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The production and crystallization of amorphous Fe-C alloys Lawrence, Benjamin 2017

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The Production and Crystallization of Amorphous Fe-C AlloysbyBenjamin LawrenceM.Sc.-Eng, Queen’s University, 2010B.Sc.-Eng, Queen’s University, 2007A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Materials Engineering)The University Of British Columbia(Vancouver)August 2017c© Benjamin Lawrence, 2017AbstractThe production and crystallization of amorphous iron-carbon alloys has been investigated experimentally.A physical vapour deposition (PVD) technique has been developed at UBC to create films with a variety ofcarbon contents. A system using controlled flow of reactive gas has been developed to allow the variationof carbon content, and films have been shown to have a reproducible amorphous structure and consistentchemistry. Characterization of the chemistry and structure of the as-sputtered alloys has been performed.Amorphous films were annealed to assess the kinetics of crystallization. For films containing less than25 at.% carbon, a two-stage crystallization involving the formation of ferrite followed by cementite was ob-served at low temperatures. The structure and chemistry of these crystallization products were characterizedby x-ray diffraction, electron microscopy and atom probe tomography. In-situ annealing was also per-formed in transmission electron microscopy, allowing for direct observation of the nucleation and growthof the product phases. This annealing study showed a significant decrease in the nucleation and growthrate of ferrite within the amorphous matrix. Simple models of diffusion-controlled and interface-controlledgrowth were not able to capture this slowing of the transformation. In addition to thermodynamic factors, itis proposed that the ferrite growth rate is strongly affected by a decrease in diffusivity arising from aging ofthe amorphous matrix and its enrichment in carbon during crystallization.Alloy films containing more than 25 at.% carbon were also found to crystallize in a two-stage processduring annealing. This crystallization involved the initial formation of ferrite and cementite, with a sec-ondary formation of cementite to fully consume the original structure. This two-step process has not beenpreviously reported in the related literature. The secondary crystallization led to large grains of cementitethat exhibited a systematic lattice compression in the [010] direction. The final cementite structure wasfound to have a super-stoichiometric carbon concentration that can only be possible via a process of ‘chem-ical twinning’. While faulting on the correct lattice plans was observed, no diffraction evidence for such‘chemical twinning’ could be identified. This is proposed as an area for future research.iiLay summaryThis work is based on the production of high-carbon iron amorphous films that provide both a novel routefor the strengthening of steel sheet, and a deeper understanding of the process of crystallization in theseamorphous materials. This thesis outlines the development of a method for producing these amorphousfilms, and shows that these films are chemically and structurally homogeneous. The crystallization of thesefilms was studied under heating, and the products that resulted from this crystallization were determinedalong with the rate of crystallization. It was found that the products and rate of crystallization varied withtemperature and carbon content, and the underlying reasons for these differences were investigated.iiiPrefaceThe research contained within this document was designed by the author in collaboration with his Ph.D.advisor Dr. C. W. Sinclair. This work was completed as part of a large NSERC Strategic Research Grant(called the Graded Composite Steels (GraCoS) project) involving close collaborations between ArcelorMit-tal, INSA Lyon, Universite´ de Rouen and the University of Ottawa. The author’s main responsibility withinthis project was for the preparation of films/coatings, for their characterization before and after annealingand for the interpretation of the results of these experiments.All of the experiments conducted at UBC were performed by the author. This includes the annealingof samples (Chapters 4, 5 and 6), SEM-EDX and Auger electron spectroscopy (Chapterss 4, 5 and 6), pro-filometry (Chapter 4), white light interferrometry (Chapter 4) and X-ray diffraction (Chapterss 4, 5 and 6).The development and application of the vapour deposition process described in Chapter 4 was conducted bythe author using facilities in the Department of Physics and Astronomy at UBC in collaboration with Prof.R. Parsons.In Chapterss 4, 5 and 6 results are presented from atom probe tomography and transmission electronmicroscopy. These experiments were conducted as a part of the collaboration with the Universite´ de Rouen.The author spent a portion of the summer of 2012 at the Universite´ de Rouen working with Dr. Ame´lie Fillon(post doctoral fellow) and Dr. Xavier Sauvage (CNRS researcher) learning these techniques. Subsequentexperiments were collaboratively planned between the author and Drs. Fillon and Sauvage, the experimentalimaging/data aquisition being performed by Drs. Fillon and Sauvage. The group in Rouen received materialsprepared by the author. They then prepared samples by FIB lift-out (see Section 4.2) or by floating thin filmsfrom a salt substrate, the later technique having been developed by the author at UBC. While not present forall of these experiments in France, the author is responsible for the interpretation of their results presentedin this thesis. Specifically, the images shown in Figures 4.18–4.19 and 4.21, Figures 5.9–5.14, Figures 5.22–5.25, Figures 5.38–5.39 and Figures 6.9–6.14 were collected by Drs. Fillon and Sauvage.To observe, in-situ, the early stages of crystallization in amorphous films, in-situ TEM heating experi-ments were performed using a specialized system at INSA Lyon. The experiment were performed in thiscase by Dr. Thierry Epicier and Dr. Fillon, Figures 5.15 and 5.19–5.21 are images taken during these ex-periments. Though the author was not present for these experiments, he designed the experiments, providedthe materials and performed the subsequent analysis of the results presented in Chapter 5.Parts of the work presented in Chapters 4 and 5 have been published in two journal papers. The firstivpaper (a short ‘letter’) is:A. Fillon, X. Sauvage, B. Lawrence, C. Sinclair, M. Perez, A. Weck, E. Cantergiani, T. Epicier, C.P. Scott,“On the direct nucleation and growth of ferrite and cementite without austenite”, Scripta Materialia, 95(2015)This paper focuses on the APT and TEM characterization of crystallization products following annealing.For this reason, the first two authors of the paper are the team from the Univ. de Rouen. As described above,the author prepared the samples for these experiments and identified the heat treatments for the study. Hecontributed to the interpretation of the results and to the subsequent writing of the manuscript.The second paper focuses on the mechanical properties of IF steel sheet after annealing.E. Cantergiani, A. Fillon, B. Lawrence, X. Sauvage, M. Perez, C. Scott, A. Weck “Tailoring the mechanicalproperties of steel sheets using FeC films and diffusion annealing”, Materials Science & Engineering A, 657(2016)The author’s contribution to this work was in the creation of all samples used to create diffusion-graded steelstructures. He also contributed to planning of the experiments/heat treatments, to discussions on the resultsand to the editing of the manuscript.While the work does not appear in this document, a third publication has been produced during thisthesis.B. Lawrence, C. Sinclair, M. Perez “Carbon diffusion in supersaturated ferrite: A comparison of mean-fieldand atomistic predictions”, Modelling and Simulation in Materials Science and Engineering, 22 (2014)This work, conducted early in the Ph.D. program, was initiated under the expectation of finding supersatu-rated ferrite following PVD deposition. While this expectation was a result of prior work in the group (seereference [1]), changes in the methodology employed in this thesis meant that supersaturated ferrite wasnever observed under the experimental conditions employed. For this reason the contents of this paper donot directly aid the core developments in this thesis.vTable of contentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiLay summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xixDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1 Diffusion graded steel - aims of the GraCoS project . . . . . . . . . . . . . . . . . . . . . . 32.2 Physical vapour deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.3 Structure of iron-carbon thin-films produced by PVD . . . . . . . . . . . . . . . . . . . . . 92.4 Crystallization of amorphous alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.4.1 Crystallization in the iron-carbon system . . . . . . . . . . . . . . . . . . . . . . . 112.4.2 Ferrite formation on crystallization of amorphous Fe-C . . . . . . . . . . . . . . . . 122.4.3 Comparisons between the behaviour of amorphous iron-carbon and iron-boron ma-terials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.5 Carbides formed by crystallization from amorphous iron-carbon films . . . . . . . . . . . . 152.6 Directly-deposited iron-carbon crystalline films . . . . . . . . . . . . . . . . . . . . . . . . 182.7 Diffusion in crystalline and amorphous iron-carbon alloys . . . . . . . . . . . . . . . . . . . 192.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21vi3 Scope and objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 Development of a method for the controlled sputtering of iron-carbon thin films . . . . . . . 244.1 Deposition methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.1.1 Description of existing PVD system . . . . . . . . . . . . . . . . . . . . . . . . . . 244.1.2 Development of reactive methane voltage control . . . . . . . . . . . . . . . . . . . 274.1.3 Substrate preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.1.4 Summary of deposition procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.2 Characterization methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.2.1 Structure and appearance of the film . . . . . . . . . . . . . . . . . . . . . . . . . . 314.2.2 Phase determination of the film . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.2.3 Chemistry of films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.3 Results: Characterization of as-deposited iron-carbon films . . . . . . . . . . . . . . . . . . 424.3.1 Appearance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.3.2 Film thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.3.3 Carbon content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.3.4 Microstructure and phases present . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.3.5 Stress state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504.4 Summary of production of iron-carbon films . . . . . . . . . . . . . . . . . . . . . . . . . . 515 Crystallization of amorphous iron-carbon alloys containing <25 at.% carbon . . . . . . . . . 525.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.1.1 Film deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.1.2 Annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545.1.3 Characterization: Structure and composition of the annealed films . . . . . . . . . . 545.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575.2.1 Decomposition kinetics on isothermal annealing as measured by XRD . . . . . . . . 575.2.2 Microstructure observation by TEM . . . . . . . . . . . . . . . . . . . . . . . . . . 675.2.3 Atom probe tomography measurements . . . . . . . . . . . . . . . . . . . . . . . . 795.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 845.3.1 Sequence of phase formation on crystallization . . . . . . . . . . . . . . . . . . . . 845.3.2 Nucleation of ferrite in amorphous iron-carbon . . . . . . . . . . . . . . . . . . . . 875.3.3 Growth of ferrite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 905.3.4 Crystallization and growth of cementite . . . . . . . . . . . . . . . . . . . . . . . . 995.3.5 Effects of carbon content and annealing temperature on crystallization . . . . . . . . 1035.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106vii6 Crystallization of amorphous iron-carbon alloys containing >25 at.% carbon . . . . . . . . . 1076.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1086.1.1 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1086.1.2 Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1086.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1086.2.1 XRD analysis of crystallization during isochronal annealing . . . . . . . . . . . . . 1086.2.2 XRD analysis of crystallization during isothermal annealing . . . . . . . . . . . . . 1136.2.3 Microstructural analysis of fully crystallized films by TEM . . . . . . . . . . . . . . 1186.2.4 Local chemistry of the film during crystallization . . . . . . . . . . . . . . . . . . . 1206.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1236.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1287 Conclusions and future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133viiiList of tablesTable 2.1 Variables associated with PVD systems and their effects on film production [23]. . . . . . 8Table 2.2 Crystallization products of amorphous iron-carbon films with varying carbon contents . . 17Table 4.1 Composition of ARMCO iron target supplied by Goodfellow Science, all elements inatomic ppm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Table 4.2 Chemistry of IF steel provided by ArcelorMittal and used as substrate in depositions . . . 29Table 5.1 Ideal position of peaks in XRD spectra for ferrite (α) and cementite (θ ) in the range 42◦≤2θ ≤ 48◦ with corresponding intensity ratios [85, 86] . . . . . . . . . . . . . . . . . . . 57Table 5.2 Analysis of XRD peaks for low-carbon films annealed for one hour at temperatures rang-ing from 250◦C to 500◦C, corresponding to Figures 5.1 and 5.2 . . . . . . . . . . . . . . 60Table 5.3 Analysis of XRD peaks for low-carbon films annealed at 250◦C showing the total inte-grated intensity of all peaks of each phase . . . . . . . . . . . . . . . . . . . . . . . . . 64Table 5.4 Analysis of XRD peaks for low-carbon films annealed at 300◦C showing the total inte-grated intensity for all peaks of each phase . . . . . . . . . . . . . . . . . . . . . . . . . 65Table 5.5 Composition (at.%) of carbon rich and carbon lean sub-volumes illustrated in Figure 5.22for an APT tip taken from a sample annealed at 250◦C for one hour. . . . . . . . . . . . . 79Table 5.6 Composition (at.%) of carbon rich and carbon lean sub-volumes illustrated in Figure 5.24for an APT tip taken from a sample annealed at 300◦C for 1 hour. . . . . . . . . . . . . . 81Table 5.7 Comparison of theoretical d-spacings of cementite based on structure of Wood et al. [85]based on SAED pattern shown in Figure 5.38b. . . . . . . . . . . . . . . . . . . . . . . . 102Table 6.1 Carbon concentration (determined by EDX) and annealing conditions for each of thesamples used in this study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Table 6.2 Peak positions of theoretical cementite and cementite measured for samples with 20 at.%carbon annealed at 300◦C and 39.6 at.% carbon annealed at 630◦C following the fittingprocedure given in Section 5.1.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112Table 6.3 Comparison of strains found in fitting cementite structure (sharp peaks) of samples with30.7, 33.2 and 39.6 at.% carbon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116ixTable 6.4 Comparison of measured and theoretical d-spacing for SAED shown in Figure 6.10 forselected diffraction planes of proposed zone-axis and orientation. . . . . . . . . . . . . . 119Table 6.5 Comparison of measured and theoretical d-spacing for SAED shown in Figure 6.12 forproposed zone-axis and orientation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121xList of figuresFigure 2.1 Stress strain curves for heat treatment of PVD coated IF steel (left), showing an increasein yield strength after annealing. Also a Lu¨der’s plateau is clearly seen at 535◦C, but notat 425◦C. Surface appearance of deformed sample after coating (right), annealing andtensile testing. From [12] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Figure 2.2 Basic components of a sputter deposition system, including working gasses, sputteredtarget, and film deposited on the substrate . . . . . . . . . . . . . . . . . . . . . . . . . 6Figure 2.3 Cross-section of a magnetron sputtering target, showing the magnetic field extendingabove the surface of the target [23] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Figure 2.4 a) Selected area TEM diffraction of the structure of an amorphous iron-carbon thinfilm and b) the associated radial intensity showing broad primary and secondary peakscommonly seen in amorphous materials [27] . . . . . . . . . . . . . . . . . . . . . . . 10Figure 2.5 Crystallization temperatures and products of iron-carbon films including as-depositedamorphous, supersaturated ferrite and carbides with varying carbon concentration fromliterature [26]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Figure 2.6 Growth of spherical ferrite precipitates in an amorphous splat-quenched iron-carbonmatrix during annealing at 300◦C [29] . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Figure 2.7 Crystallized amorphous splat-quenched film showing initial ferrite (light coloured) sec-ondary carbides (striated grains) forming in the amorphous matrix [27] . . . . . . . . . 14Figure 2.8 Plot of the crystallization of iron-boron amorphous film as reported by Nakajima (•) [54]and Kanamaru (4) [55] showing the two-stage crystallization of the amorphous phaseat low boron content, and the local maxima in crystallization temperature at roughly33 at.% boron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Figure 2.9 a) A single carbide showing chemical twinning from Fe3C to Fe5C2 to Fe7C3 as has beenobserved in amorphous crystallization [59] and b) the structure of chemical twinning,each trigonal prism having iron atoms at its vertices and containing one carbon atomshowing the Fe3C (top) and Fe5C2 (bottom) structures [57] . . . . . . . . . . . . . . . . 16xiFigure 2.10 Two forms of Fe7C3 , hexagonal and orthorhombic, identified in iron-carbon film withcarbon content of 30 at.%, where the larger striated grains are the hexagonal phase, andthe smaller ovoid grains are the orthorhombic phase[26] . . . . . . . . . . . . . . . . . 17Figure 2.11 Three films prepared by Weck at −70, −450 and −600 V bias voltage, showing theTEM dark-field image (DF) and electron diffraction pattern (DP) for each structure [61] 19Figure 4.1 PVD system chamber used at UBC showing A) sample drum B) bias voltage source C)magnetron/target D) exhaust E) argon inlet F) methane inlet . . . . . . . . . . . . . . . 25Figure 4.2 Target used in all depositions, showing geometry of the ARMCO iron facing materialand carbon backing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Figure 4.3 Schematic curve showing the expected relation between the reactive gas flow rate andthe composition of the produced film adapted from Ohring [23]. . . . . . . . . . . . . . 28Figure 4.4 A profilometry trace measured across a masked edge of a sample deposited with V40 for24 minutes on silicon wafer. The masked region is lower, on the left, while the thicknessof the film is measured at the edge shown at 2400 μm. . . . . . . . . . . . . . . . . . . . 32Figure 4.5 Excavated TEM window of iron-carbon film (through-thickness) deposited on IF steelprior to extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Figure 4.6 The production of an Auger electron from the excitation of a core shell electron, in thiscase K level, resulting in an L1 electron dropping to the K level, ejecting the paired L2shell electron as an Auger electron. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Figure 4.7 Auger electron spectra showing the observed changes (particularly in carbon and oxy-gen peaks) with sputtering time (depth). The surface contamination due to oxygen andcarbon is seen to result in large peaks at short sputtering times. The apparent carbon andoxygen content, however, decreases and eventually stabilized with further sputtering. . . 37Figure 4.8 Steel sample used for EDX calibration, in as-polished condition (5 μm diamond) withlarge equilibrated ferrite grains, surrounded by chains of cementite as shown. . . . . . . 38Figure 4.9 APT system schematically showing the evaporation of ions from the atom probe tipunder pulsed voltage, with the geometric arrangement of the electrostatic lens and twodimensional detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Figure 4.10 Silicon micropillar tops (3.5 μm diameter) showing flat surface as-recieved (left) andafter iron-carbon film deposition (right) . . . . . . . . . . . . . . . . . . . . . . . . . . 41Figure 4.11 APT blank for iron-carbon film deposited on IF steel substrate (right) as machined fromexcavated TEM window (left) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Figure 4.12 Sequential FIB annular milling of APT test samples showing the original (left) and finalradius of the APT tip at far right for film deposited on silicon micropillars . . . . . . . . 42Figure 4.13 Optical image of as-deposited iron-carbon film (right) on a glass slide and brass-coatedsteel disc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43xiiFigure 4.14 V40 iron-carbon film as-deposited on IF steel substrate, deformed using Vicker’s micro-hardness indenter, imaged by SEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Figure 4.15 Cross section of as-deposited films on silicon wafers. The images show the similarcolumnar structure regardless of deposition conditions (different Vx level). The width ofthe individual columns is of the order of 50 nm. . . . . . . . . . . . . . . . . . . . . . . 44Figure 4.16 Thickness of samples deposited on a masked silicon wafer with increasing depositiontimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Figure 4.17 Carbon and oxygen content of films deposited on Si substrates as a function of relativesystem voltage (Vx) measured by AES (with calibration point by EELS [1]) and by EDX(calibrated independantly at 25 at.% carbon). . . . . . . . . . . . . . . . . . . . . . . . 47Figure 4.18 Three dimensional reconstructions of APT samples with methane voltage control at V40showing consistent distribution of iron, carbon and oxygen (trace, at 1.0 at.%) . . . . . . 48Figure 4.19 Comparison of the mass/charge spectrum of samples deposited on silicon micropillars(left) showing a clear thermal tail (towards higher mass/charge), to that of samples de-posited on IF steel substrates (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48Figure 4.20 XRD pattern of as-deposited film deposited under the V40 voltage condition on silicon,showing a fully amorphous single broad peak . . . . . . . . . . . . . . . . . . . . . . . 50Figure 4.21 Diffraction pattern of as-deposited iron-carbon film under the V40 voltage condition,showing only broad rings associated with amorphous structure . . . . . . . . . . . . . . 50Figure 5.1 XRD spectra measured from five different Fe-C samples annealed for one hour at 250,300, 350 and 500◦C. The theoretical intensity and position of peaks for ferrite [86] andcementite [85] are also shown along the x-axis. The spectra have been artificially offsetin the vertical direction to help with visualization. Note that, as explained in the text,the carbon content of the films varied between 16 and 22 at.%C for these samples (seeTable 5.2). Full fitting of these samples shown in Figure 5.2 . . . . . . . . . . . . . . . 58Figure 5.2 XRD spectra from samples annealed for one hour. Samples shown a) as deposited,and annealed at b) 250◦C, c) 300◦C, d) 350◦C, e) 500◦C. The theoretical intensity andposition of ferrite [86] and cementite [85] are shown along the x-axis. The least-squarebest fit for the ferrite (orange), amorphous (green), and cementite (purple) are shownalongside the raw data (symbols) and total fit (black). . . . . . . . . . . . . . . . . . . . 59Figure 5.3 XRD spectra from samples containing 17.5 at.%C after annealing at 250◦C for A) 1hour and B) 2 hours. The theoretical intensity and position of ferrite [86] (circle) andcementite [85] (triangles) are shown along the x-axis. The least-square best fit for theferrite (orange), amorphous (green), and cementite (purple) are shown alongside the rawdata (symbols) and total fit (black). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61xiiiFigure 5.4 XRD spectra from samples containing 20.4 at.%C after annealing at 250◦C for A) 7.5,B) 15, C) 30, D) 60, E) 75, F) 105, G) 135 and H) 270 minutes. The theoretical intensityand position of ferrite (circle) [86] and cementite [85] (triangles) are shown along the x-axis. The least-square best fit for the ferrite (orange), amorphous (green), and cementite(purple) are shown alongside the raw data (symbols) and total fit (black). . . . . . . . . 62Figure 5.5 Normalized integrated intensities (I˜) for the amorphous, ferrite and cementite phasesestimated from the XRD spectra in Figure 5.4 and Table 5.3 as a function of annealingtime at 250◦C for a sample containing 20.4 at.%C. The solid lines are simply intendedas guides to the eye. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64Figure 5.6 XRD spectra from samples containing 16.1 at.%C after annealing at 300◦C for A) 7.5minutes, B) 15 minutes, C) 30 minutes and D) 60 minutes. The theoretical intensity andposition of ferrite [86] and cementite [85] are shown along the x-axis. The least-squarebest fit for the ferrite (orange) and cementite (purple) are shown alongside the raw data(symbols) and total fit (black). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Figure 5.7 XRD spectra from samples containing 20.1 at.%C after annealing at 300◦C for A) 7.5minutes, B) 30 minutes and C) 60 minutes. The theoretical intensity and position offerrite [86] and cementite [85] are shown along the x-axis. The least-square best fit forthe ferrite (orange), amorphous (green), and cementite (purple) are shown alongside theraw data (symbols) and total fit (black). . . . . . . . . . . . . . . . . . . . . . . . . . . 67Figure 5.8 Normalized integrated intensities (I˜) for the amorphous, ferrite and cementite phases asa function of annealing time at 300◦C for the film containing 20.1 at.%C. The bold solidlines are intended as a guide to the eye, while the dashed lines show the same guidesused in Figure 5.5 for the sample containing 20.4 at.%C annealed at 250◦C. . . . . . . . 68Figure 5.9 Selected area diffraction pattern from an Fe-C sample prepared in the low-carbon con-dition, annealed for one hour at 200◦C. No evidence of crystallization was observed,consistent with XRD observations presented above. . . . . . . . . . . . . . . . . . . . . 69Figure 5.10 a) Cross-sectional TEM image of film containing 15.8 at.%C prepared by FIB sectioningafter annealing on an IF-steel substrate for one hour at 250◦C showing spherical ferriteprecipitates and some cementite crystallites embedded in an amorphous matrix, with b)higher magnification of the interface region between an IF-steel substrate . . . . . . . . 70Figure 5.11 EFTEM imaging near the interface between the Fe-C film containing 15.8 at.%C afterannealing at 250◦C for one hour. One can see the presence of a thin oxide layer at thesubstrate-film interface. The layer of ferrite crystals aligned along the interface on thefilm side is also observed as a region of low carbon on the film-side of the oxygen richlayer. As expected, the substrate is observed to contain lower levels of carbon. . . . . . . 70Figure 5.12 HRTEM image taken from the same film as shown in Figure 5.10. The inset shows ahigher magnification view of the interface between the amorphous and crystalline BCCphases illustrating its atomic sharpness. . . . . . . . . . . . . . . . . . . . . . . . . . . 71xivFigure 5.13 Bright field TEM images of a ∼15 at.% carbon film deposited on sodium chloride,floated onto a copper grid and annealed for one hour at 300◦C. Inlaid SAED imageshows a pattern with points corresponding to the low-contrast grains and streaking cor-responding to the faulted (striped) grains. The faulting in this case gives rise to extensivestreaking in the selected area diffraction pattern. The spacing between streaks was foundto correspond to 2.26 A˚. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Figure 5.14 a) Bright field TEM image b) energy filtered (EFTEM) image for iron and c) carbon . . 73Figure 5.15 Sequential images of in situ TEM annealing at 5 (a), 10 (b) and 40 (c) minutes for 250◦Cannealing of a V10 methane voltage sample. Two ferrite grains (1, 2) have been labelledas landmarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Figure 5.16 Number density of ferrite crystals obtained from quantitative image analysis of the im-ages shown in Figures 5.15 and 5.19. The thickness of the samples was estimated basedon the deposition rate as described in the text. . . . . . . . . . . . . . . . . . . . . . . . 75Figure 5.17 Average equivalent area diameter of ferrite crystals measured from observation of Fig-ures 5.15 and 5.19. All measurements shown are during the stage of annealing whenonly ferrite and amorphous phases were identified. . . . . . . . . . . . . . . . . . . . . 76Figure 5.18 Evolution of the volume fraction of ferrite in Figures 5.15 and 5.19 assuming the ferritecrystals to have the average EQAD from Figure 5.17 and number density from Fig-ure 5.16. The large symbols indicate the volume fraction assuming the average samplethickness while the small symbols show the upper and lower bound based on using thelargest and smallest sample thicknesses based on the deposition rate. . . . . . . . . . . 77Figure 5.19 In-situ annealed sample observed through thickness in BF-TEM showing the evolu-tion of the microstructure as the sample was heated from 250◦C to 400◦C at a rate of50◦C/min. The only significant change apparent is growth of pre-existing ferrite crys-tals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Figure 5.20 The same area of in-situ annealed sample observed at 400◦C (left) and 450◦C (right)with one minute between the images. A single faulted cementite crystal is highlightedin the in image on the right and the same corresponding area is similarly highlighted(prior to cementite formation) in the image on the left. . . . . . . . . . . . . . . . . . . 78Figure 5.21 Evolution of the microstructure as the in situ heated TEM sample was held at 450◦C.The main microstructural change in this case corresponded to the nucleation and growthof cementite. Dark ring corresponds to the contamination from higher magnificationobservations made at the lower temperature (Figure 5.15) . . . . . . . . . . . . . . . . . 78Figure 5.22 Left, APT volumes of sample containing 15.8 at.%C after annealing for one hour at250◦, showing position of both carbon (pink) and iron (black). Right, the carbon andiron concentration profile of the sample within the region indicated at left. . . . . . . . . 80xvFigure 5.23 The same APT volume as shown in Figure 5.22 showing two profiles of analysed sub-volumes along lines 1 and 2 as marked, calculated in slices perpendicular to the axis ofthe sub-volume. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Figure 5.24 Left, APT volumes of sample containing 15.8 at.%C after annealing for one hour at300◦, showing position of both carbon (pink) and iron (black). Right, the carbon andiron concentration profile of the sample within the region indicated at left. . . . . . . . . 82Figure 5.25 Left, The same APT volume as shown in Figure 5.24 showing a sub-volume crossingthe interface between carbon rich and carbon lean regions. Right, carbon compositionaveraged in slices along the length of the sub-volume shown at left. . . . . . . . . . . . 83Figure 5.26 Gibb’s free energy of system variation with carbon content at 250◦C as calculated byThermo-Calc [99], where the free energy of the liquid is used as a proxy for the freeenergy of the amorphous phase. The shaded box illustrates the composition range ofinterest in this study, i.e. 16-20 at.% carbon. . . . . . . . . . . . . . . . . . . . . . . . . 85Figure 5.27 Total free energy change of a transformation of the system from liquid (a) into ferrite(α), austenite (γ), a combination of ferrite and cementite (α+Fe3C, and a combinationof ferrite + liquid (α+a) a) shown schematically and b) calculated change in Gibb’s freeenergy for each transformation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86Figure 5.28 Free energy change of initial nucleation of carbon-free ferrite, shown schematically ina) and the probability of nucleation b) calculated based on the ∆G∗ calculated from a) . . 89Figure 5.29 Effect of shifting liquid free energy curve with increasing factors shown as a) a functionof carbon content and b) the change in free energy to nucleate carbon-free ferrite. . . . . 90Figure 5.30 Diameter of sub-set of ferrite particles which crystallized and grew at earliest times ofannealing from insitu-TEM (circles), see Figure 5.18, compared to parabolic growth(linear fit) and the total population of ferrite (crosses). . . . . . . . . . . . . . . . . . . 91Figure 5.31 Schematic description of the growth of ferrite into amorphous limited by diffusion ofcarbon away from the interface, showing important concentrations that are used in thediffusion growth model used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Figure 5.32 Volume fraction of ferrite formed over time by insitu-TEM showing parametric fit andfitting parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93Figure 5.33 Result of diffusion controlled growth fit of experimental data by Equation 5.12. In-tegration was performed using Euler’s method with the change in radius calculated atmidpoints of sections. The numerical integration was performed with a step size of30 seconds using the carbon diffusivity in the amorphous phase (Dac) and initial ferriteradius (r0) as adjustable parameters to fit the experimentally measured ferrite size . . . . 95Figure 5.34 a) Description of total Gibb’s free energy, and energy associated with trans-interfacediffusion and for moving the interface of the ferrite as it grows into the amorphousmatrix as defined by Hillert [115], and b) the variation of these free energy levels withincreasing carbon content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96xviFigure 5.35 EQAD ferrite particle size from growing particles compared to and interface controlledgrowth model where the mobility was fit and thermoCalc data was used to calculate thedriving force available to move the equilibrium as shown in Figure 5.34 . . . . . . . . . 97Figure 5.36 Equilbrium carbon content predicted for liquid iron-carbon and ferrite at temperaturesfrom 250◦C to 450◦C as calculated from the common tangent of ThermoCalc data . . . 98Figure 5.37 Gibb’s free energy of nucleation at 0 at.% carbon for ferrite and 25 at.% carbon forcementite, as shown schematically a), and as a function of amorphous carbon content b) 100Figure 5.38 TEM image (a) and associated SAED pattern (b) showing identified planes (red linesadded as guide to diffraction spot positions measured) . . . . . . . . . . . . . . . . . . 101Figure 5.39 HRTEM detail of cementite region of sample annealed at 300◦C for 1 hour, for the samegrain that is shown in Figure 5.38. A simulated cementite structure, viewed in the [100]direction identified from diffraction, is shown in detail at right at the same scale. . . . . 102Figure 5.40 Schematic representation of the crystallization process observed by XRD and TEM.Each image indicates increasing annealing time (linearly) from left to right, the relativesize of the phases, and their volume fractions are designed to match experimental data ateach stage of annealing. Ferrite is shown in orange, amorphous in green (with darknessindicating carbon content) and cementite by striped purple. . . . . . . . . . . . . . . . . 104Figure 6.1 XRD of as-deposited sample (30.7 at.% carbon), and samples annealed at 300◦C (31.7at.%) (identical to the as-deposited sample), 430◦C (39.6 at.%), 530◦C (39.6 at.%) and630◦C (33.2 at.%) for one hour. Symbols indicate the expected position of ferrite (◦)and cementite (4) peaks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Figure 6.2 Detail and fitting of sample annealed at 430◦C for one hour with 39.6 at.% carbon show-ing cementite and ferrite peaks. Symbols indicate the expected position of ferrite (◦) andcementite (4) peaks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110Figure 6.3 Detail and fitting of sample annealed at 530◦C for one hour with 39.6 at.% carbon show-ing cementite peaks. Symbols indicate the expected position of ferrite (◦) and cementite(4) peaks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110Figure 6.4 Detail and fitting of sample annealed at 630◦C for one hour with 33.2 at.% carbon show-ing cementite peaks. Symbols indicate the expected position of ferrite (◦) and cementite(4) peaks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111Figure 6.5 Sample with 30.7 at.% carbon annealed at 530◦C for a total of A) 7.5 minutes, B) 15minutes, C) 30 minutes and D) 60 minutes showing fitting with cementite and ferritepeaks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114Figure 6.6 Extended detail of sample with 30.7 at.% annealed at 530◦C for 7.5 minutes showingrelation of ferrite and cementite positions to observed peaks in A) low angles and B)high angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114xviiFigure 6.7 Detail of cementite peak position of sample with 30.7 at.% carbon annealed for 30 min-utes at 530◦C showing detail of convolution of broad and sharp peaks, along with theshifted position of the sharper peak. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Figure 6.8 Comparison of observed sharp peak pattern for a sample with 33.2 at.% carbon with aselection of known carbides for comparison, including a) three possible Fe2C structures[35, 88, 89], b) cementite [85] and ε Fe3C [90], c) two possible Fe7C3 structures [91]and d) Fe5C2 (Ha¨gg Carbide) [92]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Figure 6.9 Through-thickness TEM image of sample annealed at 530◦C for one hour showing largethrough-thickness grains with pronounced faulting. The interface between the film andIF steel substrate can be seen as the bright line near the top of the image. The IF-steelsubstrate is the bright area above this. . . . . . . . . . . . . . . . . . . . . . . . . . . . 118Figure 6.10 A) Detail of grains in crystallized sample (annealed at 530◦C, one hour) along withSAED pattern (B) taken at the indicated position where no faulting is visible. . . . . . . 119Figure 6.11 HRTEM image showing detail of a grain in an orientation where striping is visible. . . . 120Figure 6.12 SAED pattern based on image shown in Figure 6.11 with measured planes indicated.Striping of diffraction pattern indicates planar structural defects in the (010) planes.Red lines added as a guide to indicate where planar spacings are measured. . . . . . . . 121Figure 6.13 EF-TEM images coming from a region containing the substrate/film interface as wellas a grain boundary between cementite grains in a film fully crystallized by annealingat 530◦C for one hour. Higher levels of carbon and oxygen are observed at the IFsteel interface but a relatively homogeneous carbon distribution is observed within thecrystallized film. This is to be contrasted to the EF-TEM images made on the (partiallyand fully) crystallized samples in Chapter 5. . . . . . . . . . . . . . . . . . . . . . . . 122Figure 6.14 APT reconstruction and atomic profile measured in a sample whose bulk composition(based on EDX) was 30.7 at.% carbon observed after annealed at 530◦C for one hour.The distribution of carbon is seen to be homogeneous (30±1 at.%) and close to the bulkcomposition despite the fact that the sample is expected to be nearly 100% cementiteafter this annealing treatment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123xviiiAcknowledgementsI offer my deep gratitude to my supervisor Dr. Chad Sinclair whose dedication, support and patience wereintegral to the success of this thesis, and to Dr. Michel Perez for his enthusiasm and thoughtful guidance.Many thanks are also owed to the members of the GraCoS Project, Dr. Xavier Sauvage, Dr. Ame´lie Fillon,Dr. Arnaud Weck, Dr. Elisa Cantergiani and Dr. Colin Scott whose work, expertise, thoughts and conversa-tions drove this research. Sincere thanks are extended to Dr. Robert Parsons whose skill and vast knowledgeof deposition technology made this work possible.xixxxDedicationTo my wife, Rachel.xxiChapter 1IntroductionThe history of steel design has been one of continual advancement in strength and toughness. The increasingdemands for stronger and tougher steel product have driven advances in chemical alloying and microstruc-tural refinement through traditional heat treatment. As most commercially viable options for alloying el-ements have been exploited, and traditional microstructural strengthening methods such as grain size re-finement are reaching their physical limits [2] the future for steel design may lie in spatially architecturedmaterials and novel processing techniques [3]. This thesis is part of a larger collaboration, the Graded SteelComposites (GraCoS) project, which aims to develop architectured packaging steel sheet product throughthe novel use of vapour deposition to produce a diffusion reservoir for flexible strengthening treatments bycarbon diffusion. The production of the vapour deposited film also allows for the direct creation of materialwith structure and chemistry that is difficult to obtain through traditional processing techniques. The goalsof this project are to both develop and test the coating process used in order to support the broader work ofimproving mechanical properties of packaging steel sheet, and also to develop a deeper understanding of thestructure and crystallization of the vapour deposited coating itself.The production of packaging steel, for use in food and beverage cans is a $30 billion global industry. Ademand exists for packaging steel that can be formed into thinner gauge cans of the same, or higher strengthwithout reducing formability [3–5]. The impetus for this derives from the potential for reduced materialand transportation cost. Reducing weight also has a large positive environmental impact as a full third ofthe carbon footprint of some food products is due to the production and transport of the steel packaging[6]. There are major challenges facing the improvement of these steel products. Steel cans are handledindividually, and are expected to withstand axial stacking forces up to 50 times their weight. They must alsobe designed to withstand variable pressures from food processing [5]. The packaging steel industry is alsovery cautious in its use of new materials due to concerns of chemical interactions between the packaging,corrosion coatings and food products. Over the years, health concerns about lead soldering of seams [7], tincoatings [8] and bisphenols in polymer coatings [9] have increased public awareness of problems associatedwith new materials and have informed strict national guidelines for the materials used in food packaging[10].1To achieve strengthening within packaging steels without sacrificing formability, the main method usedis bake-hardening. Bake-hardening relies on small amounts of carbon in solid solution that, followingan appropriately designed heat treatment, will segregate to dislocations. The carbon effectively ‘pins’ thedislocations causing the yield strength of bake hardened packaging steels to be increased by 50–60 MPa[11]. If this thermal treatment is performed after forming the packaging steel, one can benefit from a lowyield strength and high formability for the forming operation and a higher yield strength for the final product.Recent work has revealed that diffusing carbon into packaging steels from a carbon rich surface coatingcan lead to higher strength compared to traditional bake hardening [12]. An additional benefit is a loss ofthe so-called ‘discontinuous yielding’ that typically arises from bake hardening.In this thesis, continuous vapour coating, a relatively new technique for steel processing [13], has beenexplored for achieving Fe-C coatings containing a high carbon (10–40 at.% carbon) content. These thincoatings (∼1 μm thick) have been applied to the top and bottom surfaces of thin (∼100 μm thick) packagingsteel sheet. The technique developed in this thesis allows the tailoring of chemistry and structure of the filmduring deposition. In this project films with a range of carbon contents have been produced having a wellcontrolled chemistry and structure. This has been used as a starting point to a deeper analysis into the effectof annealing on evolution of the microstructure of the coatings. The results of this annealing study shedlight on to the crystallization products and kinetics of transformation that are important both in the specificcase where the film is used as a diffusion reservoir and also in a more fundamental understanding of theproperties of this far-from-equilibrium iron-carbon system.2Chapter 2Literature reviewAs noted above, this project focuses on the use of physical vapour deposition (PVD) as part of a processingscheme for achieving graded microstructures in packaging steel sheet. Some recent examples of the appli-cation of graded/hybrid approaches to improving the mechanical response in other steel systems will be firstpresented in this chapter to illustrate the potential of this approach. Following this, a very brief review ofthe steels used in packaging applications will be presented. The basic elements of PVD processing are nextintroduced with a focus on magnetron sputtering (the technique used in this work). Examples of the varietyof materials achieved by PVD processing in the iron-carbon system are reviewed, and unanswered questionssurrounding the stability and structure of these materials are highlighted.2.1 Diffusion graded steel - aims of the GraCoS projectThe over-arching aim of the GraCoS project is to produce interstitial free (IF) steel sheet coated with aniron-carbon film that can be annealed to form a material that is graded in carbon through-thickness, therebyimproving the bulk mechanical properties of the steel sheet. This type of ‘architectured’ material withspatially tailored microstructures and/or compositions is an area of significant current interest (see e.g. [3]).By spatially tailoring the composition of a material one can achieve improvements in functional properties(e.g. catalyst particles [14]) as well as mechanical properties (e.g. strength and toughness [15–17]).In the case of steels, the use of carbon composition gradients is far from a new concept. Carburizing,bringing a carbon rich gas into contact with a steel surface, is one of the oldest techniques in ferrous met-allurgy for increasing the hardness and wear resistance of surfaces. Typically, this process is carried out athigh temperatures (between 871◦C and 982◦C) where the steel is in the austenite phase [11]. High tempera-tures are chosen so as to work under conditions where the equilibrium solubility of carbon is highest in thesteel, and where the kinetics of carbon diffusion are highest. Under such conditions, however, precipitationof carbides can readily occur, either during the carburization or during the cooling from the carburizationtemperature [18]. Moreover, the solubility of carbon, even at high temperatures, is limited to be 0.1 at.%3(0.02 wt.%) [19] 1 and, depending on the cooling rate, it is also possible for the surface of the material towarp and/or crack.One innovative way to circumvent these problems was developed by the Swagelok company for thehardening of stainless steel components [20]. In this case, it has been shown that very high levels of carbonin solid solution can be achieved in austenitic stainless steels (12 at.%C) by performing carburization at lowtemperatures (470 ◦C). Compared to the equilibrium solubility of carbon at this temperature (<0.015 at.%C)the level of carbon in solid solution is enormous. This supersaturated phase has been shown to greatlyincrease the surface hardness of the steel [21] and to improve the fatigue resistance [20]. The surprisingsupersaturation in this case was attributed to a sort of ‘para-equilibrium’, where not all solute species are inequilibrium due to some elements having very low atomic mobility at the temperature of interest. In thiscase para-equilibrium exists due to the high diffusivity of carbon relative to that of the substitutional alloyingelements (Cr in particular in this case) it was found that carbide precipitation, which normally determinesthe equilibrium carbon solubility, could be completely suppressed.A similar concept has been used in an attempt to increase the strength of ferritic steels. Rather thancarburizing, however, PVD was used to produce amorphous iron-carbon coatings containing 60–70 at.%Con a 130 μm thick IF-steel sheet [12]. Annealing the coated sheets at 535◦C for one hour led to an increasein yield strength of 125 MPa but also the appearance of a Lu¨der’s plateau (Figure 2.1). In contrast, whenthe material was annealed at 425◦C for one hour, a similar increase in yield strength was observed (86MPa) but without a clear Lu¨der’s plateau (Figure 2.1). The observed increase in strength is much largerthan that typically obtained for bake aging (50–60 MPa) and the lack of a clear Lu¨der’s plateau raisesinteresting questions about the role of chemical heterogeneity on the stability of plastic flow. These results,the questions they raise, and the potential commercial impact of this processing route motivated the initiationof the GraCoS project.2.2 Physical vapour depositionAs opposed to surface chemistry modification by carburizing, the study by Scott et al. [12] explored the useof physical vapour deposition (PVD) combined with annealing. Industrial PVD units can rapidly producethin coatings continuously onto sheet products. In the steel industry, PVD processing has been developedto allow for coils of steel to be passed through a chamber at speeds of up to 1 m/min and to achieve coatingthicknesses of up to 1 μm in that time. Recently developed high speed processing techniques such as jetvapour deposition (JVD) [13, 22] have been used to take advantage of the high speed of PVD performedby evaporation. Full scale continuous JVD processing facilities are currently used by ArcelorMittal as ameans of producing aesthetic and scratch resistant coatings on a variety of steel products [13], but thistype of in-line coating has not yet been investigated as a method for improving bulk mechanical properties.As an alternative to evaporation based techniques, PVD can be performed using plasma-based sputtering1For the purposes of this thesis atomic percent will be preferred when referencing solute content in order to make relations tostoichiometric carbides more obvious. At the high range of carbon discussed in this work weight percent can be estimated by thereader as the atomic percent divided by 44Figure 2.1: Stress strain curves for heat treatment of PVD coated IF steel (left), showing an increase inyield strength after annealing. Also a Lu¨der’s plateau is clearly seen at 535◦C, but not at 425◦C.Surface appearance of deformed sample after coating (right), annealing and tensile testing. From[12]techniques. While sputtering tends to be slower than evaporation, there is significant benefit due to the factthat sputtering offers a greater degree of control over microstructure and chemistry of the coating [23].Following the work of Scott [12], this thesis focuses on using sputtering for the controlled production ofiron-carbon coatings/thin films. In sputtering based PVD systems (schematically illustrated in Figure 2.2), alarge voltage differential is imposed between the target and the substrate which creates a plasma conductingcurrent by accelerating the inert working gas towards the target and sputtering ions and atoms from thetarget to the substrate. The sputtering occurs as the inert atoms are ionized positively and hit the targetsurface (held at a large negative voltage) at high velocities, ejecting atoms from the target by momentumtransfer (Figure 2.2). The sputtered atoms travel from the target and will tend to coat any surfaces placed intheir path. Placing a substrate facing the target will lead to the development of a surface layer of sputteredmaterial on the substrate. As this film of material grows, processes similar to those occurring on the targetoccur at the substrate. High-velocity atoms and ions impact into the growing film creating defects (e.g. self-interstitials and vacancies) while also making the growing film more dense[24]. Low velocity depositioncan lead to porous films as PVD deposition is inherently a line-of-sight process which allows small surfaceroughness to develop into large voids due to self-shadowing in the growing film. Increased atomic velocityincreases the film density by allowing more mobility in the growing film surface which can collapse smallvoids or prevent them from forming.The electrical properties of PVD systems is well reviewed by Ohring [23], the following provides onlya brief overview of the type of system used in this thesis. During sputtering the system maintains whatis known as glow discharge, where charge is transferred from the cathode (target) to the anode (substrate)through the movement of electrons and negative sputtered ions. When a negative voltage is applied tothe target free electrons will be accelerated towards the substrate, if the applied voltage is large enough5Figure 2.2: Basic components of a sputter deposition system, including working gasses, sputtered tar-get, and film deposited on the substratethe electrons will have sufficient energy to ionize the neutral working gas (in this case argon) through asimple ionization process, e− + Ar→ 2e− + Ar+, which releases an additional (secondary) electron. Theproduction of secondary electrons (and the cascading ionization of the working gas) will be self sustainingif a) there is a sufficient applied voltage and b) the working gas pressure is high enough to provide a largedensity of ionization events, but c) not so high that the mean-free path of electrons (and their developedenergy) is inadequate to ionize the working gas. This self-sustaining glow discharge results in the transitionof the system from an insulating gas to a highly conductive plasma. The acceleration of the ionized workinggas towards the target (cathode) results in large numbers of neutral atoms being ejected from the surface ofthe target through momentum transfer, after which they travel through the partial vacuum of the system andcondense on the substrate to form a growing film [23]. With the large flux of electrons during depositionthe substrate will develop a slight negative (∼10–100 V) charge referred to as a floating bias, even when thesubstrate is grounded.Increasing the pressure of inert gas in the PVD chamber allows larger numbers of ions to be sputtered,but the increased pressure also increases the likelihood of sputtered species interacting with the inert gasbetween the target and the substrate. It is this interaction which makes the deposition rate generally slowerthan evaporation coating processes which can be performed at high-vacuum. In order to increase the yieldof the sputtering system it is possible to use a magnet to confine the secondary electrons in a loop near thesurface of the target and increase their local density. Called magnetron sputtering, this method increases thelikelihood of secondary electrons ionizing the working gas, which in turn increases the number of atomssputtered from the target without increasing the overall working gas pressure. The magnet used in thismethod has a specific geometry, shown in Figure 2.3, which produces loops of magnetic field in a continuouscircle around the surface of the target, and that extend above the surface [23]. When using a magneticallysoft material such as iron to form the target it is important to ensure that this magnetic field extends far6enough above the surface of the target to interact with the working gas. To do this holes can be made in thetarget to prevent the magnetic field from simply “shunting” through the soft material [25].Figure 2.3: Cross-section of a magnetron sputtering target, showing the magnetic field extending abovethe surface of the target [23]The chemistry of the material formed by magnetron sputtering is directly related to the chemistry of thetarget. Every element has a characteristic yield of sputtered atoms for a given number of impacting ions[24]. The ratio of any two element’s characteristic yields, multiplied by their atomic fraction within thetarget will give the atomic fraction of that species expected within the growing film. The chemistry of filmsproduced can therefore be controlled directly by the composition of the target.It is also possible to use reactive species to form part of the plasma in the system in a process knownas reactive sputtering [23]. These reactive species are then incorporated into the deposited film. In reactivePVD systems the reactive species is ionized by the high energy of the system and combines with evaporatedspecies in transit from the target. Within the sputtering system the reactive ions will coat the target due tothe bias voltage and are sputtered along with the target material forming mixtures of the two species in thedeposited film. In this way the chemistry of the film can be controlled without changing the geometry of thetarget, or any other parameter in the system. The chemistry can also be dynamically controlled, changing thechemistry of the film within or between depositions. Using reactive gas therefore makes the system muchmore flexible in the production of films with varied compositions.A large number of variables can be controlled in the PVD system to affect the film produced. Thetarget composition, the sputtering atmosphere (composition and flow of species), the working pressure ofthe system, the voltages (either DC or AC) of both the target and substrate, the proximity of the substrateto the target and the temperature of the substrate can all have an impact on the composition, structure andinternal stresses of the growing films. The main parameters which can be adjusted, and their effects on filmsproduced are summarized in Table 2.1This myriad of control variables, the broad chemistries possible, and the high-energy environment of thegrowing film, all combine so that the film can be grown with nearly any chemistry, structure and stress state.7Table 2.1: Variables associated with PVD systems and their effects on film production [23].PVD System Variable Effect on Films ProducedSystem pressure Increasing pressure of the system increases the number of ionization eventsand increases the sputtering rate. High pressures can prevent the directtransport of sputtered material to the substrate, decreasing the sputteringrate. Low pressure is associated with dense, compressively stressed filmswhile high sputtering pressure will result in more porous, tensile stressedfilms.Target voltage Target voltage must be high enough to maintain plasma discharge in the sys-tem, a level which will depend on the working gas species and the pressureof the system. Alternating current applied to the target increases the yieldof non-metallic speciesSubstrate voltage Negatively biasing the substrate can induce increased ion bombardment ofthe growing film, reducing the deposition rate, and increasing the densityand altering the crystallinity of the growing film.Substrate temperature Higher substrate temperatures tends to promote crystallization of depositedfilms. The temperature of the substrate at the film surface can be controlleddirectly (heating or cryogenic holders) or through the thermal conductivityof the substrate which alters the temperature achieved for a given heat fluxof deposition.Target-substrate distance Short distances lead to higher levels of ion-bombardment of the growingfilm and high substrate temperatures. A smaller area of the substrate iscoated. Longer distances decrease substrate heating and result in a largerarea being coated at a lower deposition rate.Target composition The target composition has a direct impact on the composition of the grow-ing film. The composition of the substrate will depend upon both the targetcomposition and the sputter yield of each species in the target. Metallicspecies generally have higher yields than non-metallic species, so that thefilm composition is more metallic than the target.Reactive gases Gases introduced into the system can react with the target and be co-sputtered with the target material so that they are incorporated into thegrowing film. The relationship between reactive gas flow rate and film com-position is complex and highly non-linear though in general more reactivegas will increase the composition of reactive species in the film.8This is particularly interesting in systems such as that of iron-carbon where there exist many possible phases.The possibility exists to directly form far-from-equilibrium phases such as complex carbides, supersaturatedferrite [1] and amorphous mixtures of iron and carbon [26].2.3 Structure of iron-carbon thin-films produced by PVDOne of the basic questions to arise from the original work of Scott et al. [12] is: What is the structure andchemistry of the material at the interface of their IF-steel substrate and amorphous iron-carbon thin filmcoating upon annealing? While detailed examination of the substrate/coating interface was not attemptedin the work of Scott et al., it was reported that there was no obvious formation of carbides or other phaseswithin the IF-steel sheet. Moreover, annealing experiments on the amorphous iron-carbon coatings revealeda remarkable stability at low temperatures (no changes in structure were observed after holding at 400◦Cfor 20 min) and a complex sequence of crystallization and carbide precipitation when annealed at highertemperatures [12].There is a rich literature related to the structure and stability of iron-carbon based materials produced byfar-from-equilibrium processing routes such as rapid solidification [27–30], high energy surface processing[31], mechanical mixing [32], and by vapour deposition [1, 25, 26, 33–37]. A wide range of phases havebeen achieved via these different processing routes ranging from supersaturated ferrite [38] amorphousmaterials (e.g. [26]) to metastable crystalline phases such as Fe7C3, e.g. [1]. This points to the rich potentialof the simple binary Fe-C system for achieving a wide range of interesting metastable microstructures and acorresponding wide range of properties.PVD processing of iron-carbon targets commonly result in the formation of an amorphous phase. Theiron-carbon system is a poor glass-former, with a required cooling rate greater than 107 K/s even for largelevels of carbon [27]. Splat-quenching as a means of achieving binary iron-carbon amorphous materials islimited by cooling rate, sample thickness and chemistry variations [30], meaning that amorphous ribbonshave only been produced for carbon contents between 12 and 20 at.% [29]. PVD processing, on the otherhand, has been shown to reliably produce films having controlled chemistry, thickness and structure over amuch wider composition range (8.3 at.% to >60 at.%C) [26].Amorphous films exhibit a diffuse electron diffraction pattern (Figure 2.4), with several wide peakscharacteristic of the natural nearest-neighbour spacing of a glassy metal [27]. Bulk techniques such asX-ray diffraction and Mo¨ssbauer spectroscopy have further confirmed the bulk amorphous nature of thesefilms [36]. Above a critical carbon concentration of 32 at.%C, the magnetic and Mo¨ssbauer signatures ofamorphous films are observed to change. At these high levels of carbon it is believed that amorphous areasboth rich and poor in carbon coexist within the film [39]. At one extreme, conditions have been foundleading to ‘granular’ films composed of amorphous carbon surrounding isolated grains of iron, the magneticproperties of such materials being of significant interest [40]. A more recent study has suggested that evenwithin films having 19 at.%C the composition may not be homogeneous. In this case it was reported thatamorphous iron-rich areas were found to be dispersed within regions having a composition closer to that of9the bulk material composition [37].Figure 2.4: a) Selected area TEM diffraction of the structure of an amorphous iron-carbon thin filmand b) the associated radial intensity showing broad primary and secondary peaks commonlyseen in amorphous materials [27]2.4 Crystallization of amorphous alloysAmorphous materials undergo several transitions during annealing which bring the material from a fullyamorphous structure to a stable or meta-stable crystalline phase. With heating the amorphous structure will“relax” (“age”) so that local arrangements of atoms are optimized, removing free volume from the structureand decreasing the free energy of local atomic arrangements within the amorphous phase. The amount towhich an amorphous structure can relax depends on the methods used to create the structure initially, butthe end point of this relaxation is thought to be a single ideal amorphous phase which does not dependon processing [41]. The amorphous material will fully relax with long holding times and low annealingtemperatures [41].Crystallization can theoretically occur in an amorphous structure at any temperature, but at low tempera-tures the time required becomes so large the material can be treated as functionally stable [41]. In practice, acrystallization temperature is defined using slow ramp-heating (usually <1 K/s) and measurement by differ-ential scanning calorimetry (DSC) or diffraction methods (XRD, or more rarely TEM/neutron diffraction).For kinetic reasons, glasses can crystallize at temperatures well below the reported crystallization tempera-ture if held for longer times, or heated more slowly.The driving force for nucleation and growth of crystalline phases is generally explained by the largefree energy of the amorphous phase relative to stable or meta-stable crystalline phases. The free energy/-composition of the amorphous phase is hypothesized to be similar to that of a super-cooled liquid, having10a high free energy and weak relationship between composition and free energy [30, 41]. In the literaturethree types of crystallization reactions have been reported from amorphous samples, polymorphic crystal-lization where the amorphous phase crystallizes directly to a crystalline phase with an identical composition,eutectic where the amorphous phase crystallizes into two phases of higher and lower solute composition,and primary where a crystalline phase grows directly by ejecting solute elements into the amorphous bulk.[41, 42].Prior to crystallization the amorphous phase has also been reported to decompose into two separateamorphous phases. In systems such as Zr-Y-X [43, 44] and Pd-Au-Si [45], amorphous phase separation hasbeen observed prior to crystallization. This separation is explained as occurring due to a miscibility gap inthe amorphous phase, where the energy of the system can be reduced by the separation into two phases ofdifferent composition. After phase separation either of the two new amorphous phases can undergo one ofthe three types of crystallization resulting in a mixture of crystallization products [41].2.4.1 Crystallization in the iron-carbon systemThe amorphous nature of iron-carbon thin films produced by PVD leaves them in an out-of-equilibriumstate. Annealing of these materials under the correct conditions will, therefore, result in their decompositioninto more stable crystalline phases. The path that these transformations take can be complex, leading to theformation of metastable phases either as precursors to the final equilibrium phases or as metastable phases.The thermal stability of iron-carbon amorphous films having compositions between 10 at.%C and 50 at.%Chas been studied by several authors, with a large body of work from Bauer-Grosse who has studied thecrystallization of exotic carbides from amorphous vapour deposited films over the past thirty years [46].Figure 2.5 summarizes the crystallization behaviour of binary amorphous iron-carbon illustrating certaintrends in terms of the observed phases. Black symbols represent the work of Bauer-Grosse et al. [26]and Shingu [29], Boswell and Chadwick [27]. Starting from a fully amorphous state (the homogeneityof this starting material, as reported by Bauer-Grosse et al. is indicated along the bottom of the chart),the graph shows temperature/carbon composition regimes where certain phases have been reported [25, 26,36]. Little information about the volume fraction or chemical composition of the crystallized phases ispresented in the literature and cannot be inferred from this plot. Moreover, little information is availablein the literature regarding the kinetics of transformation or phase composition. The studies which form thebasis of this plot were performed either by in-situ ramp annealing of TEM samples [36] or by differentialscanning calorimetry [26], in both cases the time and temperature increase in tandem. The crystallizationdata therefore is a good guide of the relative stability of the film with carbon content, but should not beinterpreted as a measure of the absolute start temperatures for the various crystallization reactions.The stability of amorphous iron-carbon films increases with increasing carbon content, the least stablecomposition being pure iron. This is expected as the thermal stability of a metallic glass is generally in-versely proportional to the melting point of the material at that composition [47]. While the general trendof the system is for increasing stability with carbon content up to at least 50 at.%, there is a clear local11Figure 2.5: Crystallization temperatures and products of iron-carbon films including as-depositedamorphous, supersaturated ferrite and carbides with varying carbon concentration from litera-ture [26].maximum in the crystallization temperature between 23 and 27 at.% carbon. The composition of this localmaximum corresponds with the composition of cementite the most stable carbide in the iron-carbon system[26]. The presence of a maximum in the film stability at the composition of cementite is interesting, butthe reason for this relation is not clear from the current literature. Whatever the reason, binary amorphousiron-carbon alloys are very stable in this composition range, and will remain uncrystallized after annealingof up to one hour at 400◦C [26].2.4.2 Ferrite formation on crystallization of amorphous Fe-COne of the most interesting observations involving the crystallization of amorphous iron-carbon is that fer-rite can form directly from relatively high-carbon amorphous films. This transformation occurs in films withup to 25 at.% carbon, with small ferrite grains growing into the amorphous matrix [26]. This is an incom-plete transformation, and is followed (at higher temperatures, or longer times) by a transformation of theremaining amorphous phase into cementite. Interestingly, rather then crystallizing to form carbides alongwith the iron rich phase, annealing at just above the initial crystallization temperature has been observed toresult in the formation of an iron rich, body centred cubic phase, identified as ferrite by diffraction studies, incontact with the amorphous matrix. This ferrite phase forms from a matrix with very high carbon contents,relative to the carbon solubility in ferrite at these temperatures. The ferrite formed from splat-quenched andvapour deposited amorphous films nucleates as small “precipitates” [26] or “spherical particles” [29]. Theseparticles form uniformly through the iron-carbon film and grow rapidly, quickly reaching a maximum radius12as shown in Figure 2.6. At this point growth of the ferrite stops with the phase representing a small total vol-ume fraction, and the particles having a radius less than 70 nm [29]. To date, no experimental measurementsin the literature exist which directly report how or why carbon is redistributed during this process.This crystallization product has been previously related to supersaturated ferrite produced via otherroutes. Super-saturated ferrite has been reported to form as a consequence of severe plastic deformation ofsteels (e.g. heavily drawn pearlitic wire [48]) and has been related to the “white etching layer” in rail steels[49]. More relevant to the present work, a supersaturated ferrite phase containing between 12 and 25 at.%Chas been reported to form directly during PVD processing in the binary iron-carbon system [1, 12, 38, 50].Compared to the PVD processing routes used to obtain amorphous iron-carbon films, the routes used toform a supersaturated ferrite structure involved high-energy deposition techniques such as ion plating [1],or systems expected to produce high velocity atomic deposition [38], that allow for greater mobility ofatoms in the growing film. These techniques are known to produce far-from-equilibrium crystalline phases[1, 12, 38].Figure 2.6: Growth of spherical ferrite precipitates in an amorphous splat-quenched iron-carbon matrixduring annealing at 300◦C [29]If the ferrite/amorphous system is heated to higher temperatures (less than 100 K above the temperatureof the initial ferrite crystallization) it undergoes a second stage of crystallization. This second transformationconsumes a much larger volume fraction of the amorphous matrix [27] and represents a completely distinctcrystal structure from the initially formed ferrite [26, 29]. The products of the first and second stages ofcrystallization are shown in Figure 2.7. Boswell and Chadwick describe the structure as twinned ferriteinterspersed with laths of cementite, or perhaps a complex carbide [27], whereas in all of the work of Bauer-13Grosse et al. the structure was identified as Fe3C cementite.Figure 2.7: Crystallized amorphous splat-quenched film showing initial ferrite (light coloured) sec-ondary carbides (striated grains) forming in the amorphous matrix [27]2.4.3 Comparisons between the behaviour of amorphous iron-carbon and iron-boronmaterialsThe crystallization of iron-boron amorphous alloys has received more attention than iron-carbon alloys asboron is a much better glass-forming agent in iron due to its much lower eutectic temperature compared toiron-carbon alloys [19]. This means that amorphous iron-boron can be more readily produced by processessuch as splat quenching [47]. There is also industrial interest in iron-boron-X metallic glasses due to theirsoft magnetic properties [51]. Boron has many similarities to carbon in amorphous iron alloys, and so itis not surprising that there are similarities in the amorphous phase stability of the iron-carbon and iron-boron systems. In contrast to the iron-boron system, iron-nitrogen amorphous materials cannot be producedby direct quenching and there are no industrial products based on this system, there is therefore a muchsmaller body of work in this system consisting of a handful of deposition based studies [52]. The stability ofiron-boron amorphous materials, which has been characterized in a relatively large number of studies, canpossibly offer insights into the stability of iron carbon films.In crystallization studies of iron-boron alloys it has been shown that at low boron contents and tempera-tures it is possible to crystallize ferrite within the amorphous matrix without an accompanying boride phase,just as in the iron-carbon system. The growth of this phase, and it’s apparent stability within the iron-boronamorphous phase has been explained as a simple diffusion controlled growth with the assumption that borondiffusion within the amorphous phase is much slower than it is in ferrite. The growth of the ferrite grains isthen slowed by the enrichment of boron in the surrounding amorphous material [53, 54]. This hypothesishas not been directly tested, however, due to the difficulty of measuring diffusion of boron and the local14boron content in the amorphous matrix.Another similarity between the iron-boron and iron-carbon systems can be found in the presence of alocal maximum in amorphous stability. In the iron-carbon system this maximum exists at 25 at.% carbon,corresponding to cementite, but in the boron system this local maximum coincides with Fe2B, the moststable boride at 33 at.% boron as shown in Figure 2.8. The coincidence of the maximum stability withthe composition of the crystalline boride is explained as possibly arising from local atomic arrangementsin the amorphous phase which mirror that of the crystalline phase [55]. This type of local structure hasbeen reported previously in other metallic amorphous materials and could lead to higher stability of theamorphous alloy at the composition of a known equilibrium phase [56].Figure 2.8: Plot of the crystallization of iron-boron amorphous film as reported by Nakajima (•) [54]and Kanamaru (4) [55] showing the two-stage crystallization of the amorphous phase at lowboron content, and the local maxima in crystallization temperature at roughly 33 at.% boron2.5 Carbides formed by crystallization from amorphous iron-carbon filmsIn the production and annealing of iron-carbon films several crystalline products can be found in the lit-erature. Setting aside the possibility of supersaturated ferrite, there is a large variety of carbides whichhave been reported to form in the amorphous phase at varying temperature and carbon contents. Reports ofcrystallized phases include Fe3C cementite [26], Fe5C2 Ha¨gg carbide [35], as well as two types of Fe7C315[46]. One of the more interesting possible products is the non-stoichiometric twinned carbide based on thestructure of cementite which has been extensively studied in the literature[57, 58].Above a critical annealing temperature (this temperature tending to increase with increasing carboncontent) the films will crystallize into one of several different phases (Table 2.2). For compositions above25 at.%C the films transform largely into carbides, where the type of carbide (or carbides) depending onthe composition of the amorphous phase. In the work of Scott et al. it was found that carbon rich filmscontaining 60-70 at.%C transformed to a carbide surrounded by amorphous carbon (i.e. the carbide rejectscarbon during growth into the surrounding matrix) [12]. The carbon content of the carbides can be varied byvarying the structural arrangement of carbon that describe the structure of carbides such as cementite (Fe3C).Non-stoichiometric carbon contents in these carbides are possible by an irregular “chemical twinning” of thestructure. This allows cementite-like carbides (or “sheet carbides”) to vary continuously in carbon contentfrom Fe3C to Fe2C while maintaining the same orthorhombic structure of iron atoms [57].This form of structural variation by chemical twinning in orthorhombic carbides has also been widelyreported in the crystallization of carbides during the third stage of tempering in martensite [58]. In temperedmartensites several variants of these carbides are seen to co-exist, with the frequency of chemical twinningallowing for the coherent variation of carbides structures from Fe3C to Fe5C2 to Fe7C3, all of which canoccur within a single carbide grain as shown in Figure 2.9 [59].Figure 2.9: a) A single carbide showing chemical twinning from Fe3C to Fe5C2 to Fe7C3 as has beenobserved in amorphous crystallization [59] and b) the structure of chemical twinning, each trig-onal prism having iron atoms at its vertices and containing one carbon atom showing the Fe3C(top) and Fe5C2 (bottom) structures [57]With higher levels of carbon, one of two basic variants of Fe7C3 have been reported to form directly fromthe amorphous matrix. In the first, Fe7C3 can be formed as one composition level in the chemically twinned16Fe3C structure [46]. The second variant is a true stoichiometric hexagonal Fe7C3 phase formed in filmshaving exactly 30 at.% carbon [60]. The orthorhombic Fe7C3 structure is observed in films containing atleast 30 at.%C, where it co-exists with hexagonal iron carbide up to 33 at.% C, after which the orthorhombicvariant is the only carbide formed. The two distinct forms of Fe7C3 are shown in Figure 2.10 where thelarger carbides are hexagonal FexC1−x, and the smaller ovoid carbides have the orthorhombic structure [26].Figure 2.10: Two forms of Fe7C3 , hexagonal and orthorhombic, identified in iron-carbon film withcarbon content of 30 at.%, where the larger striated grains are the hexagonal phase, and thesmaller ovoid grains are the orthorhombic phase[26]Table 2.2: Crystallization products of amorphous iron-carbon films with varying carbon contentsCarbon Content Crystallization Products< 25at.% Two stage crystallization1. Super-saturated ferrite, unknown C%2. Fe3C carbide, higher C% than bulk25at.%,< 30at.% One stage crystallizationSheet carbides with C% varying by twin structure30at.%,< 33at.% One stage crystallizationMixture of Fe7C3 and sheet carbides of varying C%> 33at.% One stage crystallizationFe7C3, excess carbon ejected to amorphous bulk172.6 Directly-deposited iron-carbon crystalline filmsFor low-energy processing with cooled targets and higher levels of carbon, iron-carbon films can be consis-tently produced in the amorphous state [26]. This is, however, not the only structure available through PVDprocessing. One of the great advantages of PVD processing is that by changing processing variables it ispossible to produce material of the same chemistry in many different phases. It has been shown that iron-carbon films can be directly deposited in a variety of structures including amorphous, a variety of carbides,and supersaturated ferrite [1] [38] [12]. These films produced and characterized by Weck et al. show inter-esting relations to those discussed above. In this work iron-carbon films were produced using AC magnetronsputtering with three different average bias voltages applied to the substrate. The application of negative biasvoltages to the target acts to encourage re-sputtering of atoms from the film, increasing the mobility of atomsat the film’s surface [23]. When no bias voltage is applied, fully amorphous films of 8 at.% carbon are pro-duced. At a bias voltage of −450 V the carbon content increases to 12 at.% and the film becomes fullycrystalline. The structure was found to be BCC, and so represents ferrite similar to those found from heatingamorphous films, but without a second phase it seems more likely that this phase is supersaturated in carbon.The major difference from the ferrite produced by annealing amorphous films is that in this case the filmis fully crystalline instead of consisting of small precipitates in an amorphous matrix. In this as-depositedsupersaturated ferrite the lattice parameter was calculated using electron diffraction to be 0.352 nm, whichis much larger than the spacing found in annealing studies [29], which possibly indicates that the ferriteproduced by Weck et al. is more consistently super-saturated in carbon. An increased lattice spacing is alsoreported by Merz and Dahlgreen in a study which also produced directly-deposited homogeneous films ofsupersaturated ferrite [38]. When the bias voltage is increased further the carbon content increases 30 at.%and the structure changes again so that it is fully composed of Fe7C3. The three films are shown below inFigure 2.11 as they appear in TEM dark field imaging and diffraction [1]. The morphology of the ferriteproduced directly by deposition is also very different from that produced by annealing of amorphous films.Whereas the annealed structure presents as small spherical particles, directly-deposited supersaturated fer-rite is found in grains which are columnar with a high aspect ratio, and oriented perpendicular to the growthof the film [1] [38]. This form of grain growth is often found in vapour deposited materials and reflects thelimited mobility of the incorporated atoms as they quickly cool on the film surface [23].The lattice parameter and tetragonality of the supersaturated ferrite phase has been reported by sev-eral authors as being much smaller than that predicted for martensite of the same atomic fraction of car-bon [27, 38, 61], with the films having a lattice c/a ratio increasing from 1 at no carbon to 1.1 at 15 at.%carbon[50]. This phase has also been shown to be thermally stable, not changing in structure even after an-nealing at 400◦C for 30 minutes [1]. How such stability is achieved when one would expect the diffusivityof carbon in ferrite to be very rapid at these temperatures remains a mystery, and the source of this ap-parent supersaturation remains unanswered. Possible avenues for exploration include interactions betweencarbon and defects, complex ordering of the carbon, or large local segregation at defects and/or surfaces[1]. It has also be postulated that the stability of the supersaturated ferrite phase may be a result of a sort of18Figure 2.11: Three films prepared by Weck at−70, −450 and−600 V bias voltage, showing the TEMdark-field image (DF) and electron diffraction pattern (DP) for each structure [61]para-equilibrium condition such as that stabilizing high carbon supersaturation in austenitic stainless steels[21].Interesting similarities do exist between the directly-deposited structures of Weck et al. and the mi-crostructures that develop upon annealing amorphous iron-carbon alloys. By thinking of the kinetic energyadded by the bias voltage as analogous to thermal energy added during annealing, it is possible to conceptu-ally position the structures created by Weck et al. on the same graph as the annealing results of Bauer-Grosseet al. shown in Figure 2.5. At low bias voltages (low carbon levels and kinetic energy) the film is amor-phous as is found for films at low annealing temperatures [26]. Increasing carbon levels and kinetic energyby increasing the bias voltage brings the films into an area of supersaturated ferrite as defined by annealingexperiments, and finally at high carbon levels and kinetic energy the structures found are fully crystalline,consisting solely of Fe7C3.2.7 Diffusion in crystalline and amorphous iron-carbon alloysIn order to predict the transformation of high-carbon iron films and the movement of iron and carbon fromthese films to underlying steel substrates it is important to understand diffusivity in crystalline and amor-19phous iron-carbon systems. The two phases of greatest interest here are ferrite and the amorphous iron-carbon phase. The self-diffusion of iron in ferrite is very slow compared to that of carbon which can travelthrough interstitial sites in the iron. The diffusivity of iron in ferrite follows an Arrhenius expression withpre-exponential D0 = 6.8× 10−4 m2/s and activation energy of Q = -2.95 eV for temperatures below theCurie point at 770◦C. The diffusivity at 500◦C is 10−22 m2s−1 [62], roughly 6 orders of magnitude slowerthan diffusivity of carbon at the same temperature [63] .The diffusivity of carbon in ferrite at the low concentration found at equilibrium with cementite has beenstudied extensively by experiment and is well understood physically, especially as it varies with temperature(see ref. [63] for a review of experimental data). It has been shown that for low carbon concentrationsand low temperatures the diffusivity is Arrhenius with D0 = 2.7181×10−2 cm2s−1 and Q = 0.836eV/atom[63]. The equilibrium concentration of carbon in ferrite is extremely low (with a maximum of 0.095 at.%at 727◦C [19]), and so for the vast majority of applications the diffusivity of carbon can be assumed to beconstant with concentration.Some authors have made attempts to measure the concentration dependence of the diffusivity of carbonin ferrite , either in high temperature ferrite where higher carbon solubility is possible [64], or in the initial-stages of diffusion of carbon in deeply quenched “virgin” martensite, where the carbon is homogeneouslydistributed [65, 66]. Neither of these methods have proven to be accurate enough to develop a clear model ofthe variation in diffusivity. A slower carbon diffusion is however supported by the fact that many models forthe early stages of tempering of martensite require the assumption of a slower diffusivity of carbon than isobserved in equilibrium ferrite [67]. The slower diffusion of carbon is also supported by a theoretical modeldeveloped by C. Zener in 1948 [68] which relates the activation energy of carbon diffusion to the energydifference between favoured and unfavoured octahedral positions in the tetragonal martensite structure. Theactivation energy is predicted to vary with increasing linearly with carbon content by the relation:∆Q = 3.11× c eV/atom (2.1)where ∆Q is the increase in activation energy and c is the carbon content of the BCC iron in atomicpercent. This corresponds to roughly a three orders of magnitude decrease in diffusivity for every weightpercent carbon at room temperature [65].The diffusion of carbon and iron in amorphous alloys has not been unambiguously quantified in theliterature. The limitation in measuring the diffusivity in this phase is the low crystallization temperature ex-hibited by the material which makes the distances over which it is possible to measure diffusion very short.The other main complication in these measurements is that the diffusion of species within an amorphousalloy is expected not to be constant in time, decreasing markedly as the system relaxes in the early stagesof annealing [69]. In general, for an amorphous alloy the diffusivity is expected to decrease with increasingatomic radius [70] and so the diffusivity of iron is expected to be several orders of magnitude slower thanthat of carbon. Direct measurements have been made in other more stable amorphous systems such as Fe-Zrwhich show the diffusion of iron to be roughly 5 orders of magnitude slower than self diffusion in ferrite20[69]. In their studies of the iron nitrogen system, Chakravarty et al. measured the diffusivity of both iron andnitrogen in the amorphous state [52] at temperatures below 200◦C. The diffusivity of nitrogen was foundto be roughly five orders of magnitude slower in the fully relaxed amorphous matrix (10−21m2/s) than incrystalline ferrite at the same temperature (10−16m2/s [71]). The diffusivity of iron, while two orders of mag-nitude slower at 10−21 m2/s than the nitrogen is much faster then the self-diffusion of iron in ferrite at similartemperatures (10−37 m2/s [62]). In contrast to the very slow diffusivity of nitrogen measured by Chakravartyet al. atomistic simulations of carbon diffusivity in amorphous iron predict diffusion levels somewhat fasterthan that found in crystalline ferrite, and much faster than the values reported by Chakravarty [72]. It isnot clear what value should be taken for the carbon diffusivity in amorphous iron-carbon systems given thepaucity of information in the literature on this subject, and the large differences between simulations of theiron-carbon system and measurements of the iron-nitrogen system.2.8 SummaryThis literature review has illustrated that, while many experiments have been performed on the productionand crystallization of amorphous iron-carbon alloys, there are many key features that remain unknown.In particular, most of the prior studies of crystallization have focused on the crystallographic structure ofmetastable carbides formed in PVD produced thin films containing >25 at.% carbon. There is little work onthe mechanisms that control the formation of these phases or of the sequence of phase formation at lowercarbon contents. Basic information regarding important details such as the diffusivities of species in suchamorphous alloys are not known.21Chapter 3Scope and objectivesAs noted in the introduction (Chapter 1), this thesis contributes to a multi-partner project (NSERC StrategicGrant, GraCoS) whose aim was to develop a method for the strengthening of packaging steel sheet by themeans of the controlled diffusion of carbon from a thin, carbon-rich surface coating into the bulk of the steelsheet. This thesis focuses on the challenges of developing a robust process for coating the steel sheet andfor understanding the microstructural changes that occur in the coating during the annealing treatment. Thebulk mechanical properties resulting from this diffusion annealing were studied in a parallel Ph.D. projectconducted at the University of Ottawa [73].Specifically, this thesis has two coupled goals:1. Develop a new, robust processing route for preparing amorphous carbon rich Fe-C coatings2. Quantify the microstructural changes occurring during elevated temperature annealing of carbon richamorphous Fe-C coatingsThe first goal has been achieved by building on prior work conducted at UBC [1] to develop a newphysical vapour deposition (PVD) method that can reproducibly produce amorphous Fe-C alloy thin films/-coatings containing between 15 at% and 40 at% carbon with structural and chemical homogeneity. As hasbeen shown in the Literature Review (Chapter 2), the structure and properties of Fe-C alloys produced byPVD methods can vary greatly depending on the conditions of deposition. It was therefore essential to thesuccess of this project that a thorough characterization of the as-deposited films/coatings be performed as aprecursor to further studies.The second goal was identified to support the design of diffusion strengthening heat treatments butalso to unravel some of the yet unexplained phenomena described in the Literature Review (Chapter 2).Isothermal annealing treatments, rather than the more common ramp heating experiments presented in theliterature, have been performed so as to quantify the isothermal transformation kinetics. The products ofcrystallization have been characterized by using a wide range of experimental characterization techniques22allowing for bulk analysis (e.g. x-ray diffraction, energy dispersive x-ray analysis) and local, atomic scaleanalysis (atom probe tomography and transmission electron microscopy). By separating the experimentsinto observations on samples containing < 25 at.% carbon and > 25 at.% the role that carbon content playsin both transformation products and transformation kinetics has been deduced. Classic continuum kineticand thermodynamic models for solid state transformations are applied to the results and used to interpret thegoverning mechanisms controlling both the observed phases and their rates of formation.23Chapter 4Development of a method for the controlledsputtering of iron-carbon thin filmsCentral to the aims of this thesis, and to the broader GraCoS project, is the development of a reliable methodfor producing thin-films with high carbon contents of known structure, consistent chemistry and repro-ducible thickness. As part of this thesis, a technique for the robust preparation of films using magnetronsputtering has been developed. This magnetron sputtering system has been modified from previous work inwhich carbon was controlled by biasing the substrate of the film. In particular, the aim of this part of theproject was to develop a way to decouple the film composition from its structure. In the previous work atUBC the carbon content was varied with substrate biasing, resulting in the variation of both carbon contentand phase fraction (i.e. crystallinity, and crystalline phase type) [1]. In order to decouple the compositionfrom structure, the PVD system at UBC was redesigned to incorporate reactive methane sputtering as themethod for carbon composition variation in the growing film. Moreover, a much more extensive character-ization of the correlation between deposition parameters and the film’s structure, chemistry and variabilitywas conducted in this study.This chapter starts with a description of the sputtering system used in this thesis, including the modifi-cations made as part of this work. Next the characterization methods used to characterize the as-depositedfilms are described. Finally, the results of the chemistry and structure of the as-deposited films is described.These observations are discussed in relation to results previously presented in the literature.4.1 Deposition methodology4.1.1 Description of existing PVD systemThe PVD system used at UBC consists of a 1 m wide cylindrical chamber, roughly 0.75 m deep with a largeoctagonal sample drum (Figure 4.1A) onto which the deposition substrate was attached via steel clips. Thesample drum is electrically isolated from the chamber with insulating attachments, but can be grounded24or attached to a secondary voltage source (Figure 4.1B). The drum can be rotated during deposition via astepper motor so as to allow multiple depositions to be carried out on multiple substrates without breakingvacuum. In all cases depositions were made on orthogonal surfaces of the drum, keeping all but the intendedsubstrate out of line-of-sight of the target in order to prevent partial deposition from earlier or later deposi-tions. The drum has one face which is reserved for sputter cleaning the target. At the start of each depositionthe system is held with this face in line with the target, and the system is sputtered until a steady state isreached. This face is also used for the methane voltage control calibration, described in Section 4.1.2, whichis performed at the start of each set of depositions. A magnetron target holder (Figure 4.1C) sits roughlyparallel to the drum, with a separation of 10 cm between the target face and the substrate.Figure 4.1: PVD system chamber used at UBC showing A) sample drum B) bias voltage source C)magnetron/target D) exhaust E) argon inlet F) methane inlet25The target used for all depositions in this study is a 50.8 mm diameter, 0.5 mm thick disc of ARMCOiron (with the composition shown in Table 4.1) with a grid of 57, 3.97 mm diameter holes as shown inFigure 4.2.Table 4.1: Composition of ARMCO iron target supplied by Goodfellow Science, all elements in atomicppmIron Manganese Carbon Phosphorus Sulphur OtherBulk < 800 < 200 < 200 < 150 TraceFigure 4.2: Target used in all depositions, showing geometry of the ARMCO iron facing material andcarbon backingThe iron target is backed with a sheet of carbon graphoil. The carbon of the graphoil is exposed throughthe holes of the iron target and represents 34.8% of the surface of the composite formed. The number ofatoms which are ejected from the target surface for each incident sputtering atom (the sputter yield) willdepend on the mass of the target element, it’s bonding with the surface and the mass and energy of theimpacting atom. Carbon has a much lower sputter yield at 0.9 atoms per impacting ion, compared to thesputter yield of iron at 5.66 atoms per impacting ion for argon sputtering gas [74]. Based on these sputteringyields and the area fraction of the elements in the target, the system is expected to form films with a carboncontent of 6.2 at.%, despite over a third of the target being made of carbon.The composite geometry for the target is essential to prevent the applied magnetic field from shuntingthrough the iron. The circular magnetron creates a toroidal magnetic field which extends above the surfaceof the target so that sputtering occurs most strongly from a diffuse 30 mm ring around the centre of thetarget. As sputtering continues the target thins and was found to eventually fail after 30–40 hours of activedeposition time, when the iron facing target thins fully through at a given region, creating a small gap in thetarget which causes sparking over this gap. To prevent the target from failing during a deposition, targetswere replaced before they had failed after 30 cumulative hours of active sputtering. During the lifetime ofthe target the area of exposed carbon increased due to the thinning of the covering iron; a used target hasroughly a 10% decrease in area of the target iron.At the back of the chamber is an outlet leading to a turbo-pump (Figure 4.1D). When the target andsamples are loaded and the system is closed the turbo pump is used to evacuate the chamber. A target pres-26sure of 4.0×10−4 Pa is used, and the system is left under vacuum for at least 24 hours prior to deposition toallow out-gassing of the sample, target and chamber to prevent contamination of the deposition. Once thetarget pressure and vacuum time has been reached a small amount of argon is introduced into the chamber(through inlet marked E in Figure 4.1). The flow rate of argon is maintained at 30 standard cubic centimetersper minute throughout the deposition, and the vanes at the system outlet (Figure 4.1D) are adjusted dynam-ically to maintain a system working pressure of 0.40 Pa. The working pressure is high enough to maintaina glow discharge in the system, and the continual introduction of argon and pumping acts to maintain thepurity of the atmosphere as sputtering by-products and out-gassed species are continuously removed.To begin sputtering the target anode is brought to −30 kV ionizing the working gas. The system iscontrolled under a constant power condition. Under constant power the system is expected to maintain aconstant sputtering rate assuming the target composition remains the same. The higher the power appliedto the system, the faster the sputtering and deposition rate will be. Higher deposition rates will howeverincrease the temperature of the growing film (with a higher flux of condensing ions on the surface) and canincrease the porosity of the film [23]. A constant power of 69 W was chosen as it showed a reasonabledeposition rate, and no problems related to heating or porosity in the films.After the target had been sputter cleaned and the system reached a steady state, the drum is rotated tobring a substrate into line with the target, and the film deposition begins. The system was activated for a settime in order to produce a given film thickness, which was calibrated using thickness measurements fromseveral depositions. At the end of the deposition the system was rotated to the next sample on the drum andthe process repeated.4.1.2 Development of reactive methane voltage controlIn order to increase the carbon content of the film above the 6.3 at.% predicted for the composite targetdescribed above there are a few options in modifying the processing conditions. The simplest method wouldbe to increase the carbon content of the target, though there are several draw-backs to this. Firstly, the carboncontent would have to be very high in the target, either achieved through a homogeneous target (whichwould introduce magnetic shunting problems with the magnetron) or by decreasing the iron facing areaof the composite target (which would make the target less structurally sound decreasing target life). Bothof these options would also necessitate the design of a separate target composition or geometry for everydesired carbon level in the deposition. Another option is to use bias voltages to induce some sputtering ofthe growing film, which again would preferentially remove iron enriching the film in carbon. This systemwas previously explored at UBC as reported in Weck et al. [1]. It was found that while it is possible tocreate films with increasing content (up to 30 at.%, −700 V applied bias) this system has two significantdraw-backs as a general method. As the bias is increased the deposition rate drops as the film is re-sputteredmaking this system much slower, and secondly this method has been shown to induce crystallization of thefilm. This method therefore does not allow for the decoupling of the carbon content and structure of thefilm. This is important for the broader goals of the GraCoS project where the diffusion of carbon from a27highly metastable surface coating into an IF-steel substrate is desired.In order to increase the carbon content in the film without changing the target or electrical setup ofthe system, carbon must be introduced through the plasma atmosphere. Reactive deposition has been usedin other iron-carbon systems [37] and has been shown to be able to produce a range of carbon contentsin the produced films. Methane is commonly used to enrich the system in carbon. The simplest methodto introduce reactive gasses is to use a constant flow rate. This method has been used successfully tocreate films of varying carbon contents but poses significant problems for the reproducibility of the carboncontent. In physical vapour deposition systems the correlation between carbon content and flow rate ofreactive species is not unique. As shown in Figure 4.3 the properties of a PVD system and deposited filmare not stable with concentration of reactive species. For a given flow rate of reactive methane the systemis expected to tend towards either very high or low levels of carbon as the target is saturated or cleared. Inorder to maintain intermediate levels of carbon coverage in the target (and incorporation in the growing film)a dynamic system of feedback is required to introduce methane into the chamber.Figure 4.3: Schematic curve showing the expected relation between the reactive gas flow rate and thecomposition of the produced film adapted from Ohring [23].Developing a control system for the methane introduction requires a measurement of carbon contentin the plasma or at the target. A measure of the carbon content can be gained indirectly from the voltageat which sputtering occurs in the system. As the system operates at constant power by controlling theapplied current, a changing resistance of the plasma will change the voltage applied at the target [23]. Theconductivity of the plasma will drop with increasing carbon content, which leads to a corresponding increasein voltage. The voltage at which the system operates can therefore be used as a measure of the carbon in theplasma and therefore the amount of carbon incorporated into the film.At the start of each deposition, the target is sputter-cleaned until the system reaches a steady state in-dicating that the target is fully cleaned of adsorbed species. The voltage is measured at this point, anddesignated as V0. Methane is then released into the system along with a constant flow of argon working gasuntil the system saturates in carbon, and the voltage of the target reaches a maximum, which is designated28V100. Using these two extremes intermediate levels of carbon can be achieved and maintained through a sim-ple binary control of the methane flow. In this system a set point voltage is chosen between the minimumV0 and maximum V100 values. The voltage is then measured continuously throughout the deposition and ifit falls below the set point a small amount of methane is introduced into the system via the pulsed openingof a piezoelectric valve. If the system voltage is above the set point the valve remains closed. This mea-surement/introduction cycle is repeated at a frequency of 100 Hz throughout the deposition. This method ofcarbon control makes no assumptions about the electrical properties of the system other than a relationshipbetween the amount of sputtered carbon and the resistance of the plasma. The voltage level maintained is notexpected to vary linearly with the carbon content of the film, and the direct relation between the controlledvoltage and the resulting carbon content of the film must be calibrated by secondary measurements of theproduced films. This method is expected to result in a more reproducible carbon content in the films thanwould be possible with a static flow of reactive methane, and allow for the production of a wide range ofcarbon contents in the films.4.1.3 Substrate preparationSeveral different substrates were used in this project, the type of substrate used depending on the typeof subsequent experiments performed. Films were produced for GraCoS colleagues at the University ofOttawa who studied carbon diffusion from the films into an IF-steel substrate. In this case an IF-steel sheet(composition in Table 4.2), 185 μm thick was provided by ArcelorMittal. This material is used commerciallyfor packaging applications and so was received in an annealed/skin-passed condition. The sheet has a smallcharacteristic roughness in the rolling direction resulting from roll marks. It had an initial microstructureconsisting of uniform equiaxed ferrite grains with a diameter of ∼10μm through the thickness. Due to theskin pass the very near surfaces exhibited smaller elongated grains with a thickness normal to the sheet of500 nm and transverse diameter of 5 μm.Table 4.2: Chemistry of IF steel provided by ArcelorMittal and used as substrate in depositionsFe C Ti Mn Si P N OBulk <0.003 <0.1 0.05–0.06 <0.03 <0.02 <0.01 <0.01Before placing the substrate in the chamber for deposition, the IF steel sheet was cleaned with ethanol,then immersed in a solution of 5 vol.% nital for 20 seconds, after which it was rinsed in water, then ethanol,before being wiped dry using a paper laboratory wipe. IF steel samples were cleaned directly before de-position (within one hour of being introduced into the chamber) to limit oxidation on the surface of thesample.Other substrates were chosen to aid in characterization of the film, and also to determine the properties ofannealed film without the possibility of carbon loss into the substrate. Silicon wafers were used to measurethickness, chemistry, stress state and structure of the films, while silicon micropillars were used for atomprobe tomography. Large crystals of sodium chloride were used for the preparation of samples for general29TEM analysis.The standard silicon wafers used in the majority of non-steel depositions were purchased in the form ofa 101.6 mm diameter wafer with a thickness of 525 μm. Smaller and thinner samples were used in curvaturestress analysis of the films, in this case 50.8 mm diameter wafers with a thickness of 275 μm were usedto aid in the measurement of small stresses in the deposited film. These wafers were received as singlecrystals having one side polished. The crystal direction of the sample was chosen as normal to the (100)plane. In X-ray diffraction this creates a very strong diffraction peak at the (400) d-spacing at 69.3◦2θ forCu-Kα radiation and no signal from the substrate at other angles of study. Silicon samples were thereforeused as a substrate for all XRD analysis as they had no contribution to the XRD spectra at the angles withthe largest peaks for the crystallized phases of interest (ferrite, austenite, various carbides). To prepare thesilicon wafers for deposition they were cleaved to needed sizes using a diamond scribe, and split along theorthogonal cleavage planes of the silicon. The samples were then cleaned by soaking in methanol, thenwiped clean with laboratory paper.Silicon samples were also used for thickness measurements as the polished surface provides a welldefined base with which to compare film thickness. In this case the samples were cleaned and then wrappedtightly with aluminum foil to mask part of the sample before deposition. The foil was removed after coatingto reveal a flat reference surface on the silicon wafer which can be compared to the height of the surface ofthe film.Silicon micropillars were also used for some of the depositions intended for atom probe tomography(APT) analysis. The micropillars were received from colleagues at the University of Rouen as an array ofhundreds of silicon pillars having a diameter of 3.5 μm and a height of 50 μm. The samples were carefullysoaked in methanol and dried by wicking the methanol off with laboratory paper, any contact with thesurface was found to break the pillars. The samples thus soaked and dried were used directly for deposition.After deposition the samples were coated with nickel using an evaporation system to a thickness of 150 nmto prevent oxidation during shipping and storage before analysis at the Universite´ de Rouen.Samples for TEM analysis were either deposited on IF steel and windowed using focused ion beam(FIB) milling, or deposited on sodium chloride crystals which could be dissolved to release the depositedthin film. The methodology used for preparing samples by FIB milling can be found in Section 4.2.2. Forsodium chloride depositions, large cubes (∼1 cm by 1 cm in cross-section) from SPI Supplies were cleavedinto thin sheets 2 mm thick using a razor blade. These salt substrates were cleaved immediately prior todeposition in order to prevent surface contamination.4.1.4 Summary of deposition procedureThe sequence of procedures which are used for each deposition are as follows:• Substrates are cleaned as discussed above and are transferred to the deposition chamber where theyare attached to the drum which is oriented with a blank (no-substrate) surface towards the target.• The drum is sealed and it is pumped down to 4×10−4 Pa over the course of 24 hours.30• The deposition started by introducing argon gas into the system and starting the continual venting tomaintain a system pressure 0.4 Pa.• Voltage is applied to the target to spark the system and establish the plasma of the system.• The target is sputtered and the voltage applied is monitored throughout until it reaches a steady-statewhich indicates that the target is clean surface contamination.• This steady state is established as the zero voltage V0 condition and methane is introduced into thechamber until the system reaches it second steady-state at the high voltage V100 condition.• The system is powered off and the sample drum is rotated to bring the first substrate into alignmentwith target.• The system is started again and the applied target voltage is maintained at the specified voltage controllevel Vx via monitoring and dynamically adjusting the methane flow rate.• The deposition continues for the set amount of time and the system is powered down and rotated againto the next substrate position.• Deposition are repeated for all substrates, following which the system is powered down, and thesamples are extracted from the chamber.4.2 Characterization methodsCareful characterization is central to understanding the connection between processing and resultingproperties of the iron-carbon films produced by PVD. This characterization is also vital in the inves-tigation of crystallization of the thin films. A variety of characterization methods have been used tomeasure the composition and crystal structure of the films (over macroscopic and atomic distances),as well as the morphology, thickness and stress state in order to have a full picture of the propertiesof the system. The methods outlined below have been used to characterize both as-deposited andannealed films on a variety of substrates and processing conditions.4.2.1 Structure and appearance of the filmScanning electron microscopyThe surface and through thickness microstructure of iron-carbon films were imaged using a ZeissSigma Schottky Field Emission Gun SEM. In order to image the through-thickness structure of films,depositions were made on single crystalline silicon wafers which were then cleaved using a diamondscribe. When cleaving samples the film generally broke cleanly and adhered well to the silicon inter-face which could be imaged easily in cross section.31Contact profilometryIn order to characterize the thickness of as-deposited films, samples deposited on silicon wafer sub-strates were masked prior to deposition using tightly wrapped aluminum foil. A DekTak brand contactprofilometer was used to measure the thickness of the masked edge. The machine uses a stylus with atip radius of 12.5 μm, contacting the sample with a force of 3 mg. The height of the stylus is measuredevery 4 μm as the sample moves under it, and is reported with a resolution of 0.1 A˚. Five scans weremade, evenly spaced over the edge of the masked region. The raw height output from the DekTakis dominated by the tilt and slight warp of the silicon substrate, and so a cubic fit, filtered to removepeaks caused by contamination and scratches, is used for the coated and uncoated halves of the scanlevelling and flattening the underlying substrate. The distance between these fitting curves is mea-sured (normal to the curve) at the interface. A representative scan, with this fitting curve subtractedfrom the raw data is shown in Figure 4.4, along with the measured thickness of the sample at theinterface.����������������������������� ���� �� ���� �� ���� �� ���� �� ������������������������������ ����������������������������������� �����Figure 4.4: A profilometry trace measured across a masked edge of a sample deposited with V40 for24 minutes on silicon wafer. The masked region is lower, on the left, while the thickness of thefilm is measured at the edge shown at 2400 μm.32White light interferometryIn order to determine the stress state of as deposited film, samples were prepared on very thin wafersof silicon. The curvature of these wafers after deposition was measured to determine the stress in thefilm itself. This process used the Stoney equation [75], modified from it’s original formulation forthin strips to apply to the biaxial stress of films deposited on a circular planar substrate [23],σ =Ysd2s6R(1−νs)d f (4.1)where Ys is the biaxial modulus of the substrate, ν the poisson ratio of the substrate (160 GPa and 0.22respectively for silicon from [76]), L the radius of the substrate, ds the thickness of the substrate andd f the thickness of the film. This formula assumes that the film is much thinner than the substrateonto which it is deposited, that the planar size of the substrate is very large compared to its thickness,and that the stress in the film is equibiaxial.In order to determine an accurate curvature for the coated wafer a Wyko NT1100 white light interfer-ometer profiling system was used. Using this method a three-dimensional image of the wafer surfacecan be obtained by analyzing the interference pattern formed from polarized light reflected off thesurface of sample. The system allows for a sampling of an area measuring 2 cm by 2 cm and measuresa vertical difference of up to 2 mm with a precision of 0.05 μm. Measurements were taken at thecenter of the silicon wafer so as to avoid edge effects. The resulting curvature was fit to a sphere togive a radius (R) which is used in the Stoney equation. The shape of the resulting interference imagescan also be used to qualitatively show the type of stress state on the film, and confirm that the stressis equibiaxial. The wafers of silicon were chosen to be as thin as possible (300 μm) to increase theresulting curvature caused by the iron-carbon film, while still being much thicker than the sub-micronthickness of the films so as to satisfy the assumptions of the Stoney equation. Films deposited at theV10 and V40 condition were found to impart a slight concave curvature to the substrate, implying asmall tensile stress in the film. The largest curvature measured was 70±2 m which corresponds to amaximum stress of 90 MPa within the film.4.2.2 Phase determination of the filmX-ray diffractionIn order to characterize the structure of the as-deposited films, an x-ray diffraction system was used.This system was a Rigaku Multiflex X-ray diffractometer using a copper Kα monochromatic X-raysource and a graphite scintillation detector located at the University of British Columbia. Sampleswere deposited on the silicon wafer substrates described above. Films of three hundred to five hundred33nanometer thickness were found to give adequate signal provided the analysis time was long enoughand sampling window was small enough to reduce noise in the system.Due to the long sampling times necessary to reduce noise in the scans the analysis was restricted toa 6 degree window between 42 and 48 degrees 2θ . A small analysis window is also preferred as itlimits the geometric effect of increasing measurement angle on the sampling volume, which could notbe perfectly accounted for without knowing the exact thickness of each sample. Each sample was alsomeasured from 68.5 to 70◦ for the silicon (100) peak, the position of which was used as a calibrationon the angle of measurement (which can vary by up to 0.2 degrees due to mechanical play in thediffractometer).Transmission electron microscopyIn order to obtain local information about the volume fraction of each phase and their morphologywithin the films, transmission electron microscopy (TEM) imaging and diffraction were used. Thismethod complements the general identification of phases given by XRD analysis. TEM imaging wasused in specific cases to identify the structure of as-deposited and crystallized films and to determinethe volume fractions and morphology of the phases which crystallize in the films.Two methods were used to produce electron transparent samples. In the first, samples were depositedat very low deposition times (to produce films of ∼50 nm thick) onto freshly cleaved single crystalsof sodium chloride. After deposition the samples were then immersed in high-purity methanol, whichdissolved the sodium chloride substrate. The very thin films can then be floated off of the top of thesubstrates and caught on copper grids for TEM analysis. The samples were annealed on the grids afterpreparation as they were found to oxidize heavily if heated on the sodium chloride substrates.The second method used was to deposit thicker films onto IF steel substrates and to excavate thinwindows of film and substrates normal to the surface using FIB milling. The FIB system used wasa cross-beam NVISION-40 Zeiss instrument. Samples are first coated with a cap layer in order toprevent the film from damage during FIB milling as shown in Figure 4.5. Platinum was used as a capmaterial and was deposited via ion-beam induced deposition as a 100 nm thick strip over the intendedwindow section which measured 20 μm in length.Milling is performed using Ga+ ions. The sample was excavated by milling ramped wedge shapedsections on either side of the target window of material which is then enough to be electron transparent.The window as imaged after milling, and before extraction is shown in Figure 4.5. The edges of thesample window were then milled and the TEM window was extracted using a micro-manipulator. Thismethod was more time consuming and expensive, but produced cleaner film surfaces and provided acheck on the influence of the substrate in crystallization of the film as well as through-thicknessimaging of the film. Being able to analyse samples deposited on IF steel is also beneficial as itallows the direct comparison to samples intended for mechanical testing and the creation of diffusion34gradients which were related to the broader goals of the GraCoS project.Figure 4.5: Excavated TEM window of iron-carbon film (through-thickness) deposited on IF steelprior to extractionAll of the TEM analysis presented in this Chapter was carried out at the GPM laboratories, Universite´de Rouen using a JEOL ARM 200F microscope equipped with a schottky field ion gun and a EDXdetector capable of qualitative composition mapping. Dr. Ame´lie Fillon (post doctoral fellow) oper-ated the microscope for these experiments. Samples were imaged in both regular and high-resolution(sub-nanometer) modes, as well as analysed using selected area diffraction for phase identificationand energy-filtering imaging to qualitatively identify changes in local composition.4.2.3 Chemistry of filmsAuger electron spectroscopyAs noted above, one of the first tasks undertaken was to calibrate the PVD system with regards to thecarbon content of the deposited films as a function of the percentage of methane voltage range. Inorder to confirm the composition of these films Auger electron spectroscopy (AES) has been used.AES is especially attractive to this work as it allows measurements of chemistry with a high spatialresolution (8 nm) through the film thickness. Auger electrons are produced as a consequence of theexcitation of atoms by an incoming electron beam. As shown in Figure 4.6, incoming electrons caneject core electrons from an atom. An outer shell electron can fill the hole created by the removedcore electron. In dropping to this lower (core) energy state, the outer shell electron emits energy thatcan interact with an electron in a paired shell causing it to be emitted from the sample as an Auger35electron. The resulting energy of the Auger electron is therefore determined by the energy levels ofthe core and higher-level electrons and will be characteristic of a specific element and bonding state[77]. The number of Auger electrons produced by each element will be related by a known Augerelectron yield factor to the volume fraction of that element present in the sample surface. By mea-suring the relative integrated intensities of the Auger electron energy peaks of two or more elements,scaled by a known intensity factor, it is possible to quantitatively determine the chemical compositionof the sample surface. The system used at UBC combines scanning electron, sputtering and AEScapabilities. To improve measurement statistics, all measurements were performed using a raster of10 by 10 measurement spots, each spot measuring an area approximately 10 nm in diameter. AESmeasurements were made on the surface of samples (plan view) directly after they were introducedinto the chamber, and then periodically following argon sputtering at intervals of 120 seconds. Thepurpose of this process is two-fold. First, the sputtering allows for the removal of surface contami-nation (oxidation, carbon contamination from handling) and also allows for the confirmation that thecomposition through thickness is approximately constant. Normally the depth of the sputtering is notmeasured in these experiments. Instead the sputtering is performed until two subsequent scans arefound to give nearly identical carbon measurements. At this depth it is assumed that the contaminatedsurface layer has been removed. Other experiments, however, have been performed where the sputter-ing is continued to ensure the constancy of composition to larger depths into the film. Example AESspectra measured from a sample after increasing sputtering times are shown in Figure 4.7. The initialoxygen and carbon contamination can be clearly seen in the initial, and first-sputtered scans. In thiscase the carbon-iron ratio stabilizes between sputtering times of 600 and 720 seconds. The spectraacquired after 600 s was used in this case for quantitative analysis. Samples are generally sputteredfor 720–1080 seconds before the spectra stabilize in this manner.Figure 4.6: The production of an Auger electron from the excitation of a core shell electron, in thiscase K level, resulting in an L1 electron dropping to the K level, ejecting the paired L2 shellelectron as an Auger electron.For the quantitative analysis performed in this thesis, the derivative of the Auger electron intensity wasused, measuring the peak-peak height of clearest carbon and iron peaks (KL1 and LM2 respectively).36Figure 4.7: Auger electron spectra showing the observed changes (particularly in carbon and oxygenpeaks) with sputtering time (depth). The surface contamination due to oxygen and carbon isseen to result in large peaks at short sputtering times. The apparent carbon and oxygen content,however, decreases and eventually stabilized with further sputtering.Unlike X-ray diffraction where the intensity peaks are simple (near-gaussian), the Auger intensitypeaks have a complex shape making it difficult to de-convolute overlapping peaks and directly mea-sure the integrated intensity. Using the peak-peak height of the derivative gives a good estimate of therelative integrated peak intensities assuming a consistent peak shape and allows for a more consistentmeasure of the sample composition [77] It has been found in our measurements on samples contain-ing different levels of carbon that the detection limit of carbon via AES is limited to approximately5 at.%C. For carbon contents below this level the strongly varying background around the carbonpeak precludes an accurate estimate of the integrated peak intensity. To compare and validate the useof these AES measurements, samples were prepared without any methane reactive gas (V0). Sampleswere subjected to both AES as well as electron energy loss spectroscopy measurements (performed bycolleagues at ArcelorMittal Research, France) [12]. Both techniques measured carbon contents closeto the theoretically expected composition of the film (6.3 at.%C) estimated based on the sputteringefficiency of C and Fe and the area fraction of these species in the sputtering target.37Energy dispersive x-ray spectroscopyAs Auger electron spectroscopy is costly and time consuming, after the voltage/carbon content curvehad been established (Figure 4.17) a simpler EDX method was used for more general carbon mea-surements. Samples were measured on the same SEM microscope described in section 4.2.1. In orderto avoid measuring contamination from adhered surface carbon and oxygen the samples were cleanedin chamber using a low energy oxygen plasma cleaner. An accelerating voltage of 10 keV was usedfor the primary beam, as this was high enough to fully resolve the iron K peak in the spectrum, but assmall as possible so that the beam does not pass through the film and create signal from the substratefor the thicker films produced. Even with this low accelerating voltage small contributions from thesubstrate could be seen in thinner films and so only films deposited on silicon wafers were character-ized using this method. The EDX system was calibrated using a equilibrated pure iron-carbon steelsample with large (10×50 μm) cementite particles shown in Figure 4.8. These particles were used asa reference standard at 25 at.% carbon. The ratio of the integrated intensity between the Fe-K andC-K peaks in the spectrum was used as a one-point calibration for the carbon content of film samples.Though calibrated on this single point, this method is expected to yield reliable results for all filmstested as their carbon content (at 15–40 at.%) is close to that of the reference standard. Using this cal-ibration the system also showed very close agreement in carbon measured by AES (14.5 at.% carbon)and EDX (13.8 at.% Carbon) for the average of three measures of a comparison sample deposited atV10 voltage control of methane.Figure 4.8: Steel sample used for EDX calibration, in as-polished condition (5 μm diamond) with largeequilibrated ferrite grains, surrounded by chains of cementite as shown.38Atom probe tomographyOne key aspect of this thesis is understanding the local arrangement of carbon in as-deposited andannealed samples. This local, nanometer scale information is impossible to obtain through traditionalmethod, but can be obtained from atom probe tomography (APT). The basic components of a 3DAPT system are shown schematically below in Figure 4.9. A thorough review of the fundamentalsof this technique can be found in [78]. Like the TEM observations presented in this chapter, all APTexperiments were performed at the Universite´ de Rouen, Dr. Ame´lie Fillon conducting the APT tippreparation, measurement and analysis.APT is directly related to the earlier technique of field ion microscopy where a high electric fieldapplied to a very sharp tip of material which accelerates ionized gas to a two-dimensional detector,giving an image of the atomic-scale structure and electric environment of the material. In APT thetip of material is placed under a high enough positive electric potential that atoms of the tip itselfare ionized and accelerated to the detector. The tip used in such studies must be extremely thin (tensof nanometers) in order to develop a high enough electrical field on individual atoms so that theyevaporate independently. This destructive technique allows for the measurement of the material sub-surface through the center of the tip. By applying voltage to the tip in discrete pulses, it is possibleto measure the interval between the evaporation of ions from the tip and their measurement at thedetector, giving a time-of-flight measure of the mass/charge ratio of the ions. If this technique iscombined with a two-dimensional detector it is possible to determine the angle at which the ionleaves the sample tip, and therefore its lateral position. The sequential evaporation of many ions byvery fast electrical pulsing at the tip (at 100 kHz) allows for depth profiling, and three dimensionalinformation for the position and mass of each measured ion through a volume in the material tip. Thevolume available for analysis has a small radial distance (of the order of 10 nm) due to the limitedsolid angle over which the positional detector of the APT measures ions. The volume analysed hasa longer axial dimension into the tip (50 nm), as in this direction the only limitation is the length oftime the experiment can be run before the tip becomes too rounded or breaks due to the high stressesapplied to this very fine tip by the electrical field. The total number of measured atoms can thereforeexceed 1×107 for a single sample.As atoms are sequentially evaporated the axial position of the atoms can be determined with precisionon the order of the atomic lattice spacing, while the accuracy of the radial position of atoms has alarger associated error, on the order of 0.3 nm, due to the difficulty in accounting for all effects onatom trajectory due to the evaporation process [79]. The chemical determination of a species dependson the accuracy with which the time-of-flight can be determined, which is generally a function of theaccuracy of measuring pulse/measurement events and of the length of the flight-path of the evaporatedions.In the case where the tip material is electrically insulating, the applied pulsed voltage will not be able39Figure 4.9: APT system schematically showing the evaporation of ions from the atom probe tip underpulsed voltage, with the geometric arrangement of the electrostatic lens and two dimensionaldetector.to effectively evaporate atoms from the end of the tip. In order to encourage evaporation the tip canbe heated by applying very short pulses of laser light, focussed close to the end of the tip. Lasersystems used in this type of APT measurement are capable of producing pulses of light on the scale offemtoseconds. In this way, laser system have been used to effectively analyse a variety of insulatingmaterials [78]. One negative aspect of this system is that the thermal energy applied is less localizedin time as the sample will have a necessary cooling time, and atoms have a (diminishing) chanceof being evaporated at any point during this cooling. This creates a “thermal tail” where insteadof a sharp signal at a given mass/charge level a single species will present a sharp front edge (foratoms ejected at the start of the heating) and long tail towards higher mass/charge levels (for atomsevaporated during cooling).For use in APT the first step in analysing samples is to produce the very fine tips required by thetechnique with the iron-carbon film of interest at the top of the APT needle. Two methods wereused to produce these needles, one was to deposit iron-carbon films directly onto silicon micropillars,produced by selective etching of silicon wafers. These micropillars were received for this purposefrom the Universite´ de Rouen and are shown in Figure 4.10 in as-received and iron-carbon coatedconditions. The exposed surface area of these films was large, and it was found that they showedproblems with oxidation in early APT attempts, after which samples were evaporation coated withnickel cap layers (150 nm thick) directly after deposition of the film to reduce oxidation. The sampleswere coated with a second thicker layer of silicon to prevent damage of the film during subsequentFIB milling.40Figure 4.10: Silicon micropillar tops (3.5 μm diameter) showing flat surface as-recieved (left) and afteriron-carbon film deposition (right)The second method used to produce APT samples was to locally excavate films deposited on IF steel,using the windowing method described in Section 4.2.2. The window was then extracted and weldedonto a steel spike using platinum deposition, oriented so the film is at the end of the spike. Theremainder of the window is then cut away to leave a thin rectangular section of IF steel and iron-carbon film as shown in Figure 4.11.Figure 4.11: APT blank for iron-carbon film deposited on IF steel substrate (right) as machined fromexcavated TEM window (left)In order to use these samples for APT analysis the silicon micropillar or IF steel rod must be sharpenedto a fine tip with a radius less than 50 nm. This is achieved using an annular FIB milling technique toremove material from the edges of the sample. The annular milling operates using the FIB along theaxis of the tip, and a set of concentric circular masks allow the sides of the tip to be milled withoutremoving material from the centre of the tip. The radius of these circular masks are sequentiallyreduced to sharpen the tip to the desired radius, and to finally remove the cap layer protecting the filmso that the film is exposed for APT analysis. This sequential milling process is shown in Figure 4.1241for a silicon micropillar sample.Figure 4.12: Sequential FIB annular milling of APT test samples showing the original (left) and finalradius of the APT tip at far right for film deposited on silicon micropillarsAfter FIB milling, samples were transfered to the APT analysis chamber, where they are brought toultra-high-vacuum (10−10 mbar) and cryogenic temperatures (analysis is carried out at 80 K). The APTsystem used at Universite´ de Rouen was a CAMECA energy compensated tomographic atom probeequipped with an advanced delay line detector. This system was used in direct electrical evaporationof samples deposited on IF steel and in laser-assisted evaporation for silicon micropillar samples.The electrical system was operated with electrical pulses (and associated measurement) at a rate of30 kHz, with pulses lasting 20% of the period of each cycle. Laser assisted evaporation was carriedout at a rate of 100 kHz with laser pulses lasting 400 fs. In both cases the specific carbon quantificationmethodology proposed by Sha [80] was used.4.3 Results: Characterization of as-deposited iron-carbon filmsUsing the PVD system described above, a large number of films were produced and characterized intheir as-depsosited state. To create a variety of film properties a small subset of the control variableswere used in the PVD production. A reference condition was used at V10 voltage control of methaneflow, no applied bias voltage to the substrate and a deposition time so that the total energy of the de-position equaled 1560 Watt minutes. From this reference condition films were produced with varyingmethane flow rates (V0 to V70). It was decided based on these results to focus particularly on filmsproduced using the V10 and V40 conditions. The deposition time was varied from roughly 2 to 50minutes (156 W·min to 3300 W·min) in order to produce films of varying thickness. The properties offilms coming from different positions within the deposition chamber were also characterized in orderto confirm the effect of position relative to the target on the as-deposited film structure.The films were also characterized with a variety of spatial positions within the chamber in order toconfirm the spatial position does not affect the film properties, and to define a window in which re-42producible depositions can be made. The thickness (profilometry), stress (white light interferometry),appearance (SEM), crystal structure (XRD/TEM), chemistry (AES/EDX) and local chemical variation(APT) were all measured for a variety of deposition conditions.4.3.1 AppearanceFilms deposited onto silicon and glass for Vx < 50 are lustrous silver, generally featureless (as con-firmed by SEM observation) and well adhered to the underlying surface of the substrate. An opticalimage of the as-deposited film is shown in Figure 4.13, deposited on a brass-coated steel disc (Cana-dian one dollar coin) and a glass slide. The only obvious visual difference between as-deposited filmswas a slight brown tinge seen in films deposited at very high methane flow rates (Vx > 50). Filmsdeposited onto IF steel are similarly lustrous silver and uniformly cover the underlying roughness ofthe steel surface.Figure 4.13: Optical image of as-deposited iron-carbon film (right) on a glass slide and brass-coatedsteel discAn SEM image of a 1 μm thick film deposited onto an IF steel substrate at V40 voltage control isshown in Figure 4.14. This image shows the area close to a 30 μm micro-hardness indent. The filmsurrounding the indent can also be seen to evenly cover the roughness of the underlying IF steel. Atthe indent itself, the film conforms to the substrate with only a relatively small amount of film crackingand debonding.To observe the through-thickness structure of the films, samples deposited on silicon were cleaved,and the film was imaged by SEM (Figure 4.15). For films deposited at V10 and V40, the through-thickness structure appears the same, with columnar features aligned nearly normal to the substrate43Figure 4.14: V40 iron-carbon film as-deposited on IF steel substrate, deformed using Vicker’s micro-hardness indenter, imaged by SEMsurface (bottom of Figure 4.15). This columnar structure is a common feature of PVD films, bothcrystalline and amorphous, when the deposited material has a low atomic mobility. This structure is anatural consequence of the fact that inhomogeneities in the film or substrate can result in shadowing.This causes higher film densities in areas where the film grows the fastest, and lower densities inthe directly surrounding area [81]. This columnar structure suggests nanoscale porosity between theindividual columns, the scale of this porosity being much smaller than what was found in a previousstudy [61].(a) V10 (∼18 at.%C) (b) V40 (∼35 at.%C)Figure 4.15: Cross section of as-deposited films on silicon wafers. The images show the similar colum-nar structure regardless of deposition conditions (different Vx level). The width of the individualcolumns is of the order of 50 nm.444.3.2 Film thicknessControlling the thickness of the as-deposited films is a parameter that must be carefully controlled forthis project. In the case of films deposited on IF-steel substrates for mechanical properties measure-ments (following annealing) it must be possible to reproducibly create samples with the same carbonlevel and thickness to ensure similar properties of the final material.Thickness as a function of deposition timeWhen sputtering under constant power and operating conditions, the rate of sputtering is expectedto be constant [23]. To test this, the thickness of several masked wafers were measured for variousdeposition times. The observed relationship between deposition time and film thickness is shownin Figure 4.16. From this plot the relationship between deposition time and film thickness has beencalibrated as 12.2 nm/min with an uncertainty of ±0.50 nm/min. This fit includes samples with bothV10 and V40 methane flow rates. No significant difference was seen in the deposition rate and carboncontent.���������������������������� ��� ��� ��� ��� ��� ����������� ���������������������������������� ��� �������Figure 4.16: Thickness of samples deposited on a masked silicon wafer with increasing depositiontimesThickness as a function of position on substrateAnother concern, particularly when preparing films on large substrates (a maximum sample size of10 cm is possible in the chamber), is the potential variation of sample thickness from one side of thesubstrate to the other. To check this, a 10 cm diameter silicon wafer was masked and profilometry45measurements made in two perpendicular directions, labelled x and y, following deposition under V40for 3300 W·min. The film thickness was found to be nearly constant over this distance. The averagemeasured thickness in the x direction was 473 nm with a standard deviation of 60 nm, while in they-direction the average thickness was found to be 480 nm with a standard deviation of 57 nm.Another sample of silicon was prepared and deposited at a slight angle so that the near edge of thesample was one centimetre lower (farther from the target) and the other was one centimetre higher.Thickness measurements were made over the surface of the sample in the direction of the tilt, andagain there was no measured trend in thickness variation with the height of the sample (distance tothe target) over the range of two centimetres.4.3.3 Carbon contentReactive gas controlIn order to test and calibrate the reactive gas control of carbon content, samples deposited on siliconsubstrates with voltage saturation levels ranging from V0 to V70 were analyzed by AES following theprocedure described above (Figure 4.17). The samples showed a nearly linear relation between voltagesaturation and carbon content measured in the films. The electrical system of the PVD deposition iscomplex, and so a strictly linear relation between the voltage level and the carbon content is notrequired or expected, though in this case, over the range studied the carbon content can be predictedroughly as C (at.%) = 0.64·Vx+8 at.% for x≤ 50.At higher Vx levels oxygen contamination of the films was observed. For V70 the films were found tocontain ∼ 22 at.%O independent of Auger analysis sputtering depth. Corresponding to the increasingoxygen in the films, it was observed that the carbon content no longer varied linearly with Vx levels.For example, at V50 the films were found to contain only 39 at.% carbon. This observation couldexplain the change in coloration which is observed in samples produced at higher methane levels.This reproducible observation may be a consequence of residual water vapour within the methane gasthat reacts with the iron and/or carbon during the deposition. In a similar study on the deposition ofchromium carbides via reactive sputtering using methane, it was found that water in parts per millionled to the preferential formation of chromium oxide in place of chromium carbide [82].Spatial variation of compositionUsing a single 10 cm silicon wafer the variation of carbon content was measured in several positionsby AES. This was carried out on the same sample on which the thickness variation measurementswere made. Three measurements were taken at the center, top and right edge of the circular samplein order to give a indication of the variation of carbon content with position in the depositions. Thissample was deposited with methane controlled at V40 and so a carbon content close to 35 at.% was46 0 20 40 60 80 100 0  0.1  0.2  0.3  0.4  0.5  0.6  0.7Composition (at.\%)Voltage (Fraction of Saturation Range)IronOxygenCarbonEELS EDX AESFigure 4.17: Carbon and oxygen content of films deposited on Si substrates as a function of relativesystem voltage (Vx) measured by AES (with calibration point by EELS [1]) and by EDX (cali-brated independantly at 25 at.% carbon).expected. The samples were found to contain within±1 at.% carbon of each other, with an average of38.5 at.% carbon. Samples measured by EDX (though smaller in dimension, generally less than 1 cmacross) have not been shown to have any measurable spatial variation in carbon composition. Basedon these results, the as-deposited samples were assumed to be sufficiently uniform in compositionover the scale of the deposited region such that this was not characterized for each sample.Local composition homogeneityAPT measurements were performed for as-deposited samples at V10 and V40 methane control condi-tions. The samples were produced by depositing samples on silicon micropillars which were evap-oration coated with a layer of nickel to prevent oxidation. These samples were then milled into thenecessary needle shape and then destructively tested using APT with laser-enhanced evaporation. Inboth the V10 and V40 cases the samples showed no local or systematic variation in carbon content inthe nanometre range of the measurement. Three dimensional plots of the chemistry of the samplesare shown in Figure 4.18. The carbon and iron atoms are seen to be very uniformly distributed inthe sample, as are small amounts of oxygen, argon and hydrogen which are also contained in thefilm. These small amounts of oxygen and argon contamination are the result of the atmosphere of thechamber during deposition. No other elements from the alloying elements in the sputtering target, thesubstrate, or other sources of contamination were shown by APT in the as-deposited films. As APT47is able to measure compositions in the parts per million range it is assumed that the films are pureiron/carbon with some small contamination of argon and oxygen.Figure 4.18: Three dimensional reconstructions of APT samples with methane voltage control at V40showing consistent distribution of iron, carbon and oxygen (trace, at 1.0 at.%)The total chemical composition of the films in each case is surprisingly lower in carbon than thatmeasured by EDX and AES for similar deposition conditions. The sample deposited under the V10level of methane control shows a carbon content of 12 at.% (15–20 at.% expected) while two separatedepositions at the V40 condition were measured with carbon contents of 9 and 19 at.% carbon, whereover 30 at.% carbon was expected. It is possible this is due to large variations between depositions,though all of these measurements seem far too low compared with the smaller variation betweensamples found by EDX. APT samples produced by FIB excavation of films produced on IF steelpresented with carbon contents similar to those found by EDX, and were used exclusively for laterstudy of annealed films as shown in Section 5.2.3. Additionally the samples deposited on IF steel had amuch higher success rate (fewer breakages of tips). The initial APT samples of the as-deposited filmsshowed a consistent distribution of carbon through the film thickness, even while the absolute valuesof the film make up are significantly different from those found from other methods of measurement.Figure 4.19: Comparison of the mass/charge spectrum of samples deposited on silicon micropillars(left) showing a clear thermal tail (towards higher mass/charge), to that of samples deposited onIF steel substrates (right).48This possibility is supported by the fact that samples prepared by FIB excavation on IF substrates(which do not require laser evaporation due to the conductivity of the IF steel) have total carboncontents much closer to those expected from the deposition conditions (as will be shown in laterchapters). Though the absolute carbon content of these samples cannot be fully explained for theas-deposited samples on silicon micropillars, the distribution of the carbon that is measured indicatesthat the films are truly present as a single uniform amorphous structure without significant variationin carbon density.Composition variation between depositionsIn the small number of AES and APT samples it was not possible to estimate the extent of variationof carbon content from deposition to deposition. With EDX measurement of samples deposited onsilicon wafers a larger number of samples were measured for composition of iron and carbon. Itwas found that from one deposition to another there was a significant variation of carbon content insamples produced using the same level of methane voltage control. Over seven separate depositions inthe V10 condition the carbon content was seen to vary from 16 to 22 at.% carbon, in five measurementsin the V40 condition samples were seen to vary from 32 to 39 at.% carbon. This range is thought toaccurately represent the variation in sample carbon content for the deposition methodology, and notthe uncertainty of the EDX measurement, partly because repeated EDX measurements of the samesample produce measurements within 1 at.% of each other.This variation is thought to be a result of the unstable nature of the reactive PVD system with respectto the carbon content produced. The system naturally tends towards either a maximum or minimumcarbon content with a given methane flow rate. The voltage/methane flow feedback system used,while it does have a very fast reaction time, does not produce a stable condition for deposition, simplyholds the system as close to a set point as possible. The control on the system during depositionis fine enough to prevent the system from tending towards either carbon maximum or minima, butwill produce a film with a higher or lower carbon content depending on the inherent tendency of thesystem. Realizing this variation, EDX analysis following deposition was used as a standard step inthe deposition procedure. For each deposition a small control substrate was placed in the chamber sothat the composition of each deposition could be checked if questions arose in future experiments.4.3.4 Microstructure and phases presentThe structure of the film in the as-deposited state was found to be uniformly amorphous for both theV10 and V40 voltage methane control levels and no applied bias voltage. This amorphous structure hasbeen confirmed by X-ray diffraction on silicon substrates as well as by TEM imaging and diffractionon sodium chloride and IF steel substrates. In X-ray diffraction the system shows a single broad peakpositioned at 43.5◦ 2θ as shown in Figure 4.20. This corresponds to a lattice spacing of 0.208 nm for49copper Kα radiation and is a shorter spacing than the major ferrite (110) peak at 0.2865 nm.Figure 4.20: XRD pattern of as-deposited film deposited under the V40 voltage condition on silicon,showing a fully amorphous single broad peakWhen imaged by TEM the sample shows almost no contrast. TEM diffraction of the as-depositedsamples, Figure 4.21, shows a set of broad rings which are indicative of a fully amorphous structure,and are very similar to published diffraction patterns for iron-carbon amorphous films [27]. Filmswere found to be fully amorphous in all samples produced at V10 and V40 voltage control conditionson both sodium chloride and IF steel substrates.Figure 4.21: Diffraction pattern of as-deposited iron-carbon film under the V40 voltage condition,showing only broad rings associated with amorphous structure4.3.5 Stress stateThe stress state of as-deposited samples was measured for both the V10 and V40 methane voltage con-trol conditions using white light interferometry to determine the curvature of thin silicon substrates.50It was found that in both deposition conditions the residual stress in the film was slightly tensile, andless than 100 MPa (55 MPa for V10 and 43 MPa for V40). This stress state is lower than the 364 MPathat was measured previously by Weck et al. [61] using similar conditions, though it is possible thatthis difference is due to the reactive atmosphere of the deposition as the pressure and atmosphere usedin PVD systems has been shown to alter the stress state of deposited films [23]. The low stress statefound in these films is beneficial in many regards for the study of film crystallization as it allows theinfluence of residual stress to be ignored.4.4 Summary of production of iron-carbon filmsThe films produced by PVD deposition in this study are in many ways similar to those reported inthe literature. Single phase amorphous alloys were created at a variety of thicknesses for carbon con-tents ranging from 16–40 at.% as has been reported by other authors, e.g.[26, 27, 29]. The diffractionpattern of the amorphous phase matches well with the structures observed previously by TEM diffrac-tion [27]. The structure was also found to be consistently amorphous regardless of carbon contentas the carbon is introduced and controlled by reactive gas without otherwise altering the depositionconditions. This is in contrast to previous work by Weck et al. where the carbon content and structurewere varied in consort by altering deposition bias voltage [1].The carbon levels produced in these films are similar to those previously studied in the literature. Inthis study however, it was shown that by using voltage control of reactive methane flow that the finalcarbon content in the films could be constrained within a few atomic percent and produced on a varietyof substrates. This carbon measurement has been performed in this study using two independentlycalibrated measures of carbon which show close agreement in the total atomic fraction of carbonpresent in the films. The as deposited stress state of these films was found to be very low, this is a factorwhich has not been reported previously in the literature and though it is very process specific, this lowvalue is useful for further crystallization studies of the films as it allows residual stress to be ignoredas a variable affecting crystallization. Through analysis with APT, the carbon content within the filmswas found to be very homogeneous over the scale of several nanometers without any clear fluctuationsin local composition. This analysis, combined with the XRD and TEM analysis implies that theamorphous films produced are homogeneous in carbon content. The previously reported separation ofthe amorphous alloy into high and low carbon content regions (based on magnetic observations) hasnot been observed here, though having similar bulk carbon concentrations (15–33 at.%).51Chapter 5Crystallization of amorphous iron-carbonalloys containing <25 at.% carbonAs described in Section 2.1, one of the higher aims of this project is use the amorphous iron-carbonfilms described in the previous chapter to act as diffusion reservoirs for the strengthening of IF-steelsheet (cf. Figure 2.1). During this diffusion anneal it is expected that the coating will crystallize. Thischapter describes the crystallization kinetics as a function of annealing time and temperature for Fe-Ccoatings containing ≤ 25 at.%C. While previous work has studied the crystallization of amorphousFe-C films (e.g. [26]), the majority of studies have focused on much higher carbon content. Thereis therefor very little information on the transformation kinetics or local composition of the phasesformed during crystallization for compositions ≤ 25 at.%C.This Chapter starts with a brief review of the specific experimental techniques used, which extendthose presented in Chapter 4. In particular, details of the methodology specific to the experimentsreported in this chapter using X-ray diffraction, electron microscopy and atom probe tomography ofannealed iron-carbon films are presented. Results are then presented, first in terms of the bulk transfor-mation behaviour as observed by x-ray diffraction, followed by local structural and chemical analysisof specific conditions by transmission electron microscopy and atom probe tomography. Finally, theseresults are discussed in light of the results previously presented in the literature for the crystallizationof Fe-C glasses and other similar materials. The crystallization pathway and kinetics are discussed interms of possible governing mechanisms.525.1 Methodology5.1.1 Film depositionAll samples were deposited using the PVD technique described in Chapter 4, different film thicknessesand substrates used depending on the type of sample that was being prepared. All samples wereproduced using the V10 methane voltage control conditions as described in Chapter 4.For x-ray diffraction (XRD) analysis, all samples were prepared on silicon wafers following the pro-cedure given in the last Chapter (see Section 4.2.2). The samples were prepared to have thicknessesranging between 450–500 nm. A [100] orientated singe crystalline silicon wafer was selected as asubstrate for XRD analysis as the films could be directly annealed on the substrate without reaction.It also allowed relatively thick films to be produced without loss of adhesion to the substrate and forXRD peaks corresponding to the film to be unambiguously differentiated from those of the substrate.As these films were relatively thick, it was also possible to use energy dispersive x-ray (EDX) andAuger (AES) analysis to estimate the carbon content of these films.As described in Chapter 4, two substrates were used for preparing TEM samples. Samples weredeposited on large sodium chloride crystals, a deposition time of 2.5 minutes being used to createfilms < 50 nm thick. These films were floated off of the substrate using a methanol bath and capturedon a copper grid. These samples were rinsed in water (to dissolve residual NaCl) and then ethanol (todisplace the water and aid in drying). The grids were dried by placing the edge of the grid on lint-freepaper, wicking the ethanol off the surface. Due to the small thickness of these films it was not possibleto perform EDX analysis to determine their exact composition.Samples for TEM were also deposited on IF-steel and imaged in cross-section following FIB win-dowing to create thin foils for observation as described in the previous Chapter 4 (cf. Section 4.2.2).These films, having a deposition time of 48 minutes, were designed to have a thickness of roughly500 nm. Due to the fact that these samples were deposited on a steel substrate, it was not possible toobtain composition information from EDX analysis in the SEM.Finally, all samples for APT observation were prepared from films deposited and annealed on anIF-steel substrate following the method described in the last Chapter 4 (cf. Section 4.2.2). Thesesamples (with conductive IF steel substrates) could be used without laser-assisted evaporation, andso the quantitative chemical analysis of these samples measured by this method was not affected bythe thermal cooling of the samples, and the bulk carbon content of the films was much closer to thatmeasured by EDX and AES for the same deposition conditions.535.1.2 AnnealingHeat treatment of the as-deposited films was conducted at two locations. For X-ray diffraction, EDXand AES analysis, samples were annealed at UBC using a Lindberg electric furnace with a sealedquartz tube. The system was attached to a diffusion pump which allowed evacuation of the tubeto 4.0× 10−4 Pa. The temperature of the furnace was monitored using a thermocouple positionedadjacent to the sample in the constant temperature zone of the furnace. The temperature from thisthermocouple was logged at one second intervals, and each measurement was the average for a datasampling frequency of 100 Hz. To allow for a sample to be inserted or removed from the hot zoneof the furnace, a specifically designed magnetic sample manipulator was used that allowed for thesample to be introduced and extracted without breaking vacuum. The use of an internal manipulatorwas important for reducing the chance of oxidation or decarburization during heat treatments. In thismanipulator the sample was set in an open sample boat made of thin sheet steel (180 μm thick). Usinga thin steel boat reduced the thermal load caused by the sample holder allowing for fast heating andcooling rates on sample insertion and retraction.In a typical annealing experiment at UBC, the sample was introduced into the cold end of the quartztube (directly under a circulated water cooling jacket) and the system evacuated to 4.0×10−4 Pa. Thefurnace was then turned on and ramped to the set point temperature. Once the furnace had stabilizedat temperature (approximately 2 hours, as measured by the internal thermocouple), the sample wasinserted into the hot zone of the furnace. When the sample boat was inserted, the temperature wasobserved to drop ∼5◦C and then quickly rise back to the set point, this transient lasting less than5 minutes. After the desired length of annealing time, the sample was extracted back into the coldend of the furnace (under the water cooled jacket) and the furnace turned off. The cooling rate ofthe sample was not directly measured, but samples and the sample holder were found to be cool tothe touch (near room temperature) within five minutes after extraction out of the furnace hot zone.After extracting the sample, the furnace was opened and the sample removed. To minimize variationsin results coming from sample-to-sample variations in deposition conditions leading to variations incomposition and thickness, the same sample was annealed several times to produce the results reportedfor the isothermal annealing experiments.Annealing was conducted at the Universite´ de Rouen for observations by TEM and APT. The furnaceused in Rouen was very similar to that described above. The main differences were that a turbo pumpvacuum system was used to evacuate the chamber and a moveable furnace was used to introduce andextract the sample as opposed to a mechanical manipulator.5.1.3 Characterization: Structure and composition of the annealed filmsThe annealed iron-carbon films were studied using the same techniques as used to study the as-deposited films (cf. Section 4.2). Local observations of structure were obtained by transmission54electron microscopy using the microscopes described in Section 4.2.2 at the Universite´ de Rouen byDr. Fillon.A set of in-situ annealing experiments were also conducted in order to obtain high-frequency imagesof the growth of crystallites under specific annealing conditions. These TEM measurements wereperformed by Dr. T. Epicier in collaboration with Dr. Fillon using an aberration corrected TITANTMETEM located at The Centre Lyonnais de Microscopie in Lyon France. The samples were heatedusing a GatanTM tantalum holder at a rate of 50◦C per minute to the set point temperature.Local composition measurements were also made by TEM using Energy Filtered Transmission Elec-tron Microscopy (EFTEM). This used a GIF QuantumTM type energy filter in conjunction with theJEOLTM microscope described in Section 4.2.2. These measurements were performed on samples de-posited on sodium chloride crystal and IF steel substrates. Additionally atom probe tomography wasused to determine the distribution of carbon and other alloying elements after annealing as describedin the previous chapter (Section 5.10b).All of the above techniques were used to give very local information about structure and composition.To obtain bulk measurements, XRD , EDX and AES were performed at UBC. The EDX and AESmeasurements, used to quantify the composition of films, were performed following the proceduresdescribed in the previous chapter (4.2.2). Standard quantitative XRD analysis could not be performeddue to the small thickness of the thin films studied. Owing to limited sample thickness and thechange of incident beam geometry, particularly at high angles of incidence on the sample, observationswere limited to a narrow range of 2θ . The angles measured from 42–48◦ 2θ include the strongestpeak of both cementite and the strongest of BCC ferrite as well as the highest point of the broadamorphous peak seen in as-deposited iron-carbon films (as shown previously in Figure 4.20). In thisrange, a single peak of ferrite {110} can be measured with five peaks of cementite ({121}, {210},{022}, {103}, and {211}). The single peak from ferrite is expected to be much stronger than thoseof cementite for the same volume fraction of the two phases due to the lower multiplicity of the BCCcrystal. By the symmetry of the BCC and cementite crystals, the strongest peak of ferrite is expected tobe six times higher than that of cementite for a given volume fraction of randomly oriented crystalites.An algorithm for fitting the measured XRD spectra was developed based on the Pearson-VII peakshape [83] and a least-squares optimization of the measured peaks (from the SciPy version 0.14 library[84]). The intensity of the Pearson-VII peak shape is described as a function of the Bragg angle 2θby,I =ImaxC4Hk(1+4(21m −1)(2θ −2θ0)2Hk2)−m+ Ibackground (5.1)whereC4 =(4m(21m −1)pi(m−0.5)) 12(5.2)55From this expression, the variation of peak intensity (Imax), peak width (Hk), peak position (θ 0) can bedescribed for peak shapes that vary continuously between Lorentzian (m = 1) and Gaussian (m = ∞).The XRD spectra were fit considering the presence of amorphous, ferrite and cementite. If each peakwere treated independently then there would be 25 fitting variables for the case where all three phasesare present. This number was reduced by making some assumptions about the system. Firstly, theshape factor of the ferrite and cementite peaks (m) was assumed to be identical for all peaks, as peakshape is expected to be a result of only the sample geometry, the XRD system parameters and theangle of measurement [83]. As this fitting is made over a short range of angles, and peak intensitiesare only compared for phases within a particular sample, it is reasonable to consider m as a constant.Secondly, the width of the peaks (Hk) is expected to be the same for all peaks in a given phase,with broader peaks expected for smaller crystal sizes or higher densities of crystal defects. Withthe assumption that the crystallographic texture of the samples is weak and that all crystallographicdirections contain roughly the same concentration of defects, the value of Hk should not vary for agiven phase. For all fits the background was assumed to be a constant, which is reasonable for thesesmall angle of fitting. In all cases this constant background was fit to an (arbitrary) intensity value ofapproximately 2.0. This background contribution is present in all fitting diagrams, but not explicitlyshown. When fitting spectra that include contributions from cementite, the mean position of the fivecementite peaks were constrained to be shifted in the same manner by assuming a strain along theaxes of the cementite unit cell. This introduces three variables (strains) ea, eb and ec for the cementiteinstead of the five independent variables which would exist if the peaks shifted independently. Thevalue for θ0 is calculated in this case using the Bragg equation (eqn. 5.4) with the x-ray wavelengthsλ (for both copper Kα1 and Kα2) and the imposed d values from equation 5.3 as:d =(h2a2(1+ ea)2+k2b2(1+ eb)2+−l2c2(1+ ec)2) 12(5.3)andθ0 = sin−1(λ2d)(5.4)Using this method, a physical limit was placed on the strain applied to the three directions of both thecementite and ferrite phase. In order to prevent large unphysical shifts in the any peak positions offerrite or cementite strains were limited to 1% in any of the three crystal directions.The broad peak of the amorphous phase was not well fit by the least squares algorithm and tended tosharpen and shift to fit one of the stronger crystalline peaks in multi-phase spectra. For this reason, theshape and width factors of the amorphous peak were fit to the pure amorphous spectrum from severalas-deposited samples and averaged to produce representative values (m = 1.7, Hk = 5.8). These factorswere not allowed to vary and no strain was applied to the phase, which produced a much better fit ofthe amorphous phase when convoluted with cementite and ferrite peaks.56After fitting the spectra, the intensity of the signal was integrated using a numerical method (Rombergintegration, based on the SciPy v0.14 library [84]) and the integrated intensity under each peak wascompared to the total integrated intensity of all peaks.5.2 Results5.2.1 Decomposition kinetics on isothermal annealing as measured by XRDIsochronal annealingIn order to determine the crystallization temperatures of the amorphous material produced, an initialset of experiments were carried out on XRD samples annealed for one hour at temperatures of 250,300, 350 and 500◦C. After annealing, the samples prepared at UBC showed little evidence of oxi-dation or loss of carbon as confirmed by SEM-EDX measurement. In the case of samples annealedat Rouen similar results were found, though a few small surface oxides measuring roughly 20 to 30nm in diameter, were observed in TEM samples prepared from films grown on sodium chloride sub-strates. These oxides are not expected to contribute to the XRD signal or to be evidence of significantoxidation or decarburization of the samples.Figure 5.1 shows the XRD spectra resulting from these annealing experiments. After annealing at250◦C a strong peak was observed close to the expected peak position for the {110}α ferrite peak (cf.Table 5.1). Increasing the temperature to 300 and 350◦C further led to the appearance of additionalpeaks corresponding closely to the positions expected for cementite (cf. Table 5.1 and Figure 5.1).After annealing for one hour at 500◦C both ferrite and cementite peaks were present but the peakscorresponding to cementite were observed to be much stronger.Table 5.1: Ideal position of peaks in XRD spectra for ferrite (α) and cementite (θ ) in the range 42◦ ≤2θ ≤ 48◦ with corresponding intensity ratios [85, 86]Peak and Phase 2θ Position Interatomic Spacing (nm) Intensity Factor{110}α 44.67◦ 0.7680 100.{121}θ 42.90◦ 1.301 42.8{210}θ 43.72◦ 1.036 64.4{022}θ 44.58◦ 1.690 33.0{103}θ 44.96◦ 2.075 100.{211}θ 45.84◦ 1.236 46.2Fitting the spectra for the samples annealed at 300, 350 and 500◦C following the procedure describedabove revealed a surprising result. From the integrated intensities, the fraction of ferrite in the samples57annealed at 300 and 350◦C were very similar. In contrast, the sample annealed at 500◦C appeared tocontain much less ferrite compared to cementite. While this result could reflect a difference in theprogress of transformation depending on annealing temperature for a fixed time, it was found that themore likely explanation rested with sample-to-sample variations in carbon content (see Section 4.2.3,and carbon contents of Table 5.2). SEM-EDX analysis on the samples annealed at 300 and 350◦Crevealed a carbon concentration in the films of ∼17 at.% carbon. In contrast, SEM-EDX analysis ofthe sample annealed at 500◦C revealed that it contained 22 at.%C. If we assume that the ferrite isfree of carbon and the cementite contains 25 at.%C then based on the bulk compositions one wouldpredict, based on a mass balance, that the equilibrium fraction of ferrite would be 34 vol.% for thesamples containing 17 at.%C and 12 vol.% for the sample containing 22 at.%C.This observation that the fraction of the crystallization products is highly sensitive to the startingcomposition of the films provided the motivation for performing multiple isothermal annealing exper-iments on the same sample. Results of such isothermal annealing experiments are described below.���������������������������������� ��� ��� ��� ��� ��� �����������������������������������������������������������������������������������������������������Figure 5.1: XRD spectra measured from five different Fe-C samples annealed for one hour at 250, 300,350 and 500◦C. The theoretical intensity and position of peaks for ferrite [86] and cementite [85]are also shown along the x-axis. The spectra have been artificially offset in the vertical directionto help with visualization. Note that, as explained in the text, the carbon content of the filmsvaried between 16 and 22 at.%C for these samples (see Table 5.2). Full fitting of these samplesshown in Figure 5.2Decomposition kinetics on isothermal annealing at 250◦CThe results of the above described one-hour isothermal annealing experiments support previous work[26] that has identified ferrite and cementite as the products of crystallization for amorphous Fe-C58A) B)C)02468101214161842 43 44 45 46 47 48Intensity[Arb.Units]Diffraction Angle [2Θ °]MeasuredFull FitAmorphousFerriteCementite051015202530354042 43 44 45 46 47 48Intensity[Arb.Units]Diffraction Angle [2Θ °]MeasuredFull Fit{110}αAmorphousFerriteCementiteD)E)010203040506070809010042 43 44 45 46 47 48Intensity[Arb.Units]Diffraction Angle [2Θ °]MeasuredFull Fit{110}α{121}θ{210}θ{022}θ{103}θ{211}θFerriteCementite010203040506042 43 44 45 46 47 48Intensity[Arb.Units]Diffraction Angle [2Θ °]MeasuredFull Fit{110}α{121}θ{210}θ{022}θ{103}θ{211}θFerriteCementite0102030405060708042 43 44 45 46 47 48Intensity[Arb.Units]Diffraction Angle [2Θ °]MeasuredFull Fit{110}α{121}θ{210}θ{022}θ{103}θ{211}θFerriteCementiteFigure 5.2: XRD spectra from samples annealed for one hour. Samples shown a) as deposited, andannealed at b) 250◦C, c) 300◦C, d) 350◦C, e) 500◦C. The theoretical intensity and position offerrite [86] and cementite [85] are shown along the x-axis. The least-square best fit for the ferrite(orange), amorphous (green), and cementite (purple) are shown alongside the raw data (symbols)and total fit (black).59Table 5.2: Analysis of XRD peaks for low-carbon films annealed for one hour at temperatures rangingfrom 250◦C to 500◦C, corresponding to Figures 5.1 and 5.2Temperature [◦C] Measured CarbonContent [at.%]AmorphousIntensityFerriteIntensityCementiteIntensityR2As deposited 20.1 8.51 0.0 0.0 0.978250 17.6 1.78 28.42 0.0 0.999300 17.8 0.0 68.90 18.48 0.998350 18.0 0.0 37.62 7.32 0.999500 22.2 0.0 36.97 98.75 0.992films containing <25 at.%C. What is not clear from the above experiments is how this transformationoccurs; whether one phase forms first, as previously reported [26, 29] or whether both form together.Moreover there is no literature that has attempted to quantify the composition of the product phasesor the kinetics of the crystallization. In order to provide a set of data to experimentally evaluate theseaspects of the crystallization, isothermal annealing experiments were performed. Motivated by thefact that at 250◦C no evidence of cementite was observed after one hour, whereas clear evidence ofcementite was present after the same time at 300◦C, isothermal annealing was performed at 250 and300◦C.The first condition to be investigated in this study was the continued annealing of the 250◦C sampledescribed above. SEM-EDX analysis of this sample revealed that it contained 17.5 at.%C, close tothe low end of carbon contents investigated here. Figure 5.3A shows the same spectrum as shownin Figure 5.1 and Figure 5.2B. Upon reintroducing this same sample into the furnace and annealingfor another hour (two hours total annealing time), a significant change in the spectrum appeared(Figure 5.3B). In this case the spectrum was well fit by including only ferrite and cementite, the fitsbeing shown in Figure 5.3B.This result suggests that for the case of a sample containing 17.6 at.%C held at 250◦C the crystalliza-tion occurs in two stages. In the first stage ferrite nucleates and grows, this being followed at latertimes by the formation of cementite. A more detailed picture of exactly how this process occurs willbe offered in the next section where in situ heating in the TEM will be used to clarify this sequence.The same annealing experiment was performed on another Fe-C film produced using the same V10conditions but containing 20.4 at.%C based on SEM-EDX analysis. As noted above, the stability ofFe-C films has been shown to increase under ramp-heating with increasing carbon content [26]. Onemight therefore expect a similar crystallization process for this higher carbon film, though perhapsat a slower rate. Figure 5.4 shows the result of this experiment where the measured XRD spectraare shown as well as the optimal fits assuming the presence of a combination of ferrite, cementiteand amorphous matrix. In this case, a larger range of annealing times, between 7.5 minutes and 270minutes, were explored so as to better follow the kinetics of crystallization. It is noted in this case60A) B)051015202530354042 43 44 45 46 47 48Intensity[Arb.Units]Diffraction Angle [2Θ °]MeasuredFull Fit{110}αAmorphousFerriteCementite02040608010012014016042 43 44 45 46 47 48Intensity[Arb.Units]Diffraction Angle [2Θ °]MeasuredFull Fit{110}α{121}θ{210}θ{022}θ{103}θ{211}θFerriteCementiteFigure 5.3: XRD spectra from samples containing 17.5 at.%C after annealing at 250◦C for A) 1 hourand B) 2 hours. The theoretical intensity and position of ferrite [86] (circle) and cementite [85](triangles) are shown along the x-axis. The least-square best fit for the ferrite (orange), amorphous(green), and cementite (purple) are shown alongside the raw data (symbols) and total fit (black).that the first evidence of crystallization occurs only after 60 minutes, where a peak located roughlyat the expected position for the ferrite {110} peak is observed on the strongly varying amorphousbackground. With continued holding this peak grows relative to the amorphous background up until105 minutes of holding. At the next measured time, 135 min, a sudden change in the spectra occurswith the amorphous background being significantly lower and clear peaks appearing corresponding tothe locations expected for cementite (Table 5.1). Comparing these results with those obtained for thelower carbon containing film annealed at the same temperature (Figure 5.3) clearly shows the delayin the onset of crystallization. Whereas after 60 minutes the low carbon containing film presenteda very strong ferrite peak, crystallization has only just commenced at the same time in the highercarbon containing film. The progression of crystallization is, however, remarkably similar in the twocases. It appears that the first phase to form in both samples is ferrite and that this ferrite phasegrows (alone) into the surrounding amorphous matrix, at least initially. Just as in the lower carboncontaining sample, it appears that after a sufficient time, cementite nucleates and grows. Performinga quantitative analysis of these spectra suggests that in Figure 5.4G a mixture of ferrite, cementiteand amorphous matrix co-exist in the sample and that the evolution from Figure 5.4G to Figure 5.4Hinvolves mainly the removal of the amorphous matrix by cementite with a small amount of additionalferrite being formed.Figure 5.5 shows the estimated evolution of relative XRD intensities of the amorphous, ferrite andcementite phases for the samples containing both 17.5 at.%C and 20.4 at.%C as a function of agingtime at 250◦C. This same data is also presented in Table 5.3, where the integrated intensity and thesum of square residual (R2 error estimate) is also presented. At the longest measured time (270 min)the XRD measurements indicate a microstructure comprised of ferrite and cementite. For the given61A) B)C) D)E) F)G) H)02468101214161842 43 44 45 46 47 48Intensity[Arb.Units]Diffraction Angle [2Θ °]MeasuredFull FitAmorphousFerriteCementite024681012141642 43 44 45 46 47 48Intensity[Arb.Units]Diffraction Angle [2Θ °]MeasuredFull FitAmorphousFerriteCementite024681012141642 43 44 45 46 47 48Intensity[Arb.Units]Diffraction Angle [2Θ °]MeasuredFull FitAmorphousFerriteCementite024681012141642 43 44 45 46 47 48Intensity[Arb.Units]Diffraction Angle [2Θ °]MeasuredFull Fit{110}αAmorphousFerriteCementite024681012141642 43 44 45 46 47Intensity[Arb.Units]Diffraction Angle [2Θ °]MeasuredFull Fit{110}αAmorphousFerriteCementite024681012141642 43 44 45 46 47Intensity[Arb.Units]Diffraction Angle [2Θ °]MeasuredFull Fit{110}αAmorphousFerriteCementite0510152025303542 43 44 45 46 47Intensity[Arb.Units]Diffraction Angle [2Θ °]MeasuredFull Fit{110}α{121}θ{210}θ{022}θ{103}θ{211}θAmorphousFerriteCementite010203040506042 43 44 45 46 47Intensity[Arb.Units]Diffraction Angle [2Θ °]MeasuredFull Fit{110}α{121}θ{210}θ{022}θ{103}θ{211}θFerriteCementiteFigure 5.4: XRD spectra from samples containing 20.4 at.%C after annealing at 250◦C for A) 7.5, B)15, C) 30, D) 60, E) 75, F) 105, G) 135 and H) 270 minutes. The theoretical intensity and positionof ferrite (circle) [86] and cementite [85] (triangles) are shown along the x-axis. The least-squarebest fit for the ferrite (orange), amorphous (green), and cementite (purple) are shown alongsidethe raw data (symbols) and total fit (black).62bulk composition of these samples (17.5 at.%C and 20.4 at.%C ) and assuming the cementite to haveits stoichiometric composition and that the ferrite is in equilibrium with it (i.e. the solubility ofcarbon in ferrite is given by the Fe-C phase diagram [87]), then one would expect 34 vol.% ferritein the sample containing 17.5 at.%C and 22 vol.% ferrite in the sample containing 20.4 at.%C. Thisis consistent with the normalized integrated intensities (I˜ = I/(Iθ + Iα + Ia) ) of the ferrite peaks inthe final annealing condition containing only ferrite and cementite, where I˜α (17.5 at.%C) = 0.56 andI˜α (20.4 at.%C) = 0.32. If it is assumed that the normalized intensity is proportional to the volumefraction of that phase then we find that I˜α (17.5 at.%C)/I˜α (20.4 at.%C) = 1.75 while the expected ratioof ferrite volume fractions in these two phases would similarly be 1.67.Fitting of the XRD spectra also revealed that the peak for ferrite was located nearly in its ideal po-sition for pure iron (shifted only by 0.1%) consistent with the idea that the ferrite formed here isneither under large imposed strain due to the transformation nor that it contains a high level of carbonsupersaturation. The fit of the cementite peaks did, however, require the assumption of significantstrains to its lattice. This fitting of the strain ranged between 0.1 and 0.2 % compression in the a, band c axes. Even with the assumption of this strain, the positions and intensities of the weaker {121}and {211} peaks are not well predicted, the former having a larger d-spacing than predicted and thelatter having a smaller d-spacing. The fact that these peaks are not as well fit by the fitting procedureused here can be explained by the fact that they impact less on the residual values used in the least-squares fitting routine compared to the stronger peaks in the spectra. It was also checked to ensurethat the peaks observed here did not correspond to another known carbide of similar composition. Inparticularly, based on the prior work of Bauer-Grosse et al. the theoretical peak positions of othercarbides including the Fe7C3 (both orthorhombic and hexagonal), Fe5C2 and Fe2C (both hexagonaland orthorhombic) [35, 88–92] were checked against the experimental XRD results. In all cases thecementite structure was the only one to give a close fitting to the experimental spectra, as will bediscussed in more detail in Chapter 6, see Figure 6.8.The results of the annealing experiments described above clearly show that ferrite is the first phaseto form and that it grows into the surrounding amorphous matrix regardless of the bulk carbon con-centration of the film in the range of 17 ≤ at.%C≤ 20 . Consistent with expectations and previousliterature [26], the rate of crystallization appeared to be higher in the lower carbon film, the completetransformation to ferrite occurring within the first hour of annealing compared to more than 2 hoursin the film containing the highest concentration of carbon.An interesting observation is that, while the ferrite appears to form progressively with time startingshortly after starting to anneal the sample, the formation of cementite is delayed. Once cementite doesnucleate it appears to grow rapidly.63Table 5.3: Analysis of XRD peaks for low-carbon films annealed at 250◦C showing the total integratedintensity of all peaks of each phaseFilm with 20.4 at.% carbon annealed at 250◦CTime [minutes] AmorphousIntensityFerriteIntensityCementiteIntensityR27.5 7.98 0.0 0.0 0.97815 7.22 0.0 0.0 0.97530 7.52 0.0 0.0 0.97560 7.33 0.78 0.0 0.97775 7.18 1.16 0.0 0.979105 7.56 1.99 0.0 0.978135 3.7 9.75 29.28 0.991270 0.0 25.29 65.05 0.991Film with 17.5 at.% carbon annealed at 250◦CTime [minutes] AmorphousIntensityFerriteIntensityCementiteIntensityR20 5.63 0.0 0.0 0.98160 1.78 28.42 0.0 0.999120 0.0 90.03 39.2 0.999Figure 5.5: Normalized integrated intensities (I˜) for the amorphous, ferrite and cementite phases esti-mated from the XRD spectra in Figure 5.4 and Table 5.3 as a function of annealing time at 250◦Cfor a sample containing 20.4 at.%C. The solid lines are simply intended as guides to the eye.64Decomposition kinetics on isothermal annealing at 300◦CA similar set of experiments to those described above were performed on two Fe-C samples at anannealing temperature of 300◦C. As above, the samples selected for study had a low (16.1 at.%C) andhigh (20.1 at.%C) carbon content so as to assess the effect of variations in starting carbon compositionon the crystallization kinetics and products (the overall analysis of the XRD spectra can be seen inTable 5.4). As expected based on the results presented above, the lower carbon 16.1 at.%C filmrapidly crystallized to a mixture of ferrite and cementite within 7.5 minutes, the shortest time used forthe experiments (Figure 5.6). The only change observed on holding of this sample for longer times isa slight sharpening of the ferrite peak (Hk decreases continuously from 0.43 to 0.35 on holding).Table 5.4: Analysis of XRD peaks for low-carbon films annealed at 300◦C showing the total integratedintensity for all peaks of each phaseFilm with 20.1 at.% carbon annealed at 300◦CTime [minutes] AmorphousIntensityFerriteIntensityCementiteIntensityR27.5 3.82 3.38 3.47 0.9730 1.20 9.96 26.6 0.9960 0.0 16.17 37.37 0.99Film with 16.1 at.% carbon annealed at 300◦CTime [minutes] AmorphousIntensityFerriteIntensityCementiteIntensityR27.5 0.0 36.41 20.32 0.9915 0.0 48.59 16.07 0.9930 0.0 42.91 20.95 0.9960 0.0 51.13 18.07 0.99The sample containing 20.1 at.%C was again seen to transform to a mixture of ferrite and cementitebut, as above, at a much slower rate than the sample containing 16.1 at.%C (Figure 5.7). Crystalliza-tion had already commenced at 7.5 minutes but unlike the results of crystallization at 250◦C there isclear evidence of both ferrite and cementite growing together into the amorphous matrix. ComparingFigure 5.7B and 5.7C one sees a much stronger background in the former compared to the later. Thatis interpreted here to indicate the co-existance of some remaining amorphous matrix with the growingferrite and cementite. This is also reflected in the growing integrated intensity of ferrite and cemen-tite phases. After 60 minutes the fitting of the spectrum indicates no remaining amorphous matrix.Figure 5.8 summarizes the XRD results for this condition showing the evolution of the normalizedintensities of the ferrite, cementite and amorphous phases for this sample. Comparing to the resultsfrom the sample containing 20.4 at.%C and annealed at 250◦C one sees that the transformation is notonly shifted to shorter times but that the rate of formation of cementite is also slower. Whereas at250◦C the formation of cementite appeared to occur very rapidly after a long delay (relative to theonset of crystallization to ferrite), at 300◦C the rate of growth of ferrite and cementite appear more65A) B)C) D)0102030405060708042 43 44 45 46 47Intensity[Arb.Units]Diffraction Angle [2Θ °]MeasuredFull Fit{110}α{121}θ{210}θ{022}θ{103}θ{211}θFerriteCementite0102030405060708042 43 44 45 46 47Intensity[Arb.Units]Diffraction Angle [2Θ °]MeasuredFull Fit{110}α{121}θ{210}θ{022}θ{103}θ{211}θFerriteCementite0102030405060708042 43 44 45 46 47Intensity[Arb.Units]Diffraction Angle [2Θ °]MeasuredFull Fit{110}α{121}θ{210}θ{022}θ{103}θ{211}θFerriteCementite010203040506070809042 43 44 45 46 47Intensity[Arb.Units]Diffraction Angle [2Θ °]MeasuredFull Fit{110}α{121}θ{210}θ{022}θ{103}θ{211}θFerriteCementiteFigure 5.6: XRD spectra from samples containing 16.1 at.%C after annealing at 300◦C for A) 7.5minutes, B) 15 minutes, C) 30 minutes and D) 60 minutes. The theoretical intensity and positionof ferrite [86] and cementite [85] are shown along the x-axis. The least-square best fit for theferrite (orange) and cementite (purple) are shown alongside the raw data (symbols) and total fit(black).similar, the cementite growing over a longer period of time.As in the case of samples annealed at 250◦C, the final observed microstructure after annealing at300◦C consisted of ferrite and cementite. In this state the normalized integrated intensity for theferrite peak was found to be I˜α (16.1at.%C) = 0.73, while I˜α (20.1at.%C) = 0.31 consistent with thevery different carbon contents of the films. Comparing the ratios of these normalized intensities tothe ratios of the equilibrium volume fractions of ferrite shows that I˜α (16.1at.%C)/I˜α (20.1at.%C) =2.35, while the expected ratio of ferrite volume fractions in these two phases would similarly be0.41/0.23 = 1.78. Thus, the integrated ferrite peak intensity increases with decreasing carbon contentas expected, but the correlation between integrated intensity and volume fraction is in. This maybe attributable to the challenge in unambiguously performing peak fitting particularly in the case ofmultiple overlapping peaks or to the uncertainty in the composition of the phases (particularly ferrite)66A) B)C)0246810121442 43 44 45 46 47Intensity[Arb.Units]Diffraction Angle [2Θ °]MeasuredFull Fit{110}α{121}θ{210}θ{022}θ{103}θ{211}θAmorphousFerriteCementite051015202542 43 44 45 46 47Intensity[Arb.Units]Diffraction Angle [2Θ °]MeasuredFull Fit{110}α{121}θ{210}θ{022}θ{103}θ{211}θFerriteCementite0510152025303542 43 44 45 46 47Intensity[Arb.Units]Diffraction Angle [2Θ °]MeasuredFull Fit{110}α{121}θ{210}θ{022}θ{103}θ{211}θFerriteCementiteFigure 5.7: XRD spectra from samples containing 20.1 at.%C after annealing at 300◦C for A) 7.5minutes, B) 30 minutes and C) 60 minutes. The theoretical intensity and position of ferrite [86]and cementite [85] are shown along the x-axis. The least-square best fit for the ferrite (orange),amorphous (green), and cementite (purple) are shown alongside the raw data (symbols) and totalfit (black).in the final product. To better understand these results, a more local analysis must be performed asdescribed below.5.2.2 Microstructure observation by TEMIn order to confirm the above results a series of samples were prepared for TEM observation at theUniversity of Rouen. Following the annealing experiments described above, the first samples to beobserved by TEM were annealed for one hour at 200◦C, 250◦C and 300◦C.The first condition to be observed was a sample prepared on a salt crystal, floated off, captured on acopper grid and then annealed for one hour at 200◦C within the grid. The post heat-treatment TEMobservation through thickness showed the sample to be featureless and the selected area diffraction67Figure 5.8: Normalized integrated intensities (I˜) for the amorphous, ferrite and cementite phases as afunction of annealing time at 300◦C for the film containing 20.1 at.%C. The bold solid lines areintended as a guide to the eye, while the dashed lines show the same guides used in Figure 5.5for the sample containing 20.4 at.%C annealed at 250◦C.pattern (Figure 5.9) to exhibit only diffuse rings characteristic of a fully amorphous microstructure.A second set of samples were prepared for observation after annealing at 250◦C for one hour, in onecase samples were prepared as above from salt crystals while in the second case observations weremade on samples that had been deposited onto an IF-steel substrate and then sectioned via FIB toreveal the film structure through thickness. The results of both analyses revealed the same generaltrends (with small differences arising from the differences in the carbon content of the films). Theadvantage of the samples prepared on the IF-steel substrate was that much thicker films could bemade, thereby reducing the effects of surfaces. During the same deposition run silicon substrateswere positioned alongside the IF-steel substrate allowing for films to be produced that could be usedfor the unambiguous bulk determination of carbon content by EDX.Figure 5.10 shows the microstructure formed by annealing the film that had been deposited onto anIF-steel substrate where EDX analysis performed on material deposited during the same depositionon silicon wafer identified the carbon content as 15.8 at.%C. In this case clear evidence of the coex-istence of three phases in bright field TEM images was obtained. Selected area diffraction revealedcrystalline spot patterns superimposed on broad amorphous rings. The crystalline spots are consis-tent with the existence of both a crystalline BCC phase and a smaller amount of crystalline cementiteembedded within an amorphous matrix. Local diffraction measurements as well as lattice resolution68Figure 5.9: Selected area diffraction pattern from an Fe-C sample prepared in the low-carbon condi-tion, annealed for one hour at 200◦C. No evidence of crystallization was observed, consistentwith XRD observations presented above.TEM (Figure 5.12) confirmed that the spots in the SADP arise from the presence of these crystallinephases. The coexistence of all three phases at this time and temperature is somewhat different fromthe XRD observations reported in Figure 5.3 where after one hour for a sample containing 17.5 at.%Conly ferrite and cementite co-existed. The appearance of cementite after only one hour at this tem-perature reflects the low carbon content of this film which, as shown from the XRD results, tends toaccelerate the transformation (e.g. compare Figure 5.3 and Figure 5.4).As expected, no particular preferential crystallographic orientation of the crystalline phases was ob-served. In the case of the samples annealed on the IF-steel substrate, however, the fraction of ferriteappeared to depend on location in the film. As can be seen in Figure 5.10 there is a clear preferencefor ferrite nucleation at the IF-steel interface. Otherwise, in both samples, the ferrite crystals appearedto be distributed approximately randomly throughout the film.It is also obvious in Figure 5.10 that a compositional difference exists at the interface between the filmand substrate as indicated by the bright line delineating the interface. Energy filtered TEM (EFTEM)imaging of the near-interface region (Figure 5.11) revealed the presence of a thin oxygen rich layer atthe film-substrate interface. It was found that such a thin oxygen rich layer was present in all of thefilms studied and was likely present as a native oxide on the substrate prior to deposition. Interestingly,one can clearly see the ferrite crystals aligned along the interface on the film side of the oxygen richlayer as a region having a much lower carbon content compared to the carbon level in the amorphousportions of the film. Similarly the IF-steel substrate is seen to be much lower in carbon than the film,as expected. The composition differences between the phases will be discussed in more detail below.69(a) (b)Figure 5.10: a) Cross-sectional TEM image of film containing 15.8 at.%C prepared by FIB section-ing after annealing on an IF-steel substrate for one hour at 250◦C showing spherical ferriteprecipitates and some cementite crystallites embedded in an amorphous matrix, with b) highermagnification of the interface region between an IF-steel substrateFigure 5.11: EFTEM imaging near the interface between the Fe-C film containing 15.8 at.%C afterannealing at 250◦C for one hour. One can see the presence of a thin oxide layer at the substrate-film interface. The layer of ferrite crystals aligned along the interface on the film side is alsoobserved as a region of low carbon on the film-side of the oxygen rich layer. As expected, thesubstrate is observed to contain lower levels of carbon.70In previous literature it has been suggested that the amorphous Fe-C phase can phase separate into car-bon rich and carbon lean regions [37]. The lack of strong variations in contrast within the amorphousregion in the lattice images (Figure 5.12) suggests that this is not the case for the samples studied here.Rather, the structure of the amorphous matrix appears homogeneous over the region of observation.Figure 5.12: HRTEM image taken from the same film as shown in Figure 5.10. The inset shows ahigher magnification view of the interface between the amorphous and crystalline BCC phasesillustrating its atomic sharpness.Finally, after annealing at 300◦C for one hour, the expected mixture of ferrite embedded in a crys-talline cementite matrix was observed in TEM with no evidence of remaining amorphous matrix.Figure 5.13 shows a bright field TEM image taken through-thickness from a sample that had beenfloated off of a sodium chloride crystal and annealed showing equiaxed ferrite crystals, similar in sizeand morphology to those seen in Figure 5.10, embedded within a cementite matrix. To confirm thesephases as ferrite and cementite local selected area diffraction was performed (Figure 5.13 insert). Asin the one hour, 250◦C sample, the equiaxed crystals showed a spot pattern consistent with ferrite. Inboth the sample annealed at 250◦C and 300◦C the features of the cementite were surprising. Ratherthan the featureless amorphous matrix, the phase surrounding the ferrite crystallites was observedto contain a high density of planar defects. These give rise to streaking in the diffraction pattern inFigure 5.13. Despite this streaking, it was possible to confirm the spacing to be coincident with theexpected {004} planar spacing of cementite. Similar faulted cementite has been previously reportedas arising from the annealing of amorphous Fe-C films (see e.g. [93] and [94]).To this point, the TEM analysis has focused on qualitative observation from bright field imaging andfrom crystallographic information from diffraction. What is not known, and has not been previouslybeen reported in the literature, is the composition of the two phases formed by the transformation.71Figure 5.13: Bright field TEM images of a∼15 at.% carbon film deposited on sodium chloride, floatedonto a copper grid and annealed for one hour at 300◦C. Inlaid SAED image shows a patternwith points corresponding to the low-contrast grains and streaking corresponding to the faulted(striped) grains. The faulting in this case gives rise to extensive streaking in the selected areadiffraction pattern. The spacing between streaks was found to correspond to 2.26 A˚.To give a first, qualitative view of the expected redistribution of carbon between ferrite and matrix(cementite) phases, EFTEM imaging was performed. As shown in Figure 5.14, and consistent withFigure 5.11, EFTEM imaging reveals the ferrite crystallites to have a low carbon content, much lowerthan the surrounding cementite in the case of the samples annealed at 300◦C. Moreover, no signif-icant gradients in carbon were observed and no clear variations in the carbon (or iron) distributioncorresponding to the faults in the cementite phase. This would appear to qualitatively suggest that thefinal product of crystallization is near equilibrium in terms of the distribution of carbon. This will bereturned to quantitatively when the results of atom probe tomography are presented.The above observations appear to corroborate the bulk XRD observations, while providing furtherinsight into the chemistry and structure of the phases formed. What is not clearly seen, however,is how the transformation proceeds for a given annealing temperature. In order to pursue this thecrystallization of a sample containing between 15 and 20 at.%C was studied during in-situ heatingin the TEM. As above, samples were prepared by floating very thin films (∼ 50 nm) off of sodiumchloride crystals. As such, the exact composition of the sample was not obtained, though it is expectedthat the composition was close to 17–18 at.%C based on the similarity of the transformation kineticsto those corresponding to the sample shown in Figure 5.3. Figure 5.15 shows a series of bright fieldimages taken in-situ during the annealing of the sample. In the early stages of annealing the sampleswere homogeneous except for some surface oxide and contamination which can be seen as light and72Figure 5.14: a) Bright field TEM image b) energy filtered (EFTEM) image for iron and c) carbondark areas on the images. As annealing progresses, evidence of crystallization appeared within thefirst minute. After 5 minutes, clear evidence of several nuclei (light regions on the darker background)could be clearly seen. Post-annealing diffraction analysis confirmed these first particles to be ferrite,consistent with the discussion above.From these images, quantitative image analysis was performed to obtain the average equivalent areadiameter (EQAD) and the number of ferrite particles in the field of view (N). These were estimatedby taking each image and manually tracing the outline of the ferrite particles. These were then loadedinto ImageJ software [95] where measurements were performed. Only particles fully contained withinthe area of analysis were included. Because the same area was observed throughout the annealingtreatment, it was also possible to follow the evolution of the size of 24 individual ferrite crystals overthe entire period of observation at 250◦C.From this information the volume fraction of ferrite was estimated from,f f erriteV (t) =1Aδ[43pi(EQAD2)3∗N (t)](5.5)and the number density of ferrite particles as,N f erriteV (t) =N (t)Aδ(5.6)In these equations N (t) is the number of observed ferrite crystals at the observation time t and A isthe observation area. To estimate the volume it was necessary to estimate the sample thickness δ .This was done using the sample thickness calibration (12.2± 0.5 nm/min) given in Chapter 4 and theknown time of deposition (2.5 minutes).Figure 5.16 shows that the number density of ferrite crystals rises rapidly over the first ∼10 min-73Figure 5.15: Sequential images of in situ TEM annealing at 5 (a), 10 (b) and 40 (c) minutes for 250◦Cannealing of a V10 methane voltage sample. Two ferrite grains (1, 2) have been labelled aslandmarks.utes before it reaches a nearly constant value of ∼ 8× 1021 m−3. Comparing this plot to the plot ofEQAD (Figure 5.17) one can see that while N f erriteV saturates quickly, the particle size continues toincrease over the entire period of observation. The combination of these two observations results inthe variation in the volume fraction with time (Figure 5.18). Here it can be seen that the volumefraction continues to rise relatively rapidly beyond 10 minutes (corresponding to reaching saturationof the number density), and the volume fraction appears to saturate at around ∼23 vol.% ferrite. In-terestingly, the equilibrium fraction of ferrite for the composition of this film would be expected tobe ∼35 vol.%, thus the slowing of the transformation at 250◦C appears not to be due to reaching avolume fraction that would be predicted from the equilibrium of ferrite in contact with cementite.After holding for 40 minutes at 250◦C and observing that the evolution of the transformation hadslowed dramatically, it was decided to raise the temperature at a rate of 50◦C/min. Figure 5.19 showsbright field images of the sample after holding 40 minutes at 250◦C, the microstructure after heatingthis same sample to 350◦C (42 minutes), and 400◦C (43 minutes). In the all cases, the microstructurewas observed to remain a mixture of ferrite and amorphous matrix, but the fraction of ferrite was74Figure 5.16: Number density of ferrite crystals obtained from quantitative image analysis of the imagesshown in Figures 5.15 and 5.19. The thickness of the samples was estimated based on thedeposition rate as described in the text.observed to increase. At the same time, the number density of ferrite was observed to slightly de-crease, this being largely due to coalescence of pre-existing ferrite particles. The result of this heatingwas the observed volume fraction of ferrite increased from 23 vol.% to 36v˙ol.% by the time 400◦Cwas reached. This was accomplished by the rapid growth of the pre-existing ferrite from an averageEQAD of 39 nm after 40 minutes at 250◦C to 46 nm after heating to 400◦C.The heating was continued to 450◦C where it was almost immediately observed that a second crys-talline phase (later confirmed by SADP to be the same faulted cementite shown in Figure 5.13) nu-cleated and grew rapidly. Figure 5.20 shows the same region observed after one minute at 400◦C andafter one minute at 450◦C. The appearance of the characteristically faulted cementite phase betweena cluster of ferrite particles is clear. Identifying the location where nucleation commenced was im-possible, however, as the cementite, upon nucleation, grew very rapidly to the size that can be seenin Figure 5.20. Notably, the cementite grain size is much larger than the average ferrite grain size, itsdiameter being roughly 200 nm in size. Upon holding, at this temperature, more cementite particlessimilar to that observed in Figure 5.21 formed until, after∼3 minutes at 450◦C the microstructure ap-peared to be completely composed of ferrite and cementite, with no amorphous phase remaining. Asin the case of the first cementite particle observed, all cementite appeared faulted, and grew extremely75Figure 5.17: Average equivalent area diameter of ferrite crystals measured from observation of Figures5.15 and 5.19. All measurements shown are during the stage of annealing when only ferrite andamorphous phases were identified.rapidly to a size of between 100 and 200 nm. Thus, the number density of cementite in these samplesis expected to be more than an order of magnitude smaller than the number density of ferrite particles.The results of the in situ observations described above, qualitatively mirror the XRD observationsmade on the 17.5 at.%C film annealed isothermally at 250◦C in that these observations confirm thetwo step process of crystallization from the amorphous amorphous; first to an amorphous matrix plusferrite, where a slowing of the rate of ferrite growth is observed with time, then to a conversion ofthe remaining amorphous phase to cementite upon holding for longer times (XRD observation) orupon increasing the annealing temperature (in situ TEM). It is interesting to note that the formation ofcementite does not seem to be limited by its growth but rather by its nucleation. The other surprisingobservation here is the fact that the volume fraction of ferrite appears to stabilize at 250◦C beforeincreasing again when the temperature was raised. This increase in volume fraction does not appearto be due to nucleation of new ferrite crystals, but rather the growth of pre-existing ferrite crystals.To gain a full understanding of the crystallization behaviour of the film it is important to know thechemistry of the phases that are formed. From EFTEM observations shown in Figures 5.11 and 5.14it is clear that carbon redistributes between the ferrite and cementite phases, though these results canonly be considered as qualitative. As a final step in the characterization of these materials, the local76Figure 5.18: Evolution of the volume fraction of ferrite in Figures 5.15 and 5.19 assuming the ferritecrystals to have the average EQAD from Figure 5.17 and number density from Figure 5.16. Thelarge symbols indicate the volume fraction assuming the average sample thickness while thesmall symbols show the upper and lower bound based on using the largest and smallest samplethicknesses based on the deposition rate.Figure 5.19: In-situ annealed sample observed through thickness in BF-TEM showing the evolution ofthe microstructure as the sample was heated from 250◦C to 400◦C at a rate of 50◦C/min. Theonly significant change apparent is growth of pre-existing ferrite crystals.77Figure 5.20: The same area of in-situ annealed sample observed at 400◦C (left) and 450◦C (right)with one minute between the images. A single faulted cementite crystal is highlighted in the inimage on the right and the same corresponding area is similarly highlighted (prior to cementiteformation) in the image on the left.Figure 5.21: Evolution of the microstructure as the in situ heated TEM sample was held at 450◦C.The main microstructural change in this case corresponded to the nucleation and growth ofcementite. Dark ring corresponds to the contamination from higher magnification observationsmade at the lower temperature (Figure 5.15)78composition of the films during crystallization was measured and is described below.5.2.3 Atom probe tomography measurementsTo complement the observations made above, APT analysis was performed on films that had beendeposited onto an IF-steel substrate then annealed at 250◦C for one hour, or 300◦C for one hour.Both samples came from the same deposition and were found by EDX analysis to contain 15.8 at.%Cbased on measurements made on a film deposited on a silicon substrate during the same depositionrun. Other details of the steps involved in preparing the APT samples and analyzing the resulting datahave been discussed in Chapter 4 (see Sections 4.3.3).The first analysis, performed on the sample annealed at 250◦C produced a large dataset containing8.4 million atoms in a volume approximately 232 nm in length and 30 nm in diameter (at its base).Measurement of the atomic concentration of the full volume was shown to include mainly iron andcarbon. Quantitative analysis of this volume revealed that the film contained 86.0 at.%Fe, 13.9 at.%C,0.1 at.%O and < 0.1 at.% of any other elements.Figure 5.22 shows the three-dimensional reconstructed volume showing the position of Fe (black) andC (pink) atoms. One can clearly see from this volume that two phases appear to co-exist; a carbon richphase and a carbon lean phase. Based on the above TEM observations of samples annealed at 250◦Cfor one hour, it is likely that the carbon rich region is either the amorphous matrix or cementite, whilethe carbon poor regions are ferrite crystals.From this APT volume it was possible to analyze the distribution of C and Fe atoms within each phase.Figure 5.22 illustrates the mass spectrum for the carbon rich and carbon lean regions. Sub volumeswere taken within the carbon rich and carbon lean regions of the sample. Within the carbon rich regionthe analysed volume was 100 nm× 10 nm× 10 nm in size (containing 461,765 atoms), and within thecarbon-lean region the analysed region was × 60 nm × 10 nm × 10 nm in size (containing 204,695atoms). The The compositions of sub-volumes taken within this sample are given in Table 5.5. Ascan be seen, the carbon rich region contains approximately 25 at.%C while the carbon poor regioncontains only 0.04 at.%C (±0.01 at.%). It is also worth noting that the highest level of contaminationfrom other elements was due to oxygen at 0.15 at.% in the carbon lean region.Table 5.5: Composition (at.%) of carbon rich and carbon lean sub-volumes illustrated in Figure 5.22for an APT tip taken from a sample annealed at 250◦C for one hour.Region / Element Fe C O Si OtherCarbon Rich Sub-Volume 75.17 at.% 24.69±0.13 at.% 0.07 at.% <0.03 at.% <0.03 at.%Carbon Lean Sub-Volume 99.78 at.% 0.04±0.01 at.% 0.15 at.% <0.02 at.% <0.02 at.%Within the carbon rich region in Figure 5.22 it was found that the distribution of C and Fe atoms79Figure 5.22: Left, APT volumes of sample containing 15.8 at.%C after annealing for one hour at 250◦,showing position of both carbon (pink) and iron (black). Right, the carbon and iron concentra-tion profile of the sample within the region indicated at left.were very uniform. Figure 5.22 shows the average carbon and iron concentration in transverse slicesmeasured along the length of the sub-volume in the carbon rich region indicated at left. As can be seen,the carbon concentration does not systematically vary over the length of the analysis sub-volume.Two further parallelepiped sub-volumes were prepared from this same APT volume, these crossingthe interface between the carbon rich and carbon lean regions (Figures 5.23 and 5.23). These paral-lelepipeds were oriented so that their long axes were perpendicular to the interface. The first In thiscase, the carbon content was observed to vary smoothly between ∼0.04 at.% and ∼25 at.%C. Impor-tantly, no sharp spike in carbon content was observed in front of the interface, as would be expectedif the growth of the ferrite phase was controlled by diffusion away from the advancing interface.The APT volume measured from the sample annealed at 300◦C for one hour appeared (Figure 5.24)very similar to the one shown above (Figure 5.22). Overall, the composition of this volume was foundto be 87.3 at.%Fe, 12.3 at.%C, 0.05 at.%O and < 0.06 at.% other elements. The fact that the C con-tent of this volume is low compared to the expected bulk composition (15.8 at.%C) is likely due tothe rather small volume and the rather large portion of the volume occupied by the carbon lean (fer-rite) phase. Extracting a parallelepiped (30 nm × 8 nm × 8 nm, containing 59,700 atoms) from thecarbon rich region revealed it to contain 26.66±0.40 at.%C with the highest impurity being oxygen80Figure 5.23: The same APT volume as shown in Figure 5.22 showing two profiles of analysed sub-volumes along lines 1 and 2 as marked, calculated in slices perpendicular to the axis of thesub-volume.(0.03 at.%) (Table 5.6). The concentration profile along this volume was also very flat, showing nosignificant variations along its length (Figure 5.24). Extracting a parallelepiped (30 nm × 10 nm ×10 nm, containing 97,168 atoms) from the carbon rich region, on the other hand, showed almost ex-actly the same composition as the carbon lean phase formed at 250◦C, with 0.20±0.04 at.%C (highestimpurity, oxygen at 0.07 at.%, Table 5.6). Finally, a parallelepiped sub-volume (25 nm × 6 nm × 6nm, 259,135 atoms) was extracted across the phase interface as shown in Figure 5.25. Again, thisprofile revealed a small composition variation across the phase interface. A slight enhancement ofcarbon (∼2 at.%C) was observed just on the carbon rich side of the interface, which decreases backtowards the bulk content within 5 nm of the interface.Table 5.6: Composition (at.%) of carbon rich and carbon lean sub-volumes illustrated in Figure 5.24for an APT tip taken from a sample annealed at 300◦C for 1 hour.Region / Element Fe C O Si OtherCarbon Rich Sub-Volume 73.31 at.% 26.66±0.4 at.% 0.03 at.% <0.01 at.% <0.01 at.%Carbon Lean Sub-Volume 99.72 at.% 0.20±0.04 at.% 0.07 at.% <0.01 at.% <0.01 at.%81Figure 5.24: Left, APT volumes of sample containing 15.8 at.%C after annealing for one hour at 300◦,showing position of both carbon (pink) and iron (black). Right, the carbon and iron concentra-tion profile of the sample within the region indicated at left.It is interesting that the two atom probe tomography volumes presented above look so similar consid-ering that they come from samples where the phase mixture is expected to be predominantly ferriteand amorphous, for samples annealed at 250◦C, and ferrite and cementite for samples annealed at300◦C. Assuming the carbon-rich areas of the 250◦C sample are amorphous, these results would sug-gest that the amorphous phase becomes heavily enriched in carbon rejected from the growing ferrite.This enrichment occurs up until the amorphous phase reaches a composition of∼25 at.%C at at 250◦Cat which point the transformation stops until the amorphous matrix is able to transform to cementite atsome later time. In the case of the sample annealed at 300◦C, the APT results would suggest that thefaulted cementite phase is slightly enriched in carbon (∼27 at.%C) relative to what would be expectedin bulk cementite (25 at.%C).82Figure 5.25: Left, The same APT volume as shown in Figure 5.24 showing a sub-volume crossing theinterface between carbon rich and carbon lean regions. Right, carbon composition averaged inslices along the length of the sub-volume shown at left.835.3 DiscussionThe results presented above confirm previous reports that amorphous iron-carbon films containing≤25 at.%C crystallize to a mixture of ferrite plus cementite [26, 29], but go further by providing newinsight into the kinetics and crystallization pathway followed during isothermal crystallization. Inparticular, it is shown that crystallization occurs;1. By a two-stage crystallization where the ferritic phase precedes the formation of the cementitephase2. With kinetics of transformation that are strongly influenced by the carbon content of the amor-phous phase, the kinetics decreasing with increasing carbon content3. By ferrite forming via the rejection of carbon into the surrounding amorphous matrix, leading toa nearly carbon free ferrite phase4. With no evidence of large scale carbon inhomogeneity in the surrounding phase arising from thecarbon redistribution away from the growing ferrite5. That the formation of cementite has a long incubation time followed by rapid growth. A lownumber density of cementite grains form compared to ferrite.In the discussion that follows these observations will be considered in relation to relevant literatureand possible mechanisms controlling phase selection and formation.5.3.1 Sequence of phase formation on crystallizationAccording to the XRD, TEM and APT results presented above, the first product of crystallizationis body centred cubic ferrite containing only a very small amount of carbon in solution. The APTresults presented in Section 5.2.3 clearly reveal, for the first ferrite formed, that the amount of carbonin solution is similar to that found under conditions where ferrite is in equilibrium with cementite atlow temperatures. At 250◦C the equilibrium amount of carbon dissolved in ferrite should be 0.1 at.%carbon when in equilibrium with cementite [96], this to be compared with the 0.04±.01 at.%C mea-sured in Figure 5.23, Table 5.6. The fact that nearly carbon free ferrite is the first phase to form isnot obvious given that the composition of the ferrite is far from the composition of the amorphousmatrix. In contrast, other phases (e.g. face centred cubic austenite or carbides such as Fe3C or Fe2C)could form with carbon contents closer to those of the as-deposited amorphous film without the needfor large amounts of carbon redistribution back into the amorphous matrix. This has led previous84authors to assume that the ferrite formed on crystallization contains a high level (>1 at.%) of carbonin supersaturation, something that has been found in crystalline iron-carbon films formed directly byPVD [27].As an alternative to the formation of ferrite, one could imagine the amorphous film transforming ina massive fashion to austenite having the same (or nearly the same) composition as the amorphousmatrix. In steel processing it is possible to stabilise austenite at high carbon contents and results havebeen presented of austenite formation by carbide dissolution during severe plastic deformation (e.g.[97]). Carbon contents in the range of 1 at.% are sufficient to stabilize austenite to room temperature[98]. To examine the relative stability of these phases, the Gibbs free energy curves for the binaryiron-carbon system at 250◦C are shown in Figure 5.26. These curves have been constructed usingthe Thermo-Calc TCFE7 database [99] where the liquid phase is used as a proxy for the free energycomposition curve of the amorphous phase, as is commonly done for amorphous alloys (e.g. [30]).Extrapolation of the free energy expressions of the liquid to such low temperatures is not expected tobe fully reliable and may or may not be an adequate representation of the free energy of the amorphousphase.����������������� �� ��� ��� ��� ��� ������������������������������������������������������� ��������������������������������Figure 5.26: Gibb’s free energy of system variation with carbon content at 250◦C as calculated byThermo-Calc [99], where the free energy of the liquid is used as a proxy for the free energy ofthe amorphous phase. The shaded box illustrates the composition range of interest in this study,i.e. 16-20 at.% carbon.Figure 5.26 shows that for the composition range of interest here, the free energy of the amorphousphase is greater than the free energy of austenite but lower than ferrite when compared at the samecomposition. Thus, if a massive transformation were to occur, one might expect austenite rather than85�������������������������� �� ��� ��� ��� ��� ���������������������������������������������������������������������������������� ���������������������������������������������������(a)�������������� �� ��� ��� ��� ��� ������������������������������������������������������� ����������������������������(b)Figure 5.27: Total free energy change of a transformation of the system from liquid (a) into ferrite (α),austenite (γ), a combination of ferrite and cementite (α+Fe3C, and a combination of ferrite +liquid (α+a) a) shown schematically and b) calculated change in Gibb’s free energy for eachtransformation.ferrite as a final phase. If instead the system is free to re-distribute carbon, the lowest free energy inthe range of interest would be that of a mixture of ferrite and cementite, as shown by the commontangent in Figure 5.27a, thus a coupled eutectoid-like transformation to ferrite and cementite (pearlite)could lead to the largest free energy decrease in the system. While ferrite and cementite are the phasesthat ultimately form the final state obtained in these experiments (see Section 5.2), it is surprising thatthe system chooses the path it does; i.e. formation of low carbon ferrite prior to the formation ofcementite. The free energy change of this transformation is nearly identical to that predicted for adirect transformation to austenite as shown in Figure 5.27b, and much lower than that predicted forthe transformation directly to ferrite and cementite.To estimate the free energy change associated with the transformation of some part of the amor-phous matrix to ferrite (here for simplicity assumed to contain no carbon), a common tangent can beconstructed between the free energy curve for the liquid (amorphous) phase and ferrite. For a bulkcomposition of 16 at.% carbon, at 250◦C this common tangent is also nearly tangent to the free en-ergy curve of austenite (as shown in Figure 5.27). At this bulk composition, the crystallization ofaustenite having the same composition as the matrix would lead to a similar free energy decrease asthe formation of carbon-free ferrite.In cases like this where the parent phase is very highly supercooled it is commonly found that thefirst phase to form on crystallization is not the one that would be expected based on the considerationof free energy changes alone. Based on these observations, Ostwald [100] proposed his so-called“step rule” which states that the first phase to form from a supercooled liquid should be the one86that has a free energy most similar to that of the liquid. This has subsequently been re-examinedand re-interpreted to read that the first phase to form should be the one with the lowest nucleationbarrier [101]. Interestingly, in relation to the work in this thesis, it has been shown theoreticallythat a metastable body centered cubic phase can have a low barrier for formation, and therefore iseasy to form in “simple liquids” [102, 103]. There are numerous examples of atomistic simulationsillustrating the formation of a BCC phase in place of, or alongside, the equilibrium phase duringcrystallization of supercooled metal (and metal-like) liquids [104–107]. A very recent example frommolecular dynamics simulations illustrates how the BCC phase can be preferred during crystallizationin a range of undercoolings for pure Cu [108]. Support for the preferential nucleation of a metastableBCC phase in metallic systems is not limited to theory. Experiments on metallic alloys (e.g. Fe-Ni alloys) where the FCC phase should be the equilibrium phase also revealed the formation of apre-cursor BCC phase [109–111]. Such observations suggest that the formation of ferrite observedhere may not be explainable by equilibrium thermodynamics alone. The kinetics of formation, ascharacterized by the barrier for nucleation, may play an important role in this case.In the case of crystallization occurring at 300◦C in films containing ∼20 at.%C the observations atshort annealing times revealed the presence of both ferrite and cementite. In this case one needs todistinguish between whether,1. Cementite formed prior to ferrite2. Coupled (eutectoid) growth of ferrite and cementite occurred3. Whether (like at the lower temperature) ferrite formed first followed later by the formation ofcementiteThe ex-situ TEM observation of this condition revealed the microstructure to be identical to the fi-nal microstructure observed in samples annealed at the lower temperature where ferrite nucleationand growth precedes the formation of cementite. While this does not rule out the possibility that ce-mentite formation preceded the formation of ferrite, there is no reason to believe that such a changeshould occur between 250◦C and 300◦C. Finally, as will be seen in the next chapter, ferrite appears toform first even when the bulk carbon content of the amorphous matrix exceeds 25 at.%C (i.e. abovethe stoichiometry associated with cementite). In the next two sections, discussion will focus on theformation of ferrite in the absence of cementite. This then will be followed by a discussion of theformation of cementite.5.3.2 Nucleation of ferrite in amorphous iron-carbonAs shown above, the nucleation and growth of ferrite is an important first step in crystallization. Tosimplify analysis here, the specific case of the amorphous samples containing 16 at.%C, crystallized at87250◦C will be focused on. For this condition XRD analysis, in-situ TEM and ex-situ APT observationsprovide a robust set of results to analyze.Above it was argued, via the modified Ostwald step rule, that the first phase to form during crystalliza-tion will be the one having the lowest energy barrier. Quantitatively evaluating this activation barrieris, however, a significant challenge. In recent work on the crystallization of Al-Ni-Y metallic glasses,classical nucleation theory (CNT) was used in an attempt to rationalize the unexpected sequence ofphases observed [112]. As noted in that work, CNT is not expected to give a quantitatively correctassessment but should be useful for order of magnitude predictions and for checking whether it is pos-sible that a loss of driving force for nucleation could be at the origins of the cessation of nucleationnoted above.Assuming that nucleation of spherical ferrite particles occurs homogeneously from a chemically uni-form matrix, the rate of formation of new nuclei is represented by:dNssdt= Zβ ∗exp(−16pi3kBγ3T∆G2v)(5.7)where Z is the Zeldovich non-equilbrium parameter, β is related to the attachment kinetics of newatoms to an embryo, ∆Gv is the volumetric free energy change associated with the transformation, Tthe temperature, kB is the Boltzmann constant and γ the surface energy of the nucleus in contact withthe amorphous bulk [113]. The pre-factor in this expression depends strongly on the conditions in thematrix, at the nucleus/matrix interface and is difficult to assess. The nucleation barrier,∆G∗ =16pi3γ3∆G2v(5.8)is, on the other hand purely thermodynamic and therefore amenable to evaluation. Here we can esti-mate the magnitude of ∆G∗ based on the Thermo-Calc thermodynamic data presented in Figure 5.26for the amorphous and ferrite phases. Here, the surface energy is estimated as γ = 0.2 Jm−2 based onexperimental and atomistic simulation results for the surface energy of ferrite nuclei in contact withpure liquid iron [114]. In the following calculations it is assumed that carbon is sufficiently mobilethat it can be easily rejected to form the nearly carbon free ferrite observed experimentally by APT(Figure 5.22). Furthermore, it is assumed that ferrite nucleates into an amorphous matrix that has theaverage composition of the matrix considering its enrichment in carbon by the formation of ferrite(i.e. carbon concentration gradients are not considered). Considering the incremental formation of avery small amount of ferrite into an amorphous matrix, the driving force (per mole of ferrite formed)available for nucleation can be calculated based on the tangent shown in Figure 5.28a [115]. Here thetangent to the amorphous matrix is drawn at the bulk composition (16 at.% carbon) and extrapolatedto the expected composition of the first ferrite to form (essentially carbon free ferrite). Figure 5.28ashows how changing the bulk composition of the amorphous matrix changes this driving force for88�������������� �� ��� ��� ��� ��� ���������������������������������������������������������� ��������������������������������(a)������������������������������������� �� ��� ��� ��� ��������������������������������� ������������������������ ����������������(b)Figure 5.28: Free energy change of initial nucleation of carbon-free ferrite, shown schematically in a)and the probability of nucleation b) calculated based on the ∆G∗ calculated from a)bulk carbon compositions of between 16 and 25 at.% carbon. The observed drop in driving force issignificant to consider since the amorphous matrix will enrich in carbon as ferrite forms. Overall,while the driving force for nucleation drops with increasing carbon content of the amorphous phase,the magnitude of this driving force remains very high, starting out at above 10 kJ/mol and remainingabove 6 kJ/mol for compositions of the amorphous matrix of up to 25 at.%C at 250◦C. For reference,the driving force associated with the martensitic transformation in carbon steels is of the order of1 kJ/mol [116].While the driving force available for nucleation drops as ferrite nucleates and grows due to the increas-ing carbon content of the amorphous matrix, the driving force remains very high (above 6 kJ/mol) upto, and beyond, the point where nucleation is seen to cease experimentally. The in-situ TEM obser-vations at 250◦C (Figure 5.16) showed that the number density of ferrite particles remained constantfor annealing times beyond 20 minutes. Thus while nucleation ceased rapidly, growth continued formuch longer times. Even when the temperature is raised, to e.g. 500◦C, the driving force for nucle-ation does not drop to zero until the carbon content of the amorphous phase is raised above 25 at.%.Correspondingly, the barrier to nucleation (∆G∗) is seen to increase significantly at carbon contentsabove 20 at.%, as shown in Figure 5.28b, where ∆G∗ is calculated from the free energy change ofinitial nucleation (see Figure 5.28a, and equation 5.8.In the above analysis it has been assumed that the extrapolated free energy curve for the liquid phaserepresents a good approximation to the free energy of the amorphous phase. The strong effect smallmodifications of the free energy curve of the liquid (amorphous) phase can have on the prediction ofthe driving force can be shown by simply shifting this curve downwards, in effect making the liquid89����������������� �� ��� ��� ��� ��� ��������� �������� �������� ������������������������������������������������������ ��������������������������������(a)����������������� �� ��� ��� ��� ��� ��������� �������� �������� ������������������������������������������������������ ��������������������������(b)Figure 5.29: Effect of shifting liquid free energy curve with increasing factors shown as a) a functionof carbon content and b) the change in free energy to nucleate carbon-free ferrite.(amorphous) phase more stable relative to ferrite. This has been done in Figure 5.29 where the freeenergy curve of the liquid phase has been reduced by up to 6 kJ/mol. Making this adjustment causesthe driving force for ferrite nucleation to decrease, leading the free energy available for nucleation todrop to zero at 25 at.% carbon if the downwards shift is 6 kJ/mol. Suggesting a lower free energy forthe amorphous phase compared to the supercooled liquid may be a reasonable estimation as the liquidtransformed to the amorphous phase below the glass transition temperature [117]. That being said,there is no way of knowing quantitatively how poor the predictions using the free energy curve of thesupercooled liquid are or precisely how the shape/position of the free energy curves of the supercooledliquid and amorphous phases may differ.5.3.3 Growth of ferriteFrom the in-situ TEM observations shown in Figures 5.15 it is possible to track the time evolutionof the size of individual ferrite particles after they have nucleated. This allows for the growth rateof ferrite particles to be measured independently. This is important for tracking the growth rate inthe early stage of crystallization where the overall growth rate will have a contribution from both thegrowth of pre-existing particles and from the nucleation of new, small, particles. The difference in themeasured sizes (measured by their equivalent area diameter, EQAD) using the average of the overallpopulation of particles and the average size of the initial 25 particles is illustrated in Figure 5.30.The evolution of the average of the size of the 25 individual tracked ferrite particles were made fromthe shortest time of observation; from 5 minutes up to 26 minutes. Beyond this time some particleimpingement started to occur, influencing the growth behaviour. An important result from Figure 5.3090is that it reveals approximately parabolic growth kinetics, this behaviour often being cited as beingcharacteristic of diffusion controlled growth common in solid state phase transformations, includingthe crystallization of amorphous alloys [118]. In such diffusion controlled growth situations (seeFigure 5.31) it is assumed that the ferrite/amorphous interface is able to adjust its chemistry andstructure very rapidly allowing for local equilibrium to be maintained across the phase interface. Inthis case the rate of growth is determined by the long range diffusion of solute (in this case carbon)away from the moving interface.������������������������ �� �� �� �� �� �� ��������������� ������ ������������������������������������������Figure 5.30: Diameter of sub-set of ferrite particles which crystallized and grew at earliest times ofannealing from insitu-TEM (circles), see Figure 5.18, compared to parabolic growth (linear fit)and the total population of ferrite (crosses).The rate of change of the radius, r of spherical particles approximately including the effects of soft-impingement (overlapping solute fields from adjacent particles) can be written as [119].drdt=((C−Csat)Cα −CsatDr)(1−Y ) (5.9)Here, C the bulk carbon content of the amorphous phase and Csat the concentration of carbon in ferriteat the ferrite/amorphous interface. Cα is the carbon content of the growing ferrite, which in this caseis assumed to be zero (see Table 5.5). The factor Y is the fraction of the transformed phase, whichranges from 0 at the start of crystallization, increasing to 1 as the system reaches the saturation volumefraction. The value of Y can be calculated as Y = f/ fsat , where f is the absolute volume fraction offerrite, and fsat the volume of ferrite observed at the end of the transformation. Substituting these then91Ferrite AmorphousGrainBoundaryInterfacemotionPosition (r)Carbon prole CαCCsatFigure 5.31: Schematic description of the growth of ferrite into amorphous limited by diffusion ofcarbon away from the interface, showing important concentrations that are used in the diffusiongrowth model usedresults in,drdt=((C−Csat)−CsatDr)(1− ffsat)(5.10)To approximately account for the increase in carbon concentration in the amorphous phase (C), amass balance for carbon can be made between the growing ferrite and the amorphous phases. This isonly approximate as it ignores the solute spike ahead of the moving interface. Assuming equal molarvolume for the phases then gives,C =C0(1− f ) (5.11)and therefore a growth rate of,drdt=(( c0(1− f ) −Csat)−CsatDacr)(1− ffsat)(5.12)92The initial carbon content of the sample was taken to be 16 at.%, consistent with the final fractions offerrite and cementite that were observed at the end of the in-situ TEM annealing.In order to compare this equation to the experimentally observed growth rate, one needs to know theinitial carbon content of the amorphous phase (C0) and the time evolution of the volume fraction of theferrite ( f ). While C could not be measured directly in this case, we can make a good estimate based onthe observed final fraction of ferrite (containing no carbon) and cementite (containing 25 at.% carbon)in the film. This gives C0 = 16 at.% carbon, this being consistent with the results of XRD observationson similar samples.Rather than develop a model for the evolution of ferrite volume fraction ( f ), the experimental datashown in Figure 5.18 has been fit to an empirical expression,f (t) = fsat(1− exp(−btc)) (5.13)where fsat , b and c are fitting parameters. The final (equilibrium) volume fraction of ferrite is repre-sented by the scaling factor a, and the kinetics of this transformation are captured by the parametersb and c. A least-squares fit of the volume fraction results was performed, the result is shown inFigure 5.32.��������������������������� ��� ��� ��� ��� �������������������������������� ��� ����������� ������������������������������������������������������Figure 5.32: Volume fraction of ferrite formed over time by insitu-TEM showing parametric fit andfitting parametersThe maximum volume fraction of ferrite was found from this fitting to be fsat = 0.23. Performing amass balance suggests that the carbon composition of the amorphous phase at that volume fraction93would be:Csat =C0(1− fsat) = 20.8at.%C (5.14)It is notable that performing a common tangent construction between the ferrite and liquid (amor-phous) phase using the Gibb’s free energy curves in Figure 5.28 would predict an equilibrium com-position of 32 at.% carbon in the amorphous phase, this being much higher than the value reportedabove. One may question the suitability of this fit for fsat given that the data does not extend to verylong times. As noted above, this limitation on the data was due to the onset of particle impingementat times longer than 20 minutes. Further evidence that the volume fraction of ferrite is nearly constantfor times longer than 20 minutes, however, comes from looking at the overall average particle size (+symbols in Figure 5.30) and noting the fact that (as mentioned above) the number density of ferriteparticles saturates for times longer than 20 minutes. The data in Figure 5.30 does show a small in-crease in the average size of the ferrite particles, suggesting that saturation of the volume fraction hasnot yet occurred at 20 minutes, but the rate of growth is so slow (compared to that at shorter times)that the fit shown in Figure 5.32 is likely a good first order approximation.Equation 5.12 was integrated numerically using the carbon diffusivity in the amorphous phase (Dac)and initial ferrite radius (r0) as adjustable parameters to fit the experimentally measured ferrite size.The best fit was obtained using values of Dac = 1.3× 10−18 m2/s and r0 = 5.4 nm, the predicted andmeasured ferrite radii being shown in Figure 5.33.1The slightly non-parabolic character of this fit is due to the time dependence of the volume fraction(Figure 5.32). The diffusivity of carbon from this fit is three orders of magnitude slower than thediffusivity found experimentally for carbon in ferrite at the same temperature (4.3×10−15m2/s)[63].It has been shown that carbon diffusion decreases with carbon content in both ferrite [120] (dueto elastic interaction of carbon atoms [120]) and austenite (due to availability of interstitial sites)[121]. For ferrite containing 16 at.% carbon the diffusivity is predicted to decrease to 5×10−23m2/s[122]. Assessing the diffusivity in amorphous alloys is more complex owing to the complex energylandscape. Experimental evidence indicates a self diffusion coefficient of iron in amorphous iron is onthe order of 10−21m at 250◦C. An experimental assessment of the diffusivity of carbon in amorphousiron has not been previously performed, though the diffusivity of nitrogen [52] and boron [123] inamorphous iron have been measured to be of the order of 10−19m2/s at similar temperatures. It isnotable that this is relatively close to the diffusivity for carbon predicted above.1As shown in Figure 4.16 there is some uncertainty in values of thickness of the film, which in turn affects the estimated volumefraction and, therefore, carbon content of the amorphous phase. The procedure outlined in the creation of Figure 5.33, was repeatedfor the minimum and maximum predicted values of volume fraction (as shown in Figure 5.18). This resulted in nearly identical fitsof radius with time, and a slight variation in the diffusivity (between 1.20 and 1.31× 10−18m2/s and initial radius (between 5.31and 5.42 nm).94������������������ �� �� �� �� ��������������� ������ �����������������������������������������Figure 5.33: Result of diffusion controlled growth fit of experimental data by Equation 5.12. Inte-gration was performed using Euler’s method with the change in radius calculated at midpointsof sections. The numerical integration was performed with a step size of 30 seconds usingthe carbon diffusivity in the amorphous phase (Dac) and initial ferrite radius (r0) as adjustableparameters to fit the experimentally measured ferrite sizeThe use of a model for diffusion controlled growth to explain the behaviour shown in Figure 5.33was motivated by the fact that Figure 5.30 appeared to suggest parabolic growth. As seen, however,the fundamental problem that is faced in applying this model is the fact that the underlying thermo-dynamics are not able to predict the slowing/stopping of the growth at the volume fraction extractedfrom the analysis above. Moreover, one may question the suitability of assuming local chemical equi-librium across an interface between crystalline and amorphous phases. In the only other work that hasattempted to quantify and understand the growth of ferrite particles from an amorphous iron-carbonmatrix, Shingu et al. [29] used a different approach. In their work they assumed that the growth of theferrite was controlled by the rate at which the interface can migrate. Unfortunately, critical details ofthe experiment and model fitting were not described in the work of Shingu et al. [29], meaning that aquantitative comparison of that older work to the work performed here is impossible.In an interface controlled model, such as the one used by Shingu et al. [29], the diffusion of carbonaway from the interface into the amorphous matrix is assumed to be very fast relative to the speedwith which the interface itself can migrate. The rate of growth of spherical particles is then assumedto be given by,drdt= M∆Ginter f ace (5.15)95�������������������������� �� ��� ��� ��� ��� ������������������������������������������������������������������������������������� ��������������������������������������������������������������������������������������������������������(a)��������������������� �� ��� ��� ��� ��� ������������������������������������������������������� ������������������������(b)Figure 5.34: a) Description of total Gibb’s free energy, and energy associated with trans-interface dif-fusion and for moving the interface of the ferrite as it grows into the amorphous matrix asdefined by Hillert [115], and b) the variation of these free energy levels with increasing carboncontentWhere dr/dt is the change in radius with time, M is the mobility of the interface and ∆Ginter f ace thedriving force.The total free energy driving growth (∆Gtot) can be found using the tangent construction shown inFigure 5.28. This may then be split into the energy required to drive the interface (∆Ginter f ace) andthat available for diffusion of atoms across the interface (∆Gdi f f usion), these three terms being shownin Figure 5.34. The free energy available for diffusion, and to drive the interface can be estimated asper Hillert [115] where a line is constructed parallel to the final equilibrium tangent line that passesthrough the current carbon content of the bulk phase. The free energy available to drive diffusion isthe difference between this line and the free energy of the growing phase, and the energy required tomove the interface is the difference between the tangent of the current chemistry of the parent phaseand the parallel line.To calculate the evolution of size of the ferrite particles by this model, the driving force for growth canbe calculated at any carbon content using the thermodynamic data in Figure 5.34. The carbon contentof the amorphous phase can be related to the annealing time by again assuming carbon partitioninginto the amorphous phase and using Equation 5.13 and 5.14 as was done for the case of diffusioncontrolled growth. The mobility of the interface is not known, though it is typically assumed to beArrhenius. Here, it is assumed to be constant (for the data collected at 250◦C) and used to fit theexperimental data along with the initial ferrite radius. The resulting curve, using a mobility M =3.36×10−12 m·mol · s−1J−1 and initial ferrite radius r0 = 10.8 nm is shown in Figure 5.35.This model gives a similar prediction of the ferrite particle size evolution with time over the first 2096������������������ �� �� �� �� ��������������� ������ �����������������������������������������Figure 5.35: EQAD ferrite particle size from growing particles compared to and interface controlledgrowth model where the mobility was fit and thermoCalc data was used to calculate the drivingforce available to move the equilibrium as shown in Figure 5.34minutes of annealing compared to the diffusion controlled growth model. The primary difference be-tween the models is that the interface controlled model predicts continued growth beyond 20 minutesannealing, which (as explained above) does not seem to fit with the experimental observations. Inthis case the predicted continuation of growth arises from the fact that a significant thermodynamicdriving force (Figure 5.34) continues to exist for times beyond 20 minutes. This is the same discrep-ancy that limited the diffusion controlled model, but in that case it was circumvented by using theexperimentally observed variation in the volume fraction of ferrite. As already noted, this could be aresult of the poor estimation of the free energy of the amorphous phase from the supercooled liquid.But this alone would not seem to be sufficient to explain all of the observations.Returning to the in-situ TEM experimental results, an important observation that has not yet beenconsidered is the fact that the growth of the ferrite resumed when the temperature is raised. Thevolume fraction of ferrite increased from 23% at 250◦C to 28% at 300◦C and to 37% at 350◦C. Thisincrease in volume fraction occurred purely by growth of ferrite, as no new nuclei were observedduring heating. No cementite formed in this temperature range either. It is interesting that the 37%ferrite obtained at 350◦C is very close to what would be expected based on the equilibrium calculationsbetween liquid and ferrite phases using the ThermoCalc. Indeed, if the cessation of growth observed at97�������������������������� �� ��� ��� ��� ��� ��� ��� ��������������������������������������������������������������������������� �����������������������������������������������������������Figure 5.36: Equilbrium carbon content predicted for liquid iron-carbon and ferrite at temperaturesfrom 250◦C to 450◦C as calculated from the common tangent of ThermoCalc data250◦C was thermodynamic in origin (i.e. the driving force goes to zero) then raising the temperatureshould lead to a dissolution of some of the ferrite and therefore a decrease rather than increase involume fraction. As shown Figure 5.36 the equilibrium between liquid iron-carbon and ferrite shiftsto lower and lower carbon contents, which by the lever rule predicts lower volume fraction of ferriteat a given carbon content with increasing temperature.In the above models, the kinetics of interface migration (described by M) and solute diffusion (de-scribed by Dc) have been assumed to be independent of time at a given annealing temperature. It hasbeen shown, however, that the diffusivity of iron in amorphous iron alloys decays exponentially withtime due to ageing of the glass [69]. During aging, the free volume of the glass decreases and thedepth of the local energy wells in which individual atoms sit increases. This leads to higher activationbarriers for atomic motion and therefore slower diffusivity [69].In the present case, the diffusivity of both iron and carbon may also be influenced by the fact thatthe amorphous phase is becoming enriched in carbon as the transformation proceeds. It is notablethat the critical temperature required to crystallize amorphous iron-carbon alloys, assessed based oncontinuous heating experiments, rises drastically with increasing carbon content to a maximum at∼25 at.%C as shown in Figure 2.5 [26]. There is evidence that with increasing carbon concentrationin iron-carbon liquids [124], and boron concentration in Fe-B glasses [125], that metalloid (carbon98or boron) centred trigonal prisms become increasingly common corresponding to a decrease in icoso-hedral ordering of the Fe atoms. This decrease in icosohedral ordering in favour of polytetrahedralordering with increasing metalloid content has been referred to as ‘geometrical frustration’ in metallicglasses (see e.g. [125]). It is significant that metalloid centred prisms are the basic structural unitsfor the boride Fe2B [125] and carbides [124], these being the eventual phases that form in Fe-B andiron-carbon glasses. Such metalloid-Fe configurations might be expected to be locally more stablethan other atomic configurations, leading to a lower energy for atoms contributing to them and higheractivation barriers for atoms to migrate away from them. This interpretation would be consistent withrecent (unpublished) simulation work [126] where molecular dynamics simulations have shown thatboth the diffusivity of carbon and iron in iron-carbon glasses decreases (at a given temperature) asthe carbon content of the glass increases. This corresponds to an observed decrease in icosahedralordering of iron atoms and increase in the presence of carbon centred prisms with increasing carboncontent of the glass.In summary, it is likely that both thermodynamic and kinetic factors contribute to the surprising slow-ing of ferrite growth at 250◦C. In particular, the slowing of iron and carbon diffusion with aging time(due to aging) and carbon content (due to carbon rejection from the growing ferrite phase) seemslikely to play an important role in some of the, up to now, unexplained phenomena observed in thecrystallization of iron-carbon glasses. In particular this may play a very important role in the reportedincrease of stability of amorphous iron-carbon alloys with carbon content (Figure 2.5). Here, it seemsthe most logical way to explain the sharp increase in growth rate following an increase in temper-ature from 250◦C. It also potentially explains the unexpectedly rapid decrease in nucleation rate at250◦C described in the last section. In CNT such kinetic factors would affect the pre-factor terms(particularly) β ∗ associated with atomic attachment and trans-interface diffusion.5.3.4 Crystallization and growth of cementiteWhen iron-carbon samples were held sufficiently long at 250◦C or if the temperature was raised, bothXRD and TEM diffraction analysis revealed the formation of cementite, Fe3C. For the samples fo-cused on above containing 16at.%C annealed at 250◦C cementite appeared to form rapidly, consumingthe remaining amorphous matrix. Interestingly, it was noted that cementite rapidly formed upon thein-situ heating experiments when the temperature reached 400◦C and the faction of ferrite was 37%.This corresponds to a condition where the amorphous matrix (which is consumed by the cementite)has reached 25 at.% carbon.It is clear from all of the experiments performed that cementite forms after the onset of ferrite forma-tion and that the two phases do not form in a coupled manner. As the carbon content of the sample andannealing temperature decrease the separation of the timescale between the onset of ferrite formationand cementite formation increases. Yet, in all conditions, once the cementite does nucleate, its growth99�������������� �� ��� ��� ��� ��� ������������������������������������������������������������������� ��������������������������������(a)��������������������� �� ��� ��� ��� ��� ������������������������������������������������������������������������� �����������(b)Figure 5.37: Gibb’s free energy of nucleation at 0 at.% carbon for ferrite and 25 at.% carbon for ce-mentite, as shown schematically a), and as a function of amorphous carbon content b)is fast. It is notable that the number density of cementite grains is much lower than that of the ferrite,meaning that each cementite crystal is (in the fully crystallized sample) much larger than the ferrite.One can suggest and explanation for the above results based on both thermodynamic, kinetic andstructural factors related to the discussion developed in the last section. The Gibb’s free energy avail-able for crystallization at 250◦C per mole formed of (carbon free) ferrite and stoichiometric cementitecan be calculated as shown in Figure 5.37. As shown in Figure 5.37b, the driving force for cemen-tite formation increases with carbon content of the amorphous phase, with it having a higher drivingforce compared to ferrite for an amorphous phase containing >20 at.% carbon. Thus the formationof ferrite, resulting in the carbon enrichment of the amorphous matrix, increases the thermodynamicdriving force for the formation of cementite. At the same time, the diffusivity was argued to de-crease with carbon enrichment of the amorphous phase but this was argued to occur because of theincreasing geometric frustration due to the formation of trigonal iron-carbon prisms that are the basicbuilding blocks for the orthorhombic Fe3C structure. In the case of iron-carbon liquids there havebeen experimental and theoretical observations of the beginnings of network formation between theseprisms within the liquid [124]. With increasing carbon content of the amorphous matrix this scenariosuggests a competition between, on one hand, the increasing chemical driving force and presence ofpre-cursor trigonal-prisms which may serve as nucleation sites and, on the other, the decreasing dif-fusivity of iron and carbon. The results presented above suggest that cementite formation is delayedat 250◦C until the matrix composition was nearly the stoichiometry of cementite, the transformationthen being possible in a massive fashion with no need for long range diffusion to or from the growinginterface.100(a) (b)Figure 5.38: TEM image (a) and associated SAED pattern (b) showing identified planes (red linesadded as guide to diffraction spot positions measured)While the APT results indicate that the cementite has a rather uniform carbon composition near theexpected stoichiometry for Fe3C, the diffraction and TEM observations suggest some peculiar struc-tural aspects for this phase. In particular, the finely-space (1-5 nm), aperiodic planar faults observedin HRTEM were unexpected as such faulting is uncommon in cementite formed by diffusional trans-formations in steels.Figure 5.38 shows a bright field TEM image as well as the corresponding selected area diffraction pat-tern taken looking nearly down the [100] direction of the cementite, the good correspondence betweenspots in the diffraction pattern and the expected location of the spots being shown in Table 5.7. Figure5.39 shows a HRTEM image of the same area, showing detail of the aperiodic nature of the faults.From this image one can estimate an average fault density to be 1.4 faults/nm. Using the approximateorientation judged from the diffraction pattern in Figure 5.38, one can overlay the expected atomicpositions with the HRTEM image again showing reasonably good agreement. As can be seen, signif-icant streaking occurs parallel to the normal to the (010) plane, suggesting that the faults lie on thisplane [127]. This is a known fault plane in cementite, being the ‘chemical twinning’ plane describedby Bauer-Grosse [35] as well as a plane on which traditional stacking faults can form [128, 129].Such high fault densities have been previously observed as a consequence of high growth rates andhigh driving forces in other systems [130, 131]. Following Han et al.’s work [130], a criterion forestablishing whether such faulting is possible requires assessing whether the volumetric free energydecrease due to the crystallization of a single layer of atoms is larger than the energy consumed increating a fault plane. In other words,∆G > γ/h (5.16)Here, ∆G is the volumetric Gibb’s free energy available to drive crystallization, γ is the fault planeenergy and h is the atomic spacing perpendicular to the fault plane (0.3374 nm here [85]). If this101Figure 5.39: HRTEM detail of cementite region of sample annealed at 300◦C for 1 hour, for the samegrain that is shown in Figure 5.38. A simulated cementite structure, viewed in the [100] directionidentified from diffraction, is shown in detail at right at the same scale.Table 5.7: Comparison of theoretical d-spacings of cementite based on structure of Wood et al. [85]based on SAED pattern shown in Figure 5.38b.Plane Theoretical d-spacing (A˚) Measured d-spacing (A˚) Error (%)(012) 2.151 2.139 0.555(022) 1.868 1.874 0.308(01¯2¯) 2.152 2.139 0.590(02¯4) 1.024 1.069 4.427(01¯0) 6.491 6.732 3.707(010) 6.088 6.732 10.580(02¯2¯) 1.865 1.874 0.472(02¯4¯) 1.078 1.069 0.779(01¯4¯) 1.120 1.112 0.681(002¯) 2.256 2.256 0.015(002) 2.261 2.256 0.225(02¯2) 1.905 1.874 1.665(01¯2) 2.132 2.139 0.327(012¯) 2.101 2.139 1.798102balance is not respected then it is expected that the faulted layer will be removed prior to furthergrowth of the interface. The fault energy of the lowest energy stacking fault on the (010) plane ofcementite has been estimated by Karkina et al. [132] as 0.0128 J/m2. Using this data we find that thedriving force for cementite crystallization must be greater than 43.2 MJ/m3 or, using cementite’s molarvolume of 23.37 cm3/mol, ∆G > 1 kJ/mol. By comparison, the thermodynamic data in Figure 5.37predicted a driving force of 3.98 kJ/mol at 16 at.% carbon in the amorphous phase and 4.85 kJ/molfor 25 at.% carbon in the amorphous phase. This analysis suggests that, energetically, it would bepossible for these faults to be incorporated into the structure during its growth.5.3.5 Effects of carbon content and annealing temperature on crystallizationThe discussion above has predominantly focused on the crystallization behaviour of the iron-carbonfilm with 16 at.% carbon at 250◦C. It is of interest to apply the physical picture described above tosee whether it is able to self-consistently describe the results from XRD measurements on samplescontaining other carbon concentrations and/or samples annealed at higher temperatures. Figure 5.40attempts to schematically illustrate the dependence of microstructure evolution during crystallizationon sample composition and isothermal annealing temperature, the time increasing from left to right.Starting with the samples containing 20.4 at.% carbon annealed at 250◦C (Table 5.3), we can seethat the onset of crystallization did not commence until between 30 and 60 minutes. This should becontrasted to the in-situ TEM observations performed on a sample containing 16 at.% carbon whichrevealed the onset of crystallization for times as short as 5 minutes. While fewer measurementswere made on the sample containing 17.5 at.% carbon annealed at 250◦C (Table 5.3) one can see thatsignificant ferrite formation has occurred within the first 60 minutes of annealing. Unlike the samplecontaining 16 at.% carbon, however, a significant increase in ferrite fraction occurred for between 60and 120 minutes of annealing.While the XRD results do not allow for a precise measurement of the onset time for crystallization, itis clear that increasing the starting carbon concentration of the sample increases the time for the startof crystallization. This is interesting as it would appear to corroborate the slower diffusion in samplescontaining higher carbon concentrations. This is separate, in this case, from the slowing diffusivitythat may arise from aging that occurs during the annealing treatment itself. An interesting outcome ofthe combined slowing of diffusion due to aging is the fact that samples produced having higher carbonconcentrations should take both a longer time for crystallization to commence and an even longer timefor crystallization to complete owing to the longer time at temperature and consequently the higherdegree of aging in such samples. Again, the data presented here is not entirely conclusive in this regardbut it is notable that it took between 120-240 minutes for the sample containing 20.4 at.% carbon tofully crystallize at 250◦C (Table 5.3), while the sample containing 17.5 at.% was fully crystallizedwithin 60-120 minutes.103Figure 5.40: Schematic representation of the crystallization process observed by XRD and TEM. Eachimage indicates increasing annealing time (linearly) from left to right, the relative size of thephases, and their volume fractions are designed to match experimental data at each stage ofannealing. Ferrite is shown in orange, amorphous in green (with darkness indicating carboncontent) and cementite by striped purple.Increasing the annealing temperature unsurprisingly increases the rate of crystallization. In the case ofthe XRD measurements made on a sample containing 16.1 at.% carbon annealed at 300◦C (Table 5.4),the results showed full (or near full) crystallization within 7.5 minutes of annealing, the shortest timeof observation. This is to be compared with the in-situ TEM annealed sample which did not fullycrystallize after 40 minutes of annealing (Figure 5.15) and the cross-section TEM sample containing15.8 at.% carbon (Figure 5.10) which showed incomplete crystallization after 60 minutes of annealingat 250◦C. A more detailed analysis can be made by comparing the crystallization kinetics, measuredby XRD, for the samples containing 20.1 and 20.4 at.% carbon annealed at 250◦C and 300◦C, respec-tively (Figures 5.5 and 5.8). For the sample annealed at 300◦C the final fraction of ferrite had beenformed within the first 7.5 minutes of annealing, with nearly half the final amount of cementite alsoalready being present by that point. Full crystallization was obtained within 30 minutes. In contrast,the sample annealed at 250◦C did not start to crystallize until after 30 minutes of annealing, withcomplete crystallization not occurring until after 135 minutes of annealing. Since these two sampleshave the same starting composition, one can ascribe the acceleration of the crystallization in this case104to the effect of temperature and time at temperature, on the diffusivity.Finally, an interesting difference is observed in the sequence of crystallization for samples containing∼16 at.% carbon annealed at 250◦C and samples containing ∼20 at.% carbon annealed at 300◦C. Forlow temperature/low carbon samples, a clear separation between the time for ferrite formation andcementite formation was observed, while for high temperature/high carbon samples the overlappinggrowth of ferrite and cementite was observed (cf. Figure 5.8 and the results of the in-situ TEMexperiments). In the intermediate case of the sample containing 20.4 at.% carbon annealed at 250◦C(high carbon, low temperature), ferrite formation clearly precedes cementite formation, but someoverlap in the formation was observed at longer times (Figure 5.5).It was argued above that for the low carbon films annealed at low temperature, enrichment of the amor-phous matrix with carbon by ferrite formation served to aid the formation of cementite by increasingthe presence of the pre-cursor ‘building blocks’ for Fe3C (trigonal prisms) while also increasing thechemical driving force for cementite formation. Working against the formation of cementite is theslowing of carbon and iron diffusion due to aging of the amorphous matrix and the carbon concen-tration dependence of the diffusivities. In the case where the amorphous matrix starts out closer to25 at.% carbon, the driving force for cementite formation starts off high and carbon centred trigonal-prisms are likely already present in the amorphous matrix. Moreover, while the diffusivities are lowbecause of the higher carbon content of the matrix, the fact that this carbon content was obtainedprior to any aging means that the diffusivities should be higher than in samples that achieved the samecarbon level via aging induced carbon redistribution from ferrite formation. Its notable that based onthe above analysis of the in-situ TEM sample, it took between 30 and 40 minutes of aging at 250◦Cfor the amorphous matrix to be enriched to 20.8 at.% carbon. The combination of high initial drivingforce, presence of pre-cursor nucleation sites and no aging induced reduction in diffusivity for sam-ples produced having ∼20 at.% carbon, helps explain why ferrite and cementite can be observed toform together in these cases.In those cases where the formation of ferrite and cementite overlap, there must be some interactionin their growth kinetics. The fact that both ferrite and cementite fractions grow with time impliesthat the cementite is formed into an amorphous matrix that does not have the required stoichiometricamount of carbon (25 at.% carbon). This means that carbon must be consumed from the surroundingamorphous matrix. Interestingly, following the arguments made above, as the carbon content of theamorphous matrix is lowered by the formation of cementite, the kinetics of carbon and iron diffusionwould be expected to increase. This may help to explain why cementite appears to grow so quicklyonce it nucleates.1055.4 SummaryThis Chapter has summarized a detailed set of experiments that, for the first time, show (under isother-mal annealing conditions) the composition and temperature dependence of the crystallization of amor-phous iron-carbon alloys containing between 15 and 20 at.% carbon. While the observed phasesmatch those reported from previous investigations, the work here provides proof of the compositionand structure of these phases. It is shown that in all cases, nearly carbon free ferrite is formed asthe first phase from the amorphous matrix. The cementite which follows is nearly stoichiometric buthighly faulted, the faults being (it is believed) a consequence of the rapid growth of this phase oncenucleated. These faults, occurring on the (010) plane, are believed to be the same as those observedpreviously in bulk cementite.One of the most interesting results of this work is the evidence that the kinetics of the transformationslow with time and carbon content of the amorphous matrix. It is argued that this happens due toaging of the glass and due to structural changes (geometrical frustration) that occurs because of carbonenrichment. This may provide an explanation for the long-known experimental observation that thestability of amorphous iron-carbon alloys increases strongly with carbon content up to 25 at.% carbon.106Chapter 6Crystallization of amorphous iron-carbonalloys containing >25 at.% carbonAs noted in the literature review (Chapter 2), the crystallization behaviour of amorphous iron-carbonalloys has been found to change drastically for carbon contents >25 at.% carbon. While amorphousalloys containing <25 at.% carbon crystallize to form ferrite and cementite (as shown in Chapter 5),alloys containing more than 25 at.%C have been reported to crystallize into a range of carbides [26],the exact phases formed depending on the alloy composition, fabrication method and heat treatment.While substantial work has been done in analyzing the structure/crystallography of these phases(see Chapter 2), there has been little work aimed at quantifying the microstructural evolution dur-ing isothermal annealing.This chapter describes observations of crystallization for amorphous iron-carbon alloys containingbetween 30 and 40 at.% carbon, the samples having been produced using the procedure described inChapter 4. The higher level of carbon is also designed for the purpose of supplying more carbon inthe development of diffusion graded steel sheet [73]. The focus of the discussion in this Chapter willfocus on improving our understanding of the fundamental mechanisms governing the microstructuralevolution on crystallization. This follows directly on the observations and discussion from the lastChapter (Chapter 5).This chapter starts by presenting the results of on-hour isothermal annealing experiments analyzed byXRD. These are then followed by a more detailed study of isothermally annealed samples. A combi-nation of TEM, EDX and APT experiments are used to verify the proportion, type and compositionof phases formed. Finally, a discussion of the results is presented, relating the results obtained hereto those previously reported in the literature for similar materials and to the lower carbon containingalloys described in the last Chapter.1076.1 Methodology6.1.1 Sample preparationSamples were prepared by PVD in the manner described in Chapter 4. The control of the methane flowrate was set and maintained at 40% of the maximum saturation voltage. As shown in the descriptionof the deposition system (Section 4.3.3 and Figure 4.17) this condition was found to produce samplescontaining between 30 and 40 at.% carbon based on EDX analysis. All samples produced in thiscondition were found to be fully amorphous following deposition (Section 4.3.4), with a homogeneouscarbon distribution across the areas analyzed (see Section 4.3.3).Samples were prepared on both silicon wafers and IF steel substrates. Silicon was used for samplesto be analyzed by EDX and XRD, while IF steel was employed for samples to be analysed by TEMand APT. The samples were all produced at a nominal thickness of 550 nm, and as such all TEMand APT analysis was performed by FIB excavation as described Section 4.2.2. This resulted ina through-thickness view of the sample in contact with the IF steel substrate. All samples wereannealed under vacuum to prevent oxidation. Annealing for samples analyzed by XRD was performedat UBC, and samples analyzed by TEM/APT were annealed at the University of Rouen, as describedin Sections 5.1.2 and 5.1.3.6.1.2 CharacterizationPhase determination following annealing was conducted by XRD using samples prepared as describedin Section 4.1.3. The XRD data was analyzed through the same curve fitting algorithm previouslydescribed in Section 5.1.3, with the additional consideration of a secondary carbide phase as describedin more detail below. The microstructure of selected samples were analyzed by conventional and highresolution TEM imaging, with selected area diffraction being used to help identify phases and defects.The bulk chemistry of samples were determined by EDX analysis as described in Section 4.2.3. Thisanalysis was supported by local chemical analysis in the form of qualitative EF-TEM observations(see Section 4.2.2) and quantitative APT analysis (see Section 4.2.3). The chemistry of all of thesamples produced, along with the heat treatments they were subjected to, are shown in Table 6.1.6.2 Results6.2.1 XRD analysis of crystallization during one-hour isothermal annealingAs in the case of the samples containing <25 at.% carbon described in the last Chapter, an initialassessment of the crystallization was performed by isothermal annealing (one hour). Temperatures108Table 6.1: Carbon concentration (determined by EDX) and annealing conditions for each of the sam-ples used in this study.Carbon content from EDX [at.%] Annealing Temperature [◦C] Time(s) [min]30.7 as-deposited -31.7 300 6039.6 430 6030.7 530 7.5, 15, 30, 6039.6 530 6033.2 630 60of 300◦C, 430◦C, 530◦C and 630◦C were selected for these annealing experiments. Subsequently,XRD was performed to assess the phases present (Figure 6.1). As in the case of the films containing<25 at.% carbon, each deposition led to a different carbon content, the exact values being given in thelegend to Figure 6.1.������������������������ ��� ��� ��� ��� ��� �����������������������������������������������������������������������������������������������Figure 6.1: XRD of as-deposited sample (30.7 at.% carbon), and samples annealed at 300◦C (31.7at.%) (identical to the as-deposited sample), 430◦C (39.6 at.%), 530◦C (39.6 at.%) and 630◦C(33.2 at.%) for one hour. Symbols indicate the expected position of ferrite (◦) and cementite (4)peaks.After annealing the sample containing 31.7 at% carbon at 300◦C for one hour, no change was observedin the diffraction pattern relative to that obtained from one measured on a sample in the as-depositedstate (Figure 6.1). This contrasts sharply with the observations from the last chapter where samplescontaining < 25 at.%C were fully crystalline after annealing for one hour at 300◦C (Figure 5.1).The first signs of crystallization were observed when a sample containing 39.6 at.%C was annealed at109430◦C for one hour. As seen in Figure 6.1 and Figure 6.2, a clear set of peaks are visible above theamorphous background. While these peaks appear broad, their locations were found to be very similarto the position of the peaks in fully crystallized samples containing < 25 at.% carbon. Annealingsamples for one hour at 530◦C (39.6 at.%C) and 630◦C (33.2 at.%C) led to a progressive sharpeningand narrowing of the diffraction peaks, above a very low background (Figure 6.3 and Figure 6.4).������������������������� ��� ��� ��� ��� ��� ������������������������������������������������������������������������������������������������������������Figure 6.2: Detail and fitting of sample annealed at 430◦C for one hour with 39.6 at.% carbon showingcementite and ferrite peaks. Symbols indicate the expected position of ferrite (◦) and cementite(4) peaks.����������������������������������������� ��� ��� ��� ��� ������������������������������������������������������������������������������������������������������Figure 6.3: Detail and fitting of sample annealed at 530◦C for one hour with 39.6 at.% carbon showingcementite peaks. Symbols indicate the expected position of ferrite (◦) and cementite (4) peaks.Focusing on the sample annealed for one hour at 430◦C (Figure 6.2), one can clearly identify an110�������������������������������� ��� ��� ��� ��� ������������������������������������������������������������������������������������������������������Figure 6.4: Detail and fitting of sample annealed at 630◦C for one hour with 33.2 at.% carbon showingcementite peaks. Symbols indicate the expected position of ferrite (◦) and cementite (4) peaks.intense peak at 2θ = 44.66◦, this being at the theoretical position of the ferrite {100} peak (44.67◦).Weaker peaks are also observed, these corresponding well to the theoretical positions of the {121},{210}, {103} and {211} peaks of cementite. The pattern shown in Figure 6.2 is, in fact, very similarto the pattern shown in Figure 5.6, this from a sample containing only 16 at.% carbon. Accordingly,it was possible to adequately fit this pattern following the same procedure outlined in Chapter 5. Theposition of the cementite peaks were well fit (R2=0.99), though a larger discrepancy between thetheoretical and observed peak heights was observed in this case compared to those presented in thelast Chapter (cf. Table 5.4). The ferrite peak is also well reproduced by the fitting algorithm, thoughit is measured to be broader than that reported in Chapter 5, with a full-width at half maximum of0.46◦, compared with for example 0.22◦ seen in Figure 5.3. This may indicate smaller ferrite grains,or a higher defect density. To compare the fraction of cementite and ferrite measured by diffractionit is instructive to look at the ratio between the total integrated intensity of the ferrite peak to the sumof the integrated intensities of all cementite peaks. The ratio between the intensity of the ferrite tocementite phases was found to be 1:1, which is smaller than ratio observed in the last Chapter for fullycrystallized films containing 20 at.% carbon (1:2.6, see Figure 5.7), but larger than the ratio found forfilms containing 16 at.% carbon (1:0.188, see Figure 5.6).Aside from the position, shape and intensity of the peaks in the diffraction pattern of Figure 6.2, it isinteresting to note that the background is significantly different compared to the background observedin partially and completely crystallized samples having <25 at.%C for the same range of 2θ . In thediffraction patterns shown in Chapter 5, the background was observed to be approximately linearfor fully crystalline conditions, or non-linear with increasing intensity at lower diffraction angles(corresponding to the position of the broad amorphous peak at 2θ = 43.5◦) in partially crystallized111samples. In Figure 6.2, the background can be seen to be higher at high angles. This may suggestweak, broad diffraction peaks that have not been indexed (i.e. do not belong to ferrite or cementite),or that some retained amorphous phase exists that has a significantly different structure than that ofthe as-deposited amorphous phase.The presence of a mix of ferrite and cementite in this sample implies that some other very carbonrich phase(s) must exist in the microstructure since the carbon content of the film (39 at.% carbon) issubstantially higher than the stoichiometry of cementite (25 at.% carbon). The highest carbon con-taining carbide reported previously in such films (Fe2C) contains only 33 at.% carbon. This impliesthe presence of a carbon rich phase that is not in evidence from the diffraction ranges studied.The diffraction peaks apparent after annealing at 530◦C and 630◦C appear much sharper than thoseobserved in any of the previously described samples. The locations of the peaks are close to thetheoretical positions expected for cementite, and in both cases the peaks can be well fit using the fittingalgorithm presented previously in Chapter 5 (Figures 6.3 and 6.4). The full-width at half maximumfor the diffraction peaks was found to be 0.11◦ for the spectra in Figures 6.3 and 6.4. This should becompared to the cementite peaks identified in the low-carbon films in Chapter 5, where the averagefull-width at half-maximum was found to be 0.39◦. The peaks are sufficiently sharp that there theseparation of the peaks arising from the Kα1 (0.154056 nm) and Kα2 (0.154439 nm) wavelengths ofthe copper X-ray source are visible. 1Another difference between the diffraction peaks shown in Figures 6.3 and 6.4, and those shownpreviously in Chapter 5 is that the cementite peaks are much sharper. Moreover, they were found toalso be located further away from their ideal positions compared to those observed for cementite infilms crystallized in low-carbon films (Table 6.2).Table 6.2: Peak positions of theoretical cementite and cementite measured for samples with 20 at.%carbon annealed at 300◦C and 39.6 at.% carbon annealed at 630◦C following the fitting proceduregiven in Section 5.1.3Peak TheoreticalPeak Position[◦]20 at.%C PeakPosition [◦]20 at.%C Dif-ference inPosition [%]39.6 at.%CPeak Position[◦]39.6 at.%C Dif-ference in Posi-tion [%](211) 42.96 43.05 0.19 43.03 0.15(102) 43.87 43.82 0.11 43.95 0.19(220) 44.64 44.84 0.45 45.08 0.98(031) 45.08 45.12 0.08 45.30 0.49(112) 45.99 46.05 0.13 46.13 0.311 Both Kα1 and Kα2 wavelengths having been included in all XRD fitting. This separation was not previously seen in theanalysis of low-carbon crystallization (Chapter 5) due to the width of the diffraction peaks.1126.2.2 XRD analysis of crystallization during isothermal annealingGiven the unique characteristics of the diffraction spectrum collected from the sample annealed onehour at 530◦C, it was decided to focus on this annealing temperature for a more detailed study ofcrystallization during isothermal holding. Annealing was conducted at 530◦C for 7.5, 15, 30 and60 minutes. As for the isothermal annealing performed in the last chapter, the annealing was allperformed sequentially on the same sample, e.g. the sample was annealed for 7.5 minutes, removedfrom the furnace, a diffraction pattern collected, then returned to the furnace for a further 7.5 minutes(total annealing time of 15 min.) prior to the diffraction measurement being repeated. The samplestudied had a carbon content of 30.7 at.% as determined by EDX analysis.The time evolution of the XRD spectra is shown in Figure 6.5. After annealing for 7.5 minutes thediffraction pattern closely resembles the diffraction pattern obtained upon annealing at 430◦C for onehour (Figure 6.2). Based on the discussion above, it is also similar to the diffraction patterns obtainedin Chapter 5 (cf. Figure 5.6). The features that were distinctive in the sample annealed for one hourat 430◦C, i.e. the higher background at larger diffraction angles and the low, broad cementite peaks,are also present in this diffraction pattern.In order to confirm the phases present after annealing 7.5 minutes at 530◦C, a scan over a wider rangeof 2θ angles was performed (Figure 6.6). Both lower angles (between 35 and 50◦) and higher angles(75–84◦) were measured, the higher angle range selected to specifically identify a secondary ferritepeak, {211} expected at the theoretical position of 82.35◦. As can be seen, a strong peak was indeedfound at approximately this position, confirming the presence of ferrite. At the lower range of angles,a set of weak peaks at 47.5◦ and 50.0◦ appear, these not matching any expected diffraction peaksfrom cementite or ferrite. The peaks corresponding to the cementite {113} (at 48.58◦) and {122} (at49.12◦) planes were also not clear above the background. These discrepancies between the expectedand measured pattern suggest the presence of another phase (or phases) that are not indexed, thesemost likely being associated with a small fraction of another carbide. Given the weak intensity ofthese peaks, it is expected that the volume fraction of the phase(s) giving rise to them is small.After returning the sample to the furnace and annealing a further 7.5 minutes (total annealing time of15 minutes), the diffraction pattern remained largely unchanged (Figure 6.5 B) The pattern remainedwell fit by a mixture of ferrite and cementite, with a broad peak in the background centred at 47.5◦.After the sample had been annealed for a total of 30 minutes (Figure 6.5C) the diffraction patternappears to be intermediate between those obtained after annealing for 7.5 or 15 minutes (Figures 6.5Aand 6.5B) and the pattern obtained upon annealing for one hour (Figure 6.3). This can be seen clearlyin the {121} and {211} cementite peaks where the pattern has a very sharp peak with broad shoulders.This combination of high, sharp peaks and broad lower peaks cannot be fit satisfactorily assuming thepresence of a single cementite phase. To perform the fitting of the peaks shown in Figure 6.5C, thesame fitting procedure was undertaken as used previously, but two separate cementite phase were used,113Figure 6.5: Sample with 30.7 at.% carbon annealed at 530◦C for a total of A) 7.5 minutes, B) 15minutes, C) 30 minutes and D) 60 minutes showing fitting with cementite and ferrite peaks.Figure 6.6: Extended detail of sample with 30.7 at.% annealed at 530◦C for 7.5 minutes showing rela-tion of ferrite and cementite positions to observed peaks in A) low angles and B) high angles114each of which had separate peak width, strain and intensities but the same theoretical diffraction peakpositions. Given the complex nature of this pattern, including the possible presence of ferrite, twoseparate cementite phases and other unknown carbides, numerical interpretation of the fit is difficult.It is clear, however, that the inclusion of two separate cementite phases represents the experimentalpattern better than using a single cementite phase, as shown in the detail of the {102} cementite peakfitting of Figure 6.7.��������������������������� ����� ����� ����� ��� ������������������������������������������������������������������������������������������Figure 6.7: Detail of cementite peak position of sample with 30.7 at.% carbon annealed for 30 minutesat 530◦C showing detail of convolution of broad and sharp peaks, along with the shifted positionof the sharper peak.When annealing of this sample was continued for up to one hour at 530◦C the diffraction spectrumappears the same as the sample containing 39.6 at.%C annealed for one hour at 530◦C (Figure 6.3).The background is very close to linear, with no discernible peaks outside of the main sharp peaks,which occur at roughly the theoretically expected cementite positions. This structure was fit using thepreviously discussed algorithm with larger allowed strain in the cementite, the final predicted fittingparameters being shown below in Table 6.3. It is interesting to compare the predicted peak positionsfor the three samples found to have this type of diffraction pattern; the one containing 30.7 at.%Cannealed for one hour at 530◦C, the one containing 39.6 at.%C annealed at 530◦C for one hour andthe one containing 33.2 at.%C annealed at 630◦C for one hour. In all cases, Table 6.3 shows that thepredicted strain is largest and compressive in the [001] (c) direction, small and compressive in the[010] (b) direction and close to zero in the [100] (a) direction, the strains increasing with increasingcarbon content. A simple explanation for strains in the crystallized phases would be that it reflects amacroscopic stress on the sample (e.g. from epitaxial stresses or thermal expansion mismatch stressesbetween the film and substrate). Owing to the geometry of the diffraction measurements, the diffrac-tion vector was always oriented normal to the sample surface. In this case, any strains would be those115arising from planes oriented parallel to the sample surface. If the strains noted above arose from amacroscopic stress it would be expected that the diffraction peaks would shift in the same direction(either towards compression or expansion) rather than the case observed here where the lattice pa-rameter appears to be expanded along certain directions of the unit cell and compressed along thetwo perpendicular directions. This could not be accounted for by a global strain on the sample asthe global strain direction of the sample would not align with the planar directions of each diffractionpeak.Table 6.3: Comparison of strains found in fitting cementite structure (sharp peaks) of samples with30.7, 33.2 and 39.6 at.% carbon.Direction Strain of 39.6 at.% C(annealed 530◦C, onehour) [%]Strain of 33.2 at.% C(annealed at 630◦C,one hour) [%]% Strain at 30.7 at.%C (annealed at530◦C, one hour)[%]a = [100] −0.064 0.019 0.060b = [010] −0.844 −0.608 −0.473c = [001] −0.403 −0.151 −0.038Given this systematic difference between the experimental patterns and the theoretical peak positionsof cementite, one may wonder whether cementite is indeed the phase present in the material. To checkthis, the theoretical diffraction patterns of other known carbides were compared to the experimentalpatterns. Figure 6.8 shows a diffraction pattern measured on the film containing 33.2 at.%C annealedat 530◦C for one hour. The range of 2θ was wider (36–50◦) in this case than the one shown inFigure 6.1 so as to provide more possible peaks for comparison. The comparison was made to the the-oretical peak positions for the Fe5C2 (Ha¨gg carbide) [92], orthorhombic Fe2C [88, 89], orthorhombicFe3C (cementite) [85], hexagonal Fe3C [90] and the theoretically calculated peak positions for bothhexagonal and orthorhombic Fe7C3 [91]. Also shown here is the spectrum of Fe2C as reported byBauer-Grosse et al. in their investigation of carbides produced from amorphous iron-carbon films[35]. Each spectra was calculated using the crystallographic imaging software Mercury from TheCambridge Crystallographic Data Centre [133] based on published atom positions, except in the caseof the Fe2C carbide reported by Bauer-Grosse where the precise crystallographic positions were notavailable and so the pattern is the experimental pattern from the carbide [35]. Of the spectra shown,the closest match, other than cementite, is Fe5C2 Ha¨gg carbide. In this case the experimental patterncontains peaks at 38 and 49◦ which would not be expected to be present. Overall, the best match tothe experimental pattern remains that of cementite despite the need for the calculated strain, describedabove.116��������������������� ��� ��� ��� ��� ��� ��� ���������������������������������������������������������������������������������������������������������������������������������������������������(a)��������������������� ��� ��� ��� ��� ��� ��� ����������������������������������������������������������������� �����������������������������������������(b)�������������������������������� ��� ��� ��� ��� ��� ��� �����������������������������������������������������������������������������������������������(c)������������������������������������ ��� ��� ��� ��� ��� ��� ������������������������������������������������ �������������������������(d)Figure 6.8: Comparison of observed sharp peak pattern for a sample with 33.2 at.% carbon with aselection of known carbides for comparison, including a) three possible Fe2C structures [35, 88,89], b) cementite [85] and ε Fe3C [90], c) two possible Fe7C3 structures [91] and d) Fe5C2 (Ha¨ggCarbide) [92].1176.2.3 Microstructural analysis of fully crystallized films by TEMOwing to the unique (for this study) XRD patterns obtained upon annealing at higher temperatures(530◦C and 630◦C) for an hour (or longer), samples containing 30.7 at.%C prepared by annealing at530◦C for one hour were observed by transmission electron microscopy. As in Chapter 5, sampleswere deposited on an IF-steel substrate and then annealed. From these annealed film-on-substratesamples, TEM lamella were prepared by FIB excavation through-thickness. The microstructure ofthis condition viewed at low magnification is shown in Figure 6.9. One can see that, distinct from thefully crystallized microstructures shown in Chapter 5, this condition is characterized by large (200-400 nm wide) crystalline grains that extend across the entire thickness of the film. Also notable is thehighly regular faulting within the grains, similar to what was seen in the case of the cementite crystalsformed upon crystallization of the lower-carbon containing films presented in Chapter 5.Figure 6.9: Through-thickness TEM image of sample annealed at 530◦C for one hour showing largethrough-thickness grains with pronounced faulting. The interface between the film and IF steelsubstrate can be seen as the bright line near the top of the image. The IF-steel substrate is thebright area above this.A more detailed view of the interface between the crystallized film and the IF steel substrate is shownin Figure 6.10 along with a selected area diffraction pattern taken from the position indicated ori-ented along the [010] cementite zone axis. The diffraction pattern is indexed using the 24 diffractionspots listed in Table 6.4. The maximum error between the theoretically expected and experimentallymeasured planar spacings was 7%, this error not being associated with any particular crystallographicdirection. These errors are therefore not related to the systematic strains implied by the fitting ofthe XRD patterns described above. It is notable that the region selected for diffraction appears free of118faulting, which is also evident in the lack of streaking in the diffraction pattern. Thinking to the resultsof Chapter 5, this would be consistent with the fact that the faulting plane observed in the cementite inthe lower carbon films was on the (010) plane. When viewed along the [010] direction such faultingwould not be visible.Figure 6.10: A) Detail of grains in crystallized sample (annealed at 530◦C, one hour) along with SAEDpattern (B) taken at the indicated position where no faulting is visible.Table 6.4: Comparison of measured and theoretical d-spacing for SAED shown in Figure 6.10 forselected diffraction planes of proposed zone-axis and orientation.Plane Theoretical d-spacing (A˚) Measured d-spacing (A˚) Error (%)(202¯) 1.69 1.64 2.96(200) 2.54 2.39 6.43(202) 1.69 1.69 0.39(002¯) 2.26 2.33 3.15(002) 2.26 2.31 2.49(2¯02¯) 1.69 1.69 0.14(2¯00) 2.54 2.39 6.48(2¯02) 1.69 1.63 3.62High-resolution TEM images (Figure 6.11) and selected area diffraction patterns (Figure 6.12) werealso obtained from regions containing high densities of faults. At high magnification the faulting isseen to be composed of distinct regions, with areas which exhibit a consistent pattern (as in the topright and bottom left of Figure 6.11) and regions of alternating bright and dark planes, with the spacingbetween these contrasting planes varying. The planar defects seen here are similar to those observed inthe cementite formed in the low carbon films, but with larger regions of non-faulted material. Betweenthese un-faulted regions are several faulted planes, which form repeating twins or stacking faults. Theplanar defects again are seen in a single orientation throughout a given grain of cementite and extend119from edge to edge of the crystal.Figure 6.11: HRTEM image showing detail of a grain in an orientation where striping is visible.The selected area diffraction pattern arising from this area (Figure 6.12) shows the long, single-directional streaking associated with faulting. In this case the zone axis was identified as the [101]cementite direction, with the {101}, {010} and {121} diffraction vectors indicated in the figure Thedirection of the streaking was identified by the spacing of the bright points along the axis of the streak-ing, which most closely corresponds to the spacing between adjacent {010} planes. The measuredinterplanar spacings are compared to the theoretical values for unstrained cementite in Table 6.5.Comparing to the faulting reported in the cementite formed in the lower carbon containing films (cf.Figure 5.38) one can see that the fault planes are the same.6.2.4 Local chemistry of the film during crystallizationGiven that the initial carbon content of the films studied here contain > 30 at.%C, it is surprisingthat a mix of ferrite and cementite form only to be replaced with what appears to be a microstructurecomposed largely (if not entirely) of (strained) cementite. Neither of these microstructures would beexpected to allow for more than 25 at.% carbon to be accommodated. To determine if the remainingcarbon segregates at surfaces or grain boundaries, the films were imaged through-thickness by energy120Figure 6.12: SAED pattern based on image shown in Figure 6.11 with measured planes indicated.Striping of diffraction pattern indicates planar structural defects in the (010) planes. Red linesadded as a guide to indicate where planar spacings are measured.Table 6.5: Comparison of measured and theoretical d-spacing for SAED shown in Figure 6.12 forproposed zone-axis and orientation.Plane Theoretical d-spacing [A˚] Measured d-spacing [A˚] Error [%](303) 1.12 1.13 0.89(22¯2) 1.51 1.53 1.29(14¯1) 1.51 1.55 3.01(06¯0) 1.12 1.17 3.85(060) 1.12 1.16 3.59(1¯41¯) 1.51 1.55 3.04(2¯22¯) 1.51 1.55 2.56(3¯03¯) 1.12 1.14 1.79(242) 1.19 1.21 1.96(121) 2.38 2.42 1.43(1¯2¯1¯) 2.38 2.47 3.80(2¯4¯2¯) 1.19 1.22 2.77121filtered TEM imaging (Figure 6.12). The low magnification map shown in Figure 6.13 encompassesthe entire thickness of the film as well as the film/substrate interface and part of the IF-steel substrate.Importantly, a grain boundary between adjacent cementite crystals is captured in this region as indi-cated. The EF-TEM carbon map shows a large difference between the film and substrate, with a muchlarger amount of carbon in the film compared to the substrate, as expected. Within the film the carbonappears uniformly distributed with no obvious evidence of carbon segregation to the grain boundary.The substrate/film interface shows an enhanced level of carbon (and oxygen) but this same featurewas found in the as-deposited film and is therefore unlikely to be the source of carbon repartitioningduring crystallization. Slight surface oxidation of the IF-steel after cleaning could account for theoxygen-rich layer, and the variable initial conditions of the deposition could account for higher levelsof carbon sputtering or reactive gas flow before the system reaches steady state.It has also been found that there is not a large amount of carbon which diffuses into the IF steelsubstrate. From APT measurement of samples taken inside the IF steel after annealing at 530◦C itwas shown that the carbon content of the substrate varied from 0.02 at.% carbon near the film interfaceto 0.01 at.% carbon at the centre of the IF steel sheet [73].Figure 6.13: EF-TEM images coming from a region containing the substrate/film interface as well asa grain boundary between cementite grains in a film fully crystallized by annealing at 530◦Cfor one hour. Higher levels of carbon and oxygen are observed at the IF steel interface but arelatively homogeneous carbon distribution is observed within the crystallized film. This is tobe contrasted to the EF-TEM images made on the (partially and fully) crystallized samples inChapter 5.To see if the location of the extra carbon in the crystalline films could be identified at a more localscale, an APT measurement was performed on a crystallized film (annealed at 530◦C for one hour), theatomic (Fe and C) reconstructions being shown in Figure 6.14A and 6.14B. Also shown is an averagecarbon composition plot taken from a cylinder having a radius of 50 nm, running from the top of thevolume to the bottom (Figure 6.14C). As can be seen, in this volume the carbon content of the APTvolume was found to be nearly constant at 30±1 at.% carbon, consistent with the bulk composition ofthe sample (30.7 at.% carbon). The carbon concentration varies smoothly over the length of the tip,122with no evidence of segregation, and only a slight linear variation in the carbon content within the tip(from 31–29 at.% over the 25 nm from the tip to the base of the sample).Figure 6.14: APT reconstruction and atomic profile measured in a sample whose bulk composition(based on EDX) was 30.7 at.% carbon observed after annealed at 530◦C for one hour. Thedistribution of carbon is seen to be homogeneous (30±1 at.%) and close to the bulk compositiondespite the fact that the sample is expected to be nearly 100% cementite after this annealingtreatment.6.3 DiscussionThe key observations from the results presented above can be summarized as follows:1. Films containing between 30-40 at.% carbon crystallize first to a mixture of ferrite, cementiteand other minority phases2. Crystallization requires annealing at higher temperatures and longer times compared to alloyscontaining <25 at.%C (cf. Chapter 5)3. The ferrite/cementite mixture initially formed on crystallization is replaced, upon annealing forlonger times, by a cementite-like phase having a distinctly different XRD pattern compared tothe first cementite formed.4. The composition of the cementite-like carbide found at the end of annealing contains >30 at.%carbon1235. This cementite phase is faulted on (010) planes, the same faulting plane as that observed forcementite in Chapter 5These results have both similarities and differences with work previously reported for similar alloys.The most detailed previous work performed on the crystallization of amorphous iron-carbon films withcomparable carbon contents focused on the structure of the iron carbides formed on crystallization[35], or on identifying the temperature for the onset of crystallization [26] (cf. Chapter 2). Notably,none of these studies reported ferrite as a product of crystallization in alloys containing >25 at.%carbon.The observed increase in crystallization temperature with carbon content of the alloy is qualitativelyconsistent with the literature. For example, it was reported that films with ∼35 at.% carbon crystal-lized at a temperature ∼100◦C higher than samples containing ∼20 at.% carbon [26]. This is con-sistent with the work presented above, where annealing at 300◦C led to the samples with <25 at.%carbon being fully crystallized after one hour and those with >30 at.% carbon still being fully amor-phous.The results presented above make a more significant departure from the literature when it comes tothe phases that were observed to form. In the studies of Bauer-Grosse et al.[26] it was reported thatcrystallization of films containing > 25 at.% carbon led directly to iron-carbides (e.g. Fe3C, Fe2C andFe7C3) having compositions close to those of the bulk film composition. A series of orthorhombiccarbides having compositions ranging from Fe3C to Fe2C can be formed via the process of ‘chemicaltwinning’ described in in Chapter 2 (cf. Figure 2.9). These ‘twins’ are formed by removing a (010)plane of iron atoms and translating perpendicular to the fault plane so as to make the edges of adjacenttriangular prism structures coincide. These chemical twins are similar to the stacking faults describedin Chapter 5, sharing the same fault plane, with the difference whether one plane of iron atoms isremoved or not. Layered iron-carbides that alternate between orthorhombic Fe3C, Fe5C2 and Fe2C bythis chemical twinning mechanism have also been previously observed in carbides formed in temperedmartensitic steels [59].This difference in the sequence of crystallization and the final phases observed in this study and thosein the literature may be the result of differences in the thin film deposition technologies and annealingprocedures used in this study and in the work of Bauer-Grosse et al. [57]. In the work of Bauer-Grosse[57] the system employed for preparing thin amorphous films was a triode magnetron sputtering. Inthis technique, compared to the sputtering system described above, an additional electrode is addedbetween substrate and target to increase the density of electrons within the plasma. This has theeffect of increasing the deposition rate of the film, and consequently modifying the microstructure,chemistry and phases formed during deposition [23]. This was seen in previous work performed ondepositing Fe-C alloys at UBC where ion plating was used to increase the rate of deposition [1]. In124that work it was found that rapid deposition led to an increase in carbon content of the film and to theformation of the metastable carbide Fe7C3 during the deposition. While the films produced in the workof Bauer-Grosse et al. were reported to be fully amorphous following deposition, it is possible thatthe differences in the deposition rate led to those phases having a significantly different local structurecompared to those produced by the method used in this study. Specifically, it would be expected thatthe triode sputtering would lead to denser, more stable films compared to those produced here [23].Another important difference with the work of Bauer-Grosse [57] is the method used to anneal thesamples. The annealing performed by Bauer-Grosse et al. involved in-situ heating in a TEM using aslow ramp heating at 0.05 K/s [35]. Under these conditions the total time to reach the crystallizationtemperature is approximately 100 minutes, longer than any annealing time needed to reach crystalliza-tion at the higher temperatures of this study. Noting the comments in Chapter 5 regarding the possibleaging of the samples during annealing, this may also lead to significant changes in the structure of theamorphous phase prior to crystallization.While the products of crystallization observed by Bauer-Grosse et al. were carbides having compo-sitions very close to the composition of the amorphous matrix, the ferrite and cementite observed toform here would necessitate significant carbon redistribution. If the amorrphous phase produced bythe combination of the triode sputtering and the long, slow heating in Bauer-Grosse et al.’s experi-ments was more stable, with lower diffusivity compared to the ones studied here, then the kinetics offerrite formation may be substantially suppressed. This would be akin to the slowing of ferrite forma-tion observed in films containing 16 at.% carbon in Chapter 5, where it appeared that the formation ofcementite under this condition required the composition of the remaining amorphous phase to reach∼25 at.% carbon.It is particularly surprising that ferrite is among the first phases to form upon the annealing of samplescontaining >25 at.% carbon. Unlike in Chapter 5, it is not possible from these experiments to tellwhether ferrite is the first phase to nucleate, as all experiments showing evidence of crystallizationhave diffraction peaks consistent with both ferrite and cementite. It is notable that both ferrite andcementite have carbon contents below that of the bulk carbon content of the as-deposited film. Thatimplies that during the initial formation of ferrite and cementite carbon is being rejected back intothe amorphous matrix, enriching it well above the ∼30-40 at.% carbon present in the as-depositedstate. Above 30 at.% carbon the driving force available for the formation of ferrite rapidly goes tozero (cf. Figure 5.37). It may be that ferrite forms in the early stages of annealing for the same reasonargued for its preferential formation in the films containing <25 at.% carbon; the kinetics of ferriteformation are significantly higher than those for the crystallographically more complex carbides. Theobservation that the mix of ferrite, cementite and other unidentified phases remain stable (i.e. thediffraction pattern does not evolve significantly) when the sample was held isothermally at 530◦C forbetween 7.5 and 30 minutes (Figure 6.5) may be a consequence of the loss of driving force for furthertransformation with the enrichment of carbon in the matrix. Another possibility is that the formation125of pure amorphous or graphitic carbon in contact with the ferrite and cementite. Indeed, there havebeen reports in higher carbon containing films of graphite formation during the annealing of Fe-Cfilms. For example, in the work of Scott et al. [12] an Fe0.4C0.6 film decomposed into a mixture ofgraphite and carbides but only when annealed at temperatures of∼ 700◦C. In another study by Sinclairet al. [134] crystallization of pure amorphous carbon was studied in contact with pure amorphousiron. Tri-layers of pure amorphous carbon-iron-carbon were created by PVD. On crystallization, itwas found that this thin film initially formed cementite which consumes the iron layer. Instead ofdirectly nucleating graphite within the amorphous carbon layer, the crystallization was mediated bythe presence of cementite, with the crystallized cementite grains migrating through the amorphouscarbon layer leaving behind crystalline graphite. Consistent with both of the studies mentioned aboveis the difficulty in forming the graphitic phase. Given our lack of direct microstructural observationson this state we can’t exclude the possibility that graphitic carbon forms at the temperatures studiedhere, thereby allowing the carbon content in the amorphous matrix to be maintained at lower levelsthan those that would be required if only ferrite and cementite formed.Further annealing leads to the apparent removal of the initial ferrite and carbides, replacing themwith what has been characterized above as cementite. The cementite formed in this second step ofcrystallization has clear structural differences with the cementite that it replaces. Most obvious is thelarge size of the cementite grains in the final state, these being an order of magnitude larger than thesize of the cementite grains formed in the samples containing <25 at.% carbon. Assuming a similarinitial cementite grain size in the samples with >25 at.% carbon would help explain the drastic changein x-ray diffraction peak widths, the width of the peaks decreasing from∼0.4◦ to 0.1◦ with this secondstep of crystallization (Figure 6.9).This second step of crystallization is also rather surprising. While it replaces the initial heterogeneousproducts of crystallization (ferrite, cementite and other unidentified phases) with what appears tobe single phase cementite, this new phase’s stoichiometry would allow for only 25 at.% carbon to beaccommodated, while the overall composition of the samples were >30 at.% carbon. While cementiteis well known to allow for sub-stoichiometric compositions through vacancies on the carbon sub-lattice [135], the only way to achieve higher than 25 at.% carbon would be to invoke the chemicaltwinning described above. In this case the presence of extra peaks/spots in the diffraction patternconsistent with e.g. Fe2C should be apparent. If the extra carbon were to be be incorporated throughthe formation of distinct other crystalline phases (e.g. Fe7C3) those too should give rise to somesignature in the diffraction spectra collected. This does not seem to be the case.One might consider that decarburized during crystallization allowed the carbon level of the sample tobe reduced during annealing. This was checked by performing EDX measurements after annealingon select samples. These measurements showed that the that carbon content of the films did notmeasurably change after annealing.126While carbon rich crystalline phases should appear in the measured diffraction spectra, carbon richamorphous phases would not. Using the molar volume of cementite (23.33 cm3/mol [85]) and byestimating the molar volume of amorphous carbon as similar to that of graphite (5.30 cm3/mol [136])it is possible to show that the required volume fraction of amorphous phase would be between 1 and6 vol.% for films with bulk concentrations between 30 and 40 at.% carbon. This small fraction ofcarbon rich phase, if distributed throughout the microstructure would be difficult to observe. Thatcould explain the observed homogeneous distribution of carbon observed by EF-TEM imaging on thefully crystallized material (Figure 6.13), where the spatial resolution of the measurements made maynot be sufficient to be able to resolve such a small fraction of high carbon amorphous phase.While the above interpretation of a final microstructure that is a mix of cementite and carbon richamorphous phase is attractive, the APT results (Figure 6.14) put it into doubt. Those results showeda remarkably uniform carbon concentration of ∼30 at.% carbon in a tip extracted from a sampleannealed at 530◦C degrees for one hour. Based on XRD and TEM observation this sample shouldprimarily consist of cementite. In particular, the TEM observations shown in Figure 6.9 come fromthe same sample used to prepare the APT tip. As noted above, there is no known way for cementiteitself to accommodate more than 25 at.% carbon. It is possible that the measured APT volume wastaken from a region that contained another phase, e.g. remaining amorphous matrix. Given the factthat this material should be predominantly cementite, then this phase remnant minority phase wouldneed to be highly enriched in carbon.Another way that the cementite could accommodate additional carbon would be via the chemicaltwinning mechanism noted above. The observed (010) fault plane is consistent with the plane requiredfor chemical twinning. If chemical twinning occurred, however, it would lead to additional phases,e.g. Fe2C. As noted above, there is no evidence in the diffraction spectra (either in TEM or XRD) thatpeaks from any other phases are present. If the chemical twinning were aperiodic (e.g. extremely thin,defected layers), then perhaps the breadth of the diffraction peaks would be sufficiently reduced so asto make them difficult to see above the strong peaks attributed to cementite. The difficulty with thisargument is that the most carbon rich carbide that can be formed by chemical twinning is Fe2C. Themix of Fe3C and Fe2C required to match the measured composition of film (APT tip) would requirea higher volume fraction of Fe2C than Fe3C. This again does not match with the observed diffractionspectra. Finally, if such extremely fine planar carbon rich regions existed in the cementite then someevidence for them should have been clear in the APT volume shown in Figure 6.14.The final surprising result from this cementite-like phase are the strains required in order to matchthe experimental XRD pattern to the theoretical Fe3C pattern. While the number of peaks and theirapproximate positions were observed to be in good agreement with those of cementite (cf. Figure 6.8),rather large strains were required in the fitting. These strains were determined with high confidencedue to the sharpness of the experimentally measured diffraction peaks. It is interesting to note that thelargest strains were required to occur normal to the (010) plane (in the b direction, [010]), i.e. normal127to the plane of the observed faults. In the case of the faults observed in Chapter 5, where there wouldbe no need for chemical twinning to take place to meet the chemistry of the film, the faulting did notseem to lead to such significant strains normal to the faulting plane.It would appear that the large compressive strains are associated with the observed apparent super-stoichiometry of the film and perhaps to some form of aperiodic chemical twinning that allows foradditional carbon to be incorporated into a cementite-like lattice. The experimental results obtainedhere do not provide sufficient detail to be able to definitively prove the origins of this enhanced carbontrapping in cementite but they do provide a potential area for fruitful further research.6.4 SummaryIn this chapter the crystallization behaviour of amorphous Fe-C thin films have been studied for alloyscontaining between 30 and 40 at.% carbon. While the results share some similarities with previousexperiments reported in the literature, significant differences exist. Surprisingly, the film undergoesa two-stage crystallization process. In the first stage, the alloy crystallizes into a combination offerrite, cementite and other carbides or carbon rich phases. This appears more complex than theresults previously reported in the literature where the direct transformation to carbides having similarcompositions as the amorphous matrix are common. In a second step, this mix of phases is replacedby a single phase whose XRD pattern is best matched (when compared to a range of carbides) torelatively coarse grained cementite containing a high density of faults on the (010) plane. Thesefaults are similar to those seen in cementite formed in lower carbon films (cf. Chapter 5). EF-TEMimaging showed a homogeneous carbon concentration in this phase, though APT analysis showeda carbon concentration significantly higher than stoichiometry (25 at.% carbon). This remarkableresult is difficult to explain given that cementite is usually considered to be limited to at most 25 at.%carbon. The relatively large elastic strains measured perpendicular to the faulting plane combinedwith previous work would suggest that a form of chemical twinning may play a role in allowing forthis super-stoichiometric phase to be formed. The difficulty with this interpretation is that one wouldexpect distinct peaks from other phases that do not appear in the diffraction pattern. This would be afruitful area for further study.128Chapter 7Conclusions and future workThis thesis has investigated the production and crystallization behaviour of thin-film, Fe-C thin film-s/coatings. This has contributed to the global goals of the collaborative, multi-institutional ‘GraCoS’project, i.e. the development of processing technologies for using diffusion reservoirs for the con-trolled strengthening of packaging steel sheet products.The production of iron-carbon coatings through a voltage-controlled reactive gas PVD system, devel-oped as part of this thesis, has allowed for well-adhered, structurally and chemically homogeneousthin film coatings to be produced. A previous process was modified by the introduction of reactivemethane gas, the sample composition being controlled by monitoring the system voltage. In this wayit has been possible to produce films containing from ∼15–50 at.% carbon with thicknesses of up to∼1 µm. The advantage of this technique, compared to prior techniques, is that the carbon content ofsamples can be controlled independent of the structure of the film.To ensure a solid understanding of these as-produced materials (prior to a study of their crystalliza-tion), a suite of experimental techniques were used to characterize the material. The bulk compositionof the as-deposited samples was studied by energy dispersive x-ray (EDX) analysis in the SEM andauger electron spectroscopy (AES). These techniques were used to develop a calibration curve forrelating system voltage (methane flow rate) to carbon content of the films. To study the structure ofthe films at a more local scale, transmission electron microscopy (TEM) and atom probe tomography(APT) were used. This study is the first to have used APT to analyze the local composition of suchamorphous Fe-C films. Unlike in previous studies where the structure of as-deposited Fe-C amor-phous films was found to be compositionally inhomogeneous, the samples produced here were foundto be very uniform in structure and composition.In the second part of this work, the crystallization of samples containing <25 at.% carbon were stud-ies. A two-stage transformation was observed for samples containing <20 at.% carbon annealed at250◦C, the samples transforming first to ferrite, with the formation of cementite following at longertimes. With increasing carbon content of the samples and annealing temperature, cementite formation129was observed to become faster. While similar results have been reported previously in the literature,most studies have used complicated ramp heating. Here, the use of isothermal annealing has allowedfor the kinetics of the transformation(s) to be examined at constant temperature. For the first time, thecomposition of the product ferrite and cementite phases have been quantified by atom probe tomogra-phy. These results definitively show that the cementite forms with its stoichiometric composition andthat the ferritic phase formed has a very low carbon content. This discounts previous suggestions thatferrite might form supersaturated in carbon (relative to ferrite in conventional steels). A surprising re-sult was the high density of faults observed in the cementite formed by crystallization. It was positedthat these faults correspond to the (020)[100] stacking faults previously reported in the literature. Itwas shown, using a simple model, that the energy required for the formation of such faults would notexceed that available for driving the transformation of the amorphous matrix to cementite. Finally,the peculiar kinetics of the crystallization, particularly the slowing of ferrite nucleation and growthdespite evidence of remaining driving force for its formation, was interpreted based on a reductionof the diffusivity of iron and carbon in the amorphous matrix. It was argued that this slowing of thediffusivities of iron and carbon can be attributed to aging and enrichment of the amorphous matrix incarbon during the transformation.In the final section of this thesis, the crystallization of samples containing > 25 at.% carbon havebeen studied. This study revealed a number of surprising results. While prior studies reported thedirect crystallization of samples into carbides with compositions close to those of the bulk compo-sition of the film, this study found a more complex crystallization pathway. The first products ofcrystallization were found to be ferrite and cementite, along with other minority phases that could notbe unambiguously identified. The full XRD patterns of these samples were surprisingly similar tothose of the crystallized samples containing <25 at.% carbon. The formation of ferrite in amorphousalloys containing > 25 at.% carbon was hypothesized here to result from a kinetic advantage for fer-rite formation versus carbides. This initial ferrite/cementite mixture was replaced on longer annealingwith a second carbide phase, this phase being identified as a strained form of cementite, this carbidebeing stable for long annealing times. This two-step crystallization process has not been previouslyreported in the literature. This strained cementite phase was observed by TEM much coarser than thecementite observed in samples containing <25 at.% carbon, but containing the similar faults on the(010) planes. In contrast to the cementite observed in samples containing <25 at.% carbon, a signifi-cant compressive strain was found perpendicular to the fault plane (in the [010] direction), this strainsystematically increasing with the carbon content of the film. It was argued that these observationscould suggest the presence of chemical twinning on the (010) planes, this form of faulting in cemen-tite allowing for thin plates of other carbides to be formed having compositions of up to Fe2C. Suchchemical twinning has been reported previously in carbides formed by crystallization of amorphousfilms. This interpretation was, however, called into question by APT results which showed a remark-ably uniform carbon concentration of ∼30 at.% carbon in cementite. The mechanism by which such130carbon supersaturation can be achieved in cementite would be a valuable area of future research.From the work of this investigation several interesting questions have been uncovered which wouldbe fruitful areas of future research. In the investigation of ferrite crystallization in films containing<25 at.% carbon it was shown that the slowing growth of ferrite can be explained as a kinetic phe-nomenon, due to the dropping diffusivity of iron and carbon within the amorphous matrix. Usingthe deposition techniques of this work, which have been shown to create structurally and chemicallyconsistent amorphous iron-carbon a series of experiments could be developed which use ramp heat-ing and in-situ TEM to identify the crystallization rate of the ferrite. By annealing multiple samplesfrom the same deposition with a series of ramp heating rates, and repeating this study with a depo-sition at a higher carbon content, it would be possible to build a model which accounts for the timeand concentration dependence of the crystallization kinetics. Using such a study it would also bepossible to positively determine if the crystallization kinetics are influenced by chemical dependantlocal-ordering as has been proposed in this study and related work in the iron-boron system. Thiswould definitively answer an open question in the literature regarding the crystallization kinetics ofthis amorphous material.High-energy diffraction studies, such as those using synchrotron XRD have been used in other sys-tems to show local ordering, and could be used in this material. This would directly show any localordering, and allow the comparison the structure of as-deposited amorphous with varying levels of car-bon to the structure of samples which have been annealed but not crystallized. If such local-orderingwere observed in annealed samples this would help to confirm that this is the mechanism behind theslowing of the amorphous crystallization. This would have implication both in this system and in theother amorphous materials such as iron-boron where similar mechanisms have been proposed.In the amorphous films with >25 at.% carbon, the exact process of the two-stage crystallization dis-covered here has not been observed by TEM. Ex-situ or in-situ annealing and analysis by TEM, aswas performed for the <25 at.% carbon samples could be very informative. The process of ferritecrystallization in these high-carbon films, the identity of the un-identified secondary carbides and theprocess of the secondary cementite crystallization could all be more clearly understood in this way.Furthermore the open question as to the accommodation of carbon within the final carbide structurecould be an interesting area of future research. Developing a better understanding of this mechanismfor incorporating carbon into iron carbides would allow for a more complete understanding of the fulliron-carbon system and could have specific benefit in steel production.Finally, the deposition and characterization methods outlined in this work have the potential to beapplied in the creation of a wide variety of metallic films with tailored chemistry and structure. Thewide range of control variables involved in PVD allow for nearly unlimited ranges of as-depositedstructures and chemistries by the careful development process parameters. Also, as shown by thelarger GraCoS project the rate of deposition allows for the creation of films that provide specificmechanical improvement to sheet material. This methodology has clear possibilities both in its use131to create tailored chemical gradients in sheet product, and also in the direct creation of material withphases and chemistries that are difficult to produce through traditional processing techniques. Thedirect route of investigation would include the addition of secondary alloying elements in the film,or altering the electrical properties of the deposition to bring about films with novel chemistry orstructure, changing the crystallization properties of the film, and allowing the creation more complexchemical profiles within sheet product for specific mechanical improvements.132Bibliography[1] A. Weck, C., Sinclair, C. Scott, and C. Maunder. Supersaturated α-iron in vapour depositedFe-C thin films. 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