Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Precipitation and recrystallization in a binary magnesium-neodymium alloy Sterling, Elizabeth 2015

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata


24-ubc_2015_september_sterling_elizabeth.pdf [ 41.99MB ]
JSON: 24-1.0165747.json
JSON-LD: 24-1.0165747-ld.json
RDF/XML (Pretty): 24-1.0165747-rdf.xml
RDF/JSON: 24-1.0165747-rdf.json
Turtle: 24-1.0165747-turtle.txt
N-Triples: 24-1.0165747-rdf-ntriples.txt
Original Record: 24-1.0165747-source.json
Full Text

Full Text

Precipitation and Recrystallization in a BinaryMagnesium-Neodymium AlloybyElizabeth SterlingB.Sc., Franklin W. Olin College of Engineering, 2008a thesis submitted in partial fulfillmentof the requirements for the degree ofDoctor of Philosophyinthe faculty of graduate and postdoctoralstudies(Materials Engineering)The University of British Columbia(Vancouver)August 2015© Elizabeth Sterling, 2015AbstractThe influence of precipitate state and annealing temperature on the recrystallizationof a Mg-2.8wt.%Nd alloy has been investigated. Precipitation kinetics at 190‰,350‰ and 400‰ were studied in order to understand precipitate evolution duringrecrystallization. Precipitation was studied primarily through electrical resistivitymeasurements, and modelled using a mean radius model. It was found that predictingthe kinetics required the spatial distribution of solute to be considered.Pre-aging conditions were selected in order to study the influence of either pre-existing or concurrently formed precipitates during recrystallization. After aging, thesamples were cold rolled to a strain of 20%. The microstructures were character-ized primarily through EBSD, and also through hardness measurements. Pre-agingthe samples at 400‰ for three hours resulted in a dispersion of stable β precipitatesduring annealing. This led to a recrystallized microstructure with recrystallizationnucleation sites similar to those previously reported in the literature. Pre-aging thesample at 190‰ for 24 hours lead to the formation of metastable β′′ precipitateswhich strengthened the sample, but dissolved rapidly upon annealing at higher re-crystallization temperatures. When samples previously solutionized at 545‰ or agedat 190‰ were subsequently annealed at 350‰, recrystallization stagnated. This wasattributed to concurrent precipitation pinning grain boundaries. In all samples, ir-respective of aging condition, recrystallization was observed primarily in twins andshear bands. The twins which recrystallized were found to be {101¯1} contractiontwins and {101¯1}{101¯2} contraction-extension twins. As the nuclei forming withinthese regions were not randomly oriented, recrystallization in these alloys did notrandomize the texture.iiThe work presented in this thesis increases understanding of recrystallization inMg-Nd alloys. In particular, the means by which Nd interacts with and affects therecrystallizing microstructure have never been studied in detail. Furthermore, thiswork points to possible ways in which new magnesium alloys and thermomechanicalprocesses could be designed to improve final material properties.iiiPrefaceThe majority of the experimental work presented in this thesis was conducted atthe University of British Columbia within the department of Materials Engineeringbetween May 2009 and August 2013 by myself. In all instances I planned experi-ments, performed heat treatments, prepared samples and interpreted results underthe supervision of Dr. Chad Sinclair.The Mg-0.6wt.%Nd used in these studies was cast at McMaster University, andthe Mg-2.8wt.%Nd used in these studied was cast at the Max-Planck-Institut fu¨rEisenforschung (MPIE) by Dr. Stefanie Sandlo¨bes.The TEM observations in Chapter 6 were performed by Dr. Xiang Wang at theCanadian Centre for Electron Microscopy in McMaster University, Hamilton, ON.Samples were prepared by myself, with Dr. Wang performing the final electropolish-ing and thinning. All analysis and interpretation was performed by myself. Induc-tively coupled plasma analysis of the sample composition was performed at McMasterUniversity.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Microscale deformation mechanisms in magnesium . . . . . . . . . . . 42.2.1 Slip in magnesium . . . . . . . . . . . . . . . . . . . . . . . . 42.2.2 Twinning in magnesium . . . . . . . . . . . . . . . . . . . . . 62.2.3 Shear banding in Mg and Mg alloys . . . . . . . . . . . . . . . 72.2.4 The effect of alloying additions on shear banding . . . . . . . 82.2.5 Effect of texture on shear banding . . . . . . . . . . . . . . . . 112.3 The effect of rare earth alloying additions on deformation . . . . . . . 122.4 Recrystallization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.4.1 Static recrystallization in magnesium . . . . . . . . . . . . . . 162.5 Precipitation, deformation, and recrystallization in the binary Mg-Ndsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.5.2 Equilibrium phases in the Mg-Nd system . . . . . . . . . . . . 212.5.3 Metastable phases in the Mg-Nd system . . . . . . . . . . . . 242.5.4 Precipitation kinetics . . . . . . . . . . . . . . . . . . . . . . . 302.5.5 Deformation and recrystallization in binary Mg-Nd alloys . . . 312.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34v3 Scope and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . 354 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.2 Starting materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.2.1 Mg-0.6wt.%Nd . . . . . . . . . . . . . . . . . . . . . . . . . . 374.2.2 Mg-2.8wt.%Nd . . . . . . . . . . . . . . . . . . . . . . . . . . 384.2.3 Commercially pure Mg . . . . . . . . . . . . . . . . . . . . . . 384.3 Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.3.1 Hot rolling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.3.2 Solutionizing . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.4 Heat treatments for precipitation kinetics . . . . . . . . . . . . . . . . 404.5 Deformation and recrystallization studies . . . . . . . . . . . . . . . . 404.6 Microstructural characterization . . . . . . . . . . . . . . . . . . . . . 414.6.1 Scanning electron microscopy . . . . . . . . . . . . . . . . . . 414.6.2 Electron back-scattered diffraction . . . . . . . . . . . . . . . 414.6.3 Transmission electron microscopy . . . . . . . . . . . . . . . . 444.6.4 Electrical resistivity measurements . . . . . . . . . . . . . . . 454.6.5 Vickers hardness . . . . . . . . . . . . . . . . . . . . . . . . . 474.6.6 Automated Berkovich hardness testing . . . . . . . . . . . . . 475 Precipitation in Mg-2.8wt.%Nd . . . . . . . . . . . . . . . . . . . . . 495.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.2 Microstructural and resistivity changes occurring on aging at 190°C,350°C and 400°C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.2.1 Characterization of solutionized Mg-2.8wt.%Nd . . . . . . . . 505.2.2 Resistivity changes during aging . . . . . . . . . . . . . . . . . 535.2.3 Comparison of aging kinetics to the literature . . . . . . . . . 585.2.4 Fitting precipitation kinetics to a JMAK model . . . . . . . . 625.3 Modelling precipitation with a mean radius model . . . . . . . . . . . 685.4 The effect of spatial variations in Nd content on precipitation kinetics 775.4.1 Experimental observations . . . . . . . . . . . . . . . . . . . . 775.4.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 866 The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Nd 876.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 876.2 Initial aging treatments . . . . . . . . . . . . . . . . . . . . . . . . . . 886.2.1 Solution treated samples . . . . . . . . . . . . . . . . . . . . . 886.2.2 Samples aged at 400°C . . . . . . . . . . . . . . . . . . . . . . 906.2.3 Samples aged at 190°C . . . . . . . . . . . . . . . . . . . . . . 926.2.4 Preparation of Mg-0.6wt.%Nd samples . . . . . . . . . . . . . 936.3 Characterization of the deformed state . . . . . . . . . . . . . . . . . 946.3.1 EBSD of deformed materials . . . . . . . . . . . . . . . . . . . 956.3.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101vi6.4 Microstructure and kinetics of recrystallization . . . . . . . . . . . . . 1016.5 Recrystallization of Mg-2.8wt.%Nd aged at 400°C . . . . . . . . . . . 1026.5.1 Comparison to Mg-0.6wt.%Nd . . . . . . . . . . . . . . . . . . 1096.5.2 Observations of recrystallization nuclei . . . . . . . . . . . . . 1106.5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1186.6 Annealing of samples solutionized or aged at 190°C before deformation 1186.6.1 EBSD observations . . . . . . . . . . . . . . . . . . . . . . . . 1206.6.2 Effect of precipitates on recrystallization . . . . . . . . . . . . 1206.6.3 Origins of recrystallization nuclei . . . . . . . . . . . . . . . . 1256.6.4 Recrystallization at 400°C and 450°C . . . . . . . . . . . . . . 1316.6.5 Recovery during annealing . . . . . . . . . . . . . . . . . . . . 1346.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1367 Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . 1387.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1387.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141Appendix A Overview of the Mean Radius Model . . . . . . . . . . . 152Appendix B Processing of Berkovich Hardness Data . . . . . . . . . 155B.1 Calculation of hardness and Young’s modulus . . . . . . . . . . . . . 155B.2 Determination of Young’s modulus . . . . . . . . . . . . . . . . . . . 157B.3 Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159B.4 Comparison of Berkovich to Vickers hardness . . . . . . . . . . . . . . 162viiList of TablesTable 2.1 Summary of slip systems in Mg. . . . . . . . . . . . . . . . . . . . 5Table 2.2 Phases observed in dilute Mg-Nd alloys . . . . . . . . . . . . . . . 22Table 4.1 ICP analysis of Mg-0.6wt.% Nd. . . . . . . . . . . . . . . . . . . . 38Table 4.2 ICP analysis of Mg-2.8wt.% Nd. . . . . . . . . . . . . . . . . . . . 38Table 4.3 Composition of pure Mg. . . . . . . . . . . . . . . . . . . . . . . . 39Table 5.1 Measured electrical resistivity and calculated amount of Nd in solidsolution from Equation 5.1 for three separate solutionized samples. 51Table 5.2 Values for b and α when n = 0.5. . . . . . . . . . . . . . . . . . . . 63Table 5.3 Variables used in the mean radius model. . . . . . . . . . . . . . . 71Table 5.4 Summary of nanoindentation data on heat treated Mg-2.8Nd. . . . 79Table 5.5 Values of interfacial energy used in the modified mean radius modelwhen Q = 1.34 eV and D0 = 10−4 m2/s. . . . . . . . . . . . . . . . 82Table 6.1 Twin angles and rotation axes in magnesium. . . . . . . . . . . . . 96Table 6.2 Berkovich hardness of samples annealed at 350‰ for 16 hours. . . 135viiiList of FiguresFigure 2.1 The effect of a) extension twinning and b) contraction twinning onreorienting the basal plane in magnesium. . . . . . . . . . . . . . 7Figure 2.2 Shear bands in an AZ31 sample which failed after rolling to a strainof 20%. The hallmark chevron shape of the shear bands can be seen. 8Figure 2.3 Kernal average misorientation (KAM) map of shear bands in pureMg rolled to 10% strain and Mg-3wt.%Y rolled to 30% strain. . . 10Figure 2.4 Effect of temperature and strain on the values of the JMAK expo-nent n in AZ31. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Figure 2.5 Rolled AZ31 that has been annealed after undergoing shear band-ing. A region of smaller grains in the former shear band region canbe seen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Figure 2.6 (a) EBSD grain boundary tracing of rolled AZ31 after rolling andrecrystallization. Regions where smaller grains formed along priorshear bands can be seen. (b) Optical image of the same region ofthe sample after further compression showing an increase in surfaceroughness concentrated at the former shear bands. . . . . . . . . 19Figure 2.7 Equilibrium phase diagram of Mg-Nd system.The maximum solu-bility of Nd in Mg is 0.6 at.%, corresponding to 3.6 wt.%. . . . . 23Figure 2.8 The solvus curve of the Mg-Nd phase diagram as determined byatom probe tomography, electrical resistivity, metallography, andFactsage thermodynamic modelling. . . . . . . . . . . . . . . . . . 24Figure 2.9 TTT curve for Mg-2.9 wt.% Nd. Precipitation was measured withelectrical resistivity, and the times shown are to 50% transformed. 26Figure 2.10 Example of β′′ precipitates in Mg-2.9wt.%Nd formed after aging at240‰ for seven hours. . . . . . . . . . . . . . . . . . . . . . . . . 28Figure 2.11 TTT curve from electrical resistivity for Mg-3.4 wt.% Nd. . . . . 31Figure 2.12 Recrystallization start temperatures for various alloying elements. 33Figure 4.1 Schematic showing the representation of crystallographic directionin an IPF map. The colour of a grain represents the orientationof a crystallographic direction relative to the sample coordinates.In this example crystallographic directions are colored relative totheir relationship to the normal direction. . . . . . . . . . . . . . 44Figure 4.2 Schematic showing orientations within a grain, the average grainorientation gavg, and the misorientation angle between a point andgavg. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45ixFigure 5.1 Overview of stable particles observed during processing of Mg-2.8wt.% Nd. a) Back scattered electron image of as-received ma-terial. b) Back scattered electron image of solutionized material.RD is vertical, TD is horizontal. c) Secondary electron image ofsample annealed at 520‰ for 96 hours. . . . . . . . . . . . . . . . 52Figure 5.2 Evolution of resistivity during aging at a) 190‰, b) 350‰ and c)400‰. Open symbols represent individual data points . . . . . . . 54Figure 5.3 Nd remaining in solid solution during aging at 190°C, 350°C and400°C estimated from the average resistivity (Figure 5.2) and Equa-tion 5.2. The equilibrium solubility at each aging temperature isindicated on the graph. . . . . . . . . . . . . . . . . . . . . . . . . 55Figure 5.4 Volume fraction of precipitates with time, estimated from the av-erage resistivity (Figure 5.2) and Equation 5.15. . . . . . . . . . . 59Figure 5.5 Fraction transformed versus time during aging of Mg-Nd samples,including data from the literature. . . . . . . . . . . . . . . . . . . 61Figure 5.6 JMAK models compared to experimental data at each aging tem-perature when fit to n = 0.5. . . . . . . . . . . . . . . . . . . . . . 64Figure 5.7 (a) Bright field TEM image taken along the [0001]Mg direction ofMg-2.8wt.%Nd aged at 190 °C for 24 hours. Dark β′′ precipitates,and in particular, the strain field associated with them can be seenagainst the background of the white Mg matrix. (b) SAED pat-tern taken parallel to the [0001]Mg matrix direction showing streaksconsistent with the β′′ phase. . . . . . . . . . . . . . . . . . . . . 66Figure 5.8 Backscattered electron micrograph of Mg-2.8Nd that was solution-ized and aged at 400°C for three hours showing coarse, sparselyspaced precipitates. The RD-TD plane is imaged. . . . . . . . . . 67Figure 5.9 TTT curves for precipitation in Mg-2.8wt.%Nd, Mg-2.9%Nd andMg-3.4wt.%Nd from this analysis and the literature. . . . . . . . 68Figure 5.10 Overview of the mean radius model [1]. The model takes intoaccount the rate of change in the number of precipitate nuclei(dN/dt) and precipitate radius (dR/dt) from the nucleation andgrowth stage through growth and coarsening. At each time step theamount of solute remaining in solid solution is calculated througha mass balance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Figure 5.11 Examples of the precipitate free zone measured in Mg-2.8 wt.%Nd aged at 400‰ for three hours. The dashed lines highlight clearexamples of the precipitate free zone (PFZ) observed in this sampmle. 73Figure 5.12 The mean radius model at 400‰ compared to resistivity measure-ments and the JMAK model. . . . . . . . . . . . . . . . . . . . . 74Figure 5.13 Overview of the shell model. . . . . . . . . . . . . . . . . . . . . . 75Figure 5.14 The effect of adding in rapid precipitation at the grain boundariesto the mean radius model at 400‰. Varying values for η, whichlowers the activation energy barrier for nucleation at grain bound-aries, are shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . 76xFigure 5.15 Mg-2.8wt.%Nd aged at 400‰ for three hours showing clear bandsof precipitates alternating with regions of low preciptiate density.Regions of high precipitate density are highlighted with red dashes. 78Figure 5.16 Histograms showing Berkovich hardness of Mg-2.8wt.%Nd a) solu-tionized at 545‰ and b) aged at 400‰ for three hours. . . . . . . 80Figure 5.17 Histogram of Nd concentration calculated from hardness measure-ments. The data was truncated above 0.6at.%Nd, representing thesolubility limit of the alloy. . . . . . . . . . . . . . . . . . . . . . . 82Figure 5.18 Results of the mean radius models at 190‰, 350‰ and 400‰ whenthe heterogeneous distribution of solute is accounted for. A com-parison to the model without a concentration distribution is alsoshown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Figure 5.19 Nd in solid solution after aging three hours at 400‰ according tothe mean radius model and experimental results. . . . . . . . . . 84Figure 6.1 Texture and microstructure of solutionized Mg-2.8wt.%Nd beforedeformation. a) Normal direction IPF map, b) key to IPF mapcolouring, c) pole figures, and d) key to pole figure colouring. . . . 89Figure 6.2 Evolution of Vickers hardness during aging at 400‰. The solidsquare represents the average hardness value, while the hollowpoints are the individual measurements. . . . . . . . . . . . . . . 91Figure 6.3 A comparison of the mean Vickers hardness from Figure 6.2 withthe Vicker’s hardness calculated from electrical resistivity measuredon the same sample. . . . . . . . . . . . . . . . . . . . . . . . . . 91Figure 6.4 Evolution of Vickers hardness during aging at 190‰. The solidpoints represents the average hardness value, while the hollow pointsare the individual measurements. . . . . . . . . . . . . . . . . . . 92Figure 6.5 Aging kinetics in a sample aged at 190‰ for 24 hours followed byaging at 400‰ as found by a) Vickers hardness and b) electrical re-sistivity. The data from aging at 190‰ after solutionizing is shownin grey squares. The solid points represents the average hardnessvalue, while the hollow points are the individual measurements. . 93Figure 6.6 (a) Vickers hardness measured in between rolling passes in Mg-2.8wt.%Nd. (b) Change in hardness in between rolling passes inMg-2.8wt.%Nd. Trend lines are provided to guide the eye . . . . . 94Figure 6.7 Normal direction IPF maps with overlaid image quality data of thecold rolled samples. Examples of shear bands are highlighted withdashed lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96Figure 6.8 Image quality maps of cold rolled samples showing location of in-dexable twins in the cold rolled samples. . . . . . . . . . . . . . . 97Figure 6.9 Examples of indexed twins in Mg-2.8Nd samples: (a) double twinsin solutionized sample, (b) contraction twins in aged 190‰ sample,and (c) extension twins in aged 400‰ sample. . . . . . . . . . . . 98Figure 6.10 Distribution of misorientation angles in samples a) solutionized b)aged at 190‰ and c) aged at 400‰. . . . . . . . . . . . . . . . . . 99xiFigure 6.11 Example of precipitates (noted with red arrows) in an image qualitymap of Mg-2.8Nd aged at 400‰ before cold rolling. . . . . . . . 100Figure 6.12 Fragments of twin boundaries indexed within a shear band in Mg-2.8wt.%Nd aged at 190‰. . . . . . . . . . . . . . . . . . . . . . . 101Figure 6.13 Vickers hardness as a function of time during annealing at 350‰,400‰, and 450‰ for materials aged at 400‰. . . . . . . . . . . . 103Figure 6.14 Normal direction IPF maps of samples aged at 400‰ before an-nealing: (a) 16 hours at 350‰, (b) 1 hour at 400‰ and (c) 1 hourat 450‰. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104Figure 6.15 Grain size distributions of the annealed samples. . . . . . . . . . . 105Figure 6.16 Grain orientation spread map of Mg-2.8Nd aged at 400‰ and re-crystallized at 450‰ for 1 hours. The region shown in Figure 6.17ais circled in red. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105Figure 6.17 (a) Normal direction IPF map of grains which are marked as unre-crystallized in the GOS map. (b) Misorientation profile across thegrains. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106Figure 6.18 (a) Normal direction IPF map of Mg-2.8Nd aged at 400‰ andrecrystallized at 350‰ for 16 hours showing a grain which has notrecrystallized. (b) Misorientation profile across the grain. . . . . . 107Figure 6.19 Normal direction IPF map Mg-2.8Nd aged at 400‰ and recrystal-lized at 400‰ for four hours. . . . . . . . . . . . . . . . . . . . . . 107Figure 6.20 (a) Grain boundary (indicated by arrows) blocking growth of re-crystallized grains in Mg-2.8Nd aged at 400‰ and recrystallized at400‰ for four hours. (b) BSE image of Mg-2.8Nd aged at 400‰and recrystallized at 350‰ for 16 hours showing profuse precipita-tion onto the solutionized grain boundaries. . . . . . . . . . . . . 108Figure 6.21 Normal direction inverse pole figure maps of (a) Mg-0.6wt.%Ndand (b) Mg-2.8wt.%Nd recrystallized at 400‰ for one hour. . . . 110Figure 6.22 Image quality map of Mg-2.8wt.%Nd recrystallized at 350‰ for onehour showing regions of interest: (a) recrystallization at a heavilyprecipitated former grain boundary, (b) unrecrystallized twins, (c)recrystallization within a shear band. . . . . . . . . . . . . . . . . 111Figure 6.23 GOS map of Mg-3Nd aged at 400°C, recrystallized 350C for 1 hour.Regions (a), (b) and (c) correspond with the regions circled in Fig-ure 6.22. Also overlaid on this map are boundaries correspondingwith contraction, extension and double twins. . . . . . . . . . . . 112Figure 6.24 Inverse pole figure maps of sample recrystallized at 350‰ for onehour. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Figure 6.25 Normal direction IPF map of twins in Mg-2.8Nd recrystallized at350C for 1 hour. Traces of the (101¯2) planes (corresponding withextension twins) are shown. The dotted black lines correspond tothe closest plane traces for the {101¯1} plane. . . . . . . . . . . . . 113xiiFigure 6.26 (a) Pole figure showing the orientation of grains in the portion ofthe sample shown in Figure 6.25. (b) Guide to pole figure coloura-tion. Red corresponds to the parent grain, dark blue to extensiontwins, and light blue and green to recrystallized grains belongingto former contraction twins. . . . . . . . . . . . . . . . . . . . . . 115Figure 6.27 Normal direction IPF map with overlaid IQ data showing recrys-tallization at a grain boundary in a sample recrystallized at 350‰for one hour. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116Figure 6.28 (a) Normal direction IPF map with overlaid IQ data showing shearband obscuring recrystallized grain boundary. (b) IQ map showinglocation of formed grain boundaries (solid black line) and regionswhere the boundaries have been partially or fully obscured (dashedlines). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116Figure 6.29 Example of grain showing solely extension twins (linear blue fea-tures) where no recrystallization has occurred in the interior of thegrain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118Figure 6.30 Vickers hardness during annealing: (a) Solutionized samples, (b)samples aged at 190‰ and (c) all samples recrystallized 350‰ . . 119Figure 6.31 Normal direction IPF maps of samples annealed at 350‰ for 16hours. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121Figure 6.32 BSE images showing (a) profuse precipitation along the deformedmicrostructure in a sample solutionized before cold rolling and an-nealing at 350‰ for 16 hours. Arrows point to examples of pre-cipitation along twin boundaries, and (b) BSE of a sample aged at400‰ before cold rolling and annealing at the same time and tem-perature showing no precipitation onto the deformed microstructure.122Figure 6.33 TEM image of Mg-2.8Nd solutionized, deformed, and annealed at350‰ for 16 hours showing fine precipitates and a recovered sub-grain structure when view along the [0001]|Mg direction. Arrowspoint to dislocations which have been blocked by β1 precipitates. 123Figure 6.34 Transmission electron micrograph of a grain boundary cold rolledMg-2.8Nd solutionized before annealing at 350‰ for 16 hours. Ex-amples of β and β1 precipitates as well as the large particles presentafter casting are highlighted. . . . . . . . . . . . . . . . . . . . . . 124Figure 6.35 Solutionized sample recrystallized at 350‰ for 16 hours showinggrowth of recrystallized grains preferentially along the length of thetwin: (a) normal direction IPF map, (b) IQ map, (c) GOS maps,(d) guide to colours in the IPF map, and (e) guide to colours inthe GOS map. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Figure 6.36 Normal direction IPF maps showing crystallographic orientation,and grain orientation spread (GOS) maps showing recrystallizedgrains in samples recrystallized at 350‰ for one hour. . . . . . . 126Figure 6.37 Recrystallization within a shear band in Mg-2.8wt.%Nd solution-ized before annealing at 350‰ for one hour: (a) Normal directionIPF map, (b) GOS map. . . . . . . . . . . . . . . . . . . . . . . . 127xiiiFigure 6.38 Examples of twins which have partially recrystallized. (a-b) Solu-tionized, annealed 1 hours at 350‰. (c-d) Solutionized, annealed16 hours at 350‰. . . . . . . . . . . . . . . . . . . . . . . . . . . 128Figure 6.39 Recrystallized twins in a solutionized sample annealed at 350‰ forone hour. Black corresponds to the parent grain, red to unrecrys-tallized twins, and green to recrystallized twins. Yellow indicatesa double twin boundary. . . . . . . . . . . . . . . . . . . . . . . . 130Figure 6.40 Recrystallized twins in a aged 190‰ sample annealed at 350‰ forone hour. The color scheme is the same as in the above image, withthe addition of a blue grain showing a contraction twin remnant. . 130Figure 6.41 Normal direction inverse pole figure (IPF) maps and GOS maps ofsamples recrystallized at 400‰ for one hour. . . . . . . . . . . . 132Figure 6.42 Recrystallized shear band in rolled sample aged at 190‰ and an-nealed at 400‰ for one hour. Colours are the same as those shownin Figure 6.41. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133Figure 6.43 Examples of recrystallization in double twins in samples aged at190‰ prior to deformation, and annealed at 400‰ for one hour.Colours are the same as those shown in Figure 6.41. . . . . . . . . 133Figure 6.44 (a) Inverse pole figure and (b) image quality map of aged 190‰Mg-2.8wt.%Nd rolled and recrystallized at 450‰ for one hour. . 134Figure 6.45 Cumulative distributions of Berkovich hardness of the samples an-nealed at 350‰ for 16 hours. The distributions of the cold rolledsamples are shown for comparison. . . . . . . . . . . . . . . . . . 136Figure B.1 Typical force displacement curve for a automated microhardnessindent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156Figure B.2 An example of the effects of varying the number of data pointsand the number of points offset from the start of the unloadingcurve used to calculate Young’s Modulus. The R2 values in thefigure titles refers to the correlation between Young’s modulus andhardness for all indents in the sample. The colors of each data pointcorrespond to the R2 value of the fit of the slope of the unloadingcurve, and the corresponding scale is to the left of each image. . . 160Figure B.3 The correlation between Young’s modulus and hardness after dis-carding outlying data points. The correlation has weakened signif-icantly. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161Figure B.4 Comparison between Berkovich and Vickers hardness measurements.163xivList of SymbolsRoman Symbols (page introduced) UnitsV eqf Equilibrium volume fraction of precipitates (page 59)Aproj Projected area (page 156) nm2b Pre-exponential factor in JMAK equation (page 16)CpptMg Fraction of Mg in precipitates during aging (page 57)CpptNd Fraction of Nd in precipitates during aging (page 57)CssNd Fraction of Nd in solid solution during aging (page 57)D Diffusivity (page 72) m2/sD0 Pre-exponential for diffusion (page 72) m2/sDz Grain diameter in the presence of Zener pinning (page 109) µmEi Young’s modulus of the Berkovich indenter tip (page 158) GPaEr Composite modulus (page 158) mN/nm2 or GPaEs Young’s modulus of the nanoindentation sample (page 158) GPaf Fraction recrystallized (page 16)fs Solute fraction (page 60)gA Orientation of individual point in a grain (page 44) °gave Average grain orientation (page 44) °HB Berkovich Hardness (page 163) MPahc Contact depth of indentation (page 156) nmhi Symmetry matrix of a material (page 44)HV Vickers Hardness (page 163) MPahmax Maximum indentation depth (page 156) nmxvHtot Total hardness value (page 79) MPak Boltzmann Constant (page 72) eV/KKNd Resistivity coefficient of Nd in Mg (page 57) µW-cm/at. frac.N Number of data points (page 79)n JMAK exponent (page 16)Nv Number density of precipitates (page 69) m−3Q Activation energy for diffusion (page 71) eVR Mean precipitate radius (page 69) mR∗ Critical radius for nucleation (page 69) mT Temperature (page 55) ‰Vat Atomic volume (page 57) m3Greek Symbols (page introduced) Units∆G Driving force for precipitation (page 69) J/m3∆τ Solid solution strengthening component (page 78)√CNd−1 Geometric factor for indenter tip geometry (page 156) unitlessη Factor to reduce activation energy barrier (page 75) unitlessνi Poisson’s ratio of the Berkovich indenter tip (page 158) unitlessνs Poisson’s ratio of Mg (page 158) unitlessρ Resistivity (page 46) µW-cmρf Equilibrium resistivity (page 53) µW-cmρf Equilibrium resistivity (page 60) µW-cmρi Initial resistivity (page 53) µW-cmσ Conductiviey (page 46) MS/mσy Yield stress (page 157) MPaxviList of AbbreviationsAPT atom probe tomographyAZ31 Mg-3wt.%Al-1wt.% ZnBSE back scattered electronCI confidence indexCRSS critical resolved shear stressDFT density functional theoryEBSD electron back-scattered diffractionEDX energy dispersive x-ray spectroscopyEMPA electron microprobe analysisGP Guinier-Preston zonesGOS grain orientation spread mapHAADF-STEM high angle annular dark field-scanning transmission electron mi-croscopyhcp hexagonal close packedICP inductively coupled plasmaIPF inverse pole figure mapIQ image quality mapJMAK Johnson-Mehl-Avrami-Kolmogorov modelKAM kernal average misorientation mapND normal direction in rolled sheetRD rolling direction in rolled sheetSEM scanning electron microscopyPFZ precipitate free zoneSAED selected area electron diffractionxviiTD transverse direction in rolled sheetTEM transmission electron microscopyTTT time-temperature-transformation diagramxviiiAcknowledgmentsIt’s November 2008 and the economy is terrible. Maybe I should go tograd school.–Anonymous.And thus began a series of unfortunate events, mishaps, and, believe it or not,some of the best times of my life.First off, my thanks go to Dr. Chad Sinclair, for his years of advice, guidance, andtolerating my frantic emails about MATLAB. In addition, I would like to thank thestaff of Materials Engineering for all their help, whether it was machining samplesat the last minute or helping me navigate the paperwork of a large university. Spe-cial thanks go to Jacob Kabel, who’s talent with electron microscopes and vacuumfurnaces borders on magical.Between the sound of breaking glassware in the lab and the sound of clinkingglasses at the pub, I have a number of folks to give my thanks to. In no particularorder, my thanks go to Lina, Phil, Victor, Millie, Alyssa, Alex, Tegar, Sebastian andMarie. Furthermore, my time in Vancouver would have been sorely lacking were itnot for the Mike collection. To Mikes #1, 2 and 4: thanks for all the good times.And of course, my thanks go to my parents for tolerating all the times they had toexplain to friends and family that why yes, their daughter was still in school, in grade22 to be precise.Those who have read to this point may have noticed that mention of Mike #3has been conspicuously absent. This Mike in particular is the one who helped methrough thick and thin, made desserts when I was feeling down, and somehow orxixanother survived the perils of dating a grad student. Thus, to Michael Lee, this one’sfor you. I’m looking forward to the end of this misadventure being the start of alifetime more.xxChapter 1IntroductionThe Magnesium Strategic Research Network (MagNET) was formed in 2009 with thegoal of increasing the room temperature formability of wrought magnesium alloys foruse in the automotive industry. To acheive this, several significant barriers must beovercome. Magnesium has a hexagonal close packed (hcp) crystal structure, which in-herently limits ductility. Formability is further limited by the tendency of magnesiumto acquire a strong texture during low temperature deformation, and the texture isoften not significantly weakened during subsequent annealing.While wrought magnesium usage in cars is currently uncommon, usage is graduallyincreasing. For example, General Motors has hot formed magnesium alloy ZEK (zinc-neodymium-zirconium) at 450°C to use in trunk lid inner panels [2], and the Nd-containing alloy Elektron 717 is being used in automotive inner door panels weighing58% less than the original steel panels [3]. While hot forming is effective at creatingcomplex parts, the process causes issues with corrosion, wear on forming equipment,and is costly, making low temperature forming operations more attractive [4].Lanthanide rare earth alloying additions are one promising solution to increasingthe formability of wrought magnesium products. Neodymium in particular has beensingled out for its effects on mechanical strength, texture and ductility, and is alreadyin use in relatively common commercial alloys such as ZEK100, which contains 0.1wt.% Nd in additon to zinc and zirconium [5,6]. Despite its importance, little about1Chapter 1. Introductionthe effect of Nd on deformation and recrystallization has been reported. Nd is knownto have a significant effect on recrysatllization, dramatically altering the recrystal-lization start temperature once Nd concentration reaches a threshold value [5].This thesis explores precipitation in Mg-2.8wt.%Nd and the effect of Nd on de-formation and annealing in this alloy. It starts with a study on the precipitationin a binary Mg-2.8wt.%Nd alloy. The little information that exists in the literatureregarding phase equilibria, diffusivity and precipitation for this alloy system is oftencontradictory. This is followed by an examination of the deformed microstructure ofheat treated Mg-Nd alloys. Finally, the effect of Nd on recrystallization in binary Mgalloys has been studied, linking precipitation and the deformed state to the recrystal-lized microstructure. These results suggest ways the microstructure of deformed andheat treated Mg-Nd alloys can be tailored via the prior precipitate state.2Chapter 2Literature Review2.1 IntroductionThe relatively high strength and low density of magnesium alloys makes them idealcandidates for reducing the weight of vehicles in order to improve fuel economy.However, there are a number of issues which limit the feasibility of magnesium insuch applications. These include low ductility and strong texture, both of whichlimit the low temperature formability of Mg alloys. Pure Mg has been reported toform edge cracks after as little as a 10% rolling reduction [7], and Mg-3wt.%Al-1wt.%Zn (AZ31), one of the most common commercial alloys [8], can only be cold rolled tostrains of approximately 15-30% before failure [9, 10].Static recrystallization after cold working in many metals can improve formabilityby increasing ductility and modifying the texture formed during deformation [11].However, this rarely occurs in magnesium alloys [6, 12]. Furthermore, static recrys-tallization in Mg alloys is found to be spatially heterogeneous, making it difficult toaccurately predict the properties of the final recrystallized microstructure [10, 13].Interest in rare earth elements, especially Nd, has increased due to their abilityto increase the room temperature formability of Mg alloys (e.g. [5,9,14–16]). Nd cansubstantially increase ductility while weakening the basal texture after recrystalliza-tion. However, the underlying microstructural reasons for these effects are poorlyunderstood. In particular, static recrystallization in these alloys has received little3Chapter 2. Literature Reviewattention despite its importance to subsequent low temperature formability.This literature review will explore deformation and recrystallization in Mg. Inparticular, heterogeneous deformation on multiple length scales and its subsequenteffects on recrystallization will be examined. Next, the Mg-Nd system will be exam-ined, including the equilibrium phase diagram and metastable precipitation. Finally,the effect Nd on deformation and recrystallization will be discussed.2.2 Microscale deformation mechanisms inmagnesiumMg has a hexagonal close packed (hcp) crystal structure, and as such its deformationis inherently complex as it possesses a limited number of slip systems. Deformationinhomogeneity is seen at both the microscale, in features such as twins (i.e. [8,17,18]),and at the macroscale, with shear bands capable of traversing the entire thicknessof samples [19]. Crystallographic texture, precipitates, changes in deformation tem-perature, and alloying additions can all substantially affect the active deformationmechanisms. This section will review the effects of these factors on deformation inMg alloys. The fundamental mechanisms of deformation in Mg will be reviewed onlybriefly. For a more in depth discussion, please refer to the review by Partridge [20].2.2.1 Slip in magnesiumThe Von Mises Criterion states that a polycrystalline material must possess five activeindependent slip modes to accommodate any arbitrary shape change [20]. Fewer thanfive modes of slip are available to magnesium at room temperature, leading to lowductility for many deformation paths. There are four known types of slip sysems activein magnesium: Basal slip, prismatic slip, pyramidal slip and second order pyramidalslip, which is also known as 〈c+ a〉 slip. These slip systems are summarized in Table2.1.4Chapter 2. Literature ReviewTable 2.1: Summary of slip systems in Mg.Slip system Basal 1st order Prismatic 2nd orderpyramidal pyramidalSlip plane and direction {0001}〈112¯0〉 {101¯1}〈112¯0〉 {101¯0}〈112¯0〉 {112¯2}〈112¯3〉CRSS at room temp. 0.49 MPa [21] – 45 MPa [22] 2.3–40 [23–25]Number of slip modes 2 4 2 5Basal slip has the lowest critical resolved shear stress (CRSS) of any slip system atroom temperature. It operates on the (0001) plane in the 〈112¯0〉 directions, and there-fore only provides two independent modes of slip. Prismatic slip ({101¯0}〈112¯0〉) pro-vides two independent modes of slip, while first order pyramidal slip ({101¯1}〈112¯0〉)provides four modes. However, the strain accomplished by first order pyramidal slipcan be equivalently achieved with a combination of basal slip and primatic slip, mak-ing these four slip systems not independent. Both prismatic and pyramidal slip arebelieved to have significantly higher CRSS values than basal slip at room tempera-ture [21, 22]. Typically, prismatic and pyramidal slip will not be activated unless agrain is in a favourable orientation, or it faces strong enough constraint from surround-ing grains that these slip systems are activated [26]. Basal, prismatic and pyramidalslip cannot accommodate strain along the c-axis of the crystal lattice. Second orderpyramidal slip is able to accommodate strain along the c-axis, as it occurs on {112¯2}planes in the 〈112¯3〉 directions [23]. Second order pyramidal slip has the longestBurgers vector of any slip system in Mg. Estimates of the CRSS vary widely due tothe difficulty of measuring it experimentally [23–25,27].Grain boundary sliding is an alternative deformation mechanism to slip that canprovide an additional means of accomodating deformation. In some instances grain5Chapter 2. Literature Reviewboundary sliding can accomodate a significant portion of the applied strain: In anAZ31 sample strained 10% in tension, grain boundary sliding was estimated to ac-commodate 25% of the total applied strain [28].2.2.2 Twinning in magnesiumTwinning provides an alternate means of accommodating plastic strain parallel tothe c-axis. Twins also add complexity to deformation; for example, twins have beenreported to act as sites for damage nucleation [29, 30]. Extension twins form along{101¯2} planes in response to tensile stresses applied parallel to the c-axis. Thesetwins reorient the matrix by 86°. Contraction twins occur along the {101¯1} familyof planes in response to compressive stresses along the c-axis. They lead to thematrix being reoriented by 57°. A schematic of these twinning modes can be seen inFigures 2.1a and 2.1b. Extension twins typically have a thicker shape than contractiontwins, which tend to be narrow, and may occur in parallel bundles [8,30]. Extensiontwinning in Mg can be activated at low stresses [8], comparable to those required forbasal slip. By comparison, contraction twinning is not as easy to activate, therebyreducing the ability of Mg to accommodate c-axis compression [17], which leads todifficulties rolling basally textured Mg. Contraction twins often form contraction-extension double twins [17], which will be discussed shortly.The level of twinning observed in deformed Mg and Mg alloys is strongly affectedby grain size. Decreasing the grain size decreases the amount of twinning seen duringdeformation [31], which is believed to be due to the smaller grain size increasing thecritical stress necessary to nucleate a twin [32]. Twinning itself is considered to bean athermal process [32], in that the stress necessary to nucleate a twin is unaffectedby temperature. However, increasing the deformation temperature does decreasethe amount of twinning seen [31]. This is likely due to the thermal activation ofslip systems (i.e. lowering of the CRSS below that of the twinning activation stress)6Chapter 2. Literature Review(a) (b)Figure 2.1: The effect of a) extension twinning and b) contraction twinning onreorienting the basal plane in magnesium.relative to the stress for twinning as deformation temperature increases.Once magnesium has twinned, it is possible for the twinned volume to undergotwinning a second time, leading to double twinning. If the secondary twin reorientsthe material favourably, the twinned volume may be able to undergo further slip. Thiscan be seen when grains that are compressed perpendicular to the basal plane form{101¯1}{101¯2} (contraction-extension) double twins [33]. This twinning leads to a 37°rotation of the basal plane. This favours basal slip within the double-twinned volume.The strain within the double twinned volume can be extremely high. For example,dynamic recrystallization at room temperature was observed in {101¯1}{101¯2} doubletwins in pure Mg [9,33], indicating a high level of strain within the twins.2.2.3 Shear banding in Mg and Mg alloysShear bands are regions of intense, highly localized deformation seen in Mg and Mgalloys after deformation, most notably after rolling [7,9,19] and compression [34,35].The most extreme cases of shear banding can result in a series of cracks on thetransverse edges of the sample. These edge cracks take on a regular spacing, andoccur at a consistent angle relative to the rolling plane. An example of edge crackingcaused by shear banding in AZ31 can be seen in Figure 2.2.7Chapter 2. Literature ReviewIn recent years shear bands have received an increasing amount of attention inthe literature, as they are representative of extreme strain localization, and havesignificant effects on both the deformed and recrystallized microstructure. As thisthesis is focused on sheet products, and the the shear bands occurring during extrusionform under different conditions than those during rolling, only shear bands formedduring rolling will be discussed here.Figure 2.2: Shear bands in an AZ31 sample which failed after rolling to a strainof 20%. The hallmark chevron shape of the shear bands can be seen. Imageis from [19]. Reprinted from: Springer and JOM: Journal of the Minerals,Metals and Materials Society, Volume 57 No. 5, 2005, pgs. 57-61, “Macro-scopic damage by the formation of shear bands during the rolling and deepdrawing of magnesium sheets”, F.W. Bach, M. Rodman, A. Rossberg, B.A.Behrens, and G. Kurzare, Figure 1, original copyright notice) is given tothe publication in which the material was originally published, by adding;with kind permission from Springer Science and Business Media2.2.4 The effect of alloying additions on shear bandingWhile shear bands in Mg have recently become a subject of interest, shear bandshave been observed in Mg alloys for decades. For example, Couling et al. observedextensive shear banding in a Mg-0.5%Th alloy and in Mg-0.2%MM-0.4%Zn [36] in1959, where “MM” refers to lanthanide mischmetal. Both of these alloys could becold rolled to a strain of 87% using small (1-2%) reductions in height per pass. Thisexceptionally high degree of ductility was attributed to the extensive shear bandingseen in both alloys. Polarized light microscopy showed that the shear bands were8Chapter 2. Literature Reviewcomposed of {101¯1}{101¯2} double twins which reoriented the material favourably forbasal slip. Interestingly, these alloys showed a strain softening effect when deformedin tension after rolling, as increasing the rolling strain resulted in a decrease in tensileyield strength. This was believed to be due to the easy activation of basal slip withinthe shear bands [36].Alloying additions can have a striking effect on the formation of shear bands.An example of this can be seen in Figure 2.3, which compares shear banding inpure Mg cold rolled 10% to Mg-3wt.%Y cold rolled 40% through kernal averagemisorientation (KAM) maps. KAM maps compare the misorientation of a centralpoint (“kernal”) to that of neighboring points [37]. The pure Mg could not be coldrolled past 10% strain without forming edge cracks. By comparison, the Mg-3wt.%Yalloy was cold rolled to 40% strain before forming edge cracks. The Mg-3wt.%Ysample shows significantly more shear bands which are smaller and more denselyspaced, and are confined to one grain or the region between two grains. This contrastsstarkly to the shear bands in pure Mg, which are hundreds of microns long and spanmultiple grains. The shear bands in Mg-3wt.%Y are numerous enough that theauthors speculate that the high ductility of Mg-Y alloys are due to the shear bandspreventing the extreme strain localization and damage nucleation seen in pure Mg.The significant differences in the behaviour of the shear bands has been attributedto an increase in the activity of 〈c+a〉 slip in Mg-Y alloys, caused by a decrease in thestacking fault energy with the addition of yttrium [7,38]. This results in a significantchange in the twinning behaviour of the alloy compared to pure Mg. The shear bandsin pure Mg were composed primarily of contraction twins and double twins. At thesame time, the regions of the sample without shear bands showed a low density oftwins, and those that formed were extension twins. Extension twins in rolled Mgwith a basal texture has been observed by other authors, and are believed to be dueto backstresses on grains during unloading [9, 33].9Chapter 2. Literature Review(a) Pure Mg (b) Mg-3%YFigure 2.3: Kernal average misorientation (KAM) map of shear bands in pureMg rolled to 10% strain and Mg-3wt.%Y rolled to 30% strain. Reprintedfrom: Acta Materialia, Volume 59 No.2, S. Sandlo¨bes, S. Zaefferer, I. Sches-takow, S. Yi, and R. Gonzalez-Martinez, “On the role of non-basal defor-mation mechanisms for the ductility of Mg and Mg-Y alloys”, pg. 429-439,2011, with permission from Elsevier.The twinning response of the Mg-3wt.%Y alloy differs from that seen in pureMg. The shear bands were described as bundles of narrow bands. These bands werealternately oriented parallel to the parent grain and in an orientation consistent with{101¯1}{101¯2} double twinning. Unlike pure Mg, the regions of the sample which werenot shear banded still contained a large number of extension and double twins. Thisis the same type of double twinning within shear bands observed by Couling et al. inMg alloys containing either Th or lanthanide mischmetal alloys [36].The effect of alloying additions on shear banding was also studied by Barnett,Nave, and Bettles on pure Mg, AZ31 and Mg-0.2wt.%Ce [9]. All alloys had a pre-dominantly basal texture before rolling. The Ce alloy was substantially more ductilethan the other two alloys, and could be cold rolled to a strain of 90% before failure.This is a marked improvement over the 15% strain before failure in pure Mg, and10Chapter 2. Literature Review10% strain in AZ31. In all the alloys, the number of shear bands increased as therolling strain increased. Interestingly, the increase in shear bands was accompaniedby a decrease in the number of {101¯2} extension twins. Furthermore, the textureof the samples did not change substantially past a rolling strain of 10%. This wasinterpreted as being due to a large amount of deformation being accommodated solelywithin the shear bands, leaving the non-shear banded region relatively undeformed.The shear bands in all of the alloys were identified as being a combination of {101¯1}contraction and {101¯1}{101¯2} double twins.2.2.5 Effect of texture on shear bandingThe studies on shear bands conducted by Sandlo¨bes et al. [7] and Barnett et al. [9]both used materials with initial basal textures. As crystallographic orientation affectsthe slip and twinning systems active in Mg alloys, it stands to reason that a changein the starting texture of the material will impact the shear banding behaviour.Chun and Davies studied shear banding between room temperature and 250°C inAZ31 rolled to a strain of 10% [39]. The starting texture of the plate was varied suchthat the c-axes of grains were oriented parallel to either the normal direction (ND),rolling direction (RD), transverse direction (TD) of the sheet, as well as at an anglehalfway between ND and RD. The samples with an initial basal texture showed thehighest degree of shear banding. These shear bands were located at approximately30° to the rolling plane, which is similar to the angle reported by other authors [7,9].The authors reported a high density of twins in and around the shear bands, thoughthe twin types within the shear bands were not reported. The authors also noted adifference in the texture between the regions with and without shear bands, with thec-axes of grains within a shear band formed during hot rolling at 250°C being rotatedapproximately 20° toward the rolling direction.In the same study, shear banding was completely suppressed in samples oriented11Chapter 2. Literature Reviewsuch that the majority of the c-axes were oriented parallel to the transverse direction.This was believed to be due to this texture favouring prismatic slip over twinning [39].However, the authors did not comment on whether suppressing shear banding hadany impact on the ductility of the alloy [39]. When the starting texture of the sheethad the majority of the c-axes oriented toward the rolling direction, shear bands didform during rolling, albeit at a 50-60° angle relative to the rolling plane instead ofthe 30° seen in the basal textured material.2.3 The effect of rare earth alloying additions ondeformationThe beneficial effects of rare earth alloying additions on enhancing ductility have beenknown for decades [5, 36]. The first rare earth element to be alloyed with Mg wasthe actinide rare earth thorium, although it was phased out of use due to its weakradioactivity [40]. Since then, Ce, La, Dy, Nd and Gd have been added to magnesiumas lanthanide rare earths. In addition, Y has been categorized as a rare earth elementdue to having a similar effect on formability [5]. The effect of Nd in particular ondeformation will be discussed in further detail in Section 2.5.5.Historically, the lanthanide rare earths have been used as alloying additions in theform of mischmetals, which are mixtures of lanthanides that reflect the compositionof the parent ore, and typically contain La, Ce, Dy, and Nd [41]. This was due toboth the high expense of refining individual lanthanides, and to the belief that thestrong chemical similarities amongst the lanthides would cause them to behave almostidentically when used as alloying additions [42]. The individual elements do, however,have significantly different effects on the deformation of Mg alloys, e.g. [5]. In general,rare earth alloying additions are able to increase the ductility of magnesium alloys,decrease tension/compression asymmetry and anisotropy, and increase formability[6, 15,36,43].12Chapter 2. Literature ReviewStudies on binary Mg-rare earth alloys are uncommon as most studies have beenperformed on commercial alloys usually containing two or more alloying additions.Furthermore, most of these studies concentrate on hot rolling or extrusion, wheredynamic recrystallization occurs, leaving only a few papers to concentrate on theeffect of rare earth alloying additions during low temperature deformation and staticrecrystallization.Perhaps the most notable effect of rare earth elements on deformation is an im-provement in ductility compared to pure Mg or commonly used commercial alloyssuch as AZ31. As noted previously, Mg-0.2wt.%Ce was cold rolled to a 90% rollingreduction prior to failure compared to only 15% for AZ31 [9]. Similarly, a Mg-3wt.%Y alloy was cold rolled 40% before failure due to edge cracking, compared to 10%for pure Mg rolled under the same conditions [7]. Extruded Mg alloys fare similarly,with tensile elongation in an Mg-0.2%Ce alloy reaching a strain of 31%, compared to9% in pure Mg [44].In extruded Mg-rare earth alloys, the enhancement of ductility has been attributedto a change in the recrystallized texture. In extruded Mg alloys that do not containrare earth elements, the c-axes of grains are aligned nearly perpendicular to the ex-trusion direction. In rare earth containing alloys, the texture after recrystallization isdescribed as having a crystallographic orientation where an angle between the 〈0001〉and 〈112¯0〉 directions in Mg is parallel to the extrusion direction. This texture changeis attributed to recrystallization occurring within shear bands during or immediatelyafter extrusion [45]. While this texture shift in extruded materials is not paralleledin rolled Mg-rare earth alloys, it does demonstrate the significant effect that rareearth elements can have on recrystallization. In the extruded Mg-0.2%Ce mentionedabove [44], the enhanced ductility of the alloy is attributed to this texture shift. Thealloy also had a lower yield strength than pure Mg, which is believed to be due tomore grains being oriented such that slip systems with low CRSS values, such as basal13Chapter 2. Literature Reviewslip, can be activated.In contrast to extruded billets, rolled binary Mg-rare earth alloys do not show ashift away from a basal texture, but rather a reduction in the intensity of the basaltexture [9,14]. The mechanisms behind this texture weakening are poorly understood,though it may be attributable to recrystallized grains growing out of shear bands [43],as shear bands differ in crystallographic orientation than the surrounding grains.However, in general the relationship between the deformed microstructure in Mg-rare earth alloys and the recrystallized microstructure and texture has not been fullyexplored.The texture weakening effects and enhanced ductility found in Mg-Y alloys havebeen attributed to Y affecting the active deformation mechanisms. The change indeformation characteristics has been attributed to a change in the stacking faultenergy, ultimately changing the activity of 〈c+ a〉 slip and twinning in Mg-Y [7] andMg-Ce [46] alloys, or to an increase in prismatic slip activity at the expense of basalslip in Mg-Nd alloys [16] .As a result of the increased ductility and reduced texture, Mg-rare earth alloys areconsidered to be highly formable by the standards of magnesium alloys [6]. Rare earthalloying additions show great promise in improving the low-temperature formabilityof magnesium alloys, and this is supported by the number of commercial Mg-rareearth alloys currently available. Despite this, there are many aspects of deformationin Mg-rare earth alloys which merit further study. Many studies on rare earth alloysinclude additional alloying elements such as zinc or zirconium [6, 47], which make itdifficult to determine the effect of a single element on the deformation and texturechanges in the alloy. For example, the addition of 1wt.%Zn and 0.6wt.%Zr to Mg-1wt.%Ce lead to a modified texture compared to the same alloy without Zr and Zn.Furthermore, most studies have focused on deformation where dynamic recrystalliza-tion is active (extrusion and hot rolling, for example), which reveals little about the14Chapter 2. Literature Reviewroom temperature formability of these alloys. However, the evidence that does exist(e.g. [9]) shows that rare earth alloying additions are important to improving roomand low temperature formability.2.4 RecrystallizationIn the previous section, deformation in magnesium was discussed, with an emphasison the heterogeneity of deformation. Recrystallization in magnesium is also complex,in no small part due to the effects of heterogeneous deformation [10, 13, 48, 49]. Thissection will give an overview of recrystallization in metals, followed by a review ofrecrystallization in magnesium in particular. This section will conclude with a briefreview of the literature on the effect of Nd on recrystallization in Mg. A compre-hensive overview of recovery and recrystallization can be found in Humphreys andHatherly [11], and only a short summary of the microstructural changes occurringduring annealing of metals will be given here.The microstructural changes that occur during annealing can be divided into re-covery, recrystallization, and grain growth. These stages may overlap. Recovery isdriven by the stored energy of dislocations, and may decrease the hardness of the ma-terial, but microstructural changes will not be observable through optical microscopy.In the process of recovery, dislocations will annihilate or rearrange into subgrain struc-tures. During recrystallization, new grains with low dislocation densities nucleate andgrow into the deformed surroundings. During grain growth, large recrystallized grainscoarsen at the expense of smaller grains; this process leads to a reduction in grainboundary area/energy. Under certain circumstances (usually annealing at high tem-peratures or extended times), abnormal grain growth may occur, leading to a bimodalgrain size distribution.Recrystallization kinetics are often modeled using the empirically derived Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation [11]. The JMAK equation describes the15Chapter 2. Literature Reviewrecrystallized fraction as a function of time during isothermal annealing as:f = 1− exp(−btn) (2.1)where f is the fraction recrystallized, b is an experimentally derived constant atconstant temperature, and n represents the dimensionality of growth. The values ofn and b can be calculated by plotting ln(ln(1/(1−f))) versus ln(t) for a given annealingtemperature. The slope of the resulting line and the y-interecept correspond to n,and ln(b) respectively. For three-dimensional growth, the theoretically derived valueof n is 3 or 4, depending on whether all recrystallization nuclei are present at thebeginning of recrystallization (site saturation) or the nucleation rate is constant. Inpractice, values of n are often much lower [11, 50], as the JMAK equation assumesthat nucleation sites are randomly distributed and growth occurs in three dimensions,which does not often happen in experiments.2.4.1 Static recrystallization in magnesiumRecrystallization after low temperature deformation in Mg has not received muchattention in the literature, but has generally been found to be highly spatially het-erogeneous. In both pure Mg [51] and AZ31 [10,13,52,53], recrystallization nuclei arefirst seen in twins after room temperature deformation, as well as shear bands [7, 9].Recrystallization nuclei are also often seen at grain boundaries [48]. Twin nucleationhas been found to occur primarily within contraction and double twins [52–54]. Thesenuclei often have a non-basal orientation [51,52], which may reflect the orientation ofthe twinned region [43]. Despite the proliferation of nuclei within twins, these nucleioften fail to grow outside the original boundaries of the twin [10, 48, 51, 52]. As aresult, the recrystallized microstructure remains dominated by basal-oriented grains.The reasons behind the slow motion of the twin boundaries are poorly understood.Furthermore, particle stimulated nucleation in Mg alloys is ineffective at promoting16Chapter 2. Literature Reviewrecrystallization in more than a small percentage of the microstructure [55]Annealing magnesium for extended periods of time or at high temperatures maycause abnormal grain growth. With few exceptions, abnormal grain growth is consid-ered detrimental, as it leads to local areas with different mechanical properties fromthe bulk material. Abnormal grain growth has been observed in pure Mg [7] andMg-Nd alloys [56].As a result of this heterogeneous nucleation and grain growth, recrystallizationkinetics in Mg and Mg alloys cannot be accurately described using a simple JMAKmodel with a constant value of n, as was demonstrated by Su et al. in AZ31 [13].Varying the temperature and strain caused a change in n, the JMAK exponent, whichcan be seen on a plot of ln(ln(1/(1−f))) versus ln(t) in Figure 2.4 This is indicative of amaterial which does not recrystallize in a homogeneous manner, as varying strain andtemperature will lead to a change in the density and location of nucleation sites [13].Zou argued that two n values (one to describe the beginning of recrystallization, andthe other for the latter stages) for a given temperature were needed to model thefraction recrystallized [50]. Similarly, recrystallization kinetics have been describedby Okrutny using two distinct stages of recrystallization [10]. In this type of model,recrystallization is modeled using one set of parameters for recrystallization occurringwithin twins, and a second set for recovery and recrystallization within the untwinnedportions of grains.The effect of shear banding on the recrystallized microstructureAs with deformation, recrystallization can also be heterogeneous at the macroscalelevel due to shear bands. As shear bands are regions of higher localized strain thannon-shear banded regions [9, 19], the recrystallization response between the two re-gions differs significantly. In addition, as the texture of the shear bands is differentfrom the surrounding grains, recrystallization in shear bands will alter the properties17Chapter 2. Literature ReviewFigure 2.4: Effect of temperature and strain on the values of the JMAK expo-nent n in AZ31. XV is the fraction recrystallized as determined by hardness.Image is reprinted from [13] with permission from Taylor and Francis.of the annealed microstructure. Figure 2.5 highlights the difference in recrystallizationbetween shear banded and non-shear banded regions in rolled AZ31.Figure 2.5: Rolled AZ31 that has been annealed after undergoing shear band-ing. A region of smaller grains in the former shear band region can be seen.From [19] Reprinted from: Springer and JOM: Journal of the Minerals,Metals and Materials Society, Volume 57 No. 5, 2005, pgs. 57-61, “Macro-scopic damage by the formation of shear bands during the rolling and deepdrawing of magnesium sheets”, F.W. Bach, M. Rodman, A. Rossberg, B.A.Behrens, and G. Kurzare, Figure 2, original copyright notice) is given tothe publication in which the material was originally published, by adding;with kind permission from Springer Science and Business Media.Another example of the effect shear banding can have on the recrystallized mi-18Chapter 2. Literature Reviewcrostructure can be seen in Figure 2.6, in which AZ31 sheet was rolled, inducing shearbands, then annealed [49]. The annealed regions corresponding to shear bands had acrystallographic texture believed to similar to that of the parent shear bands, whilethe non-shear banded regions had a basal texture. During subsequent compressionperpendicular to the rolling direction, these shear band were oriented favourably forbasal slip, causing significant surface roughness due to the formerly shear bandedregions deforming from the surrounding areas. This highlights the importance of theprior deformed texture and microstructure on future deformation, even when stepssuch as annealing are taken to lessen these effects.(a) (b)Figure 2.6: (a) EBSD grain boundary tracing of rolled AZ31 after rolling andrecrystallization. Regions where smaller grains formed along prior shearbands can be seen. (b) Optical image of the same region of the sample afterfurther compression showing an increase in surface roughness concentratedat the former shear bands. Image is from [49]. Reprinted from ScriptaMaterialia, Vol. 57 No. 12, M.R. Barnett and N. Stanford, “Influenceof microstructure on strain distribution in Mg-3Al-1Zn,” pgs. 1125-1128,2007, with permission from Elsevier.In pure Mg, the effects of strain localization within shear bands can include room19Chapter 2. Literature Reviewtemperature dynamic recrystallization. This has been observed by Barnett, Naveand Bettles as well as Sandlo¨bes et al. [7, 9]. In both cases, the recrystallized grainswere small, typically under 10 µm in diameter. This room temperature dynamicrecrystallization was also seen in {101¯1}{101¯2} twins (i.e. the twins common seen inshear bands) by Wonciewicz and Backofen [33].As shear banded regions have a texture significantly different from the basal rollingtexture (where the grains are tilted approximately 35° away from a basal texture dueto double twinning), one might assume that shear bands are able to reduce the textureupon annealing. Whether or not this occurs appears to be highly dependent uponalloying additions. Basu and Al-Samman found that in a Mg-1wt.%Gd alloy, shearbands formed during hot rolling were responsible for significantly reducing the numberof grains with their c-axes perpendicular to the rolling direction, thus weakening thebasal texture [43]. In contrast, the same study found that the shear bands in Mg-1wt.% Ce were not able to significantly reduce the texture upon recrystallization. Thiswas attributed to Mg-Ce intermetallic particles pinning the grains forming within theshear bands, thus preventing them from growing beyond the shear bands [43].2.5 Precipitation, deformation, andrecrystallization in the binary Mg-Nd system2.5.1 IntroductionThe previous sections have discussed many of the issues surrounding the thermo-mechanical processing of magnesium alloys at low temperatures. Rare earth alloyingadditions are able to substantially improve the formability and mechanical propertiesof magnesium alloys, though the effects of individual alloying additions are still beingstudied. Out of the lanthanide rare earths, neodymium has been singled out for itseffects on mechanical strength, texture reduction and formability improvements [5].Both stable and metastable phases in binary Mg-Nd alloys play a significant role in20Chapter 2. Literature Reviewgoverning the mechanical properties and recrystallization of these alloys [5, 57–59].Advances in understanding the phases present in Mg-Nd alloys include the recentdiscoveries of new metastable phases formed during casting [57] and hot rolling [59],as well as several studies to characterize the metastable precipitates that form duringartificial aging [59–63]. This section will review the literature on binary Mg-Ndalloys, with the goal of further understanding the effects of Nd on precipitation,deformation, and recrystallization. This section will begin with a summary of knownstable and metastable precipitates, followed by an overview of precipitation kinetics.Next, deformation in these alloys will be discussed, followed by brief mention of theeffect of Nd on recrystallization kinetics.2.5.2 Equilibrium phases in the Mg-Nd systemThe phase diagram for the Mg-Nd system can be seen in Figure 2.7. There are regionsof solid solubility on both the Mg- and Nd-rich sides of the phase diagram, as wellas four stable intermetallic compounds in the system: Mg41Nd5, Mg3Nd, Mg2Nd andMgNd [64]. The solid solubility of Nd in Mg is limited at most to 3.5 wt.% (0.6at.%), as will be discussed in greater detail below. In discussions of precipitation inmagnesium alloys, Mg41Nd5 is often referred to as the β phase, and forms at the Ndconcentrations typically used in commercial Mg-Nd alloys. Mg41Nd5 forms a eutecticwith Mg in solid solution at a temperature of approximately 550°C [5], and at higherNd concentrations decomposes into Mg3Nd and liquid in a peritectic reaction [65].In some literature, Mg41Nd5 is given as having a range of stoichiometries [5], thoughmore recent works have argued for a purely stoichiometric composition [66]. Therelevant stable and metastable phases found in dilute alloys (<1 at.%Nd) in thissystem are shown in Table 2.2.Pike and Noble observed equilibrium Mg41Nd5 (β) precipitates after aging at tem-peratures from 300°C to the melting point of Mg-2.9 wt.%Nd. These precipitates21Chapter 2. Literature ReviewTable 2.2: Phases observed in dilute Mg-Nd alloysName Composition Notes ReferenceStable β Mg41Nd5 [5, 67]— Mg3Nd [5,66,68]Metastable GP zones Needles orthin plates[58,60,62,67]β′′ Mg6Nd [60–62,67]β′ Mg7Nd [62]β1 Mg3Nd Plate-like, Latticeparameters notgiven[62,63]– Mg12Nd Observed in castalloys[5, 68]– Mg3Nd Equiaxed, latticeparameter differsfrom stable Mg3Nd[59]nucleate preferentially onto dislocations [67] and grain boundaries [5]. Deforming asolutionized Mg-2.9wt.%Nd sample to a strain of 10% prior to aging increased thenumber density of precipitates compared to an undeformed sample [67].Pike and Noble found the crystal structure of Mg41Nd5 to be a body centeredtetragonal (bct) structure with lattice parameters of a = 1.031 nm and c = 0.593 nmthrough transmission electron microscopy (TEM) and selected area electron diffrac-tion (SAED) [67]. However, these lattice parameters do not match with subsequentinvestigations, which have found a values between 1.466 and 1.474 nm, and values forc between 1.000 and 1.040 nm [5,68,69].The equilibrium Mg3Nd phase is cubic with a lattice parameter of 0.7397 nm[68]. While it is shown on the phase diagram as being stoichiometric, recent electronmicroprobe analysis (EMPA) measurements on Mg-Nd diffusion couples show thatit is non-stoichiometric, with a maximum composition range of 75-80 at.% Mg atapproximately 500°C, with the composition range decreasing as temperature decreases[66].22Chapter 2. Literature ReviewFigure 2.7: Equilibrium phase diagram of Mg-Nd system. N.B.: The maximumsolubility of Nd in Mg is 0.6 at.%, corresponding to 3.6 wt%, and a moredetailed view of the solid solubility of Nd in Mg can be seen in Figure 2.8.Figure is from [64]. Reprinted from: Springer and Journal of Phase Equi-libria and Diffusion, Vol. 28 No. 4, 2007, pg. 405, “Mg-Nd”, H. Okamoto,Figure 1, original copyright notice is given to the publication in which thematerial was originally published, by adding; with kind permission fromSpringer Science and Business Media.Solid solubility of Nd in MgThe Mg-rich portion of the phase diagram contains a region of solid solubility, al-lowing limited age hardening in Mg-Nd alloys [5]. The maximum solid solubilitywas extrapolated using electrical resistivity measurements, and was found to be 3.6wt.%Nd at 552°C [5]. The solubility as a function of temperature from experimentsand the calculated solubility from FactSage thermodynamic modelling can also beseen in Figure 2.8. It is interesting to note that between La, Ce, and Nd, Nd has thehighest solid solubility in Mg, and also the strongest age hardening response [5].23Chapter 2. Literature ReviewFigure 2.8: The solvus curve of the Mg-Nd phase diagram as determined byatom probe tomography [60], electrical resistivity [5], metallography [70],and Factsage thermodynamic modelling [70].2.5.3 Metastable phases in the Mg-Nd systemMg-Nd alloys are known to form a number of metastable phases. These phases maybe formed through casting, hot rolling or aging after solutionizing. Some, such as anon-equilibrium variant of Mg3Nd, have only recently been identified and character-ized [59]. These metastable phases are important as they can significantly alter themechanical properties of Mg-Nd alloys. For instance, the non-equilibrium phases incast Mg-Nd alloys are thought to be responsible for the observed high degree of creepresistance [57], while the metastable precipitates formed during artificial aging canstrengthen the material [5, 58,71].Metastable phases after casting and hot workingMg12Nd is commonly seen in as-cast Mg-Nd alloys. It has been observed in alloysthat were cooled rapidly by casting into steel moulds [68], as well as alloys cooled24Chapter 2. Literature Reviewslowly, at 2°C/min [5]. Recent thermodynamic calculations show that slow coolingrates favour the formation of Mg12Nd, while fast cooling rates in Mg-Nd alloys canlead to the formation of Mg3Nd [57]. Older phase diagrams [72] often incorrectlyincluded Mg12Nd in the equilibrium phase diagram, likely due to the wide range ofconditions where Mg12Nd forms.Recent TEM analysis of Mg-Nd alloys ranging from 0.6-1.9 wt.%Nd have revealedthat a metastable precipitate with a composition of Mg3Nd forms when hot rolledat 400°C. This form of Mg3Nd is not the same as that of the equilibrium Mg3Ndphase. While the crystal structure of this newly found phase is also cubic, the latticeparameter, 1.09 nm, differs from that of equilibrium Mg3Nd [59].Metastable phases formed during artificial agingMg-Nd alloys can be heated close to the eutectic temperature to dissolve all Nd intosolid solution, quenched rapidly and then aged at temperatures below 320°C in orderto form a series of metastable precipitates [58,60–63,67] that can modestly age hardenthe material [58]. The precipitation sequence in Mg-2.9wt.%Nd was described by Pikeand Noble as [67]:Mg (ss) −−→ GP zones (DO19) −−→ β′′ −−→ β′ −−→ β (Mg41Nd5) (2.2)Since then this sequence has been modified to include metastable β1 precipitatesforming after β′ precipitates [63]. The precipitates formed at early stages of aging aresmall, with the thinnest dimensions of the smallest precipitates detected being lessthan 10 atoms thick [61]. This makes characterization of the precipitates difficult, asit requires techniques with atomic-scale resolution. As a result, the early stages ofprecipitation have been characterized only relatively recently (i.e. [60–62]), and thereis still some ambiguity regarding the nature of the precipitates.25Chapter 2. Literature ReviewThe first systematic study of the effect of aging time and temperature on pre-cipitation kinetics in binary Mg-Nd alloys was performed on an Mg-2.9wt.%Nd alloyby Pike and Noble [67]. The kinetics were studied primarily through electrical resis-tivity measurements, with transitions between precipitate types being inferred usingan Avrami analysis. In an Avrami analysis, a change in the slope of log(t) plottedagainst log(log(1/(1 − f))) indicates a transition of the dominant precipitate type,with f indicating the fraction transformed. While Pike and Noble report naturalaging at room temperature, this was not observed by Rokhlin or Kopp [5, 60]. Pikeand Noble were able to determine the precipitation kinetics using resistivity mea-surements, and constructed a time-temperature-transformation (TTT) diagram. Theresults indicating the time required to reach 50% transformed for each precipitatetype can be seen in Figure 2.9.Figure 2.9: TTT curve for Mg-2.9 wt.% Nd. Precipitation was measured withelectrical resistivity, and the times shown are to 50% transformed. Data isfrom [67].Guinier-Preston ZonesGuinier-Preston (GP) zones are the first precipitates to form during low tempera-ture aging [67]. After aging at 180°C, Pike and Noble described GP zones as being26Chapter 2. Literature Reviewneedle-like, with the long axis of the precipitate parallel to the [0001] direction in themagnesium matrix. No GP zones could be directly seen through TEM observationsbelow 180°C, though their presence was inferred by streaks seen in SAED patterns.Subsequent studies have not seen the needle-like precipitates observed by Pike andNoble, with GP zones typically being classified as thin plates. Wilson et al. observedtwo types of plates, with thin plates laying parallel to the {112¯0} planes, and shorter,thicker plates laying parallel to the {11¯00} planes [61]. However, Wilson et al. didnot differentiate between β′′ precipitates and GP zones [60].GP zones identified by both Saito and Hiraga [62] and Hisa et al. [58] take the formof plates arranged in the form of triads parallel to the {112¯0} planes when viewedparallel to the [0001]Mg direction. Both studies found that the precipitates were small,at 5-15 nm in length, and under 1 nm thick. According to Saito and Hiraga, at peakaging conditions conditions (100 hours at 170°C), the GP zones lengthen to 20-50nm in length, and can be seen coexisting with precipitates they classified as β′. Thisresults in a complex, interconnected network of precipitates. Hisa et al. further triedto determine the atomic arrangement of Nd atoms with the precipitates using bothexperimentally derived and simulated SAED patterns. The Nd was described as beingarranged in a “quasi-DO19” structure, in which substitutional Nd atoms take on aperiodic arrangement, forming a superlattic structure [58].β′′ PrecipitatesThe presence of β′′ precipitates in Mg-Nd alloys aged at low temperatures is morefirmly established than that of GP zones. They have been observed following agingat temperatures from 150°C to 260°C [60,62,67]. β′′ precipitates sometimes take theform of triads with arms at 120° angles when viewed along the matrix [0001] directionand have a morphology of thin plates that are fully coherent with the matrix. Anexample of these precipitates is shown in Figure 2.10.27Chapter 2. Literature ReviewFigure 2.10: Example of β′′ precipitates in Mg-2.9wt.%Nd formed after agingat 240‰ for seven hours. Image was taken at 20,000x magnifcation parallelto the [0001] matrix direction. Image is from [67]. Reprinted from Journalof the Less Common Metals, T.J. Pike and B. Noble, “The formation andstructure of precipitates in a dilute magnesium-neodymium alloy”, Pgs.63-74, Copyright 1973, with permission from Elsevier.Pike and Noble found that these precipitates were often arranged in triads, withthe arms of the triads laying along the {112¯0} planes. However, atom probe tomog-raphy (APT) by Kopp found that the precipitates lay parallel to the {11¯00} familyof planes [60]. The high angle annular dark field-scanning transmission electron mi-croscopy (HAADF-STEM) study by Lefebvre et al. confirmed that β′′ precipitatesin an Mg-2.9wt.% Nd sample aged at 150°C lay parallel to the {11¯00} planes [61].Pike and Noble [67] as well as Kopp [60] have found that β′′ precipitates have a DO19structure [60, 67]. Lefebvre et al. found that β′′ precipitates are comprised of “nano-pillars” of Nd in a periodic arrangements, with models based off the HAADF-STEMresults showing a stoichiometry of Mg6Nd.Saito and Hiraga also examined metastable precipitates through HAADF-STEMimaging [62]. They found several types of precipitates during aging which are inpartial agreement with the results of Lefebvre et al. and Kopp. At lower aging times28Chapter 2. Literature Reviewand temperatures, e.g. 170°C, a different type of precipitate labeled β′ was observed.These β′ precipitates start out as triads with arms parallel to the {112¯0} planes. Asaging progresses to peak aging conditions (100 hours at 170°C), these precipitatesevolve from a collection of discrete triads to an interconnected network of triadsconnected by plates identified by the authors as GP zones. Interestingly, after over-aging at 250 °C for nine hours, triad-shaped precipitates with arms parallel to the{11¯00} planes could be seen. Saito and Hiraga labeled these precipitates as the β1phase. These precipitates have also been observed by Bamberger et al. [73] andLiu et al. [63]. The β1 precipitates are approximately 10 times larger than the β′precipitates. In addition to differing in habit plane, the β′ and β1 precipitates appearto differ in composition. Models based off the HAADF-STEM imaging identify Saitoand Hiraga’s β′ phase as having a stoichiometry of Mg7Nd, while the β1 phase isMg3Nd [62].β′′ precipitates versus GP zonesWith the exception of Pike and Noble’s classification of GP zones as needles, GPzones appear to have many similarities to β′′ precipitates. Both GP zones and β′′precipitates take the form of thin plates, albeit with some ambiguity with regardsto the habit plane and the orientation of the plates relative to the matrix. The GPzones found by Hisa et al. and Saito and Hiraga take the form of triads when viewedalong the [0001] matrix direction, which is similar to the β′′ triads seen by Kopp. Inaddition, the GP zones identified by Hisa are classified as having a DO19 superlattice-type structure, which is the same structure that Pike and Noble as well as Koppfound for β′′ precipitates. From these observations it seems likely that GP zones andβ′′ precipitates are the same species.29Chapter 2. Literature Reviewβ′ PrecipitatesPike and Noble made direct TEM observations of β′′ and β′ precipitates coexistingduring aging and found that β′ precipitates tend to nucleate onto dislocations duringaging at 240°C. The precipitates seen by Pike and Noble took the form of diskslaying parallel to the {101¯0} planes when viewed along the [0001]Mg direction. Theprecipitates are partially coherent with the matrix.APT on Mg-2.9wt.%Nd found β′ precipitates after aging for 24 hours at 190°C.These precipitates were substantially larger than the β′′ precipitates seen in the samesample, and were surrounded by a precipitate free zone. The structure and mor-phology of the precipitates could not be determined with APT. Interestingly, com-positional analysis of the precipitates showed an unusually high Nd concentration,estimated to be 79±8.1 at%Nd. Such a high Nd concentration within a precipitatehas been seen once before in a TEM study by Lorimer [60], who estimated the Ndconcentration of β′ precipitates to be 89 at.%, corresponding to a stoichiometry ofMg2Nd17.Further study of β′ precipitates using HAADF-STEM showed that the thin edgesof the disks typically lay parallel to the {112¯0} planes [61], which differs from theresults of Pike and Noble. β′ precipitates appear to be comprised of the same nanopillars as the β′′ precipitates, albeit with a different arrangement of the pillars them-selves [61].2.5.4 Precipitation kineticsPrecipitation kinetics from Mg-2.9wt.%Nd and Mg-3.4 wt.%Nd can be seen in Fig-ures 2.9 and 2.11. Precipitation between 300-400°C occurs rapidly, with 50% beingtransformed in under 10 minutes [5,67]. According to Pike and Noble, in this temper-ature range, the precipitates most likely to form during aging are the equilibrium βor β′ [67]. Given the rapid precipitation kinetics seen at typical recrystallization tem-30Chapter 2. Literature Reviewperatures, there is speculation that simultaneous precipitation during annealing ofMg-Nd alloys can pin grain boundaries, causing stagnation [5]. As noted previously,this pinning has also been observed in a Mg-1wt.%Ce alloy [43].Figure 2.11: TTT curve from electrical resistivity for Mg-3.4 wt.% Nd. Datais from [5].2.5.5 Deformation and recrystallization in binary Mg-NdalloysStudies focusing on deformation and recrystallization in binary Mg-Nd alloys are un-common, as most studies focus on commercial alloys, which typically contain alloyingelements in addition to Nd. While commercial alloys containing Nd such as ZEK100(1wt.%Zn, 0.1wt.%Zr, 0.1wt.% Nd) exhibit weaker textures and greater ductility com-pared to pure Mg or AZ31 [14], the individual contribution of Nd to these effects isunknown. In this section, studies on the effect of Nd in binary Mg-Nd alloys will bediscussed.Effect of Nd on deformationRokhlin reports that the addition of 0.16 wt.%Nd to pure Mg increased tensile elon-gation from 3.8% strain to failure in pure Mg to 9.6% strain to failure in the Mg-31Chapter 2. Literature Review0.16wt.%Nd alloy [5]. While the prior annealed grain size was lower in the Mg-0.16wt.% alloy than in the pure Mg (140 µm versus 860 µm), which may have beenpartially responsible for the increase in ductility, the authors speculated that some ofthe enhanced ductility was due to Nd binding impurity atoms at grain boundaries [5].Nd alloying additions have been shown to influence the deformed microstructurein binary alloys. For example, in hot rolled binary Mg-Nd alloys, a concentration of0.06 wt.%Nd leads to a microstructure of predominantly tensile twins in the unre-crystallized regions. At an Nd concentration of 0.24 wt.% Nd, the sample showedsignificantly more compression and double twins arranged into what were termed“deformation bands” when viewed along the RD-TD plane [14]. In extruded andsolutionized Mg-3wt.% Nd that was tested in tension and compression, the volumefraction of twins seen in the samples was typically less than the fraction seen in aMg-6.2Zn-1.2Mn alloy tested under the same conditions [71]. Aging the Mg-3wt.%Ndsamples at 190°C for five hours further decreased the area fraction of visibly twinnedmaterial for all deformation paths except for compression along the tranverse extru-sion direction. For both the as-solutionized and the aged conditions, this led to achange in the yield surface, accompanied by a reduction in the tension-compressionasymmetry.The reduced texture of Mg-rare earth alloys requires a critical level of alloying ad-ditions. Hantzsche et at. found that in binary Mg-Nd alloys, Nd concentrations below0.24wt.% Nd were found to have no effect on weakening the deformation texture. Theintensity of the basal texture is steadily reduced with increasing Nd concentrationsfrom 0.24 wt.% to 0.47 wt.%Nd, after which point increasing the Nd concentrationhas little to no effect on decreasing the texture [14].32Chapter 2. Literature ReviewEffect of Nd on recrystallizationRokhlin et al. have studied the effect of a number of binary alloying additions onthe temperature necessary to initiate recrystallization [5]. These results, summarizedin Figure 2.12, show that Nd has the strongest effect on the recrystallization starttemperature of the elements studied. While this phenomenon has not yet been ex-plained, it is believed that the recrystallization temperature is strongly affected bysimultaneous precipitation during recrystallization [5]. Couling et al. [36] also notedthat a cold rolled alloy containing mischmetals required a significantly higher tem-perature for recrystallization than a deformed AZ31 sample, requiring annealing at260°C versus 150°C in the AZ31 to recrystallize. Hantzsche et al. [14] noted thatthe texture weakening effects of RE elements (including Nd) may be due to pinningduring recrystallization, e.g. there is no grain growth during annealing that wouldfavour growth of predominantly basal oriented grains.Figure 2.12: Recrystallization start temperatures for various alloying elements.Data is from [5].33Chapter 2. Literature Review2.6 SummaryDespite increased interest in the use of magnesium to reduce the weight of vehicles,poor formability limits its practical uses. These difficulties begin with deformation,which is often heterogeneous as is shown by the prevalence of twinning and shearbands. Recrystallization is spatially heterogeneous, and fails to substantially weakenthe basal texture of rolled Mg. Furthermore, recrystallization in Mg alloys is not fullyunderstood, with few studies focusing on static recrystallization.While the addition of Nd to Mg alloys can alleviate some of these difficulties,there remains much to be learned about this system. For example, the effect of Ndon static recrystallization is poorly understood, especially in instances where theremay be an interaction between precipitates and grain boundaries. Furthermore, moststudies on Nd-containing alloys use two or more alloying additions, making it difficultto discern the effect of Nd alone. Further research into the effect of Nd on staticrecrystallization is necessary if the microstructure and mechanical properties of thesealloys are to be fully understood and utilized.34Chapter 3Scope and ObjectivesThe Literature Review found that Mg-Nd alloys undergo a complex precipitationsequence, and that Nd has a substantial effect on recrystallization. Despite the po-tential commercial importance of Nd additions in alloys such as ZEK, there are nostudies that have systematically linked the deformed microstructure and precipitationstate to the kinetics and microstructural evolution during static annealing. This isnecessary for predicting the final microstructure, which ultimately affects formabilityand mechanical properties.As such, the objective of this thesis is to quantify the effect of Nd on precipitationkinetics, deformation, and recrystallization in Mg-2.8wt.%Nd. In particular the aimof this thesis is to determine the means by which Nd interacts with the recrystallizingmicrostructure, whether it be via Nd in solid solution or in precipitates. This hasbeen accomplished in two stages: i) quantifying precipitation kinetics, precipitatetype, Nd in solid solution, and the volume fraction of precipitates during aging, andii) quantifying the effect of prior aging state on deformation and recrystallization,and in particular on recrystallization kinetics and the annealed microstructure.In the first part, precipitation kinetics were studied at 190‰, 350‰ and 400‰.These experiments were performed on undeformed Mg-2.8wt.%Nd to investigate thekinetics, type, and spatial distribution of precipitates during heat treatment. Thesewere used to further understand and quantify precipitation during heat treatment, and35Chapter 3. Scope and Objectivesto select aging conditions to be used before deformation. Precipitation was studiedthrough scanning electron microscopy (SEM) observations, electrical resistivity andVickers hardness measurements.In the second part, deformation and recrystallization were studied in the samealloy. The deformed state was studied in samples cold rolled to a 20% strain thatwere either solutionized, aged at 190‰ for 24 hours, or aged at 400‰ for 3 hoursin order to determine if the precipitate state would affect the deformed state in amanner that would in turn affect recrystallization. Recrystallization kinetics werestudied in order to determine the effect of precipitates, either pre-existing or formedduring recrystallization, on the temperature and time for recrystallization. Usingthe results of the precipitation kinetics experiments, samples were heat treated tocontrol concurrent precipitation during recrystallization. In particular, the effect ofNd on the nucleation of recrystallizing grains, the growth of grains, and the effect ofprecipitation on recrystallization was focused on in this alloy. The microstructuresof the samples were characterized with scanning electron microscopy and EBSD, andmicrohardness measurements were used to study microstructural evolution duringannealing.36Chapter 4Methodology4.1 IntroductionThis chapter will introduce the materials used in this thesis, followed by the ther-mal and mechanical treatments performed on them. Characterization and analyticaltechniques will also be described.4.2 Starting materials4.2.1 Mg-0.6wt.%NdMg-0.6wt.%Nd was cast in 200-230 g batches using arc melting at McMaster Univer-sity from master alloys of Mg-3.8wt.% Nd and 99.98% purity Mg. The Nd concen-tration of the ingot was measured using inductively coupled plasma (ICP) chemicalanalysis. In order to ensure that Nd was not being disproportionately lost to oxida-tion during subsequent processing, ICP measurements of the Nd concentration weretaken after casting, hot rolling and solutionizing. Three measurements per samplewere taken for each state. The results can be seen summarized in Table 4.1 Theaverage Nd concentration for all measurements was found to be nearly 0.6wt.% Nd,with a maximum relative error of 0.293% as determined by calibration curves of theinstrument. While the Nd concentration does fluctuate slightly (by a maximum of0.15 wt.%), it appears that if Nd is being lost to heat treatments, it does not occur37Chapter 4. Methodologyin sufficient amounts to affect the bulk composition. After casting, the ingot wasmachined into blocks with approximate dimensions of 1.3x30x60 mm.Table 4.1: ICP analysis of Mg-0.6wt.% Nd.Sample Nd conc. (wt.%)As-cast 0.60Solutionized 0.57Hot rolled 0.604.2.2 Mg-2.8wt.%NdMg-2.8wt.%Nd was cast at the Max Planck Institute fu¨r Eisenforschung using aninduction furnace backfilled with argon to a pressure of 2.5 MPa. After casting theingot was homogenized at 535°C for 24 hours. After homogenization, the ingot wascut into strips 6-8 mm in height. As with the Mg-0.6wt.%Nd, the composition wasmeasured after casting, hot rolling and solutionizing using ICP. The results can beseen in Table 4.2. The average composition of the alloy was found to be 2.8 wt.% Nd.Table 4.2: ICP analysis of Mg-2.8wt.% Nd.Sample Nd conc. (wt.%)As-cast 2.74Solutionized 2.85Hot rolled 2.884.2.3 Commercially pure MgCommercially pure Mg was used during electrical conductivity measurements. Mghaving 99.98% purity was supplied by US Magnesium LLC. Composition data canbe seen in table 4.3. The pure Mg was cut into blocks directly from a cast slab andused in its as-cast state, with a grain size on the order of millimeters. For simplicitythis will be referred to as “pure Mg” throughout this thesis.38Chapter 4. MethodologyTable 4.3: Composition of pure Mg.Element Al Si Cu Zn Fe Ni Ca Na Mn Sn PbConc. (ppm) 39 < 20 < 10 < 10 27 4 < 10 < 10 36 < 20 < 204.3 Processing4.3.1 Hot rollingAfter casting, the Mg-0.6wt.%Nd and Mg-2.8wt.%Nd blocks were hot rolled intosheets using a laboratory rolling mill at the University of British Columbia. A con-vection furnace with flowing argon was used to heat the sample to 530-535°C for tenminutes prior to rolling and between each pass. The temperature near the sampleswas monitored with a thermocouple. The samples were reduced in height by 0.4-0.5mm per pass to a final height of 1.5-2 mm.4.3.2 SolutionizingThe Mg-0.6wt.%Nd and Mg-2.8wt.%Nd strips were solutionized after hot rolling inorder to homogenize the microstructure and dissolve any precipitates present. Thesamples were placed in stainless steel foil heat treatment bags to minimize oxidation.The samples were solutionized at 545°C for 8 hours, following the procedure previ-ously used by Kopp for a similar alloy [74]. The temperature was monitored witha thermocouple placed close to the samples. After solutionizing the samples wereimmediately quenched in their bags in room temperature water to minimize precip-itation during cooling. In addition to confirming the amount of Nd in solid solutionusing electrical resistivity measurements, the samples were found to be cool to thetouch in 30 seconds or less after quenching, indicating a rapid cooling rate.39Chapter 4. Methodology4.4 Heat treatments for precipitation kineticsMg-2.8wt.%Nd samples were artificially aged after solutionizing in order to studyprecipitation kinetics in undeformed samples. Aging treatments at 190°C used eitheran oil bath or a convection furnace. The samples aged in the oil bath were placed intosteel foil bags before heat treatment, and an electric stirrer was used to minimize anytemperature gradients within the oil bath. Samples aged in the convection furnacewere either placed in stainless steel foil heat treatment bags before heat treatment orheat treated under flowing argon. After aging, all samples were quenched into water.Aging treatments at 350°C and 400°C were performed in either a salt bath ora convection furnace. The salt bath was used primarily for heat treatments of fiveminutes or less. Samples heat treated in the salt bath were placed into steel foil bagsprior to heat treatment. Samples heat treated in the convection furnace were heatedunder flowing argon or placed in steel foil bags. All samples were quenched into waterimmediately after heat treatment.4.5 Deformation and recrystallization studiesRecrystallization in Mg-0.6wt.%Nd and Mg-2.8wt.%Nd samples was studied by so-lutionizing and aging samples, cold rolling, and annealing them. Solutionizing andaging treatments were performed using the methods described in Section 4.4. Coldrolling to a nominal reduction of 20% was performed with a laboratory rolling millusing unlubricated rolls.After cold rolling the samples were cut into smaller pieces (approximately 10x10mm) using a slow speed saw and annealed individually in either a salt bath or aconvection furnace depending on the length of the heat treatment. Heat treatmentsof five minutes or less took place in a salt bath, with the samples being placed in asteel foil bag during heat treatment. Heat treatments longer than five minutes weredone in a convection furnace in either flowing argon or a steel foil bag. After annealing40Chapter 4. Methodologyall samples were immediately quenched into water.4.6 Microstructural characterization4.6.1 Scanning electron microscopyThe microstructure of the samples, and in particular the precipitate state, was charac-terized with SEM. Samples selected for SEM observation were prepared by grindingwith 800 grit, 1200 grit, and 1200 fine grit silicon carbide grinding papers using wateras a lubricant. The 1200 fine grit paper had a smaller particle size distribution andsmoother surface finish than the normal 1200 grit grinding paper. The samples werepolished with 1 µm diamond suspension without lubricant or compound extender. Insome cases, the samples were then polished with 0.05 µm colloidal silica. Towards theend of each polishing step the polishing clothes were rinsed with running tap waterto prevent a film from forming on the surface of the sample. After every grinding andpolishing step the samples were washed briefly with tap water, immediately rinsedwith denatured ethanol, and immediately dried with hot air. After the final polishingstep the samples were ultrasonically cleaned in ethanol.SEM observations were made using either a Hitachi S-570 Scanning Electron Mi-croscope or a Carl Zeiss NTS Ltd. Sigma Scanning Electron Microscope. Both micro-scopes were equipped with backscattered electron detectors. Images taken with theHitachi S-570 SEM used a 20 kV accelerating voltage, while images from the ZeissSEM were taken at 10-20 kV.4.6.2 Electron back-scattered diffractionSample preparationSamples analyzed with electron back-scattered diffraction (EBSD) required a samplesurface with no deformation induced by polishing. While this is commonly accom-41Chapter 4. Methodologyplished with electropolishing, attempts to electropolish the alloys were unsuccessfulas the electropolishing solutions used would preferentially dissolve precipitates, leav-ing behind a rough, dimpled surface that was unsuitable for EBSD. Thus, samplesfor EBSD were prepared through a combination of mechanical polishing and chem-ical polishing. Samples were prepared by grinding with 1200 grit and 1200 fine gritgrinding papers, then polished with 1 µm diamond suspension and 0.05 µm colloidalsilica. After each grinding and polishing step the samples were chemically polishedin a solution of 5-10% nitric acid (68-70% concentration) in absolute ethanol (Nital),then rinsed thoroughly in ethanol and dried with hot air. Nital polishing for eachgrinding and polishing step was considered adequate when the deformation inducedby the previous preparation step was minimized. Deformation was typically visibleas dark scratches on the sample surface or occasionally series of twins when viewedwith an optical microscope.Texture measurementsLow resolution EBSD measurements were used for texture evaluation. This wasperformed with a Hitachi S-570 SEM equipped with a tungsten filament, and anHKL Technology EBSD detector with a Nordif electron back scatter pattern (EBSP)processor. Maps were acquired using HKL Flamenco Software. Typical step sizeswere between 1 and 5 µm. For texture measurements, a minimum of 500 grains in asample were analyzed in order to gain sufficient statistics [75]. The EBSD maps wereprocessed with HKL Tango software by removing wild spikes, iteratively cleaningbased off of the orientation of neighboring points, and exported. Pole figures werecreated using EDAX TSL OIM Anslysis 6 software.High resolution mapsHigh resolution EBSD was performed with a Zeiss SEM with a field emission source.EBSD patterns were captured with a Digiview detector, using EDAX TSL Orientation42Chapter 4. MethodologyImaging Microscopy (OIM) Data Collection software.The post processing of the EBSD data was performed using EDAX TSL OIMAnalysis 6. The maps were cleaned as follows:ˆ Grains were defined as a cluster of points containing a minimum of 5 pointswithin 5° of the same orientation as the neighbouring points.ˆ All points which did not belong to grains were discarded.ˆ The confidence index (CI) of each grain was standardized using the “Grain CIstandardization” cleanup method. This ensured that low CI points that hadthe same orientation as the surrounding grain were not discarded.ˆ A single iteration of grain dilation was performed, and the results were visuallyinspected to ensure that this did not create any false grains.After processing the data was rendered into maps, including inverse pole figure(IPF) maps and grain orientation spread (GOS) maps. IPF maps represent thecrystallographic direction at each point in the map using color. Figure 4.1 shows anexample of this, with grains with their c-axes parallel to the normal direction beingrepresented in red, and grains with their c-axes perpendicular to the normal directionbeing represented as blue or green.The recrystallized fraction was determined using GOS maps. Grains were de-fined using two parameters: a minimum average size and a maximum acceptablemisorientation between two points [37]. In this analysis, the minimum grain size wasconsidered to be five indexed points, and the maximum misorientation to be 5°. TheGOS was calculated using the TSL software. To do this, the average orientation ofeach grain was first calculated. From here, the minimum misorientation angle betweeneach point in the grain (gA) and the average grain orientation (gave) was calculated,and the average of all misorientations calculated [37,109]:43Chapter 4. MethodologyFigure 4.1: Schematic showing the representation of crystallographic directionin an IPF map. The colour of a grain represents the orientation of a crys-tallographic direction relative to the sample coordinates. In this examplecrystallographic directions are colored relative to their relationship to thenormal direction.GOS =1NN∑A=1×mincos−1trace[gave(higA)−1]− 12(4.1)In this equation, the inverse cosine term is used to calculate the misorientationangle between each point in the grain and the average grain orientation (gave). Thevariable hi is the symmetry matrix, which is calculated for each symmetry element,with the resulting minimum value of misorientation being used [109]. A schematicshowing the average grain orientation of a grain is shown in Figure Transmission electron microscopySamples for TEM were prepared by grinding Mg-2.8wt.%Nd sheet to 120-150 µmthickness using 1200 grit and 1200 fine grit grinding papers, with water as a lubri-44Chapter 4. MethodologyFigure 4.2: Schematic showing orientations within a grain, the average grainorientation gavg, and the misorientation angle between a point and gavg.cant. Disks with a diameter of 3 mm were then punched out of the sheet. Thediscs were mounted onto a disc grinder designed for TEM sample preparation usingcyanoacrylate glue and ground using 1200 fine grit grinding paper to 100 µm in thick-ness. After grinding the samples were removed from the disk grinder by dissolving theglue in acetone in an ultrasonic bath. The samples were electropolished at McMasterUniversity using a solution of 5.3 g lithium chloride (LiCl) and 41.16 g magnesiumperchlorate [Mg(ClO4)2] dissolved in a solution of 500 mL methanol and 100 mL butylcellosolve. Electropolishing was carried out at -50°C with an applied voltage of 45 V.The samples were examined at the Canadian Centre for Electron Microscopy usinga Philips CM12 TEM equipped with a LaB6 filament. Samples were imaged in brightfield and dark field modes, and SAED patterns were used to assist in identifying typesof precipitates.4.6.4 Electrical resistivity measurementsElectrical resistivity was measured using a Foerster Sigmatest 2.069 Portable EddyCurrent Tester. After each aging treatment the sample was lightly ground with a file45Chapter 4. Methodologyto remove any oxide which may have formed. The conductivity was measured betweenone and three times at frequencies of 240 kHz and 480 kHz, and the average mea-surement for both frequencies reported. Before taking every set of measurements theinstrument was calibrated using pure copper and stainless steel calibration standards.The probe’s internal temperature correction was used to compensate for fluctuationsaround ambient temperature, which varied from 16-25°C. The intrinsic error of theconductivity tester is ±0.5% [76], which in the samples studied here will yield an errorof ±0.04 µW-cm or less. The conductivity was converted into resistivity (ρ) with:ρ (µW-cm) =100σ(MS/m) (4.2)Eddy current testing is sensitive to the thickness of the material being tested.Lower testing frequencies increase the penetration depth, and if the penetration depthis too deep relative to the sample thickness, the conductivity measurements will notbe accurate. Conversely, a higher testing frequency with a low penetration depthmay be susceptible to the influence of an oxide layer lowering the conductivity. Theeffective penetration depth δeff for the type of probe used is given by [76,77]:δeff =503√σf(4.3)where δeff is in mm, σ is the conductivity in MS/m, and f is the testing frequencyin Hz.The guideline for accurate eddy current testing is that the sample should be aminimum of three times thicker than the effective penetration depth [76]. Using theworst case scenario for pure Mg, which has the highest conductivity (and therefore thehighest penetration depth) of any of the alloys tested, at 22.9 MS/m, the minimum46Chapter 4. Methodologyrecommended sample thickness at 240 kHz is 0.21 mm and at 480 kHz is 0.15 mm,well below the thickness of the samples measured here.4.6.5 Vickers hardnessSamples were prepared for Vickers microhardness measurements by polishing thesheet normal surface. The samples were ground with 1200 grit and 1200 grit finegrinding papers, and polished with 6 µm and 1 µm diamond suspension. Vickersmicrohardness measurements were taken using a Buehler Micromet 3 Micro HardnessTester equipped with a diamond tip. Ten measurements were taken and averaged foreach data point. All samples were tested using a 50 g load.The Vickers Hardness (Hv) values were converted into MPa by:H (MPa) = 9.81Hv (kg/mm2) (4.4)4.6.6 Automated Berkovich hardness testingA subset of samples was chosen for Berkovich hardness testing in order to studylocal variations in the microhardness of the samples in further detail as well as togain better statistics on the hardness measurements. Samples for Berkovich hardnesstests were prepared using the same mechanical and chemical polishing technique usedfor EBSD sample preparation described in Section 4.6.2, as the shallow depth of theindent (1-1.5 µm) requires a surface free of deformation. EBSD image quality mapsof samples prepared this way showed no evidence of deformation such as scratches orregions of poor index induced from grinding and polishing that could influence thehardness results. Measurements were made on the rolling plane.Indentations were made using an MTS Nano Indenter XP testing system runningTestworks software. All tests were performed in “XP Load, displacement, time”47Chapter 4. Methodologymode. Indents were made on a square grid with 100 µm between each indent. Theindenter drift rate was set at 0.3 nm/s, as it offered a reasonable compromise betweenspeed and accuracy. Indents were made using a diamond Berkovich indenter. Theprojected area to depth ratio of a Berkovich indenter is the same as that of a Vickersindenter, making comparison of results to Vickers hardness measurements easier [78].During each indent, the applied force and depth were recorded.Each indent consisted of three phases:ˆ Loading the sample to a maximum load of 5 g (49 mN force) over a 30 s periodof time.ˆ A hold period of approximately 10 seconds to stabilize the indenter and toreduce the effect of creep on calculating the Young’s modulus [79] before mea-suring the value of the maximum force, Pmax and maximum indentation depthhmax.ˆ An unloading period where the force was withdrawn while monitoring the depthof the indenter.As the grain size in the as-aged samples was on the order of 100 µm, placing theindents at 100 µm intervals allowed for sampling a wide variety of grains in additionto ensuring that that the region of plastic deformation under the indents did notoverlap. This spacing, as well as an acceptable drift rate was determined by makinga series of indents within a single grain of pure magnesium, and checking that theYoung’s Modulus for each indent was consistent.The methods used to calculate the hardness of the material and screen out anamolousindents can be found in Appendix B.48Chapter 5Precipitation in Mg-2.8wt.%Nd5.1 IntroductionThough the literature pertaining to the static recrystallization in binary Mg-Nd alloysis limited [5], it does suggest an interaction between precipitation, deformation in-duced defects (e.g. twins and dislocations) and recrystallization [5, 67]. As discussedin the literature review, out of six alloying additions studied by Rokhlin, Nd hadthe strongest impact on static recrystallization [5]. This interaction between precip-itation and recrystallization could aid with the design of Mg alloys with good creepresistance and microstructural stability at elevated temperatures [57] similar to whathas been achieved in some Al alloys via alloying additions [80, 81]. One might alsospeculate that by controlling precipitation, deformation and recrystallization, it maybe possible to modify grain size, grain size distribution and texture in novel ways.To this end, the goal of this chapter is to quantify precipitation kinetics in Mg-2.8wt.%Nd as a function of aging time and temperature. In particular, the evolutionof precipitate volume fraction and Nd in solid solution as a function of time at 190°C,350°C, and 400°C will be determined with electrical resistivity measurements. Se-lect microstructural observations using back scattered electron (BSE) SEM imaging,and limited TEM imaging will also be presented to support the resistivity results.Temperatures of 350°C, and 400°C were selected for study as these are close to therecrystallization start temperature and nose of the TTT curve for precipitation, as49Chapter 5. Precipitation in Mg-2.8wt.%Ndreported in the literature [5]. The behaviour at 190°C was investigated since it isexpected that a much finer distribution of metastable precipitates will form [60, 61].In the following chapter the effect of these pre-existing precipitates on the deforma-tion and recrystallization of the material will be evaluated. The information obtainedfrom these experiments will be used in order to create a model of precipitation kinet-ics that can determine precipitate volume fraction and concentration of Nd in solidsolution during aging. This information will be used to aid with the interpretation ofrecrystallization observations in Chapter 6.5.2 Microstructural and resistivity changesoccurring on aging at 190°C, 350°C and 400°C5.2.1 Characterization of solutionized Mg-2.8wt.%NdStudying aging kinetics requires beginning from a well-characterized, fully solution-ized material. To solutionize the Mg-2.8wt.%Nd alloy studied here, the material washeat treated for eight hours at 545‰ in order to place all Nd in solid solution. Thissolutionizing method was inspired by the work of Kopp et al. [74]. The level of Nd insolid solution was quantified using electrical resistivity measurements to ensure thatthe length and temperature of the solutionizing treatment was adequate. These samestrips of as-solutionized material were subsequently used for the aging experiments.Directly following this solutionizing treatment the resistivity of the samples wasmeasured, the results being shown in Table 5.1. For reference, the resistivity of apiece of 99.98% purity cast Mg was also measured. The impurity content of the castMg is reported in Section 4.2 of Chapter 4. As the electrical resistivity of Mg isanisotropic (the ratio of resistivity parallel versus perpendicular to the basal plane is0.83 [82]), measurements were made on three perpendicular faces of the sample andthe average taken in an attempt to reduce the effect of crystallographic texture of thecast material. The resistivity of the Mg was found to be 4.37 ± 0.03 µW-cm, which50Chapter 5. Precipitation in Mg-2.8wt.%Ndis the same (within experimental error) as the value reported in the literature (4.39µW-cm) for randomly textured polycrystalline Mg [83].According to Bijvoet et al. [84], the presence of Nd in solid solution increases theresistivity of Mg by 8.2 µW-cm/at.%Nd. This allows the resistivity of a sample witha known amount of Nd in solid solution CNd (in at.%) to be calculated as:ρ = 8.2CNd + 4.37 (µW-cm) (5.1)If all of the Nd in the Mg-2.8wt.%Nd samples (0.48 at.%) was in solid solution,then according to Equation 5.1, the resistivity is 8.3 µW-cm. The difference betweenthe calculated resistivity and the measured resistivity was used to estimate the amountof Nd in solid solution (Table 5.1). From this it is estimated that 0.45-0.47 at.%Nd(2.6-2.7 wt.%) was in solid solution following solutionizing, this amounting to 94-98%of the total Nd in the alloy.Table 5.1: Measured electrical resistivity and calculated amount of Nd in solidsolution from Equation 5.1 for three separate solutionized samples.Sample ρ (µW-cm) Nd in solid solutionMg-2.8wt.%NdSample 1 8.07 0.45 at.% (2.6 wt.%)Sample 2 8.24 0.47 at.% (2.7 wt.%)Sample 3 8.07 0.45 at.% (2.6 wt.%)Pure Mg 4.37 –Several factors could account for this slightly lower level of Nd in solid solutioncompared to the composition measured by ICP. These include the effect of traceelements, texture, or errors in the resistivity coefficient calculated by Bijvoet et al.[84]. Given the lack of observed trace elements in energy dispersive x-ray spectroscopy(EDX) analysis and the use of high purity starting materials in casting, it is felt thatthis is an unlikely source for the solutionized resistivity. On the other hand, due51Chapter 5. Precipitation in Mg-2.8wt.%Ndto the dimensions of the samples tested here, the resistivity was measured only onthe RD-TD plane. Given that the rolled sheet should have a basal texture (c-axispreferentially aligned with ND), the assumption of a random texture may be calledinto question. Evaluating the possible magnitude of this effect is difficult howevergiven the measurement technique used (eddy current probe).It is believed that the most likely source for the low resistivity following solu-tionizing was the presence of Nd that was not dissolved into solution during thesolutionizing treatment. SEM observations of the solutionized sample revealed coarseparticles that were very bright compared to the surrounding matrix when viewed withBSE imaging. These particles, having diameters ranging from 1-10 µm, were foundto be very stable upon heat treatment, the same particles being found in both theas-received material as well as in a sample annealed at 520‰ for 96 hours (Figure5.1).(a) As-received (b) Solutionized (c) Annealed 520°CFigure 5.1: Overview of stable particles observed during processing of Mg-2.8wt.% Nd. a) Back scattered electron image of as-received material. b)Back scattered electron image of solutionized material. RD is vertical, TDis horizontal. c) Secondary electron image of sample annealed at 520‰ for96 hours.Analysis of the particles with EDX was inconclusive, in part due to the interactionvolume of the electron beam being of a similar size or larger than the precipitatesthemselves. However, all precipitates showed peaks corresponding to oxygen, mag-52Chapter 5. Precipitation in Mg-2.8wt.%Ndnesium and neodymium, and a small carbon peak. The carbon peaks are likelycontamination from sample preparation. The magnesium, neodymium and oxygenpeaks suggest that these particles are oxides that formed before or during casting,as the alloy was cast from large pieces of pure Mg and pure Nd. Pure Nd oxidizesrapidly to form non-adherent Nd2O3, which could break up and become entrainedin the melt. Indeed, similar particles can also be observed in the binary Mg-Nd al-loys studied by Rokhlin, Kopp, and Safi-Naqvi et al. [5, 60, 71]. While no previousattempts have been made to analyze the composition or structure of these particles,it is interesting to note that Kopp, whose bulk alloy composition was reported 0.51at.%Nd, found via APT that after solutionizing the amount of Nd in solution was0.49 at.%. This is similar in magnitude to the apparent loss of Nd from solid solutionfound here [60].5.2.2 Resistivity changes during agingHaving confirmed that the vast majority of the Nd in the alloy was successfullydissolved into solid solution by the selected solutionizing treatment, the next step wasto perform isothermal aging experiments using the procedure described in Section 4.4,in Chapter 4. As noted above, the same strip samples used to study the resistivityin the as-solutionized state were also used for studying the resistivity change uponfurther aging. The resistivity measurements made following aging for various times at190°C, 350°C, and 400°C can be seen in Figures 5.2a through 5.2c. Here, the averageresult is shown as a solid symbol while individual measurements are shown as opensymbols. As noted in Section 4.6.4, between two and six measurements were made persample. The intrinsic error of the eddy current tester (±0.05%) [76] is smaller thanthe dispersion of the data points at a given time and temperature. In all samples,the resistivity decreases with time, indicating that Nd is being depleted from solidsolution.53Chapter 5. Precipitation in Mg-2.8wt.%Nd(a) 190‰ (b) 350‰ (c) 400‰Figure 5.2: Evolution of resistivity during aging at a) 190‰, b) 350‰ and c)400‰. Open symbols represent individual data pointsAs noted previously, the change in resistivity measured during aging can be at-tributed to the process of precipitation. Thus, it should be possible to estimate theevolution of Nd in solid solution as well as the volume fraction of precipitates from thedata given in Figure 5.2. If it is assumed that it is the loss of solute from solid solutionthat dominates the change in resistivity (it is also possible that interfacial scatteringcontributes to the resistivity when the precipitates are small), then an estimate of theamount of solute in solid solution in atomic percent is,CNd =ρ− 4.378.2(at.%) (5.2)where CNd is in atomic percent and ρ is the electrical resistivity in µW-cm. Theamount of Nd in solid solution during aging at 190°C, 350°C and 400°C is shown inFigure 5.3.Upon aging, the amount of solute in solution should approach the equilibriumsolubility based on the phase diagram. Kang et al. have reported the temperaturedependence of the solubility of Nd in Mg (in equilibrium with Mg41Nd5) as [70]:54Chapter 5. Precipitation in Mg-2.8wt.%NdCNd = 100exp(−6.48(1000T + 273)+ 2.82)(at.%) (5.3)where T is the temperature in Celsius. From Equation 5.3, the level of Nd remainingin solid solution during aging of Mg-2.8wt.%Nd can be seen in Figure 5.3.Based on Equation 5.2 the equilibrium solubility corresponds to the followingresistivity:ρ = 1.25× 104 · exp(−6.48(1000T + 273))+ 4.3(µW-cm) (5.4)Figure 5.3: Nd remaining in solid solution during aging at 190°C, 350°C and400°C estimated from the average resistivity (Figure 5.2) and Equation 5.2.The equilibrium solubility at each aging temperature is indicated on thegraph.55Chapter 5. Precipitation in Mg-2.8wt.%NdThe measured resistivity was also used to estimate the volume fraction of pre-cipitates present during aging. These calculations assumed that only equilibriumMg41Nd5 precipitates are present. Although the literature clearly has shown thataging at lower temperatures leads to the formation of metastable precipitates [5,58, 60–62, 67], there is not enough information available regarding the properties ofthese precipitates, such as the molar volume and stoichiometry, to perform a moresophisticated analysis.The atomic fraction of Nd in the precipitates (CpptNd) can be defined as the fractionof Nd atoms in solid solution at the start of aging (C0Nd) minus the remaining fractionof Nd atoms in solid solution following aging (CssNd):CpptNd = C0Nd − CssNd (5.5)Furthermore, the total atomic fraction of Mg and Nd atoms in precipitates, Cppttotal,is the sum of the fraction of Nd atoms and Mg atoms (CpptMg) in precipitates:Cppttotal = CpptNd + CpptMg (5.6)As it is assumed that all precipitates are stoichiometric Mg41Nd5, there are 5 Ndatoms for every 41 Mg atoms in each precipitate, i.e. there are 415 Mg atoms persingle Nd atom in each precipitate. As such, Equation 5.6 to be written as:Cppttotal = CpptNd +(415)CpptNd (5.7)Cppttotal =(465)CpptNd (5.8)56Chapter 5. Precipitation in Mg-2.8wt.%NdThe volume fraction of precipitates(V pptf)is the volume of precipitates Vppt dividedby the total volume of the sample (Vsample), and can be expressed by converting thefraction of atoms in precipitates to a volume by dividing by the atomic volume:V pptf =VpptVsample(5.9)V pptf = Cppttotal ×V pptatV matrixat(5.10)Where V pptat is the atomic volume of Mg41Nd5, and Vmatrixat is the atomic volume ofthe matrix, taken as the atomic volume of pure Mg. The atomic volume of Mg41Nd5was given as 2.46× 10−29 m3 by Delfino et al. [68]. As the concentration of Nd in thealloy is dilute, it was assumed that Nd in solid solution would have no effect on theatomic volume of Mg, and a value of 2.32× 10−29 m3 for the atomic volume of pureMg was used [68].Substituting Equation 5.8 into the previous equation gives:V pptf =(465)CpptNdV pptatV matrixat(5.11)As was stated previously in Section 5.2.1, the resistivity of a sample is consideredto be linearly proportional to the concentration of Nd in solid solution. Equation 5.1can be restated as:CssNd =1KNd(ρ− ρMg) (5.12)where KNd is the resistivity coefficient of Nd in Mg, given as 820 µW-cm/atomicfraction [84], CssNd is the fraction of Nd in solid solution during aging and ρMg is the57Chapter 5. Precipitation in Mg-2.8wt.%Ndresistivity of pure Mg, which was found to be 4.37 µW-cm.Equation 5.12 can be substituted into Equation 5.5 resulting in:CpptNd =1KNd(ρ0 − ρMg)−1KNd(ρ− ρMg) (5.13)CpptNd =1KNd(ρ0 − ρ) (5.14)where ρ0 is the resistivity of the fully solutionized alloy. Substituting the previousequation into Equation 5.11 allows the volume fraction of precipitates to be calculatedbased on the change in resistivity measured during aging:V pptf =1KNd465V pptatV matrixat(ρ0 − ρ) (5.15)The volume fraction of precipitates versus time can be seen in Figure 5.4. Al-though the atomic volume of Mg41Nd5 is close to that of Mg, the approximately 8:1ratio of Mg atoms in each precipitate to Nd atoms causes the volume fraction of pre-cipitates to rise quickly relative to the amount of Nd being depleted in solid solutionduring aging.5.2.3 Comparison of aging kinetics to the literatureThe previous section reported data on the amount of Nd in solid solution and thevolume fraction of precipitates during aging at 190‰, 350‰, and 400‰. Using elec-trical resistivity measurements and APT, Rokhlin [5] and Kopp [60] respectively havestudied precipitation in binary Mg-Nd alloys. Because neither presented data in aform that was directly comparable with the experiments in this thesis, the data fromthis thesis, Kopp, and Rokhlin was converted into the fraction transformed versusaging time. The equilibrium volume fraction of precipitates will decrease as aging58Chapter 5. Precipitation in Mg-2.8wt.%NdFigure 5.4: Volume fraction of precipitates with time, estimated from the av-erage resistivity (Figure 5.2) and Equation 5.15.temperature increases, and so by comparing the fraction transformed it is possible totake into account the differences in the volume fraction across varying temperatures,as well as allowing for a more direct comparison to the results in the literature.The fraction transformed at each aging time and temperature was calculated fromthe volume fraction data using:f =V pptfV eqf(5.16)With V eqf being the volume fraction of precipitates expected at equilibrium. Theequilibrium volume fraction of precipitates was calculated by using Equation 5.4 todetermine the expected resistivity of a sample aged to equilibrium. This value wasthen used in Equation 5.15 to determine the expected volume fraction of precipitatesin a fully aged sample.Rokhlin presented data on Mg-3.4 wt.%Nd (0.59 at.%) solutionized at 510‰ before59Chapter 5. Precipitation in Mg-2.8wt.%Ndaging at 150‰, 200‰, 250‰, and 300‰. While there is a difference in the Ndconcentration of the alloy used by Rokhlin versus the alloy studied here, it is assumedthat the low differences in the atomic concentrations of the alloy (0.48 at.% versus 0.59at.%) will lead to similar precipitation kinetics. The data by Rokhlin was presented inthe form of ρ/ρ0 versus time, where ρ0 was the resistivity of the solutionized material.The concentration of Nd in solid solution was estimated from Equation 5.3 to be 2.5wt.%Nd (0.43 at.%), and by using Equation 5.1, ρ0 was estimated to be 7.9 µW-cm inthe solutionized material. While micrographs of the solutionized material presentedby Rokhlin show coarse precipitates believed to be similar to those discussed earlierin this chapter, it is not possible to account for the magnitude of the effect that theymay have had on ρ0. Similarly, ρf , the equilibrium resistivity of the sample, wascalculated using Equation 5.4. The fraction transformed was calculated from:f =ρ0 − ρρ0 − ρf(5.17)Kopp reported APT data for Mg-2.9wt.%Nd (0.5 at.%) for samples aged at 150°Cfor aging times between 54 and 1324 hours. This data was reported as the solutefraction fs, which was given as the number of atoms of Nd in the APT sample thatwere within precipitates, divided by the total number of Nd atoms sampled. Thismakes 1− fs equal to the number of Nd atoms remaining in solid solution divided bythe total number of Nd atoms sampled. Multiplying 1−fs by the overall concentration(C0 =0.5 at.%) of Nd atoms therefore yields the concentration of Nd remaining insolid solution: CNd = C0(1− fs). Once the concentration of Nd in solid solution wasknown, the fraction transformed for Kopp’s data could be calculated using Equations5.2 and 5.17.When compared to data gathered by Rokhlin for shorter aging times and a higher60Chapter 5. Precipitation in Mg-2.8wt.%Ndconcentration of Nd, Kopp’s data appears to follow the same behaviour. Figure 5.5shows the fraction of Nd that has precipitated in Mg-2.9wt.%Nd and Mg-3.4wt.%Ndfrom the literature, as well as the Mg-2.8wt.%Nd studied here. The rate of trans-formation to f=0.5 increases from 150°C to 300°C. Above this temperature the ratedecreases. Interestingly, the majority of the samples appear to have failed to reachequilibrium (ρ = ρf ) even after prolonged aging times. This is particularly interest-ing in light of the TTT curve constructed by Rokhlin showing rapid precipitation tof=0.5 at 300-350°C. (in Figure 2.11 of Chapter 2).Figure 5.5: Fraction transformed versus time during aging of Mg-Nd samples,including data from the literature. The data from Rokhlin [5] (open sym-bols) used Mg-3.6wt.%Nd, and the data from Kopp (open symbols withdots) [60] used Mg-2.9wt.%Nd.61Chapter 5. Precipitation in Mg-2.8wt.%Nd5.2.4 Fitting precipitation kinetics to a JMAK modelThe precipitation kinetics presented above were fit using a Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation so as to allow for interpolation of the precipitationbehaviour to intermediate times and, perhaps, temperatures. Rather than attempta fully physical application of the JMAK model, it was used as a phenomenologicalexpression with the aim being to capture the general trends shown in Figure 5.5.The general form of the JMAK model is:f = 1− exp (−btn) (5.18)The variable n depends on the geometry of precipitate growth, as well as whetherall precipitate nuclei are present at the start of nucleation (site saturation) or ifthe nuclei form over time. In theory, for site saturated nucleation with precipitatesgrowing in three dimensions, n = 3. This situation is not expected to hold true inprecipitation reactions where a value of n ≈ 1 is often found. This was the case, forexample, in Al alloys [85, 86], and is consistent with the kinetics predicted by morecomplex precipitation models, as will be seen later in this chapter. In the simplestversion of the JMAK expression, n is solely a geometric factor and it is thereforeexpected to be independent of temperature. The parameter b, on the other hand,incorporates both the nucleation rate and growth rate of precipitates and is thereforeexpected to vary with diffusivity and supersaturation, and therefore temperature.When fitting the JMAK equation to experimental data, the values of n and b areinterdependent to a degree. To reduce the number of fitting parameters, n was firstassumed to be constant for all of the isothermal precipitation reactions. As such, thedata was fit to a constant value of n, while b was allowed to vary for each annealingtemperature. The value of n was lowered until a good fit could be obtained by varying62Chapter 5. Precipitation in Mg-2.8wt.%Ndb. The highest value where this was achieved was n = 0.5. Once n was fixed at thisvalue then the value for b was set for each aging temperature.Although this provided good fits to the initial stages of the precipitation kinetics, itwas found that the JMAK expression often over-estimated the approach to saturation,similar to Figure 5.5 showing that few samples reached equilibrium during aging. Inthese instances, adjusting n or b alone was found to be insufficient to achieve a goodfit. Instead, it was found necessary to multiply the fraction transformed obtainedfrom the JMAK expression by a factor α < 1. The results of fitting the model ton = 0.5 are shown in Figure 5.6, and values used for α and b are summarized in Table5.2.Table 5.2: Values for b and α when n = 0.5.Temperature b (s−0.5 ) α150‰ 0.11 0.85190‰ 0.30 0.75200‰ 0.30 0.95250‰ 1.9 0.95300‰ 5.5 0.85350‰ 1.8 0.8400‰ 1.6 0.75While no physical interpretation is given for the specific values of b, it is importantto note that they show the expected trend. Starting at low temperatures, b increasesas the temperature is increased. This is a reflection of the increase in the kineticsowing to the temperature dependence of diffusivity. As the temperature goes above300‰, however, the value of b decreases. This is a consequence of the decrease indriving force for precipitation. Such behaviour is consistent with a material thatexhibits “C” curve like reaction kinetics.While the JMAK model appears to do a good job of capturing the overall kineticsof precipitation, the fact that the predicted saturation volume fraction is not the63Chapter 5. Precipitation in Mg-2.8wt.%Nd(a) 150°C (b) 190°C(c) 200°C (d) 250°C(e) 300°C (f) 350°C(g) 400°CFigure 5.6: JMAK models compared to experimental data at each aging tem-perature when fit to n = 0.5.64Chapter 5. Precipitation in Mg-2.8wt.%Ndone predicted by the phase diagram (the difference being the factor α) requires somediscussion. The fact that α < 1 suggests that upon aging the concentration of Ndin solid solution never reaches the value predicted from the phase diagram. Focusinginitially on the data at low temperatures (T < 300‰), there are several possiblereasons for this discrepancy. First, there is no experimental study on the solubility ofMg-Nd precipitates below 300‰. Indeed, the solvus expression given by Equation 5.3is fit based on extrapolating from high temperature where the equilibrium Mg41Nd5phase forms, rather than the metastable β′′ observed at low temperatures.Also important is the fact that at the lowest temperatures examined here, theprecipitates are small in size and closely spaced. Kopp found that Mg-0.5at.%Nd(2.9 wt.%) aged at 150‰ for 864 hours contained precipitates approximately 10 nmin length with approximately 20 nm of space between particles [60]. After 100 hoursof aging Mg-0.5at.%Nd (2.9 wt.%) at 170‰, Saito and Hiraga observed precipitatesapproximately 20 nm in length that formed an almost continuous network [62]. Inaddition, after aging the same material at 200‰ for ten hours, the precipitates werestill found to form a nearly continuous network. However, after aging at 250‰ for 9hours, the precipitates were found to be relatively widely spaced, with several hundrednanometers between precipitates [62]. This is consistent with TEM observations madein this study (Figure 5.7a) after aging at 190‰ for 24 hours. In Figure 5.7 an SAEDpattern of these precipitates is shown, with the diffuse streaks shown being consistentwith the GP zones identified by Hisa et al. [58].Such small precipitates may effect the results of the resistivity measurements intwo ways. First, the Gibbs-Thomson effect for small precipitates can cause an appar-ent shift in the solvus curve towards higher Nd solubility. This alone could accountfor the apparently high level of Nd in solid solution. Another, perhaps equally impor-tant effect, could arise directly from the effect of small precipitates on the resistivity.Precipitates can cause electron scattering during electrical resistivity measurements65Chapter 5. Precipitation in Mg-2.8wt.%Nd(a) (b)Figure 5.7: (a) Bright field TEM image taken along the [0001]Mg direction ofMg-2.8wt.%Nd aged at 190 °C for 24 hours. Dark β′′ precipitates, and inparticular, the strain field associated with them can be seen against thebackground of the white Mg matrix. (b) SAED pattern taken parallel tothe [0001]Mg matrix direction showing streaks consistent with the β′′ phase.when the precipitates are closely spaced [87,88]. Raeisinia et al. found in an Al-Mg-Si-Cu alloy that between 15-25% of the total measured resistivity could be attributedto scattering when the precipitates were spaced at approximately 10 nm. When theprecipitate spacing was increased to ∼100 nm, the contribution of interface scatter-ing to the resistivity decreased to 10-15%. When precipitate spacing increased toapproximately 1 µm, the contribution of precipitate spacing to scattering droppedto approximately 5% [87]. The results presented here show that precipitates at andbelow 200‰ are spaced closely enough for scattering to have a significant contributionto the resistivity. This would lead to an anomalously high resistivity measurement.While these effects could explain the high resistivity measured for samples agedat low temperatures, none of them adequately explains the fact that a high resistivityat the end of precipitation appears for samples aged at 300‰ and above. In thesecases, the precipitates are expected to be mainly the equilibrium Mg41Nd5 phase forwhich the phase diagram has been constructed. Moreover, given that the precipitates66Chapter 5. Precipitation in Mg-2.8wt.%Ndare clearly visible in low magnification SEM images (e.g. Figure 5.8) it is unlikelythat they are small enough for either the Gibbs-Thomson effect or anomalous electronscattering to contribute significantly to the resistivity results.Figure 5.8: Backscattered electron micrograph of Mg-2.8Nd that was solution-ized and aged at 400°C for three hours showing coarse, sparsely spacedprecipitates. The RD-TD plane is imaged.In order to present the results of the JMAK model in a way that would be moreuseful when it comes to correlating the precipitation and recrystallization kineticsin future chapters, a TTT diagram was constructed (Figure 5.9), where iso-volumefraction lines are shown for f = 0.25, 0.5 and 0.75. On the same graph, the TTT datafor f = 0.5 from Rokhlin (see Figure 2.11) was also plotted. The agreement betweenthe data is good, the largest deviation being at 200‰.Despite the possible uncertainty in precipitation kinetics at low temperature, asdescribed above, the adjusted JMAK expression provides a good point of referencefor comparing the relative kinetics of precipitation and recrystallization. This isparticularly true given that it is expected that recrystallization will require annealingat temperatures greater than 300‰. While this empirical fit is useful for the the nextchapter of this thesis, the fact that an unexpectedly low value of n is required andthat, even at high temperatures, the expected equilibrium level of Nd in solid solutionis never achieved on aging suggests additional complexities. In order to go one step67Chapter 5. Precipitation in Mg-2.8wt.%NdFigure 5.9: TTT curves for precipitation in Mg-2.8wt.%Nd, Mg-2.9%Nd andMg-3.4wt.%Nd from this analysis and the literature [5, 60].further in this analysis, a simple but more physical model for the precipitation kineticshas been developed and fit the experiments described above. This is presented in thenext section.5.3 Modelling precipitation with a mean radiusmodelIn this section the experimental data presented above is discussed in relation toa mean radius model [1] for precipitation kinetics which was originally developedfor predicting precipitation in aluminum alloys by Deschamps and Bre´chet [1]. Asummary of the key equations used in this model is shown in Figure 5.10, and a morecomplete overview can be found in Appendix A. The model divides precipitation intotwo separate regimes. In the first stage of precipitation, precipitates nucleate andgrow simultaneously. In the second stage, precipitates grow and coarsen at the sametime. All precipitates are treated as being spherical and having the same average68Chapter 5. Precipitation in Mg-2.8wt.%Ndradius, R.In the mean radius model, precipitates nucleate when the average precipitateradius in the system is equal, to or greater than, the critical radius for precipitation,R∗. The driving force for precipitation ∆G is a function of aging temperature andthe difference between the current solute concentration and the equilibrium soluteconcentration. During the nucleation and growth stage of the model, the numberdensity (Nv) of precipitates and the average precipitate radius will both increase.The transition between growth and coarsening occurs when the rate at which smallprecipitates dissolve is greater than the rate at which new nuclei appear. This tran-sition is assumed to be gradual, with the fraction of precipitates that are coarseningsteadily increasing with time. Coarsening does not remove Nd from solid solution.Finally, at each timestep the amount of Nd remaining in solid solution is calculatedwith a mass balance, while the number density, volume fraction and average radiusof the precipitates are numerically integrated.The mean radius model assumes that all precipitates are spherical, and are equi-librium Mg41Nd5. As was the case with the JMAK model, these are simplifying as-sumptions made because of a lack of information on the composition of the metastableprecipitates, as well as consistent details on the aging times and temperatures at whichthese precipitates are present.The physical parameters used as model inputs are summarized in Table 5.3. Theseparameters can be divided into known values and estimated values. The known valuesinclude the lattice parameter of Mg on the basal plane (a), aging temperature (T ),precipitate composition (Cppt) and the equilibrium solubility (Ceq) as a function ofaging temperature. Equation 5.3 was used to determine the equilibrium solubility.In addition to these known parameters, the model incorporates three variablesfor which experimental values do not exist in the literature: The activation energyfor diffusion of Nd in Mg (Q), the pre-exponential factor for diffusion (D0), and the69Chapter 5. Precipitation in Mg-2.8wt.%NdFigure 5.10: Overview of the mean radius model [1]. The model takes intoaccount the rate of change in the number of precipitate nuclei (dN/dt) andprecipitate radius (dR/dt) from the nucleation and growth stage throughgrowth and coarsening. At each time step the amount of solute remainingin solid solution is calculated through a mass balance.70Chapter 5. Precipitation in Mg-2.8wt.%NdTable 5.3: Variables used in the mean radius model.Variable Value UnitsC0 0.48 at.%Cppt 10.9 at.%a 3.2× 10−10 m [89]Vat 2.32× 10−29 m3 [68]surface energy of Mg41Nd5 precipitates (γ). As a starting point, results from recentdensity functional theory (DFT) calculations were used to guide the selection of avalue for Q since experimental results for the diffusivity of Nd in Mg do not exist.Huber et al. found that the activation energy for an Nd atom to diffuse within thebasal plane is 1.14 eV [90]. In the same DFT study it was found that the activationenergy for self diffusion of Mg is 1.23 eV/atom, this being significantly lower thanthe values reported from experiments (1.40-1.44 eV) [91, 92]. While DFT is able toshow trends in activation energy to a high degree of precision (0.01 eV), its ability toaccurately predict the exact value of the activation energy is more limited. The exactvalue for activation energy calculated through DFT can vary depending on factorssuch as the approximations used to account for electron correlation effects, and thepseudo potentials used to simplify the interaction of core electrons [93].Given the variance between DFT and experimental results for self diffusion, 1.14eV was used as the lower bound for the value of Q. The upper bound for Q wasdetermined by adding the magnitude of the discrepancy between DFT and experimentfor self-diffusion in the basal plane, which was 0.19 eV [91]. This gave an upper boundof 1.34 eV for the value of Q used in the model. Here the small anisotropy in Q [90,92]in and out of the basal plane has been ignored.As with the activation energy for Nd diffusion in Mg, the pre-exponential, D0,is also unknown. In this case neither experimental nor calculated values exist. Aswas originally suggested by Brown and Ashby [94], the value of D0 for substitutional71Chapter 5. Precipitation in Mg-2.8wt.%Ndalloying elements (or for vacancies) should not vary strongly in a given material.Indeed, recent DFT calculations [95] show that the D0 for Ca, Sn, Al and Zn in Mgwere all of the same order of magnitude as the value of D0 for vacancy diffusion inpure Mg [96]. Given the complete lack of experimental data for diffusivity of Nd inMg alloys, but the apparent similarity of D0 for vacancy and solute diffusion in Mgit was chosen here to use the value of D0 for vacancy diffusion in Mg as an estimateof the D0 for Nd in Mg.Unfortunately, experimental and DFT calculated values of D0 for vacancy diffu-sion differ by two orders of magnitude. Shewmon [92] reported a value of between1 × 10−4 m2/s and 1.5 × 10−4 m2/s for vacancy diffusion in pure Mg while the re-cent DFT calculations cited above [96] report a value of 4.5 − 4.9 × 10−6 m2/s. Tocheck which value of D0 is most consistent with the experiments performed here, thepredicted vacancy diffusion distance was compared against the width of precipitatefree zone (PFZ) observed near grain boundaries in samples aged at high temperature(i.e. Figure 5.11). It has been previously argued that the width of the PFZ can beapproximately correlated to the rate of vacancy diffusion to grain boundaries [97],with the width L, being approximately given by:L ≈ 2√Dt (5.19)Where D is the diffusivity of Nd in Mg, and t is in seconds. D is further definedas:D = D0exp(−QkT)(5.20)where k is the Boltzmann constant, with a value of 8.62× 10−5 eV/atom.72Chapter 5. Precipitation in Mg-2.8wt.%NdFigure 5.11: Examples of the precipitate free zone measured in Mg-2.8 wt.%Nd aged at 400‰ for three hours. The dashed lines highlight clear examplesof the PFZ observed in this sampmle.If values for D0 and Q are assumed to be those given by Shewmon [92] as 1.0×10−4m2/s and 1.4 eV respectively, then the width of PFZ in a sample aged at 400‰ forthree hours is expected to be 12 µm in width. This is close to the 11 ± 2 µm widthof the precipitate free zone in an Mg-2.8wt.%Nd sample aged at the same time andtemperature, which can be seen in Figure 5.11.This result gives good confidence that the vacancy diffusivity is consistent herewith what was suggested by Shewmon. Based on the suggestion of Brown and Ashby[94] and the similarity of vacancy and solute D0 in DFT calculations [95,96], a valueof D0 = 1× 10−4 m2/s has been assumed here for the D0 of Nd in Mg.The final parameter in the model is the surface energy of precipitates (γ). Thiswas used as the main adjustable parameter in the mean radius model. In general, γis either supposed to remain constant with respect to aging temperature, or increasewith increasing aging temperature as metastable precipitates lose coherency with thematrix [98]. Typical values for surface energy are γ < 1 J/m2 [99].The values of Q and γ, constrained to the limits described above, were systemat-73Chapter 5. Precipitation in Mg-2.8wt.%Ndically varied in order to tune the mean radius model to the experimental data shownin Figure 5.2c. The results of running the model at 400‰ are show in Figure 5.12.The model was found to be very sensitive to the value of surface energy selected, asshown in Figure 5.12, where the effect of changing γ between 0.043 J/m2 and 0.046J/m2 is shown in addition to varying Q from 1.14− 1.34 eV. Under no condition wasthe model able to adequately predict the experimental precipitation kinetics. Also itis important to note that the precipitate radius was strongly dependent on the valueof γ used. For example, at 400‰ when γ = 0.046 J/m2 and Q = 1.14 eV, the averageprecipitate radius after three hours of aging is 1.4 µm, while when γ = 0.043 J/m2and Q = 1.34 eV, the average precipitate radius is 270 nm. This is despite bothscenarios leading to similar aging kinetics as shown in Figure 5.12.Figure 5.12: The mean radius model at 400‰ compared to resistivity measure-ments and the JMAK model.In Figure 5.12, the JMAK fit for the same temperature is also shown. It isinteresting to note that if one attempts to compare the mean radius model with aJMAK curve one requires a value of n ≈ 1.7 − 2.0 regardless of the values of D0, Qand γ used. As noted earlier, in order to fit the JMAK model to the data a value of74Chapter 5. Precipitation in Mg-2.8wt.%NdFigure 5.13: Overview of the shell model.n ≤ 0.5 was required.Precipitation at grain boundariesAs Figure 5.8 clearly shows, precipitation occurs profusely along grain boundariessuggesting a possible importance for heterogeneous nucleation. Assuming a low dis-location density in the solutionized material, heterogeneous precipitation on grainboundaries was incorporated into the mean radius model through the use of a shellmodel. Each grain was assumed to be a series of ten concentric spherical shells ofequal radius, with the outermost shell representing the grain boundary. A parameter,η, was assigned to each shell, with η adjusting the height of the activation energybarrier to nucleation [1]. For the inner shells, η = 1 while for the shell representingthe grain boundary, η was set to a lower value to decrease the activation energy bar-rier for precipitation. At the end of each time step, the flux of solute between eachshell was calculated using Fick’s second law, and the amount of Nd in solid solutionwas adjusted accordingly. An overview of the model can be seen in Figure 5.13.The results of running the model for varying values of η at the grain boundaryshell can be seen in Figure 5.14. For all values of η, the model used γ = 0.046 J/m2,75Chapter 5. Precipitation in Mg-2.8wt.%NdFigure 5.14: The effect of adding in rapid precipitation at the grain boundariesto the mean radius model at 400‰. Varying values for η, which lowers theactivation energy barrier for nucleation at grain boundaries, are shown.D0 = 1.0 × 10−4 m2/s, and Q = 1.14 eV. The aging kinetics given by this modelcan be divided into two regimes. In the first, the grain boundary undergoes rapidprecipitation. Precipitation then stagnates before entering the second regime wherethe interior of the grain undergoes precipitation. This sort of behaviour is typicalof models incorporating heterogeneous precipitation where the density of nucleationsites is limited [1, 100].Incorporation of heterogeneous precipitation on grain boundaries is clearly unableto account for the aging kinetics seen in this system. After solute is exhausted atthe grain boundary precipitation proceeds in much the same way as it did in theunmodified version of the mean radius model, with aging kinetics being too rapidrelative to the experimentally measured kinetics. This is consistent with the fact thatthe material used here has a large grain size (approximately 100 µm) and thereforea relatively large diffusion distance for solute and low number density of sites forprecipitate nucleation. Thus, under these conditions one can infer that the effect of76Chapter 5. Precipitation in Mg-2.8wt.%Ndheterogeneous precipitation on defects is a second order effect on the precipitationkinetics.5.4 The effect of spatial variations in Nd contenton precipitation kineticsThe material used in this study began as a small laboratory-scale casting and there-fore did not undergo industrial scale thermo-mechanical processing consistent withcommercial alloys. Treatments such as these serve to reduce casting induced varia-tions in composition in the sample through diffusion of solute over the scale of thesample. The homogenization treatment used was taken from previous studies [60,61]on similar laboratory cast alloys, where the question of large scale compositionalfluctuations following processing were not considered.These considerations present the possibility that some of the unusual featuresseen following aging of this alloy could be attributed to variations in Nd concentrationthroughout the sample. For instance, a region of low Nd concentration might undergominimal precipitation, leading to regions where Nd may never fully precipitate. Inthis section, the possibility of a spatially heterogeneous distribution of Nd will beinvestigated, with the findings used to modify the mean radius model previous used.5.4.1 Experimental observationsA first piece of evidence suggesting such large scale chemical inhomogeneity is shownin Figure 5.15. This figure shows Mg-2.8wt.%Nd that was aged at 400‰ for threehours. In this low magnification micrograph, alternating bands of coarse and fineprecipitates aligned parallel to the rolling direction are seen. At this magnificationit is the coarse precipitates (circled in red) that are the most apparent, these bandsbeing spaced at 50-100 µm intervals. This spatial heterogeneity in the distribution ofprecipitates was commonly observed at low magnification.77Chapter 5. Precipitation in Mg-2.8wt.%NdFigure 5.15: Mg-2.8wt.%Nd aged at 400‰ for three hours showing clear bandsof precipitates alternating with regions of low preciptiate density. Regionsof high precipitate density are highlighted with red dashes.If composition variations exist in the sample then it should be possible to presentevidence of them in the as-solutionized state. As noted above, the small atomicfraction of Nd in solution makes its measurement by EDX or even EMPA difficult. Asan alternative, however, one can take advantage of the large solid solution hardeningeffect of Nd in Mg. Evidence of this comes from the DFT calculations of Yasi etal. [101] who have shown that the effect of Nd on increasing the critical resolvedshear stress for basal dislocations (∆τ) can be quantified as:∆τ = 150√CNd (MPa) (5.21)where CNd is the concentration of Nd in solid solution in atomic percent.This level of strengthening is high compared to other common alloying additions inMg such as Al and Zn, which have strengthening coefficients of 21 and 32 MPa√CNd−178Chapter 5. Precipitation in Mg-2.8wt.%Ndrespectively [101]. This strong effect of Nd on solid solution strengthening was usedas a means of approximating the solute distribution of Nd in the solutionized samples.To measure the spatial variation of solute content in the Mg-2.8wt.%Nd samples,the variations in solid solution strengthening in a single sample were used. To char-acterize this the hardness of a solutionized sample and a sample aged at 400‰ forthree hours were measured using Berkovich hardness testing. The techniques used tomeasure hardness and process the results are described in Section 4.6.6. The meanand median hardness, as well as the width of the hardness distribution and numberof points measured (N , after discarding outliers) are summarized in Table 5.4. Thestandard deviation of each sample was used as the width of the hardness distribu-tion. Histograms of the hardness of the samples can be seen in Figures 5.16a and5.16b. While crystallographic orientation may be responsible for up to 20% of thevariations in hardness [27], this variation is smaller than the variation observed hereof up to 65% of the mean if the width of the hardness distribution is taken to be thestandard deviation. Thus, the variation that is measured cannot be attributed solelyto variations in the orientations of the grains tested.Table 5.4: Summary of nanoindentation data on heat treated Mg-2.8Nd.Heat treatment Mean hardness Median hardness Width N(MPa) (MPa) (MPa)Solutionized 763 761 167 279Aged 400°C 576 570 202 128For the solutionized sample, the hardness Htot can be approximated as the sum ofthe hardness contributions from unalloyed Mg (HMg) and the strengthening contribu-tion from Nd in solid solution. Using the assumption of Yasi et al. that solid solutionstrengthening is proportional to the square root of concentration (i.e. H ∝√CNd),the hardness of an indent can be related to the level of Nd in solid solution with:79Chapter 5. Precipitation in Mg-2.8wt.%Nd(a) Solutionized (b) Aged 400‰Figure 5.16: Histograms showing Berkovich hardness of Mg-2.8wt.%Nd a) so-lutionized at 545‰ and b) aged at 400‰ for three hours.Htot = HMg + ∆τexp (5.22)where ∆τexp is the strengthening coefficient to be solved for. It is assumed that0.46 at.%Nd is in solid solution (from the average of the three samples in Table 5.1),and Htot is the mean hardness of the solutionized sample, 763 MPa. The value ofHMg was found to be 457 MPa from indention of a sample of commercially pure Mg,the composition of which was listed in Section 4.2 of the Chapter 4. A series of 16indents were made in the sample using the same parameters as those used for theother samples in one grain. Using these values it was found that ∆τexp = 451 MPa√CNd, where CNd is in at.%.It is interesting to note that the solid solution hardness coefficient obtained above(451 MPa) is roughly three times the coefficient reported by Yasi et al. from DFTsimulations, which is roughly the correlation expected between flow stress and hard-ness [102]. Of course, a direct comparison is difficult as one expects other deformationmechanisms under the indent to be active, (e.g. twinning [103]) but the fact that thesevalues are similar gives some confidence in the interpretation of these results.80Chapter 5. Precipitation in Mg-2.8wt.%NdUsing this value of ∆τ in Equation 5.22 allows the concentration of Nd at a givenindent to be determined from the measured Berkovich hardness:CNd =(Htot − 457451)2(5.23)Equation 5.23 was applied to the set of indents obtained from both samples, andused to construct the normalized histogram shown in Figure 5.17. The solutionizeddata set shows a concentration distribution from 0.05-0.7 at.%Nd, with a small frac-tion of points above this. The histogram of the as-solutionized hardness distributionwas approximated using a normal distribution. The mean value of the distributionwas set to 0.46 at.%, as that was the average amount of Nd in solid solution accordingto the samples in Table 5.1, and a value of 0.1 was used as the standard deviation.The experimentally derived histogram is shown in Figure 5.17. As the maximum solidsolubility of Nd in Mg is 0.61 at.% [70], the indents in bins above this amount werediscarded, these possibly having been influenced by the proximity of nearby secondphase particles.This normal distribution was next used with the mean-radius model to predict theinfluence of having regions of different composition in the samples. The mean radiusmodel was used in the same manner as described above. The model was run for eachconcentration represented within the normal distribution histogram in Figure 5.17.For each bin of starting Nd concentration, the amount of Nd in solid solution at eachtime step is multiplied by the volume fraction of precipitates within the bin. Theaverage Nd concentration is calculated by adding together each bin multiplied by thevolume fraction of each bin.As with the original version of the mean radius model, surface energy was usedas a fitting parameter. D0 was held constant at 1.0× 10−4 m2/s. When 1.14 eV was81Chapter 5. Precipitation in Mg-2.8wt.%NdFigure 5.17: Histogram of Nd concentration calculated from hardness mea-surements. The data was truncated above 0.6at.%Nd, representing thesolubility limit of the alloy.used for the value of Q, fitting the model required decreasing γ with increasing agingtemperature. Increasing Q to 1.34 eV weakened the temperature dependency of γ,as is shown in Table 5.5. As such, the model used 1.34 eV for the value of Q, and thebest fits of γ to each individual aging temperature were used.Table 5.5: Values of interfacial energy used in the modified mean radius modelwhen Q = 1.34 eV and D0 = 10−4 m2/s.T (‰) γ (J/m2)190 0.060350 0.054400 0.046A comparison between the kinetics predicted by the model and the experimentalresults collected in this study are show in Figure 5.18. At 350‰ and 400‰, the modelis able to capture both the extended time required for aging as well as the tendency82Chapter 5. Precipitation in Mg-2.8wt.%Ndfor the amount of Nd in solid solution to never reach the equilibrium level. At 190°C,however, the model is unable to adequately predict the precipitation kinetics. Theorigins of this will be discussed in further detail below.(a) 190°C (b) 350°C (c) 400°CFigure 5.18: Results of the mean radius models at 190‰, 350‰ and 400‰ whenthe heterogeneous distribution of solute is accounted for. A comparison tothe model without a concentration distribution is also shown.As a final check of the validity of incorporating a concentration distribution intothe mean radius model, the concentration distribution given by the model after threehours of aging at 400‰ was compared to the data obtained through Berkovich hard-ness testing. The results are shown in Figure 5.19. Both the model and experimentpredict that most of the sample will have fully precipitated to the equilibrium amountof Nd in solid solution. The model has a higher fraction of the sample containing 0.3-0.35 at.%Nd remaining in solid solution than the experimental results. In the model,these regions have not begun to precipitate after three hours of aging, although theydo at later aging times.5.4.2 DiscussionModifying the mean radius model to account for a spatially heterogeneous distributionof Nd concentration offers an explanation for the precipitation kinetics observed inthis work particularly at the highest annealing temperatures, though it still fails to83Chapter 5. Precipitation in Mg-2.8wt.%NdFigure 5.19: Nd in solid solution after aging three hours at 400‰ according tothe mean radius model and experimental results.capture the experimental results obtained for aging at 190‰.As noted above, there are several factors which likely contribute to the poor fit ofthe model at 190‰. At this temperature the model exhibits only a relatively weaksensitivity to the assumed solute distribution in the sample. This prediction is notunreasonable considering that at low temperatures the solubility of Nd in Mg is verylow, and as such the supersaturation (and therefore driving force for precipitation)does not vary as strongly with temperature as it does at high temperature where thesolvus curve varies strongly with temperature.This points to one large piece of uncertainty regarding the parameters input intothe model. The solvus curve used here was determined at high temperature forequilibrium between Mg and Mg41Nd5, not between the Mg and β′′ phases observedto precipitate at this temperature. The solubility of this metastable β′′ phase remainsunknown. If the model is employed assuming a higher solubility than that assumedhere, then the fit to the experimental data improves.The second major factor limiting the comparison between the model and exper-iments is the possible contribution of scattering from precipitates to the measuredresistivity (cf. Section 5.2.2). The concentration of Nd in solid solution predicted by84Chapter 5. Precipitation in Mg-2.8wt.%Ndthe model was converted into an equivalent resistivity using Equation 5.2, and com-pared to the measured resistivity. In all cases, the model predicts a lower resistivitythan the experimental measurements at 190‰, with the magnitude of the differencedecreasing with aging time. At the aging time with the maximum difference betweenthe resistivity given by the model versus experiment, the model resistivity is 70%of that measured experimentally. It seems not unreasonable to attribute at least aportion of this difference to interface scattering, given that Raeisinia et al. foundthat up to 25% of the resistivity in a sample with closely spaced precipitates (10 nm)could be attributed to interface scattering [87].While the model had difficulty in matching the experimental kinetics at 190‰, itwas able to accurately capture aging behavior at 350‰ and 400‰. For both tempera-tures, the model captured the wide spread in aging times as well as the failure of bothmodel and experiment to reach equilibrium. This is consistent with the observationsof the microstructure in Figure 5.15, and also would appear to confirm the previouslydiscussed speculation that there was insufficient mixing of Nd and Mg during casting,or insufficient homogenization after casting. Furthermore, this widescale variationin composition may account for the unusually large deviation seen in the resistivitymeasurements seen in Figure 5.2 in Section 5.2.2.As was previously stated, precipitation kinetics were studied primarily to be ableto quantify precipitation during future recrystallization experiments. As the recrys-tallization start temperature of this alloy is over 300‰ [5], understanding precipitationkinetics at 350‰ and 400‰ is more important than at lower temperatures. As themodel is able to account for precipitation kinetics at 350‰ and 400‰ through theincorporation of a heterogeneous distribution of solute, the model is considered suit-able for further use in determining precipitation kinetics during the recrystallizationexperiments described in the next chapter.85Chapter 5. Precipitation in Mg-2.8wt.%Nd5.5 SummaryThis chapter began with a stated goal of quantifying precipitation kinetics throughexperiments and modelling, and has done so through electrical resistivity measure-ments, scanning electron microscopy observations, and modifications to the meanradius model developed by Deschamps and Bre´chet [1]. Precipitation experiments onMg-2.8wt.%Nd (0.48 at.%) at 190‰, 350‰, and 400‰ were used to correlate volumefraction and solid solution content with results from the literature and found to be ingood agreement. Modelling precipitation kinetics proved to be challenging, as resultsfrom both a JMAK model and a mean radius model indicated that precipitation wasbeing affected by features not contained in a mean-field model. Precipitation kinet-ics could be accurately modelled at 350‰ and 400‰, however, by incorporating aspatially heterogeneous distribution of Nd concentration into a mean radius model.86Chapter 6The Effect of Precipitate State onRecrystallization in Mg-2.8wt.%Nd6.1 IntroductionThe previous chapter showed that precipitation in Mg-2.8wt.%Nd is complex, withdifferent types of precipitates forming depending on aging temperature and time.Further complexity arises from the issue that aging at high temperatures is affected bythe spatial distribution of solute. Consistent with the literature [5], it was confirmedthat precipitation is heterogeneous, as was shown by the propensity for precipitatesto form at grain boundaries. This evidence clearly points to the potential of Nd inMg-Nd alloys to alter the progression of recrystallization. Indeed, Rohklin has shownthat among the six binary alloys he studied, Mg-Nd alloys had the strongest effecton the recrystallization start temperature [5].In this chapter, the effect of Nd will be studied with an emphasis on understandingthe effect of precipitates on recrystallization in rolled sheet samples. Rolling wasselected as the mode of deformation as it aligns with the goal of the MagNET StrategicResearch Network in producing formable Mg sheet alloys. The chapter will begin witha description of the methods used to set the precipitation state and subsequentlydeform the material. The samples will be deformed and annealed from three starting87Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Ndconditions: i) The solutionized state, ii) samples aged at 190‰, and iii) samplesaged at 400‰. The deformed microstructures from these starting materials will becharacterized next. Finally, the recrystallization of these deformed samples will bestudied to assess the effect of the initial precipitation state. These results will berelated to previous reports related to recrystallization in Mg alloys.For the sake of consistency in this chapter, the following terms are defined:ˆ Aging refers to heat treating samples prior to deformation in order to formprecipitatesˆ Annealing refers to the heat treatment of samples which were deformed andthen heated in order to induce recrystallization6.2 Initial aging treatmentsAs noted above, the majority of the work performed here focuses on samples subjectedto three different initial aging treatments to give three different precipitation states.In addition, a second alloy (Mg-0.6wt.%Nd) was prepared to compare with thesematerials. In this case, the alloy is expected to be below the solubility limit for thetemperatures used for the recrystallization treatments. All of these materials wereinitially prepared from cast ingots following the procedure described in Section Solution treated samplesSamples were solution treated at 545‰ for eight hours then water quenched followingthe procedure given in Section 4.3.2. This was performed just prior to rolling thespecimen, which will be described in greater detail in the following section. Aftersolutionizing the samples were found to have a predominantly basal texture, withan average grain size of 105 µm. An IPF map of the solutionized material and polefigures are shown in Figure 6.1. Inverse pole figure maps are coloured according tothe crystallographic direction that is parallel to the specified sample direction. For88Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Ndinstance, in Figure 6.1 the colours correspond to the crystallographic direction parallelto the normal direction of the rolled sheet.(a) (b)(c) (d)Figure 6.1: Texture and microstructure of solutionized Mg-2.8wt.%Nd beforedeformation. a) Normal direction IPF map, b) key to IPF map colouring,c) pole figures, and d) key to pole figure colouring.Work by Rokhlin on solutionized Mg-Nd alloys found that temperatures in excessof 300‰ were required to initiate recrystallization in alloys similar to those studiedhere [5]. In alloys that are cold rolled in the solutionized state, it is expected thatextensive precipitation of the equilibrium β phase will occur at such temperaturesbased on the results of the previous chapter and from the literature [67]. This pre-89Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Ndcipitation will have an impact on the hardness of the material through precipitatehardening as well through changes in solid solution strengthening. As the hardnessevolution of samples during annealing will be used to track recrystallization and con-current precipitation, it is important to examine the impact of precipitation alone onthe hardness.Figure 6.2 shows that aging at 400‰ leads to a continuous decrease in hardnesswith time, from an average hardness of 508 MPa in the solutionized sample to a finalhardness of 447 MPa after 24 hours of aging. This suggests that the loss of Nd fromsolid solution provides the dominant contribution to hardness at this temperature.These observations are consistent with the resistivity evolution observed under thesame conditions (Figure 5.2c in Chapter 5). Using Equation 5.2 with Equations5.23 and B.12 in Appendix B, the resistivity data was used to estimate the expectedhardness. The comparison with the experimental hardness measurements in Figure6.3 shows good agreement, with the calculated hardness being at most 8% largerthan that found by experiment. These results suggest that precipitation from thesolutionized state will contribute to a change in the hardness of the material duringrecrystallization, the maximum magnitude being of the order of 50 MPa of hardness.6.2.2 Samples aged at 400°CThe experiments in Chapter 5 found that aging at 400‰ leads to the formation ofrelatively coarse Mg41Nd5 precipitates. As seen in Figures 5.2c and 6.2 (above), thehardness and resistivity reach a constant value after approximately one hour of aging.This is consistent with the previous chapter where it was shown that the majority ofsolute has precipitated after 3 hours, with approximately 1.2 wt.%Nd remaining insolution. While this remains above the theoretical solubility limit of 0.65 wt.%Nd,the results in the last chapter showed that the progress towards the solubility limitwas slow after three hours; this is consistent with Figure 6.2.90Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%NdFigure 6.2: Evolution of Vickers hardness during aging at 400‰. The solidsquare represents the average hardness value, while the hollow points arethe individual measurements.Figure 6.3: A comparison of the mean Vickers hardness from Figure 6.2 withthe Vicker’s hardness calculated from electrical resistivity measured on thesame sample.91Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Nd6.2.3 Samples aged at 190°CAs discussed in the previous chapter, aging at 190‰ leads to the formation of amixture of the metastable β′ and β′′ phases. It was decided to use the peak agedcondition at this temperature as the precipitation state used for these experiments,as it was hoped that this would maximize the effect of precipitates on deformation.As shown in Figure 6.4 this condition was achieved after 24 hours.Figure 6.4: Evolution of Vickers hardness during aging at 190‰. The solidpoints represents the average hardness value, while the hollow points arethe individual measurements.The results by Rokhlin on the recrystallization of Mg-Nd alloys revealed thatrecrystallization requires annealing at temperature much higher than 190‰ [5]. Toobserve the stability of the precipitates formed at 190‰ during annealing at a highertemperature, samples aged for 24 hours at 190‰ were subjected to a second agingtreatment at 400‰. In this case, it was found that the hardness of the samplecontinuously dropped on aging (Figure 6.5a), which is consistent with the conversionof the metastable β′ and β′′ precipitates into coarser β precipitates. Interestingly,92Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Ndhowever, resistivity measurements on the same material revealed a sudden increasein resistivity after only 1 minute of aging at 400‰ (Figure 6.5b). This would suggestthat the metastable precipitates dissolve prior to the formation of the beta phase.Indeed, if one plots the value of resistivity measured from these samples alongsidesamples solution treated then aged directly at 400‰, one sees that, beyond the firstdata point, the results collapse onto one another, as is shown in Figure 6.5b.(a) Vickers hardness (b) ResistivityFigure 6.5: Aging kinetics in a sample aged at 190‰ for 24 hours followed byaging at 400‰ as found by a) Vickers hardness and b) electrical resistivity.The data from aging at 190‰ after solutionizing is shown in grey squares.The solid points represents the average hardness value, while the hollowpoints are the individual measurements.6.2.4 Preparation of Mg-0.6wt.%Nd samplesA limited number of experiments were performed on samples that were expectedto be below the solubility limit during annealing. These samples were hot rolledfrom a cast ingot as described in Section 4.3 of the Chapter 4. After hot rollingthey were solutionized at 545‰ for eight hours and immediately quenched into roomtemperature water.93Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Nd6.3 Characterization of the deformed stateGiven the significant differences in the initial precipitate states of the Mg-2.8wt.%Ndsamples, it is important to know whether the initial precipitate state and concen-tration of Nd in solid solution affects the as-deformed microstructure. Cold rollingwas used to deform each of the materials described above to 20% reduction in heightin 4-5 steps, with a 3-8% reduction per step. In samples rolled past 20% strain itwas found that edge cracks rapidly developed leading to sample failure, limiting themaximum amount of deformation that could be achieved.A first check of possible differences in the rolled samples was accomplished byfollowing the evolution of hardness. Figure 6.6a shows that Mg-2.8wt.%Nd in allthree aging states hardened similarly during rolling, with the material aged at 190‰showing a higher level of hardness compared to the other two samples. This is mostclearly seen when the initial hardness is subtracted from the data, is is shown inFigure 6.6b.(a) Hardness during rolling (b) Change in hardnessFigure 6.6: (a) Vickers hardness measured in between rolling passes in Mg-2.8wt.%Nd. (b) Change in hardness in between rolling passes in Mg-2.8wt.%Nd. Trend lines are provided to guide the eye94Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Nd6.3.1 EBSD of deformed materialsDespite the modest additional increase in hardness seen in the aged 190‰ sample,these results suggest that the rolled microstructures are likely similar for the threeaging conditions. Indeed, this was found when the as-rolled materials were studiedby EBSD. Figure 6.7 shows normal direction (ND) IPF maps for the three as-rolledsamples viewed in the TD plane (the plane containing the rolling and normal di-rections of the sheet). The brightness of the IPF maps is adjusted according to theimage quality (IQ) value. IQ maps indicate the quality of the Kikuchi pattern at eachindexed point, where light points indicate a high quality Kikuchi pattern, and darkpoints indicate low quality patterns. Poor IQ values are often associated with regionsof local high misorientation such as grain boundaries, regions having undergone largeplastic strains, or fine twins [37, 104, 105]. Furthermore, the presence of fine secondphase particles will also reduce IQ.The maps in Figure 6.7 show similar microstructural features for all three ma-terials. In all cases, the maps appear to be predominantly shaded in red and pink,indicating alignment of the (0001) crystallographic direction parallel to the normaldirection, consistent with a basal texture [6,9]. Owing to the large starting grain sizeof these samples (105 µm) only a few grains appear in each map. Grain boundariesare clearly evidenced by abrupt changes in colour. Similarly, extension twins cansometimes be seen due to their 86° misorientation with the surrounding parent grain,often appearing as blue against a red background.Many regions of these appear with low IQ, as can be seen in Figure 6.8; theseare indicated by dark grey or black in these figures. These features are not randomlydistributed within the microstructure. In many cases they can be identified as twinsfrom the presence of small fragments that were successfully indexed. The twinswere identified based on their specific misorientation (summarized in Table 6.1) withrespect to the surrounding matrix with a tolerance angle of ±5° as shown in Figure95Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Nd(a) Solutionized (b) Aged 190‰(c) Aged 400‰ (d)Figure 6.7: Normal direction IPF maps with overlaid image quality data of thecold rolled samples. Examples of shear bands are highlighted with dashedlines.6.8, with more detailed views being shown in Figure 6.9.Table 6.1: Twin angles and rotation axes in magnesium.Twin type Twinning Plane Rotation axis Twinning angleExtension {101¯2} 〈112¯0〉 86.3°Contraction {101¯1} 〈112¯0〉 56.2°Contraction-extension {101¯1}{101¯2} 〈112¯0〉 37.5°96Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Nd(a) Solutionized (b) Aged 190‰(c) Aged 400‰ (d) KeyFigure 6.8: Image quality maps of cold rolled samples showing location ofindexable twins in the cold rolled samples.As was previously shown by Nave et al. and Hanzsche et al. [14,106], the prevalenceof twinning modes can be visualized if one looks at the distributions of misorienta-tion angles in Figure 6.10. In the case of the solutionized material, the misorientationdistribution clearly shows peaks at approximately 35°, 55° and 85°, these correspond-ing to the misorientations associated with contraction-extension, contraction, and97Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Nd(a) (b)(c) (d)Figure 6.9: Examples of indexed twins in Mg-2.8Nd samples: (a) double twinsin solutionized sample, (b) contraction twins in aged 190‰ sample, and (c)extension twins in aged 400‰ sample.extension twins respectively. In the case of the aged samples a strong peak close to86° corresponding to extension twins is observed, though peaks corresponding to theother two twin types are less clear. While this could point to an effect of precipitationon suppressing contraction (and therefore also, contraction-extension) twinning, it islikely that the lack of evidence for these twins in the misorientation profile comesfrom the difficulty in indexing the samples.In the sample aged at 400‰, the Kikuchi patterns were found to be of poorer98Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Nd(a) Solutionized (b) Aged 190‰ (c) Aged 400‰Figure 6.10: Distribution of misorientation angles in samples a) solutionizedb) aged at 190‰ and c) aged at 400‰.quality than those in the deformed solutionized material. The presence of precipitatesaffects the quality of the diffraction patterns in two ways. First, the diffractionfrom the precipitates contributes to the signal measured, making the overall patterncontrast weaker. On top of this, it was found that sample preparation was much moredifficult in the case of samples containing precipitates. In particular, the sample agedat 400‰ exhibited differential chemical polishing associated with the precipitates,leaving the material with a rough surface. This also strongly degrades the quality ofthe diffraction pattern, as is demonstrated by large β precipitates showing up as darkgrey or black (low IQ) in Figure 6.11.Further inspection of Figures 6.8b and 6.8c, however, shows that there are manyfine twins in these samples that are not indexed. This is qualitatively consistentwith the work of Jain et al. who found that changing the precipitate state in AZ80affected the thickness of twins, where the presence of precipitates lead to finer twinsbut with the same overall volume fraction [107]. Furthermore, Safi-Naqvi et al. notedthat aging Mg-3wt.%Nd at 190‰ for five hours decreased the fraction of visible twinscompared to the solutionized sample in extruded sheets when deforming in compres-sion parallel to the extrusion and sheet normal directions [71].A final important, but difficult to quantify feature of all of the samples in Figures6.8a through 6.8c are the relatively large band-like features that exhibit low IQ values.99Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%NdFigure 6.11: Example of precipitates (noted with red arrows) in an imagequality map of Mg-2.8Nd aged at 400‰ before cold rolling.These bands appear to be larger than individual twins and often cross more thanone grain. They also appear with an angle of between 30° and 60° with respect tothe rolling direction, regardless of grain orientation. These features are consistentwith shear bands reported in other rolled Mg alloys [7, 9, 36, 39]. For the purposesof this work, a shear band will be defined as a region of localized high strain, thisfeature crossing two or more grains at an angle of 30-60° with respect to the rollingdirection [7, 9, 36, 39]. The formation of shear bands in Mg alloys has been reportedto be moderately texture dependent [39], with the bands that form occurring ata relatively fixed angle to the rolling direction. In the literature, shear bands areconsistently found to be formed of contraction and contraction-extension double twins[7,9,36,39]. While the indexing within the shear bands shown here was poor, in manycases twin fragments could be found, an example of which is shown in Figure 6.12.This is consistent with the view that shear bands are formed when contraction, thendouble twins form leading to a re-orientation of the lattice into a condition favorablefor basal slip compared to the original texture [36, 49].100Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Nd(a) (b)Figure 6.12: Fragments of twin boundaries indexed within a shear band inMg-2.8wt.%Nd aged at 190‰.6.3.2 SummaryDespite differences in the intitial aging condition, the deformed microstructures ofthe samples studied here are similar. All microstructures share in common the typesof twins present, presence of shear bands, and the heterogeneity of the deformed mi-crostructure. As such, any differences in the annealed microstructure of the materialsin the three heat treated conditions is not expected to arise from differences in theirdeformed state.6.4 Microstructure and kinetics ofrecrystallizationFollowing rolling, samples that were solutionized, aged at 190‰, and aged at 400‰underwent static annealing. There were two primary goals for these experiments:Clarifying the role of precipitates on recrystallization kinetics in Mg-Nd alloys, andexamining the formation and growth of new grains during annealing. These experi-ments were performed between 350‰-450‰ based on the previous work of Rokhlin [5].The first aging condition studied will be that of the samples aged at 400‰. Theresults from these samples are the simplest to interpret, as the recrystallization and101Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Ndprior-aging temperatures are similar, leading to recrystallization occurring in an ap-proximately stable field of precipitates. Following this, the recrystallization responseof the samples that were either solutionized or aged at 190‰ before rolling will be de-scribed. In both of these cases precipitation was expected to occur concurrently withrecovery and recrystallization. As shown above, when the samples aged at 190‰ wereaged a second time at 400‰, it appeared that the metastable precipitates dissolvedrapidly. Based on this observation and the similarity of the deformed microstructures,the annealing response of these two conditions was expected to be similar.6.5 Recrystallization of Mg-2.8wt.%Nd aged at400°CThe Vickers hardness as a function of annealing time in Mg-2.8wt.%Nd samples agedat 400‰ and annealed at 350‰, 400‰ and 450‰ are shown in Figure 6.13. For allannealing temperatures the mean hardness of the material eventually decreases to avalue of approximately 470 MPa, compared with a value of 576 MPa for the as-rolledmaterial. This is within 20 MPa of the hardness of the samples in their as-agedcondition (451 MPa). In the case of annealing at 450‰ this occurs within the firstminute of annealing, while at 350‰ it takes approximately 4 hours, and at 400‰ ittakes about 10 minutes.The IPF maps in Figure 6.14 show that the microstructures of the fully softenedmaterials for each annealing temperature look similar. In each case the materialconsists of equiaxed grains with average grain sizes of 13 µm (350‰ for 16 hours), 14µm (400‰ for one hour) and 17 µm (450‰ for one hour). The grain size distributionis wide (Figure 6.15) similar to what has been observed in other recrystallized Mgalloys [10,13,49]. This is consistent with the maps shown in Figure 6.14 where a widerange of grain sizes is seen.To check the degree of recrystallization, GOS maps were computed from the EBSD102Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%NdFigure 6.13: Vickers hardness as a function of time during annealing at 350‰,400‰, and 450‰ for materials aged at 400‰.data [108]. A GOS value of 1° was considered the upper threshold for a recrystal-lized grain. This was in accordance with the literature [108]. Furthermore, analysisof grains with GOS values between 0.5-1° found that these grains corresponded tofeatures observed in the image quality maps that were not present in the as-deformedmicrostructure. Analysis of grains with GOS values of 1-2° found these grains oftencontain a continuous misorientation gradient consistent with deformation. A GOSmap for the sample recrystallized at 350‰ for 16 hours is shown as an example inFigure 6.16 where a wide range of grain sizes is seen.The GOS maps often identified grains containing internal misorientation spreadsof greater than 1° that upon closer inspection appeared visually to be recrystallized.These grains comprised upwards of 10% of the sample. Many of these “grains” werefound to actually be clusters of grains or large subgrains separated by low angle grainboundaries, as illustrated in Figure 6.16 and in Figure 6.17a. Figure 6.17b shows a plotof the misorientation along a line showing the sharp nature of these boundaries andthe low misorientation within each domain. This result suggests that these regions are103Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Nd(a) Annealed 350‰ (b) Annealed 400‰(c) Annealed 450‰ (d)Figure 6.14: Normal direction IPF maps of samples aged at 400‰ before an-nealing: (a) 16 hours at 350‰, (b) 1 hour at 400‰ and (c) 1 hour at450‰.recrystallized or, more likely, very highly recovered grains versus still-deformed grains.While the misorientation profile shows that some of the clusters are misoriented bymore than 5° over parts of the trace, the OIM Analysis software requires that allsegments of the grain boundary must be above the threshold value for misorientationin order to be considered a grain.While these grains could be considered “recrystallized” as their microstructure is104Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%NdFigure 6.15: Grain size distributions of the annealed samples.Figure 6.16: Grain orientation spread map of Mg-2.8Nd aged at 400‰ andrecrystallized at 450‰ for 1 hours. The region shown in Figure 6.17a iscircled in red.105Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Nd(a) (b)Figure 6.17: (a) Normal direction IPF map of grains which are marked asunrecrystallized in the GOS map. (b) Misorientation profile across thegrains.unlikely to change during further annealing, they were not included in the fractionrecrystallized to be conservative. This observation is similar to that of Levinson etal., who found that up to 20% of grains in annealed AZ31 contained orientationgradients greater than 0.75% [105]. The appearance of these types of grains sharplycontrasts with other grains in the same sample which exhibited a more continuousmisorientation profile as is shown in Figure 6.18. These grains are interpreted asbeing unrecrystallized.Based on this analysis, the sample annealed at 350° for 16 hours was found tobe 89% recrystallized, the sample annealed at 400‰ for 1 hour was found to be 87%recrystallized, and the sample annealed at 450‰ for 1 hour was found to be 85%recrystallized. Little change in the microstructure occurred with further holding ofthe samples. For example, Figure 6.19 shows the microstructure of a sample held at400‰ for 4 hours having an average grain size of 14 µm.The results presented to this point could be used to conclude that the presenceof pre-existing β precipitates formed at 400‰ do not have a large effect on recrys-tallization. They clearly do not strongly inhibit recrystallization at and above 350‰,106Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Nd(a) (b)Figure 6.18: (a) Normal direction IPF map of Mg-2.8Nd aged at 400‰ andrecrystallized at 350‰ for 16 hours showing a grain which has not recrys-tallized. (b) Misorientation profile across the grain.(a) (b)Figure 6.19: Normal direction IPF map Mg-2.8Nd aged at 400‰ and recrys-tallized at 400‰ for four hours.107Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Ndparticularly at 450‰ where recrystallization occurs within minutes. This conclu-sion would not be fully correct, as looking carefully at the results one can observethe strong tendency for heterogeneous precipitation of the β phase on the prior grainboundaries of the solutionized material. This is shown as low IQ in EBSD maps alongthese former grain boundaries. Moreover, new recrystallized grains do not cross theseboundaries as evidenced in Figure 6.20. This may strongly limit grain coarsening inthese samples.(a) (b)Figure 6.20: (a) Grain boundary (indicated by arrows) blocking growth ofrecrystallized grains in Mg-2.8Nd aged at 400‰ and recrystallized at 400‰for four hours. (b) BSE image of Mg-2.8Nd aged at 400‰ and recrystallizedat 350‰ for 16 hours showing profuse precipitation onto the solutionizedgrain boundaries.The presence of precipitates can have two main effects on the annealed microstru-cure. First, they can assist recrystallization through particle stimulated nucleation[15,55,110]. This will be discussed further below. They can also impede grain bound-ary migration through Zener drag, limiting the final grain size during coarsening [11].A simple estimate of the limiting grain size accounting for the effect of precipitateson Dz, the diameter of the recrystallized grains is [11]:108Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%NdDz =4r3Fv(6.1)where Fv is the volume fraction of precipitates.Using the results of the mean radius model incorporating a concentration distri-bution, the grain diameter predicted by Equation 6.1 at initial Nd concentrations ofbetween 0.45-0.6at.% in solid solution will give limiting grain sizes ≥5 µm. Concen-trations below 0.45 at.%Nd yield limiting grain sizes of millimeters or more. Whilethe this calculation is only a rough estimate and incorporates a number of simpli-fying assumptions (spherical precipitates, and no means of accounting for the denseprecipitation along grain boundaries), it does show that as a worst case, there maybe some minor reduction in the final grain size of the annealed material. However, itis clear that nucleation of new grains and recrystallization will still occur despite thepresence of precipitates.6.5.1 Comparison to Mg-0.6wt.%NdA solutionized Mg-0.6wt.%Nd alloy was subjected to the same rolling and recrystal-lization annealing treatments as the alloys above. This was done in order to comparerecrystallization in an alloy with precipitates to one without precipitates. This alloycomposition is below the solubility limit (0.11at.%/0.96wt.%Nd) at 400‰, meaningthat recrystallizing this material at 400‰ should lead to no precipitation. Figure6.21 shows the microstructures of the Mg-2.8wt.%Nd and Mg-0.6wt.%Nd samplesfollowing one hour of annealing at 400‰. One can see that the materials show nearlyidentical recrystallized fractions (80% for the Mg-0.6Nd alloy based on GOS analysis)and grain size, with the grain size of the Mg-0.6wt.%Nd alloy being 14 µm versus 13µm in the Mg-2.8wt.%Nd sample recrystallized at 400‰ for 1 hour. Thus, these twoalloys, which differ in their precipitation states, but have nearly identical properties109Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Ndotherwise also show similar recrystallized microstructures.(a) Mg-0.6wt.%Nd (b) Mg-2.8wt.%Nd (c) KeyFigure 6.21: Normal direction inverse pole figure maps of (a) Mg-0.6wt.%Ndand (b) Mg-2.8wt.%Nd recrystallized at 400‰ for one hour.6.5.2 Observations of recrystallization nucleiAs noted above, the presence of β precipitates could also potentially affect the earlystages of recrystallization by acting as nucleation sites via particle stimulated nucle-ation. To examine this as well as the peculiar features noted above, notably the widegrain size distributions and grains failing to recrystallize even after extended anneal-ing, it is necessary to examine the partially recrystallized state. A good example ofthis state was found in samples annealed for 1 hour at 350‰. An IQ map illustratingthe partially recrystallized microstructure of this condition is shown in Figure 6.22.Three particular regions are highlighted, illustrating: i) profuse precipitation alongthe solutionized grain boundaries (Figure 6.22a), ii) a region that appears to havebeen traversed by a shear band (Figure 6.22b), and iii) unrecrystallized features thatgive the appearance of being twins (Figure 6.22c). In all three regions there is evi-dence of new, small, recrystallized grains. Figures 6.23 and 6.24 show the same regionbut as IPF and GOS maps.According to the GOS map in Figure 6.23, 52% of the sample has recrystallized.110Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%NdFigure 6.22: Image quality map of Mg-2.8wt.%Nd recrystallized at 350‰ forone hour showing regions of interest: (a) recrystallization at a heavily pre-cipitated former grain boundary, (b) unrecrystallized twins, (c) recrystal-lization within a shear band.The newly recrystallized grains are not distributed randomly, and instead appearto be clustered, with some prior solutionized grains containing few new grains, andothers being nearly fully recrystallized. This heterogeneity could be due to variationsin Nd concentration and therefore precipitation within the sample. However, thelocation of the new grains does not appear to be correlated with regions devoid of βprecipitates, nor does there appear to be evidence of a correlation of new grains tothe location of β precipitates. This lack of evidence for particle stimulated nucleationis in agreement with previous research which has shown that magnesium alloys areresistant to particle stimulated nucleation [55]. Rather than being correlated withprecipitates, the nucleation of new grains appears to be most closely correlated to theposition of twins, shear bands, and grain boundaries.Examining the GOS and IQ maps show a number of unrecrystallized twins, anexample of which is shown in Figure 6.22. These twins, identified as described above,were all found to be extension twins by overlaying twin boundaries onto the GOSmap in Figure 6.23. The blue boundaries represent extension twins, and are the only111Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%NdFigure 6.23: GOS map of Mg-3Nd aged at 400°C, recrystallized 350C for 1 hour.Regions (a), (b) and (c) correspond with the regions circled in Figure 6.22.Also overlaid on this map are boundaries corresponding with contraction,extension and double twins.type of twin remaining in this sample. This should be contrasted with the as-rolledstate (cf. Figure 6.8c) where extension, contraction and contraction-extension doubletwins were observed.The spatial arrangement of recrystallization nuclei into bands within grains sug-gests the possibility that they have been formed at or within twins, even though noremnants of the original unrecrystallized twin orientations could be unambiguouslyidentified. This is shown in Figure 6.25, where two parallel unrecrystallized exten-sion twins (blue) are crossed by a band of new, small recrystallized grains. A secondband of recrystallized grains can be seen near the bottom of the image. This con-figuration is similar to previous reports of recrystallization in twin grains from theliterature [10,13,51].112Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Nd(a) Normal direction IPF map (b) Rolling direction IPF map (c) KeyFigure 6.24: Inverse pole figure maps of sample recrystallized at 350‰ for onehour.Figure 6.25: Normal direction IPF map of twins in Mg-2.8Nd recrystallized at350C for 1 hour. Traces of the (101¯2) planes (corresponding with extensiontwins) are shown. The dotted black lines correspond to the closest planetraces for the {101¯1} plane.No unrecrystallized portions of the prior twins could be found to confirm thesefeatures to be prior twins. Barnett et al. [104] have used the trace of twinning planesto identify twins by comparing the orientation of the long axis of the twin to overlaid113Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Ndtraces of the expected twinning plane. The upper band of recrystallized grains wasfound to deviate from traces of the {101¯1} planes of the parent grain by 3.3°, whileit deviated from the {101¯2} planes by 14.0°. If the twin did indeed form on a {101¯1}plane, this could be consistent with a contraction twin, or a contraction-extensiondouble twin. Similarly, the lower band of recrystallized grains deviated from the{101¯1} planes by 5.2° and the {101¯2} planes by 12.3°. Being definitive in this caseis difficult, however, as the trace of the original twin can only be guessed based onthe positions of the newly formed grains. Moreover, slip in the parent grain after theformation of the twin should lead to changes in orientation that would add to theerror in the twin trace analysis. Indeed, Barnett et al. found that contraction andcontraction-extension double twins could deviate from the {101¯1} planes in order toaccommodate internal stresses, and end up following a {303¯4} habit plane [104].The crystallographic orientations of the recrystallized and deformed parent grainswas also investigated, similar to that performed by Barnett [17]. Figure 6.26a showsthe {0001} and {101¯2} pole figures of the parent grain, extension twins, and recrys-tallized nuclei. As both extension and contraction twins rotate the grain about a[112¯0] axis, twins and their parent grain are expected to share a common orientationin the {112¯0} pole figure. Indeed, one can see that the unrecrystallized extensiontwins share a common orientation in the {112¯0} pole figure, and are separated by anapproximately 85° angle in the {0001} pole figure (i.e. the twinning angle associatedwith extension twinning). In contrast, common orientations in the {112¯0} pole fig-ure are much less common in the recrystallized twins. The orientation relationshipbetween recrystallized grains and twins will be discussed in further detail in the nextsection.The lack of recrystallization in extension twins has been previously noted in theliterature. In this case it is believed that extension twins are able to thicken to accom-modate strain. This contrasts with the behaviour of contraction and/or contraction-114Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Nd(a) Pole figures (b) Colour guideFigure 6.26: (a) Pole figure showing the orientation of grains in the portion ofthe sample shown in Figure 6.25. (b) Guide to pole figure colouration. Redcorresponds to the parent grain, dark blue to extension twins, and light blueand green to recrystallized grains belonging to former contraction twins.extension twins where re-orientation leads to geometric softening of the basal slipsystem leading to profuse slip in the interior of the twin [54,105].The second location where recrystallization was identified to occur was at thesolutionized grain boundaries, as is shown in Figure 6.20. As noted above, thesegrain boundaries are also effective at halting the migration of newly formed grainsowing to the presence of β precipitates. Grain boundaries have been previouslyidentified as favourable nucleation sites in AZ31 deformed in compression and rolling[10, 13, 53]. However, the nuclei that form at grain boundaries typically maintaina basal orientation, and therefore do not weaken the texture [53]. An example ofgrain boundary nucleation was provided by Ion et al. [111] who studied dynamicrecrystallization of a Mg-Be alloy. This too was attributed to the grain boundariesundergoing a higher degree of deformation than the interior of the grains [111]. Mostrecently, Martin et al. have directly measured high levels of strain amplification ofup to 5 times the macroscopically imposed strain in tension [26] and ten times themacroscopically imposed strain in plane strain compression [34] in the vicinity of somegrain boundaries during tension [26] and plane strain compression [34].115Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%NdFigure 6.27: Normal direction IPF map with overlaid IQ data showing recrys-tallization at a grain boundary in a sample recrystallized at 350‰ for onehour.Finally, perhaps the most significant microstructural change between the as-deformed microstructure and the microstructure present after annealing for 1 hourat 350°C is the lack of evidence for the shear bands observed in the as-rolled state.Regions of the sample that appear to be comprised of recrystallized shear bands arehighlighted in Figure 6.28a. The shear bands were identified from the GOS maps,where they appeared as clusters of recrystallized grains aligned at roughly 45° to therolling direction.(a) IPF + IQ map (b) IQFigure 6.28: (a) Normal direction IPF map with overlaid IQ data showingshear band obscuring recrystallized grain boundary. (b) IQ map showinglocation of formed grain boundaries (solid black line) and regions where theboundaries have been partially or fully obscured (dashed lines).116Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%NdWhile the prior solutionized grain boundaries are easily recognizable, due to thepresence of closely spaced β precipitates, in maps such as in Figure 6.28, they donot appear to cross the recrystallized region identified as coming from a shear band.This would be consistent with the very large strains in the shear bands (as large as10 times the macroscopically imposed strain according to the observations of Martinet al. in commercially pure Mg [34]) breaking up the prior grain structure, and alongwith it the contiguous layer of β precipitates. The combination of very large plasticstrains, a high density of high angle (i.e. twin) boundaries and the breaking up of theβ precipitates would all favour recrystallization in these shear bands.The prevalence of recrystallization in shear bands is coherent with several reportsfrom the literature. Chun and Davies noted dynamic recrystallization occurred muchmore readily within shear bands in hot rolled AZ31 [39] than within non-shear bandedregions. Sandlo¨bes et al. found that strain localization within shear bands in pureMg was intense enough to lead to room temperature dynamic recrystallization [7].While the alloy discussed here does not undergo room temperature dynamic recrys-tallization, the observations of Chun and Davies and Sandlo¨bes et al. [7, 39] supportthe notion that shear bands can undergo rapid recrystallization.While in this section the focus has been on identifying regions that do recrystallize,it is notable how many large regions appear to contain few recrystallization nuclei;this appears particularly true for the interior of the deformed grains that show fewcontraction twins (Figure 6.29). It is possible that the level of plastic deformation inthese regions is too low to allow for the easy formation of new nuclei. Indeed, justas large strains were measured within shear bands, in regions outside of shear bandsMartin et al. [34] showed shear strains close to zero in other parts of the microstruc-ture. This would help to explain the continued appearance of highly recovered butunrecrystallized grains even after annealing at 450°C for one hour, such as was shownin Figure 6.17. The importance of recovery as a mechanism for softening will be117Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Nddiscussed in more detail in the next section.Figure 6.29: Example of grain showing solely extension twins (linear blue fea-tures) where no recrystallization has occurred in the interior of the grain.6.5.3 SummaryRecrystallization in samples aged at 400‰ occurs in a similar manner to Mg-0.6wt.%Nd.Thus, the strong effect of Nd on recrystallization [5] does not appear to be from thepresence of pre-existing precipitates prior to deformation. In the samples studied theorigins of the twins which give rise to recrystallized grains is obscured, with this beingstudied in further detail in the next section.6.6 Annealing of samples solutionized or aged at190°C before deformationThe experiments on the samples aged at 400‰ showed that the material containeda relatively stable distribution of β precipitates. Recrystallization in rolled samplesthat were solution treated or aged to form β′′ are expected to be more complex. Thisis because the precipitation of the β phase is expected to overlap with recovery andrecrystallization. For the aged 190‰ samples, the β phase is formed following thedissolution of the β′′ phase as described in Section 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%NdIn Chapter 5 it was shown that 50% of the precipitation of the β phase is achievedin less than 10 minutes at 350‰ and 400‰, while in the section above it was shownthat recrystallization commences in under 30 minutes at 350‰, and under 1 minuteat 400‰. These results, qualitatively consistent with the reports from Rohklin [5],point to an increasing possibility for precipitation to occur ahead of recrystallizationat lower temperatures.As a starting point, the temperature dependent evolution of the Vickers hardnessof the rolled, solutionized and aged 190‰ samples are shown in Figures 6.30a and6.30b. Based on the comments made above, it was expected that the softening ofthe material would be strongly retarded by precipitation leading to materials thatretained their strength for longer times compared to those aged at 400‰, as has beenseen in some aluminum alloys (e.g. [112]). Surprisingly, it was found that all of thematerials, including those aged at 400‰, eventually softened to similar values, thisbeing the same as that of the aged 400‰ material before deformation, as is shownin Figure 6.30c. The hardness in all three cases begins to converge after less than 10minutes of annealing, and the hardness of all three samples converges to the sameconstant value after four hours.(a) Solutionized (b) Aged 190‰ (c) 350‰Figure 6.30: Vickers hardness during annealing: (a) Solutionized samples, (b)samples aged at 190‰ and (c) all samples recrystallized 350‰The hardness of the samples aged at 190‰ drops more rapidly than the hardnessof the solutionized samples. This is consistent with the results of Section 6.2.3 that119Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Ndshowed that the metastable precipitates present after aging at 190‰ dissolve rapidlybefore stable β precipitates form. While both sets of hardness data exhibit softeningfrom the loss of Nd in solid solution in addition to recrystallization (making determi-nation of the fraction transformed difficult from hardness alone), the similarities inthe final hardness values to those seen in the fully annealed aged 400‰ samples givesthe impression that these samples have fully recrystallized.6.6.1 EBSD observationsWhile the softening response shown in Figure 6.30 could be interpreted to suggest asimilar evolution of the microstructure in all three materials, the IPF maps show thatthis assumption is not true. Figures 6.31a and 6.31b show the IPF maps for samplesannealed at 350‰ for 16 hours, corresponding to the last data points in Figure 6.30c.While the microstructures of the solutionized and aged 190‰ samples are similar toeach other, they are markedly different from the sample aged at 400‰.Using the GOS analysis described above, the fraction recrystallized was deter-mined for these three materials after 16 hours of annealing at 350‰. The solutionizedsample was found to be 19% recrystallized, while the sample aged at 190‰ was foundto be 27% recrystallized. This should be contrasted with the sample aged at 400‰where it was shown above that the fraction recrystallized was 89%. Thus, unlike whathas been presented in the past (see e.g. [48]) the evolution of hardness in Mg-Nd al-loys does not appear to be a good predictor of fraction recrystallized. The continuedsoftening of the solutionized and aged 190‰ samples suggests that recovery can besignificant in these materials, with this being a topic that will be returned to below.6.6.2 Effect of precipitates on recrystallizationThe relationship between precipitation and the deformed microstructure is clearlyevidenced from BSE images. Figure 6.32b and shows BSE images of samples annealedat 350‰ for 16 hours that were solutionized and aged at 400‰ prior to rolling.120Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Nd(a) Solutionized (b) Aged 190‰(c) Aged 400‰ (d) KeyFigure 6.31: Normal direction IPF maps of samples annealed at 350‰ for 16hours.The spatial distribution of the precipitates is vastly different, with the solutionizedsample showing precipitation along features formed by deformation, particularly twinboundaries. The sample aged at 400‰, in contrast, shows profuse precipitation alonggrain boundaries but a relatively uniform precipitation occurring within the grains asdescribed above.The prevalence of precipitation on the deformed microstructure was confirmedvia TEM observations made on the solutionized sample after rolling and annealing at121Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Nd(a) Solutionized (b) Aged at 400‰Figure 6.32: BSE images showing (a) profuse precipitation along the deformedmicrostructure in a sample solutionized before cold rolling and annealing at350‰ for 16 hours. Arrows point to examples of precipitation along twinboundaries, and (b) BSE of a sample aged at 400‰ before cold rolling andannealing at the same time and temperature showing no precipitation ontothe deformed microstructure.350‰ for 16 hours (Figures 6.33-6.34). In the matrix in Figure 6.33 one can see thepresence of β1 precipitates which seem to be interacting with individual dislocations.These precipitates are believed to be the β1 phase due to their alignment along the〈112¯0〉 directions and the relatively high temperature they formed at [62]. It is difficultto determine whether precipitation has occurred on these dislocations or whether thedislocations have moved and been blocked by the precipitates. The microstructuredoes, however, appear to be well recovered with dislocations organized into relativelylow energy configurations [11]. The picture changes, however, when one views theprecipitate state close to boundaries. Figure 6.34 shows a low magnification view of agrain boundary where profuse precipitation of the β1 and β phase can be seen. Alsoseen in this image are a few large particles coming from casting (cf. Section 5.2.1).Moving away from the boundary one can see a precipitate free zone followed by theappearance of the β1 phase.122Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Nd(a)Figure 6.33: TEM image of Mg-2.8Nd solutionized, deformed, and annealed at350‰ for 16 hours showing fine precipitates and a recovered subgrain struc-ture when view along the [0001]|Mg direction. Arrows point to dislocationswhich have been blocked by β1 precipitates.In some cases it is possible to see regions where recrystallization nuclei have beenonly partially pinned by precipitates (Figure 6.35). The nuclei are able to growparallel to the length of the twins more easily than they are able to bulge out of thethickness of twin, leading to a banded structure. This indicates that precipitates thatform within twins are less effective at pinning grains than the precipitates that format twin boundaries. This could be indicative of very rapid precipitation along theboundaries followed by slower precipitation away from them.123Chapter6.TheEffectofPrecipitateStateonRecrystallizationinMg-2.8wt.%NdFigure 6.34: Transmission electron micrograph of a grain boundary cold rolled Mg-2.8Nd solutionized before annealingat 350‰ for 16 hours. Examples of β and β1 precipitates as well as the large particles present after casting arehighlighted.124Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Nd(a) (b) (c)(d) (e)Figure 6.35: Solutionized sample recrystallized at 350‰ for 16 hours showinggrowth of recrystallized grains preferentially along the length of the twin:(a) normal direction IPF map, (b) IQ map, (c) GOS maps, (d) guide tocolours in the IPF map, and (e) guide to colours in the GOS map.6.6.3 Origins of recrystallization nucleiComparing the partially recrystallized microstructures shown in Figures 6.31a and6.31b to the partially recrystallized microstructures obtained after annealing the rolledaged 400‰ samples for 1 hour at 350‰ reveals many similarities. In order to look inmore detail at mechanisms of recrystallization the microstructure evolution at 350‰for the previously solutionized as well as the aged 190‰ samples will be followed. Themicrostructural evolution of the aged 190‰ samples always appeared qualitatively thesame as the solutionized sample.Figure 6.36 shows IPF maps and GOS maps for the solutionized and aged 190‰material following rolling and annealing at 350‰ for 1 hour. These should be com-pared with the IPF maps for the aged 400‰ sample annealed under the same condi-125Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Nd(a) Solutionized, ND IPF (b) Aged 190‰, ND IPF (c)(d) Solutionized GOS (e) Aged 190‰ GOS (f)Figure 6.36: Normal direction IPF maps showing crystallographic orientation,and GOS maps showing recrystallized grains in samples recrystallized at350‰ for one hour.tions in Figure 6.24. In this case, there is relatively little change in the microstructurebetween 1 hour and 16 hours of annealing. From the GOS maps the recrystallizedfractions were found to be 8% for the solutionized sample and 13% for the aged 190‰sample after one hour. As in the aged 400‰ samples, evidence of recrystallizationalong shear bands can be seen (Figure 6.37). As in the aged 400‰ case this has tobe inferred from the geometry of the recrystallized bands rather than from any di-rect quantitative measurement as recrystallization is complete in these narrow bands126Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Ndcrossing several grains. Consistent with reports from the literature [7, 39,49], recrys-tallization within these shear bands is very rapid, allowing for the recrystallization toproceed here before precipitation can block migration of high angle boundaries.(a) ND IPF map (b) GOS map(c) Key (d) KeyFigure 6.37: Recrystallization within a shear band in Mg-2.8wt.%Nd solution-ized before annealing at 350‰ for one hour: (a) Normal direction IPF map,(b) GOS map.Clear evidence for recrystallization within twins can also be found in Figures 6.38athrough 6.38c. As in the aged 400‰ case, extension twins appear to be unfavourablesites for recrystallization, with clear evidence of extension twins devoid of recrystal-lization nuclei being apparent for up to 16 hours of annealing. Extensive nucleationof new grains within double twins, however, can be found. In comparison to the127Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Ndresults shown for the aged 400‰ case where no direct evidence of the prior contrac-tion/double twins could be found, here several regions could be found where newgrains only partially filled prior twins allowing for the twins to be unambiguouslyidentified as double twins, these being identified by their misorientation with thesurrounding matrix.(a) Normal direction IPF (b) GOS(c) Normal direction IPF (d) GOS(e) IPF key (f) GOS keyFigure 6.38: Examples of twins which have partially recrystallized. (a-b) Solu-tionized, annealed 1 hours at 350‰. (c-d) Solutionized, annealed 16 hoursat 350‰.Little evidence could be found for recrystallization within contraction twins. Itis entirely possible that contraction twins are infrequent in these samples. Indeed,128Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%NdFigure 6.10a shows that a smaller fraction of misorientation angles in the solutionizedsample are associated with contraction twins than with double twins. However, duringrolling of basally textured Mg, contraction twinning reorients the grain in a waywhich is then favorable for double twinning [17]. Thus, it is possible that most of thecontraction twins have double twinned during deformation, thus giving the impressionthat they rarely occur.The new grains which nucleated from twins were observed to have a non-randomorientation. Figures 6.39 shows an example of double twins in a solutionized samplethat was recrystallized at 350‰ for one hour, while Figure 6.40 shows double twins ina sample aged at 190‰ and recrystallized at 350‰ for one hour. In these figures, anexample of the untwinned portion of the grain is highlighted in black. Unrecrystal-lized double twins (highlighted in red and bounded by yellow lines) were determinedfrom their misorientation angle and axis relative to the matrix. Furthermore, in thepole figures in Figures 6.39b and 6.40b, it can be clearly seen that these twins sharea common rotation axis on the {112¯0} pole figures, and the twins are within approx-imately 35° of the parent grain in the (0001) pole figures. However, the orientationrelationship between the recrystallized grains (highlighted in green) and either thematrix or the double twin are unclear. While the newly recrystallized grains areclearly within approximately 55° of both, no clear orientation relationship could befound between these grains and the still-deformed grains and twins. This is similarto the results of Li et al., who found that no clear orientation relationships betweenrecrystallized grains and the matrix could be found [52], but that the orientation ofthe new grains corresponded more closely to that of the parent twin than to eitherthe matrix or to a randomized texture. The presence of multiple nuclei within twinshas been observed in the literature [52,53], and has been attributed to the formationof double twins within contraction twins leading to the presence of high angle bound-aries [105]. Furthermore, these results are consistent with the results of the previous129Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Ndsection, where the origins of the recrystallized twins in the aged 400‰ sample couldnot be conclusively determined.(a) (b)Figure 6.39: Recrystallized twins in a solutionized sample annealed at 350‰ forone hour. Black corresponds to the parent grain, red to unrecrystallizedtwins, and green to recrystallized twins. Yellow indicates a double twinboundary.(a) (b)Figure 6.40: Recrystallized twins in a aged 190‰ sample annealed at 350‰ forone hour. The color scheme is the same as in the above image, with theaddition of a blue grain showing a contraction twin remnant.The one feature missing from these cases that was observed in the aged 400‰ caseis evidence for nucleation of new grains along grain boundaries. In the cases where newgrains could be found in proximity to a grain boundary they were always associatedwith the presence of a contraction or contraction-extension double twin. The lack of130Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Ndnucleation along grain boundaries may help to partially explain the higher level ofrecrystallization in the aged 400‰ sample annealed for 1 hour at 350‰ compared tothe solutionized or aged 190‰ samples annealed under the same conditions given thesimilarity in terms of recrystallization on shear bands and contraction/double twins.These results suggest a hierarchy of the potency for the nucleation of recrystal-lization. Recrystallization in shear bands occurs most readily, followed by recrystal-lization within contraction and double twins. Finally, nucleation at grain boundariesappears to be the slowest of the three mechanisms. In this interpretation it wouldappear that nucleation within shear bands can occur prior to extensive precipitationwhile nucleation in twins occurs in competition with precipitation, thus leading tothe eventual blocking of growing nuclei. The rapid recrystallization in shear bandsappears consistent with the previously noted ease of recrystallization, even at roomtemperature [7].6.6.4 Recrystallization at 400°C and 450°CRecrystallization at 400‰ and 450‰ of the solutionized and aged 190‰ samples wasstudied to further explore the interaction between precipitation and recrystallization.While precipitation at 400‰ is nearly as rapid as at 350‰ (c.f. Figure 5.9), recrys-tallization is expected to be more rapid due to the higher annealing temperature.Samples were predominantly studied at one hour of annealing in order to comparethe competition between precipitation and recrystallization in greater detail.IPF maps of the solutionized and aged 190‰ samples annealed at 400‰ for onehour are shown in Figures 6.41a and 6.41b, while GOS maps with twin boundaries areshown in Figures 6.41d and 6.41e. Both samples are 25% recrystallized after one hour,which is two to three times the amount reported in the samples recrystallized at 350‰for one hour. While increasing the temperature clearly increases recrystallization, itdoes not alter recrystallization sites. While there are fewer unrecrystallized twin131Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Ndfragments remaining, the GOS maps show that recrystallization still occurs primarilyin shear bands (Figure 6.42) and double twins (Figure 6.43). No evidence could befound of recrystallization at grain boundaries, indicating that precipitate pinning isstill effective at blocking this type of nucleation site at this temperature.(a) Solutionized (b) Aged 190‰ (c) Key(d) Solutionized (e) Aged 190‰ (f) KeyFigure 6.41: Normal direction IPF maps and GOS maps of samples recrystal-lized at 400‰ for one hour.Recrystallization kinetics at 450‰ were found to be very rapid, with 88% of theaged 190‰ sample recrystallizing within one hour. The IPF map shown in Figure6.44a shows that the microstructure is very similar to that of the aged 400‰ sam-ple recrystallized at the same time and temperature, including the presence of grains132Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Nd(a) ND IPF map (b) GOS mapFigure 6.42: Recrystallized shear band in rolled sample aged at 190‰ andannealed at 400‰ for one hour. Colours are the same as those shown inFigure 6.41.(a) ND IPF map (b) GOS mapFigure 6.43: Examples of recrystallization in double twins in samples aged at190‰ prior to deformation, and annealed at 400‰ for one hour. Coloursare the same as those shown in Figure 6.41.which failed to recrystallize. This fraction recrystallized is similar to what was seen inthe aged 400‰ sample, indicating that precipitation has little impact on the recrys-tallization at this temperature. Indeed, Figure 6.44b shows an image quality mapof the sample showing that while there are precipitates present, they do not havethe same proclivity towards the deformation induced boundaries as in the samplesannealed at lower temperatures.From these results it would appear that increasing annealing temperature de-creases the ability of precipitates to pin the microstructure. Slower precipitationkinetics due to the lower driving force for precipitation (cf. the TTT diagram in133Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Nd(a) Normal direction IPF map (b) IQ map (c) KeyFigure 6.44: (a) Inverse pole figure and (b) image quality map of aged 190‰Mg-2.8wt.%Nd rolled and recrystallized at 450‰ for one hour.Figure 5.9) allow recrystallization nuclei to form and grow before precipitates caneffectively block the migration of moving grain boundaries.6.6.5 Recovery during annealingA recurring observation in the recrystallized samples is that regardless of aging state,annealing time, and annealing temperature, there are always grains which fail to re-crystallize. The most obvious example of this is the solutionized/aged 190‰ samplesannealed at 350‰ for 16 hours, where up to 75% of the microstructure fails to recrys-tallize. This is particularly interesting in light of Vickers hardness of these samplesbeing nearly identical to that of the aged 400‰ sample which fully recrystallizedunder the same aging conditions.The Vickers hardness measurements during recrystallization show that the so-lutionized and aged 190‰ samples continue to soften (by approximately 50 MPa)during annealing at 350‰ between 1 and 16 hours despite only a modest increase (ofapproximately 10%) in the fraction recrystallized. In comparison, the entire hardnessloss of the aged 400‰ sample was only approximately 100 MPa. A portion of thissoftening may be attributed to precipitation still occurring after one hour of anneal-134Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Nding. However, during aging of an undeformed sample at 400‰ (c.f. Section 6.2.2),the hardness of the sample remained constant during this time period, indicating thatthe loss of Nd from solid solution is unlikely to be responsible for this softening.Berkovich hardness measurements on the samples annealed at 350‰ for 16 hoursconfirmed that the hardness of the samples in all three aging states was nearly identi-cal, as is summarized in Table 6.2. Furthermore, the cumulative distributions shownin Figure 6.45 are nearly identical, particularly in comparison to the cumulative dis-tributions of the cold rolled samples which are also shown. This is surprising giventhe large differences in microstructures. These results indicate that recovery is highlyeffective at removing stored energy during annealing of this alloy. In the work ofLevinson et al., it was noted that recovery caused softening at the beginning of re-crystallization in AZ31 samples, and further found that samples believed to be fullyrecrystallized still had 20% of the grains containing high internal misorientation [53].This was also observed by Zou et al. using hardness measurements in pure Mg [48].Table 6.2: Berkovich hardness of samples annealed at 350‰ for 16 hours.Sample Mean Hardness Median Hardness Width N(MPa) (MPa) (MPa)As solutionized 695 679 239 269Aged 190‰ 689 665 292 203Aged 400‰ 651 633 286 235There are several potential explanations for the strong similarities in the Berkovichhardness distributions of the samples. The first can be related back to the hetero-geneous deformation that these samples undergo. There are regions outside of shearbands that undergo very little deformation, and the stored energy of these regionscould be insufficient to drive recrystallization. This may be consistent with the resultsof Martin et al. [26], who found low strains in the center of grains, which in this workare the regions which are the least prone to recrystallizing. It could also be the case135Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%NdFigure 6.45: Cumulative distributions of Berkovich hardness of the samplesannealed at 350‰ for 16 hours. The distributions of the cold rolled samplesare shown for comparison.that the interiors of grains do not contain enough dislocations capable of arranginginto mobile high angle grain boundaries. Misorientation profile traces across thesegrains show a continuous change in orientation across the grain (cf. Figure 6.18), withno sharp misorientations which would indicate a high angle grain boundary capableof forming a nucleus. Indeed, work by Honeycombe et al. found that single crystalsof cadmium (a hcp material) could not recrystallize when they were deformed on onlyone slip system [113]. Dislocations in these grains may then be able to recover with-out generating high angle grain boundaries due to a lack of geometrically necessarydislocations which cause the misorientation gradients within grains.6.7 SummaryIn this chapter, Mg-2.8wt.%Nd has been studied starting from choosing initial agingconditions, to studying the effect of precipitates on the deformed state, to finally ex-ploring the effect of prior aging condition on recrystallization. While recrystallizationin binary Mg-Nd alloys has been briefly explored in the literature (i.e. [5, 14]), this136Chapter 6. The Effect of Precipitate State on Recrystallization in Mg-2.8wt.%Ndwork found that simultaneous precipitation plays a stronger role in retarding staticrecrystallization than has ever been previously noted.ˆ Nd has the strongest effect on recrystallization when there is simultaneous pre-cipitation during annealing, such as in the solutionized and aged 190‰ samples.At 350‰ recrystallization occurs on a similar timescale to precipitation, leadingto stagnation.ˆ When precipitates are present before deformation, such as those in the aged400‰ sample, their impact on recrystallization kinetics is minimized. Whilethe pre-existing stable precipitates may have some role in limiting the finalgrain size, they do not impede recrystallization as they are unable to effectivelypin migrating grain boundaries.ˆ Nd does not fundamentally alter nucleation sites. EBSD analysis of the partiallyrecrystallized microstructure found that nucleation sites were predominantlydouble twins and shear bands, with the occasional grain boundary. These sitesare the same as those observed previously in the literature [10,13,48,52–54].ˆ Finally, there is a hierarchy of nucleation sites present after deformation, interms of their potential to recrystallize. Shear bands recrystallize fastest, fol-lowed by contraction/double twins. When there are no impediments to recrys-tallization such as simultaneous precipitation, recrystallization will occur alonggrain boundaries. When there are no nucleation sites, or nuclei are pinned, themicrostructure will recover instead of recrystallizing.137Chapter 7Conclusions and Future Work7.1 ConclusionsWhen work on this thesis first began, there were many unknown aspects regard-ing the recrystallization of Mg-Nd alloys. Static recrystallization had never beensystematically explored, and mention of the interaction between precipitation andrecrystallization in these alloys was limited to a single paragraph in the literature [5].As it received so little attention in the literature, it thus came as a surprise that theannealed microstructure could be so dramatically altered by changing the precipitatestate.Precipitation was studied in Mg-2.8wt.%Nd and compared to results in the lit-erature. It was confirmed that precipitation is rapid near the recrystallization starttemperature noted in the literature [5]. These results were used to construct a TTTcurve that can be used to find the fraction precipitated as a function of aging time andtemperature. Furthermore, precipitation kinetics in this alloy were linked to the pres-ence of a concentration distribution within the sample that needed to be accounted forbefore precipitation kinetics could be understood. Finally, it was found that precipi-tation occured in a highly heterogeneous manner, with precipitation occuring rapidlyat grain boundaries and onto the deformed microstructure.Studying the recrystallization behavior yielded unforeseen results, with annealingbehavior being highly entwined with the initial precipitate state. Annealing under138Chapter 7. Conclusions and Future Workcircumstances that lead to concurrent precipitation created a competition betweenthe growth of recrystallization nuclei and precipitates pinning grain boundaries. Thishas not previously been observed during static recrystallization in Mg alloys. At oneextreme, when precipitation won out, recrystallization would stagnate (e.g. in the as-solutionized and pre-aged 190‰ samples annealed at 350‰). At the other end of thespectrum, recrystallization with minimal concurrent precipitation lead to a uniformequiaxed microstructure after annealing, such as pre-aging the samples at 400‰.Despite these differences in the final microstructure, Nd was not found to fun-damentally alter nucleation sites or the annealed texture in these samples. Doubletwins and shear bands remained the most common nucleation sites, as well as grainboundaries in the samples pre-aged at 400‰. As the recrystallized nuclei typicallymaintained an orientation spread within 55° of the parent twin, recrystallization weak-ened but did not randomize the texture. It is clear that in circumstances where anequiaxed, fully recrystallized microstructure is desired, concurrent precipitation inthis system should be avoided.It was also found that recovery was able to soften the samples when recrystalliza-tion was pinned by precipitates. In the samples studied here, recovery could obscurethe differences between recrystallized and unrecrystallized samples when recrystal-lization kinetics were measured with Vickers hardness. While this has been observedto a small degree in AZ31 [105], this indicates that tracking the recrystallized frac-tion in Mg solely with hardness is not practical due to the potential for grains to berecovered instead of recrystallized.The results of this thesis provide new insights into how the microstructure andproperties of magnesium alloys could be tailored. In this work, two extremes ofprecipitation were studied: Either all precipitation was nearly complete before an-nealing, or no precipitation occurred before annealing. This lead to microstructureswhich could either fully recrystallize at 350‰ or completely stagnate at this temper-139Chapter 7. Conclusions and Future Workature. One could imagine that by tailoring the precipitate state before deformationthat the degree of recrystallization could be tailored too. If recovery could also becontrolled, this could lead to microstructures with desirable properties such as im-proved resistance to grain growth at high temperatures, or possibly creep resistance.Furthermore, this use of precipitation to control the annealed microstructure presentsa processing method that could potentially be replicated with alloying additions thatare less expensive than Nd.7.2 Future workThe Mg-2.8wt.%Nd alloy studied here highlights a new avenue for tailoring the mi-crostructures of Mg alloys through controlled precipitation and annealing. In thissystem, it was found that Nd was ineffective at halting recovery of deformed grains.This led to samples which softened during annealing despite failing to recrystallize.If an alloying addition to Mg could be found that precipitated in such a way as tostagnate recrystallization and also halt recovery (similar to what has been seen inthe Al-Sc system [112]), it may be possible to design magnesium alloys with greatlyenhanced high temperature creep resistance.Secondly, the precipitation model presented in Chapter 5 depends on a number ofassumptions due to lack of experimental evidence. The most crucial of these was thediffusivity of Nd in Mg, which has never been measured experimentally. Furthermore,other factors such as the transition between metastable phases and the resistivitymeasurements at low aging temperatures being affected by scatter made modeling ofprecipitation kinetics difficult. Further studies of diffusion and precipitation kineticswould clarify these matters.140Bibliography[1] A. Deschamps and Y. Brechet. Influence of predeformation and ageing of anAl-Zn-Mg alloy–II. modeling of precipitation kinetics and yield stress. ActaMaterialia, 47(1):293 – 305, 1998. (Cited on pages x, 68, 70, 75, 76, 86,and 152.)[2] GM pioneers use of lightweight magnesium sheet metal, 2012. (Cited onpage 1.)[3] International Magnesium Association. IMA 2014 Awards of Excellence andEnvironmental Responsibility Award Highlight Advances in MagnesiumTechnology, Processes and Products. January 30th, 2015.(Cited on page 1.)[4] F. Zarandi and S. Yue. Magnesium sheet; challenges and opportunities. InMagnesium Alloys - Design, Processing and Properties. InTech, 2011. (Citedon page 1.)[5] L. L. Rokhlin. Magnesium alloys containing rare earth metals: structure andproperties, volume 3 of Advances in metallic alloys. Taylor & Francis, London,2003. (Cited on pages 1, 2, 3, 12, 20, 21, 22, 23, 24, 25, 26, 30, 31, 32, 33,49, 50, 53, 56, 58, 61, 68, 85, 87, 89, 92, 101, 118, 119, 136, and 138.)[6] J. Hirsch and T. Al-Samman. Superior light metals by texture engineering:Optimized aluminum and magnesium alloys for automotive applications. ActaMaterialia, 61(3):818–843, 2013. (Cited on pages 1, 3, 12, 14, and 95.)[7] S. Sandlo¨bes, S. Zaefferer, I. Schestakow, S. Yi, and R. Gonzalez-Martinez.On the role of non-basal deformation mechanisms for the ductility of Mg andMg-Y alloys. Acta Materialia, 59(2):429–439, 2011. (Cited on pages 3, 7, 9,11, 13, 14, 16, 17, 20, 100, 117, 127, and 131.)[8] M. Barnett. Twinning and the ductility of magnesium alloys: Part I.“Tension” twins. Materials Science and Engineering: A, 464(1-2):1–7, August2007. (Cited on pages 3, 4, and 6.)[9] M.R. Barnett, M.D. Nave, and C.J. Bettles. Deformation microstructures andtextures of some cold rolled Mg alloys. Materials Science and Engineering: A,386(1-2):205–211, 2004. (Cited on pages 3, 7, 9, 10, 11, 13, 14, 15, 16, 17, 20,95, and 100.)141Bibliography[10] P. Okrutny. Modelling of Recovery and Recrystallization in Magnesium Alloys.Master’s thesis, McMaster University, Hamilton, Ontario, 2011. (Cited onpages 3, 15, 16, 17, 102, 112, 115, and 137.)[11] F.J. Humphreys and M. Hatherly. Recrystallization and Related AnnealingPhenomena. Elsevier, Oxford, UK, 2nd edition, 2004. (Cited on pages 3, 15,16, 108, and 122.)[12] R.D. Doherty, D.A. Hughes, F.J. Humphreys, J.J. Jonas, D.J. Jensen, M.E.Kassner, W.E. King, T.R. McNelley, H.J. McQueen, and A.D. Rollett.Current issues in recrystallization: a review. Materials Science andEngineering: A, 238(2):219 – 274, 1997. (Cited on page 3.)[13] C. W. Su, L. Lu, and M. O. Lai. Recrystallization and grain growth ofdeformed magnesium alloy. Philosophical Magazine, 88(2):181–200, 2008.(Cited on pages 3, 15, 16, 17, 18, 102, 112, 115, and 137.)[14] K. Hantzsche, J. Bohlen, J. Wendt, K.U. Kainer, S.B. Yi, and D. Letzig.Effect of rare earth additions on microstructure and texture development ofmagnesium alloy sheets. Scripta Materialia, 63(7):725 – 730, 2010. (Cited onpages 3, 14, 31, 32, 33, 97, and 136.)[15] T. Al-Samman and X. Li. Sheet texture modification in magnesium-basedalloys by selective rare earth alloying. Materials Science and Engineering: A,528(10-11):3809–3822, 2011. (Cited on pages 3, 12, and 108.)[16] J.P. Hadorn, K. Hantzsche, S. Yi, J. Bohlen, D. Letzig, J.A. Wollmershauser,and S.R. Agnew. Role of solute in the texture modification during hotdeformation of mg-rare earth alloys. Metallurgical and Materials TransactionsA, 43(4):1347–1362, 2011. (Cited on pages 3 and 14.)[17] M. Barnett. Twinning and the ductility of magnesium alloys: Part II.“Contraction” twins. Materials Science and Engineering: A, 464(1-2):8–16,August 2007. (Cited on pages 4, 6, 114, and 129.)[18] S. R. Agnew, C. N. Tome´, D. W. Brown, T. M. Holden, and S. C. Vogel.Study of slip mechanisms in a magnesium alloy by neutron diffraction andmodeling. Scripta Materialia, 48(8):1003–1008, 2003. (Cited on page 4.)[19] F.W. Bach, M. Rodman, A. Rossberg, B.A. Behrens, and G. Kurzare.Macroscopic damage by the formation of shear bands during the rolling anddeep drawing of magnesium sheets. JOM: Journal of the Minerals, Metals andMaterials Society, 57(5):57–61, 2005. (Cited on pages 4, 7, 8, 17, and 18.)[20] P.G. Partridge. The crystallography and deformation modes of hexagonalclose-packed metals. Metallurgical Reviews, 118:169–194, 1967. (Cited onpage 4.)142Bibliography[21] A. Akhtar and E. Teghtsoonian. Solid solution strengthening of magnesiumsingle crystals—I alloying behaviour in basal slip. Acta Metallurgica,17(11):1339–1349, 1969. (Cited on page 5.)[22] A. Akhtar and E. Teghtsoonian. Solid solution strengthening of magnesiumsingle crystals—II the effect of solute on the ease of prismatic slip. ActaMetallurgica, 17(11):1351–1356, 1969. (Cited on page 5.)[23] T. Obara, H. Yoshinga, and S. Morozumi. {112¯2}〈1¯1¯23〉 slip system inmagnesium. Acta Metallurgica, 21:845–853, 1973. (Cited on page 5.)[24] S. Ando, K. Nakamura, K. Takashima, and H. Tonda. 11-22¡-1-123 ¿ slip inmagnesium single crystal,. Journal of Japan Institute of Light Metals,42(12):765–771, 1992. (Cited on page 5.)[25] B. Bhattacharya. Plastic deformation behaviour of pure Mg in the temperaturerange 4.2K-300K. PhD thesis, McMaster University, 2006. (Cited on page 5.)[26] G. Martin, C.W. Sinclair, and J.-H. Schmitt. Plastic strain heterogeneities inan Mg-1Zn-0.5Nd alloy. Scripta Materialia, 68(9):695–698, may 2013. (Citedon pages 5, 115, and 135.)[27] R. Sa´nchez-Mart´ın, M.T. Pe´rez-Prado, J. Segurado, J. Bohlen,I. Gutie´rrez-Urrutia, J. Llorca, and J.M. Molina-Aldareguia. Measuring thecritical resolved shear stresses in mg alloys by instrumented nanoindentation.Acta Materialia, 71(0):283 – 292, 2014. (Cited on pages 5 and 79.)[28] J. Koike, R. Ohyama, T. Kobayashi, M. Suzuki, and K. Maruyama.Grain-boundary sliding in AZ31 magnesium alloys at room temperature to523 k. Materials Transactions, 44(4):445–451, 2003. (Cited on page 6.)[29] P. Cizek and M. R. Barnett. Characteristics of the contraction twins formedclose to the fracture surface in Mg-3Al-1Zn alloy deformed in tension. ScriptaMaterialia, 59(9):959–962, 2008. (Cited on page 6.)[30] J. Koike. Enhanced deformation mechanisms by anisotropic plasticity inpolycrystalline Mg alloys at room temperature. Metallurgical and MaterialsTransactions A, 36(7):1689–1696, 2005. (Cited on page 6.)[31] M. R. Barnett, Z. Keshavarz, A. G. Beer, and D. Atwell. Influence of grainsize on the compressive deformation of wrought Mg-3Al-1Zn. Acta Materialia,52(17):5093–5103, 2004. (Cited on page 6.)[32] M. A. Meyers, O. Vo¨hringer, and V. A. Lubarda. The onset of twinning inmetals: a constitutive description. Acta Materialia, 49(19):4025–4039, 2001.(Cited on page 6.)143Bibliography[33] B.C. Wonsiewicz and W.A. Backofen. Plasticity of magnesium crystals.Transactions of the Metallurgical Society of AIME, 239:1422–1431, 1967.(Cited on pages 7, 9, and 20.)[34] G. Martin, H. Azizi-Alizamini, C.W. Sinclair, and W.J. Poole. Local plasticstrain heterogeneities and their impact on the ductility of Mg as revealed bydigital image correlation and EBSD. Unsubmitted manuscipe, 2014. (Cited onpages 7, 115, and 117.)[35] D.K. Sun, C.P. Chang, and P.W. Kao. Microstructural study of strainlocalization in hot compressed Mg-3Al-1Zn alloy. Materials Science andEngineering: A, 527(26):7050–7056, 2010. (Cited on page 7.)[36] S.L. Couling, J.F. Pashak, and L. Sturkey. Unique deformation and agingcharacteristics of certain magnesium-base alloys. Transactions of the ASM,51:94–107, 1959. (Cited on pages 8, 9, 10, 12, 33, and 100.)[37] TexSEM Laboratories, Incorporated. OIM analysis 6 manual. (Cited onpages 9, 43, and 95.)[38] S. Sandlo¨bes, M. Fria´k, J. Neugebauer, and D. Raabe. Basal and non-basaldislocation slip in Mg-Y. Materials Science and Engineering: A, 576:61–68,2013. (Cited on page 9.)[39] Y.B. Chun and C.H.J. Davies. Texture effects on development of shear bandsin rolled AZ31 alloy. Materials Science and Engineering: A, 556(0):253 – 259,2012. (Cited on pages 11, 12, 100, 117, and 127.)[40] I.J. Polmear. Magnesium alloys and applications. Materials Science andTechnology, 10(1):1–16, 1994. (Cited on page 12.)[41] L. L. Rokhlin. Dependence of the rare earth metal solubility in solidmagnesium on its atomic number. Journal of Phase Equilibria and Diffusion,19(2):142–145, 1998. (Cited on page 12.)[42] G. V. Raynor. The Physical Metallurgy of Magnesium and its Alloys. Serieson Metal Physics and Physical Metallurgy. Pergamon Press, New York, 1959.(Cited on page 12.)[43] I. Basu, T. Al-Samman, and G. Gottstein. Shear band-relatedrecrystallization and grain growth in two rolled magnesium-rare earth alloys.Materials Science and Engineering: A, 579(0):50 – 56, 2013. (Cited onpages 12, 14, 16, 20, and 31.)[44] R. Mishra, A. Gupta, P. Rao, A. Sachdev, A. Kumar, and A. Luo. Influenceof cerium on the texture and ductility of magnesium extrusions. ScriptaMaterialia, 59(5):562–565, September 2008. (Cited on page 13.)144Bibliography[45] N. Stanford and M. R. Barnett. The origin of “rare earth” texturedevelopment in extruded mg-based alloys and its effect on tensile ductility.Materials Science & Engineering A, 496(1-2):399–408, 2008. (Cited onpage 13.)[46] J.P. Hadorn, R.P. Mulay, K. Hantzsche, S. Yi, J. Bohlen, D. Letzig, and S.R.Agnew. Texture weakening effects in Ce-containing Mg alloys. Metallurgicaland Materials Transactions A, 44(3):1566–1576, 2012. (Cited on page 14.)[47] I. Basu and T. Al-Samman. Triggering rare earth texture modification inmagnesium alloys by addition of zinc and zirconium. Acta Materialia,67:116–133, 2014. (Cited on page 14.)[48] J. Zou and C.W. Sinclair. The relationship between microstructure, textureand static recrystallization in uniaxially compressed magnesium. InMagnesium 2009, San Francisco, 2009. (Cited on pages 15, 16, 120, 135,and 137.)[49] M.R. Barnett and N. Stanford. Influence of microstructure on straindistribution in Mg-3Al-1Zn. Scripta materialia, 57(12):1125–1128, 2007.(Cited on pages 15, 19, 100, 102, and 127.)[50] J. Zou and C.W. Sinclair. Private communications. 2009. (Cited on pages 16and 17.)[51] J. Zou, J. Jain, and C. W. Sinclair. Tracing nucleation and grain growthduring static recrystallization of pure Mg by EBSD. In Magnesium Technology2009, San Francisco, 2009. (Cited on pages 16 and 112.)[52] X. Li, P. Yang, L.-N. Wang, L. Meng, and F. Cui. Orientational analysis ofstatic recrystallization at compression twins in a magnesium alloy AZ31.Materials Science and Engineering: A, 517(1-2):160 – 169, 2009. (Cited onpages 16, 129, and 137.)[53] A. Levinson, R. K. Mishra, R. D. Doherty, and S. R. Kalidindi. Influence ofdeformation twinning on static annealing of {AZ31} Mg alloy. ActaMaterialia, 61(16):5966–5978, 2013. (Cited on pages 16, 115, 129, 135,and 137.)[54] E´. Martin, R. Mishra, and J. Jonas. Deformation structures andrecrystallization in magnesium alloys. In Magnesium Alloys - Design,Processing and Properties. InTech, 2011. (Cited on pages 16, 115, and 137.)[55] J.D. Robson, D.T. Henry, and B. Davis. Particle effects on recrystallization inmagnesium–manganese alloys: Particle-stimulated nucleation. ActaMaterialia, 57(9):2739–2747, 2009. (Cited on pages 17, 108, and 111.)145Bibliography[56] J.P. Hadorn, K. Hantzsche, S. Yi, J. Bohlen, D. Letzig, and S.R. Agnew.Effects of solute and second-phase particles on the texture of nd-containingmg alloys. Metallurgical and Materials Transactions A, 43(4):1363–1375, 2012.(Cited on page 17.)[57] M.A. Easton, M.A. Gibson, D. Qiu, S.M. Zhu, J. Gro¨bner, R. Schmid-Fetzer,J.F. Nie, and M.-X. Zhang. The role of crystallography and thermodynamicson phase selection in binary magnesium-rare earth (Ce or Nd) alloys. ActaMaterialia, 60(11):4420–4430, 2012. (Cited on pages 21, 24, 25, and 49.)[58] M. Hisa, J.C. Barry, and G.L. Dunlop. New type of precipitate inMg–rare-earth alloys. Philosophical Magazine A, 82(3):497–510, 2002. (Citedon pages 21, 22, 24, 25, 27, 56, and 65.)[59] J.P. Hadorn and S.R. Agnew. A new metastable phase in dilute, hot-rolledMg-Nd alloys. Materials Science and Engineering: A, 533(0):9 – 16, 2011.(Cited on pages 21, 22, 24, and 25.)[60] V. Kopp. Analyse et mode´lisation de tranformations de phase parpre´cipitation dans des alliages de magne´sium mode`les. PhD thesis, Universite´de Rouen, Rouen, France, 2010. (Cited on pages 21, 22, 24, 25, 26, 27, 28,30, 50, 53, 56, 58, 61, 65, 68, and 77.)[61] W. Lefebvre, V. Kopp, and C. Pareige. Nano-precipitates made of atomicpillars revealed by single atom detection in a Mg-Nd alloy. Applied PhysicsLetters, 100(14):141906, 2012. (Cited on pages 21, 22, 25, 27, 28, 30, 50, 56,and 77.)[62] K. Saito and K. Hiraga. The structures of precipitates in an Mg-0.5 at%Ndage-hardened alloy studied by HAADF-STEM technique. MaterialsTransactions, 52(10):1860–1867, 2011. (Cited on pages 21, 22, 25, 27, 28, 29,56, 65, and 122.)[63] H. Liu, Y. Gao, Y.M. Zhu, Y. Wang, and J.F. Nie. A simulation study of β1precipitation on dislocations in an Mg-rare earth alloy. Acta Materialia,77:133–150, 2014. (Cited on pages 21, 22, 25, and 29.)[64] H. Okamoto. Mg-Nd. Journal of Phase Equilibria and Diffusion,28(4):405–405, 2007. (Cited on pages 21 and 23.)[65] S. Gorsse, C.R. Hutchinson, B. Chevalier, and J.-F. Nie. A thermodynamicassessment of the mg-nd binary system using random solution and associatemodels for the liquid phase. Journal of Alloys and Compounds,392(1-2):253–262, 2005. (Cited on page 21.)[66] S. Brennan, K. Bermudez, and Y. Sohn. Intermetallic growth andinterdiffusion in the Mg-Nd system. Mg2012: 9th International Conference onMagnesium Alloys and their Applications, pages 417–422, 2012. (Cited onpages 21 and 22.)146Bibliography[67] T.J. Pike and B. Noble. The formation and structure of precipitates in adilute magnesium-neodymium alloy. Journal of the Less Common Metals,30(1):63–74, 1973. (Cited on pages 22, 25, 26, 27, 28, 30, 49, 56, and 89.)[68] S. Delfino, A. Saccone, and R. Ferro. Phase relationships in theneodymium-magnesium alloy system. Metallurgical and MaterialsTransactions A, 21(8):2109–2114, 1990. (Cited on pages 22, 24, 57, and 71.)[69] E. Aghion and G. Levy. The effect of Ca on the in vitro corrosion performanceof biodegradable Mg-Nd-Y-Zr alloy. Journal of Materials Science,45(11):3096–3101, 2010. (Cited on page 22.)[70] Y.-B. Kang, L. Jin, P. Chartrand, A.E. Gheribi, K. Bai, and P. Wu.Thermodynamic evaluations and optimizations of binary mg-light rare earth(La, Ce, Pr, Nd, Sm) systems. Calphad, 38:100–116, September 2012. (Citedon pages 24, 54, and 81.)[71] S. H. Safi-Naqvi, W. B. Hutchinson, and M. R. Barnett. Texture andmechanical anisotropy in three extruded magnesium alloys. Materials Scienceand Technology, 24(10):1283–1292, 2008. (Cited on pages 24, 32, 53, and 99.)[72] A.A. Nayeb-Hashemi and J.B. Clark. The Mg-Nd system(magnesium-neodymium). Bulletin of Alloy Phase Diagrams, 9(5):618–623,1988. (Cited on page 25.)[73] M. Bamberger, G. Atiya, S. Khawaled, and A. Katsman. Comparison study ofmicrostructure and phase evolution in Mg-Nd- and Mg-Gd-based alloys.Metallurgical and Materials Transactions A, 45(8):3241–3253, 2013. (Cited onpage 29.)[74] V. Kopp, W. Lefebvre, and C. Pareige. Determination of the Mg-rich phaseboundary of the binary Mg-Nd phase diagram by means of atom probetomography. Journal of Phase Equilibria and Diffusion, 32(4):298–301, 2011.(Cited on pages 39 and 50.)[75] O. Engler and V. Randle. Introduction to Texture Analysis: Macrotexture,Microtexture, and Orientation Mapping. CRC Press, 2nd edition, 2009. (Citedon page 42.)[76] Sigmatest Foerster User Manual. (Cited on pages 46 and 53.)[77] Eddy current inspection. In Metals Handbook Desk Edition, pages 1275–1281.ASM International, 1998. (Cited on page 46.)[78] B. Rother, A. Steiner, D. A. Dietrich, H. A. Jehn, J. Haupt, and W. Gissler.Depth-sensing indentation measurements with Vickers and Berkovichindenters. Journal of Materials Research, 13:2071–2076, 8 1998. (Cited onpage 48.)147Bibliography[79] W.C. Oliver and G.M. Pharr. An improved technique for determininghardness and elastic modulus using load and displacement sensing indentationexperiments. Journal of Materials Research, 7:1564–1583, 6 1992. (Cited onpages 48 and 156.)[80] M.E. van Dalen, D.N Seidman, and D.C. Dunand. Creep- and coarseningproperties of Al–0.06 at.%S–0.06 at.% Ti at 300-450°C. Acta Materialia,56(16):4369–4377, 2008. (Cited on page 49.)[81] J. Royset and N. Ryum. Scandium in aluminium alloys. InternationalMaterials Reviews, 50(1):19–44, 2005. (Cited on page 49.)[82] J.L. Nichols. Orientation and temperature effects on the electrical resistivityof high-purity magnesium. Journal of Applied Physics, 26(4):470–472, 1955.(Cited on page 50.)[83] W. M. Haynes, editor. CRC Handbook of Chemistry and Physics, chapterElectrical Resistivitives of Pure Metals, pages 12–41 – 12–42. CRC Press, 94thedition, 2014. (Cited on page 51.)[84] J. Bijvoet, B. de Hon, J.A. Dekker, and G.W. Rathenau. The electricalresistivities of dilute Mg-Nd and Mg-Gd alloys. Solid State Communications,1(7):237–240, 1963. (Cited on pages 51 and 57.)[85] S. Esmaeili, D.J. Lloyd, and W.J. Poole. A yield strength model for theAl-Mg-Si-Cu alloy AA6111r. Acta Materialia, 51(8):2243 – 2257, 2003. (Citedon page 62.)[86] M.J. Sohi, W. J. Poole Poole, C. W. Sinclair, and M. Gallerneault. Thestrength of a twin-belt cast Al-Mg-Sc alloy after high temperature annealing.2014. (Cited on page 62.)[87] B. Raeisinia, W.J. Poole, and D.J. Lloyd. Examination of precipitation in thealuminum alloy AA6111 using electrical resistivity measurements. MaterialsScience and Engineering: A, 420(1–2):245–249, 2006. (Cited on pages 66and 85.)[88] M. Rosen. Eddy current analysis of precipitation kinetics in aluminum alloys.Metallurgical Transactions A, 20(4):605–610, 1989. (Cited on page 66.)[89] H.W. King. CRC Handbook of Chemistry and Physics, chapter CrystalStructures and Lattice Parameters of Allotropes of the Elements, pages 12–15– 12–18. CRC Press, 94th edition, 2014. (Cited on page 71.)[90] L. Huber, I. Elfimov, J. Rottler, and M. Militzer. Ab initio calculations ofrare-earth diffusion in magnesium. Physical Review B, 85:144301–1–144301–7,2012. (Cited on page 71.)148Bibliography[91] J. Combronde and G. Brebec. Anisotropie d’autodiffusion du magnesium.Acta Metallurgica, 19(12):1393–1399, December 1971. (Cited on page 71.)[92] P.G. Shewmon and F.N. Rhines. Rate of self-diffusion in polycrystallinemagnesium. Transactions of the Metallurgical Society of AIME, 6:1021–1025,1954. (Cited on pages 71, 72, and 73.)[93] D.S. Sholl and J.A. Sholl. Density Functional Theory: A PracticalIntroduction. Wiley-Interscience, Hoboken, NJ, USA, 2009. (Cited onpage 71.)[94] A.M. Brown and M.F. Ashby. Correlations for diffusion constants. ActaMetallurgica, 28(8):1085–1101, 1980. (Cited on pages 71 and 73.)[95] S. Ganeshan, L.G. Hector, and Z.-K. Liu. First-principles calculations ofimpurity diffusion coefficients in dilute Mg alloys using the 8-frequency model.Acta Materialia, 59(8):3214–3228, May 2011. (Cited on pages 72 and 73.)[96] S. Ganeshan, L.G. Hector, and Z.-K. Liu. First-principles study ofself-diffusion in hcp Mg and Zn. Computational Materials Science,50(2):301–307, Dec 2010. (Cited on pages 72 and 73.)[97] D. Porter and K.A. Easterling. Phase transformations in metals and alloys.Chapman & Hall, London New York, 1992. (Cited on page 72.)[98] J.D Robson. A new model for prediction of dispersoid precipitation inaluminium alloys containing zirconium and scandium. Acta Materialia,52(6):1409–c1421, 2004. (Cited on page 73.)[99] J. M. Howe. Interfaces in Materials: Atomic Structure, Thermodynamics andKinetics of Solid-Vapor, Solid-Liquid and Solid-Solid Interfaces. John Wiley &Sons, Inc., 1997. (Cited on page 73.)[100] H.S. Zurob, C.R. Hutchinson, Y. Brechet, and G. Purdy. Modelingrecrystallization of microalloyed austenite: effect of coupling recovery,precipitation and recrystallization. Acta Materialia, 50(12):3077–3094, 2002.(Cited on page 76.)[101] J. A. Yasi, L. G. Hector, and D. R. Trinkle. First-principles data forsolid-solution strengthening of magnesium: From geometry and chemistry toproperties. Acta Materialia, 58(17):5704–5713, 2010. With data (Cited on pages 78 and 79.)[102] A. C. Fischer-Cripps. Nanoindentation. Mechanical Engineering Series.Springer-Verlag, 3 edition, 2011. (Cited on pages 80, 155, 156, 157, and 158.)[103] H. Somekawa and C. A. Schuh. Nanoindentation behavior and deformedmicrostructures in coarse-grained magnesium alloys. Scripta Materialia,68(6):416–419, 2013. (Cited on page 80.)149Bibliography[104] M.R. Barnett, Z. Keshavarz, and M.D. Nave. Microstructural features ofrolled Mg-3Al-1Zn. Metallurgical and Materials Transactions A,36(7):1697–1704, 2005. (Cited on pages 95, 113, and 114.)[105] A. J. Levinson. The Role of Deformation Twinning on Strain Hardening andRecrystallization in Magnesium Alloy AZ31. PhD thesis, Drexel University,2012. (Cited on pages 95, 106, 115, 129, and 139.)[106] M.D. Nave and M.R. Barnett. Microstructures and textures of puremagnesium deformed in plane-strain compression. Scripta Materialia,51(9):881–885, 2004. (Cited on page 97.)[107] J. Jain, W.J. Poole, C.W. Sinclair, and M.A. Gharghouri. Reducing thetension–compression yield asymmetry in a Mg-8Al-0.5Zn alloy viaprecipitation. Scripta Materialia, 62(5):301–304, 2010. (Cited on page 99.)[108] J. Victoria-Hernandez, S. Yi, D. Letzig, D. Hernandez-Silva, and J. Bohlen.Microstructure and texture development in hydrostatically extrudedMg-Al-Zn alloys during tensile testing at intermediate temperatures. ActaMaterialia, 61(6):2179–2193, apr 2013. (Cited on page 103.)[109] S.I. Wright. Proceedings of the Twelfth International Conference on Texturesof Materials (ICOTOM 12), chapter Quantification of Recrystallized Fractionfrom Orientation Imaging Scans, pages 104–109. NRC Research Press, 1999.(Cited on pages 43 and 44.)[110] E. Ball and P. Prangnell. Tensile-compressive yield asymmetries in highstrength wrought magnesium alloys. Scripta Metallurgica et Materialia,31(2):111–116, 1994. (Cited on page 108.)[111] S.E. Ion, F.J. Humphreys, and S.H. White. Dynamic recrystallisation and thedevelopment of microstructure during the high temperature deformation ofmagnesium. Acta metallurgica, 30(10):1909–1919, 1982. (Cited on page 115.)[112] R. Roumina. Mechanical properties of a recovered Al-Mg-Sc alloy. PhD thesis,University of British Columbia, 2009. (Cited on pages 119 and 140.)[113] A.H. Cottrell. Dislocations and Plastic Flow in Crystals. Clarendon Press,Oxford, UK, 1953. (Cited on page 136.)[114] G. E. Dieter, Jr. Mechanical Metallurgy. Metallurgy and MetallurgicalEngineering Seriews. McGraw-Hill Book Company, 1961. (Cited on page 162.)[115] N.A. Sakharova, J.V. Fernandes, J.M. Antunes, and M.C. Oliveira.Comparison between Berkovich, Vickers and conical indentation tests: Athree-dimensional numerical simulation study. International Journal of Solidsand Structures, 46(5):1095–1104, 2009. (Cited on page 163.)150Appendices151Appendix AOverview of the Mean RadiusModelThe mean radius model was developed by Deschamps and Brechet to model pre-cipitation kinetics [1]. The model separates precipitation into two stages. The firststage takes into account the nucleation and growth of precipitates, with the growingprecipitates decreasing the matrix solute concentration. The second stage modelsprecipitate coarsening, with the solute in the matrix staying constant.The initial precipitate radius at the first timestep, R0 is calculated with:R0 =2γVatkT(A.1)The model calculates the driving force for precipitation at each time step, ∆G, inJ/m3:∆G(i) =kTVat[Cpln(CeqC(i))+ (1− Cp) ln(1− Ceq1− C(i))](A.2)The critical radius R∗(i) for a stable precipitate is calculated with:152Appendix A. Overview of the Mean Radius ModelR∗(i) = −2γ∆G(i)(A.3)The critical driving force to nucleate a precipitate of radius R∗ is ∆G∗(i):∆G∗ =16pi3γ3∆G(i)2(A.4)The frequency at which atoms will attach to the growing precipitate is describedusing β∗:β∗(i) =4piR∗(i)2DC020a4(A.5)Using the equations above, the change in the number of nuclei at each timestep,dNnuc/dt is:dNnucdt=β∗(i)Vatexp(−∆G∗kT)(A.6)The change in the radius of each precipitate nucleus at each timestep, dRnuc/dtis:dRnucdt=DR(i)C(i)− Ceqexp (R0/R(i))Cp − Ceqexp (R0/R(i))+1N(i)dNnucdt(i) (αR∗(i)−R(i)) (A.7)A precipitate with a radius exactly equal to R∗ will not grow, so the term α isused to ensure the precipitates with radius R∗(i) do grow. We have used α = 1.05.153Appendix A. Overview of the Mean Radius ModelThe transition between growth and coarsening is governed with:f(i) = 1− erf(4R(i)R∗(i)− 1)(A.8)When f = 0, the precipitates are in the growth stage, and when f = 1, theprecipitates will coarsen.During coarsening, the radius of the precipitates will change by:dRcoarsedt(i) =427Ceq1− CeqR0DR(i)2(A.9)Coarsening will cause larger precipitates to grow, while smaller precipitates willshrink and eventually disappear. The rate at which precipitates will disappear isgoverned by:dNcoarsedt=427CeqCp − CeqR0DR(i)3[R0C(i)R(i)(Cp − C(i))(34piR(i)3−N(i))− 3N(i)](A.10)At the end of each timestep, the amount of Nd in solid solution is recalculatedusing a mass balance:C(i+ 1) =C0 −4pi3N(i)R(i)3Cp1−4pi3N(i)R(i)3(A.11)154Appendix BProcessing of Berkovich HardnessDataB.1 Calculation of hardness and Young’s modulusAn example of a load-displacement curve during indentation of an Mg-2.8wt.%Ndsample can be seen in Figure B.1. Even the initial portions of the loading curvewill undergo a mixture of elastic and plastic deformation, which makes accuratelydetermining the Young’s Modulus difficult. As a result, the stiffness of the material,which is used to calculate both Young’s Modulus and hardness is calculated from theinitial portion of the unloading curve, where the material is most likely to behave ina linear-elastic manner [102].The contact stiffness, S is determined by caluclating the slope of the initial portionof the unloading curve:S =dPdh(B.1)Extrapolating the linear-elastic region to P = 0 allows the indentation contactdepth hc to be calculated. The variable hc is defined as the distance the indenterwill travel during unloading during which the indenter remains in full contact with155Appendix B. Processing of Berkovich Hardness DataFigure B.1: Typical force displacement curve for a automated microhardnessindent.the sample. This makes it possible to determine the portion of the depth of theindentation that can be attributed solely to plastic deformation [79]:hc = hmax − PmaxdPdh(B.2)The variable  is used as a geometric factor to account for simplifying assumptionsregarding the geometry of the Berkovich tip, as the calculations assume an axisym-metric tip instead of the three-sided pyramidal construction of an actual Berkovichindenter. In this work, we have used  = 0.75 in accordance with experimental resultsin the literature [102].As the indenter tip has a known geometry, the projected area of the indent, A, ofthe indent can be calculated from the indentation depth. With a Berkovich indenter,the area as a function of indentation contact depth is [102]:156Appendix B. Processing of Berkovich Hardness DataA = 24.49h2c (B.3)After determining hc and A, the hardness of the indent is determined with:H =PmaxA(mNnm2)(B.4)The hardness can be converted into units of MPa with:H =PmaxA× 109 (MPa) (B.5)The indentation hardness of metal is significantly higher than the yield stress(σy) due to the material under the indenter being constrained from deforming bythe surrounding material. In this case, we have approximated the yield stress of theindents when necessary using [102]:H ≈ 3σy (B.6)B.2 Determination of Young’s modulusThe Young’s modulus of each indent was calculated as a way of verifying the data.As there are few factors that can cause the Young’s Modulus to diverge from anarrow range of values, indents with Young’s Moduli that fell outside this range wereconsidered to be erroneous. In our analysis, all indents with Young’s Modulus whichwere not withing one standard deviation of the average of all indents in the sample157Appendix B. Processing of Berkovich Hardness Datawere discarded.The Young’s modulus is calculated by first calculating the composite modulus,Er. Er is the combined modulus of the indenter and the sample as measured at thestart of the unloading curve [102]:Er =1√A√pi2dPdh×mNnm2(B.7)Or in GPa:Er =1√A√pi2dPdh× 106(GPa) (B.8)The composite modulus is also defined as a function of the Poisson’s ratios andYoung’s moduli of the sample and indenter [102]:Er =11− ν2sEs+1− ν2iEi(B.9)Es and Ei are the Young’s Moduli for the sample and indenter respectively, whileνs and νi are the Poisson’s ratio. Values from the literature were used for νi and νs,with νi = 0.07 and νs = 0.35 for pure Mg. A value of Ei specific to the Berkovich tipused in these experiments was used, with Ei = 1141 GPa.Setting Equations B.8 and B.9 equal to each other and solving for Es yields:158Appendix B. Processing of Berkovich Hardness DataEs =1− ν2s2√A√pidPdh× 106−1− ν2iEi(GPa) (B.10)Substituting Equation B.3 for the projected area of the indenter gives:Es =1− ν2s2√24.49h2c√pidPdh× 106−1− ν2iEi(GPa) (B.11)B.3 Data processingCalculating the Young’s modulus of each indent required calculating a best fit linefor the stiffness during unloading with a sufficient number of points, all the whileensuring that the modulus was calculated solely from the linear elastic portion of theunloading curve. To further complicate calculations, there was occasionally a smallamount of scatter in the measured depth of the indenter at the beginning of theunloading curve, making it necessary to offset measurement of the unloading curve.The number of data points used to calculate the Young’s modulus, as well as theoffset from the peak of the unloading curve was systematically varied in order todetermine the effect of varying each on the calculated Young’s modulus. In addition,the R2 value for each best fit line was calculated.An example of the effects of varying the number of data points used as the offsetcan be seen in Figure B.2. This particular sample was Mg-2.8wt.% aged at 400°C,but all samples showed the same trend. Increasing the number of points used tocalculated the modulus, as well as increasing the offset causes an increase in the159Appendix B. Processing of Berkovich Hardness DataFigure B.2: An example of the effects of varying the number of data pointsand the number of points offset from the start of the unloading curve usedto calculate Young’s Modulus. The R2 values in the figure titles refers tothe correlation between Young’s modulus and hardness for all indents inthe sample. The colors of each data point correspond to the R2 value ofthe fit of the slope of the unloading curve, and the corresponding scale isto the left of each image.correlation between Young’s Modulus and hardness. This can be seen in the best fitlines and R2 values displayed in Figure B.2. There are also a few noticeable outlierswith low R2 values for the best fit of the unloading curve. Given these results, thedata was analyzed and filtered in the following ways:1. All indents with R2 < 0.95 for the slope of the unloading curve were discarded.2. All indents where the Young’s Modulus was not within one standard deviationof the average Young’s Modulus of the sample were discarded160Appendix B. Processing of Berkovich Hardness DataFigure B.3: The correlation between Young’s modulus and hardness after dis-carding outlying data points. The correlation has weakened significantly.3. The slope of the unloading curve was determined using three data points, andoffset from the peak of the unloading curve by two data points.The results of filtering the data in this way can be seen in Figure B.3. Thecorrelation between hardness and Young’s modulus has decreased significantly. Afterprocessing, the data was further analyzed in order to determine trends from heattreatment, cold rolling and annealing. Each data set was made into a histogramwith bins 25 MPa in width, and the data was normalized by dividing the numberof counts in each bin by the total number of data points. This made it possible tocompare trends across data sets. A cumulative distribution function for each samplewas calculated by summing each bin and the total of all the bins preceding it. Thewidths of the hardness distributions were calculated as being two times with thestandard deviation. In addition, the arithmetic mean and median hardness of eachsample was calculated.161Appendix B. Processing of Berkovich Hardness DataB.4 Comparison of Berkovich to Vickers hardnessThe samples were characterized after aging, deformation and recrystallization usingVickers and Berkovich hardness measurements, EBSD and BSE. The basic proceduresassociated with these techniques are described in Section 4.6 of the Methodologychapter. Vickers hardness was used to track the softening during recrystallizationannealing. Ten measurements were taken on all samples, the measurements havingbeen made on the sheet normal plane of the sample. The samples were groundafter heat treatment and polished up to a 1 µm diamond suspension before takingmeasurements.Berkovich hardness was used on a subset of samples to examine changes to thedistribution of hardness values following pre-aging, cold rolling, and recrystallizationannealing. As was shown in the previous chapter, the starting material has a hardnessdistribution arising from the distribution in solid solution content and, in the case ofaged samples, precipitation state. The Berkovich hardness measurements were ableto provide more detailed data than the Vickers hardness measurements due to thelarger number of indents per sample, although fewer samples could be analyzed.As the depth of an indent and the geometry of the indenter used can affect themeasured hardness [114], the Berkovich hardness data was plotted against the Vickershardness data for the same samples to see if the data could be correlated (Figure B.4).The Berkovich hardness measurements consistently had a larger standard deviationthan the Vickers hardness. As the Berkovich indents were systematically screened bythe slope of their unloading curves (as was described in Section 4.6.6 of the Method-ology chapter), this variation is believed to be due to the smaller indent size of theBerkovich indents (approximately 10 µm versus 50 µm per side). The small size ofthe Berkovich indents may have made the indents more sensitive to variations in themicrostructure such as proximity to twin or grain boundaries, as well as localizeddifferences in the solute concentration and precipitate state. As expected based on162Appendix B. Processing of Berkovich Hardness Datathe work of Sakharova et al. [115], a linear correlation between the Vickers Hardness(HV ) and the Berkovich hardness (HB) was found when data measured on the samesamples using the two techniques was plotted (Figure B.4). It was found that therelationship:HB = 1.41HV (B.12)gave the best fit agreement to this data.Figure B.4: Comparison between Berkovich and Vickers hardness measure-ments.163


Citation Scheme:


Citations by CSL (citeproc-js)

Usage Statistics



Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            async >
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:


Related Items