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Phase transformations in titanium-rich alloys with iron and nickel Polonis, Douglas Hugh 1955

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PHASE  TRANSFORMATIONS ALLOYS  WITH  IRON  IN T I T A N I U M - R I C H AND  NICKEL  by Douglas Hugh Polonis —0O0-—  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in METALLURGY 0O0  We accept this thesis as conforming to the standard required from candidates for the degree of Doctor of Philosophy K.C. Mann W.M* Armstrong J»0. Parr Members of the Departments of Mining and Metallurgy and Physics THE  UNIVERSITY  OF B R I T I S H October 1955  COLUMBIA  THE UNT^ERST/FY OF BRITISH COLUMBIA Faculty of Graduate Studies  PROGRAMME OF THE FINAL ORAL EXAMINATION FOR "THE DEGREE OF DOCTOR OF PHILOSOPHY  of  DOUGLAS HUGH POLONIS B.A.Sc. ( B r i t i s h Columbia) 1951 M.A.Sc. (Toronto) 1 9 5 3 FRIDAY, September 2 3 , 1 9 5 5 at 4:00 p.m. i n ROOM 2C4 PHYSICAL METALLURGY BUILDING COMMITTEE IN CHARGE H.F. Angus, Chairman W.A. J.B. M.F. W.M.  Bryce Brown McGregor Armstrong  B.A. Dune11 C.E. Borden F.A. Forward K.C. Mann  External Examiner: Dr. H.W. Worner, B a i l l i e u Laboratory, University of Melbourne, A u s t r a l i a  GRADUATE STUDIES F i e l d of Studys  Metallurgy Jo Halpern  Theory of Reactions ~ D i f f u s i o n and Phase Transformations i n MetaTs Theory of Alloys -Magnetic Properties —  WoMo Armstrong JoGo Parr HoPo Myers  Other Studies: Oo Theimer JoBo Brown B.A. Dunell and JoGo Hooley WoAo Bryce  Quantum Mechanics -= Atomic Physics == Topics i n Physical Chemistry — Chemical Kinetics -=  THESIS PHASE TRANSFORMATIONS IN TITANIUM=RICH ALLOYS. WITH IRON AND NICKEL Phase transformations have been studied i n titaniumr i c h binary alloys with iron and nickelo Particular attention has been given' to the formation and decompose i t i o n of metastable phases i n powder specimens. A l l a l l o y s were prepared by a l e v i t a t i o n melting technique and precautions were taken throughout the experimental work to minimize contaminationIn the Ti=Fe system martensitio & i s produced When powder specimens containing up to 12$ iron are quenchedfrom 1000"C. The hardness of hypoeutectoid specimens increases with iron content to a maximum at 12$ Fe» The eutectoid temperature f o r the system has been r e assessed at 10*C„ During tempering the decomposi t i o n rates of retained § phase are slow but the appearance of FeTi i s accompanied by an increase i n slope of the gj / l o g time curve* The hardness of tempered a l l o y s f  625 +  increases as the FeTi content increases. Contrary to the results of other Investigators--Ti Fe has been found to exist in sensibly oxygen-free -alloys. This phase forms at 1000*C in-crushed .powder specimens but decomposes below the euteetoid temperature. In the Ti-Ni system the .constitution of quenched alloys Is found to depend on both «rjmpcsitioTi and cooling rate from the grange. An 'inverse stabilization' of the g phase has been observed and the 100$ {$ phase exhibits two types of substructures which have been attributed to polygonization and stacking faults. The hardness of quenched alloys is higTier for higher nickel contents and for faster cooling rates. Orientation relationships were observed between (3 and a and a shear mechanism suggested by Burgers for Zr is proposed- for this system. Decomposition ^studies have shown thatoa breaks down by a growth^controlled process similar to that described by Johnson.^and--Mehl.''"Ah activation energy of 8^000 cal/mole has been determined and a model "has been proposed which involves planar interfaces of .TigNi advancing into o regions to produce a Widmanstatten-type micrestructure. The self-diffusion of titanium is believed "to be the •growth -controlling factor. Hardness values decrease with longer tempering times and higher tempering temperature. Retained g decomposes on tempering by a two stage process % 2  -  9  -  p-*a"-*a, + TicNi X-ray diffraction data indicate that a'" has the same dryetal structure as a ' . The fHx"reaction appears to "be a -diffusion process although reaction curves are similar to those-observed for Isothermal martensite formation in steels. During the first stage of the reaction ( g-*a" ) the hardnesses and x=ray diffraction line"breadths.initiially show -a sharp increase, probably due to coherence between g and a „ - The reaction a"-*• a + TigNi proceeds In a similar-way to the 'decomposition of ttf 3 but with a shorter induction period f o r Ti Ni formation. Further, the. activation energy-for the a'' -» a + Ti' Ni growth process (71000 cal/mole) is lower than t h a t ' for o' decomposition,, These ^observations suggest t h a t Ni-rich regions exifct in t h e ct" phase and accelerate t h e nucleation and growth processes. ,s  -  2  2  LIST OP PUBLICATIONS Levitation Melting Titanium and Titanium Alloys: D.H. Polonis, R.G. Butters, J.G. Parr,. Research, 7 (2), 195^*512 Some Techniques for Melting Reactive Metals: D.H. Polonis, R.G. Butters,. J.G. Parr, Research, VTI, P. 272 Phase Transformations.in-Titanium-Rich Alloys of Iron and Titanium: D.H. Polonis, J.G. Parr.-Journal of MetaId, Oct. 195^; Trans. A.I-.M.E. (195^),"200, P. 1148. Martensite Formation in Powders and Lump Specimens of Ti-Fe Alloys: D.H. "Polonis,: J.G. Parr, Journal of Metals, January 1955' Non-Equilibrium Structures in Ti-Alloys: D.H. Polonis, J.G. Parr, Journal.of the Institute of Metals,.• Oct. 195^« Isothermal Decomposition Kinetics of Transformed-Phase in TiNi Alloy: D.H.Polonis,. J.G. Parr,, Acta Metaliurgica, in press.  ii  TABLE.OP.CONTENTS Page  FOREWORD  ,  '  x  INTRODUCTION . . . . . . . . . . . . . . .  .....  1  PART I - TITANIUM-IRON SYSTEM GENERAL . . . . . .  •  5 7  EXPERIMENTAL' . , CONSTITUTION, MICROSTRUCTURE AND HARDNESS OF HYPO-EUTECTOID ALLOYS  7  CONSTITUTION OF HYPER-EUTECTpID ALLOYS  11  EUTECTOID TEMPERATURE  11  DECOMPOSITION'OF oi' AND ^> THE PHASE Ti Fe . . 2  12  , ,  l6 21  SUMMARY AND CONCLUSIONS PART II - TITANIUM-NICKEL SYSTEM ' GENERAL  .;  2k  EXPERIMENTAL  26  CONSTITUTION, MICROSTRUCTURE AND HARDNESS.OF QUENCHED ALLOYS. .  27  CONSTITUTION OF RETAINED j& PHASE  31  ORIENTATION RELATIONSHIP ft -» c  <  EFFECT OF QUENCHING RATE ISOTHERMAL DECOMPOSITION STUDIES . Decomposition of ©* Decomposition of Retained P SUMMARY OF CONCLUSIONS  .  "Jft ».  .. « «,  i l h2 45 6b 7^  iii  page REFERENCES  77  APPENDIX I  - -LEVXTATION MELTING  APPENDIX II  - HEAT TREATMENT AND QUENCHING . ,  82 .  86  APPENDIX III - MICRO-HARDNESS TESTING .  90  APPENDIX IV - HIGH TEMPERATURE X-RAY GONIOMETRY  91  APPENDIX V  '9&  - CONTAMINATION OF ALLOYS  96  APPENDIX VI - PHASE RATIO DETERMINATIONS APPENDIX VII - METHODS OF DETERMINING ACTIVATION ENERGY -  102  SIGNIFICANCE OF COEFFICIENT 'n*. . APPENDIX VIII - SUMMARY OF SIGNIFICANT EXPERIMENTAL DATA . . . . .  106  APPENDIX IX - ABSTRACTS OF PUBLICATIONS  11^  .  TABLES page  I.  HABIT PLANES OF C*' IN /6 PHASE OF TITANIUM ALLOYS . . . .  "II. . ORIENTATION RELATIONSHIPS-BETWEEN  .  56  DECOMPOSITION  52  KINETIC RESULTS - ^"DECOMPOSITION  67  III. . KINETIC RESULTS IV.  ' AND/8 . . . . . .  56  V  ILLUSTRATIONS page 1.  Ti-Fe -phase, diagram after Van Thyne, Kessler and Hansen . . . .  2.  Photomicrograph showing 100$ martensite in a 0.2$ Fe alloy powder (-200) of titanium which was quenched from 1000"C. . . .  3.  6  5  Photomicrograph showing representative martensitic structure of a lump specimen of 0.2$ Fe alloy quenched from 1000*C . . i . ;  8  k.  Constitution and Hardness of Ti-Fe alloys quenched from 1000°C.  10  5.  Constitution of Ti-Fe alloys tempered at 570*C  1^  6.  Hardness of alloys tempered at 570*C for 1000 hours  .... .  15  7-  Microstructure of crushed powder of 33«3$ Fe alloy, as-cast . .  19  8.  Microstructure of crushed 33.3$ Fe alloy after heat treatment I for 3 hours at 1000°C.  9.  19  Microstructure of 33.3$ Fe alloy, remelted and crushed after heat treatment at 1000"C  10.  19  Microstructure of crushed powder taken from lump specimens after 2h hours at 1000°C  If  11.  Phase diagram of the Ti-Ni system after Margolin et al ..?!„'. . . *2ij>  12.  Graph of VPN Hardness versus composition for as-quenched sintered alloy,powders; and percentage retained B versus composition 28  for"the helium quenched specimens 13.  Photomicrograph^showing quehched from IQOO'C  ik.  structure ip a 1$ Ni alloy powder .... 30'  Photomicrograph showing 100$ retained y& in a quenched 6$ Ni alloy powder  32  vi page 15.  Photomicrograph showing two adjacent grains of 100$ retained ^  16.  in a quenched 6# Ni alloy:.  Photomicrograph of retained  32  showing twin-like sub-structure  observed "in some grains and attributed to clusters of stacking ' faults  3^  17.  Stereographic projection on (Oil) of a body-centred cube . . .  38  l8»  Stereographic projection on (Q001) of a hexagonal cell with c/a = I.58  . .  • '.  19.  Photomicrograph of 100$ oi' in quenched 6% Ni powder . . . .  20.  Graph of $ Ti Ni versus log time for decomposition of 2  transformed j&  39  h6  10  ( oi* ) at U-5P', 500*, 525*, 550* . . . . . .  .  MT  at 500*C . . . . . .  ^9  21. . Photomicrograph of 6# Ni alloy ppwder showing Widmanstatten structure after 90# decomposition of 22.  Photomicrograph of 6$ Ni powder specimen after. 90$ decomposition at 550*C  23.  40  Photomicrograph showing spheroidal precipitate of Ti Ni in ah 2  matrix after -100$ transformation . . . . . . . . . . . .  Uo,  2k. Graph of hardness versus log time, during the isothermal 50  decomposition of cA 25.  Plots of 'logiplogio of  26.  oi'  1 l-/(t)  versus logio time for decomposition 53  Graph of logio K. • 2,.3n  versus  activation energy 27. 28.  Graph of logiotime versus  1  "¥*"  for determination of ......  1 . for 50$ decomposition of o^'. .  "T"  Proposed model for growth of Ti Ni from transformed p 2  . . . .  55 55 58  page 29.  Graph-of activation energy for self^diffusion Q versus melting s  6l  temperature T^j for several metals « . . . . . . . . . . . . . . 30.  (a), (b),;(c) Graphs showing the fractioriof ^transformed, hardness, anqjl line.breadths-as a function of -time during62-64  tempering at ij-OO*, -425*, and 450*0 •31• Photomicrograph of 100^  structure showing original  grain boundaries . . . . . . . . . 32.  Isothermal reaction curves for the reaction  33*  Plot of logiologio  66  ... . . -pi'-* o4 • +  TI2NI  .  1 . versus log time for the decomposi - / ( t ) i: ^ . .  68  1  ition of ^ " 34.  .-.  Plot of log v,.,-K- versus 1 for the decomposition of o i . 2.3'n T  . •  69 70  APPENDIX I - Figure.!.  Diagram of levitation melting.unit . . . .  85  APPENDIX I - Figure 2.  Levitation Melting Unit in Operation . . . .  85  APPENDIX II - Figure 1.  Gas Quenching Furnace  . 88  APPENDIX II - Figure 2.'. Arrangement for Rotating Specimen during . 88  , Heat Treatment . . . . . . . APPENDIX TV - Figure 1.  X=ray attachment for spectrometer  APPENDIX IV - Figure 2.  Photo of high temperature attachment in position in the spectrometer  APPENDIX VI - Figure 1.  ......  •••• . . . . v 93  Standard curve for determining phase ratios from intensity measurements . . . . . . . .  APPENDIX VI - Figure 2. i APPENDIX VI - Figure $•  93  .100  Microstrfacture of 6$ Ni alloy powder which was slowly cooled from the  temp, range . . 101  Photomicrograph of 6# alloy heated 17 hours at 750'C to agglomerate TiaNi in oi matrix . 101  THESIS PHASE TRANSFORMATIONS IN TITANIUM-RICH ALLOYS WITH IRON AND NICKEL  by D.H.Polonis viii  ABSTRACT  Phase transformations.have. been.studied in titanium-rich binary alloys with, irdn .and.nickel. Particular attention has been given to the formation and decomposition-of.metastable phases'In-powder specimens. All alloys were prepared-by-a .levitatlon melting technique and precautions were taken throughout the~.experimental work- to minimize contamination. . In the Ti=Fe system .martensitic oi ' is-produced when powder specimens containing up -to.12$ iron are quenched-from 1000°C. The hardness of hypoeutectoid^ specimens increases with iron content to a maximum at 12$ Fe. The eutectoid temperature.-for the. system has been reassessed at 625 + 10*C. retained ^  During tempering the -decomposition rates of  phase are slow but the^appearance =of FeTi Is accompanied  by an increase in slope of the - ^ / l o g time curve. The hardness of -  tempered alloys increases - as the FeTi.content -increases. Contrary to the results of other-investigators TiaFe has been, found to exist in sensibly oxygen-free alloys. -This,.phase forms~at...1000*C in crushed powder specimens but decomposes--"toe-low .the eutectoid temperature. In "the Ti-Ni •system the ...constitution of: quehched alloys is found "to depend oh both compositiGn..and .pooling.r^te from the j& An 'inverse stabilization* of the 100$ jS  range.  -phase-has -been-observed and the  phase exhibits two types-of sub-structures which have been  attributed to pblygonization and stacking faults-. The hardness of quenched alloys is higher for higher.nickel contents-and -for faster cooling rates. Orientation relationships were observed between  /&  and  ABSTRACT  Phase transformations,have> been.studied in titanium-rich binary alloys with iron .and.nickel. Particular attention has been given to the formation and deeomposition-of.metastable phases in-~powder specimiens. All alloys were prepared by-a.levitation melting technique and precautions were taken throughout the,..experimental work-to minimize coritaminat ion. . Tri the Tl-Fe system .martensitic oi ' is produced when powder specimens containing up-to 12$ iron are quenched'from 1000°C. The hardness of hypoeutectoid specimens increases with iron content to a maximum at 12$ Fe. The eutectoid temperature.-for the system has been reassessed at 625 + 10"C. During;tempering the-decomposition rates of retained ft phase-are "slow but the-appearanee -of PeTi is accompanied by an increase In slope of the  ft/log  time curve. The hardness of  tempered alloys increases•as the PeTi.content .increases-. Contrary to the results of other-investigators. TigPe has been, found to exist in sensibly oxygen-free alloys. -This-phase forms:~at-..1000"C in crushed powder specimens but decomposes-«beiow .the euteotoid temperature. . In the Ti-Ni "system the ...constitution ..of: quenched alloys is found to depend oh both compos it ion.„and -cooling , rate, .from the An 'inverse stabilization' of the ^:?phase-.has..been-observed  range.  and the  100$ ft phase exhibits' two types of ..sub-structures which have been attributed to pblygonization and stacking faults-. The hardness of quenched alloys is higher for higher-nickel contents and -for faster cooling rates. Orientation relationships were observed between  $ and  ix  Of- and a shear mechanism suggested by Burgers f o r Z r is proposed for r  this system. Decomposition studies have shown that  tA ' breaks down by a  growth-controlled process similar to that described by Johnson and Mehl. An activation energy-of 84000 cal/mole has been determined and a model has been proposed"which involves planar interfaces of Ti Ni advancing into 2  oi  regions to produce a Widmanstatten-type microstructure. The selfr-  diffusion of titanium is believed to be the growth controlling factor. Hardness values decrease with longer tempering times and higher tempering temperature. . Retained ^ /8 -»  decomposes on tempering by a two stage process %  oi •-* oi + Ti Ni H  2  X-ray diffraction data indicate that oi" has the same crystal structure as o(' . The  r*  reaction appears to be a  diffusion process although reaction curves are similar to those observed for isothermal martensite formation in steels. During the first stage of the reaction (  -» o<" ) the hardnesses and X-ray.diffraction line  breadths initially show-a sharp increase, probably due to coherence between . P and of" • The reaction o(* -* xA + Ti' Ni proceeds in a similar way ' \ to the decomposition of ol' J but with a shorter induction period for 2  Ti Ni formation.- Further, the activation energy for the 2  «* '•** oi. + Ti Ni 2  growth process (71000 cal/mole) is lower than that for </.' decomposition. These observations suggest that Ni-rich regions exist in the and accelerate the nucleation and growth processes.  oi phase  Of- and a shear mechanism suggested by Burgers f o r Z r is proposed for this system. »  Decomposition studies have shown that  e*  breaks down by a  growth-controlled process similar to that described by Johnson and Mehl. An activation energy-^of 84000 cal/mole has been determined and a model has been proposed'which involves planar interfaces of Ti Ni advancing into 2  ©<  regions to produce a Widmanstatten-type microstructure. The self-  diffusion of titanium is believed to be the growth controlling factor. Hardness values decrease with longer tempering times and higher tempering temperature. . Retained ^ ->  decomposes on tempering by a two stage process %  c*" -* oi + Ti Ni 2  X^ray diffraction data indicate that ©<" has the same crystal structure as ot' . The  -*  reaction appears to be a  diffusion process although reaction curves are similar to those observed for isothermal martensite formation in steels. During the first stage of the reaction (  -* o<" ) the hardnesses and X-ray.diffraction line  breadths initially show-a sharp increase, probably due to coherence between . J& and o4  H  • The reaction of* ^ (A + Ti Ni proceeds, in a similar way 2  to the decomposition of o^' J but with a shorter induction period for Ti Ni formation. Further-, the activation energy for the 2  ol + Ti Ni 2  growth process (71000 cal/mole) is lower than that for o<' decomposition. These observations suggest that Ni-rich regions exist, in the and accelerate the "nucleation and growth processes.  of* phase  X  FOREWORD  Many recent studies have been carried out on the constitution of binary alloys of titanium with the transition metals. Phase diagrams for these systems are s t i l l subject to revision since slow diffusion rates are involved in most cases and i t is therefore^uncertain whether equilibrium has been achieved. Some isothermal decomposition curves have been developed for selected commercial titanium alloys of doubtful purity and complex composition. Howevery most'previous workers-on titanium systems have devoted little attention to metastable phases and the mechanism of their decomposition during- tempering. Non-equilibrium conditions and rate processes warrant careful quantitative study In titanium alloys since equilibrium conditions are rarely achieved Irr practice and, in most cases, are probably not desired. In previous work the Interpretation of results has been based almost entirely on optical metallography with very little X-ray evidence to support the conclusions which have been made.. In the present work extensive X-ray diffraction studies have been made and new techniques have been used for detailed -analysis of transformations in Ti-Fe and Ti-Ni alloys. The occurrence of martensitic ot and retained ft .have 1  been studied with particular emphasis on the effects of cooling rate and composition. Further, the-decomposition kinetics of these phases have been studied "quantitatively :and analysed in terms of current nucleation and growth theories. D. H. P.  PHASE TRANSFORMATIONS IN.TITANIUM-RICH BINARY ALLOYS WITH IRON AND NICKEL  INTRODUCTION  Pure titanium undergoes an allotropic transformation at 882"C (l). The stable structure above this temperature is body centred cubic /£ and at lower temperatures hexagonal close-packed  . The temperature range over  which each of these structures is stable can be altered by alloy additions and depends on both types and quantity of solute present (2,3). In addition, the rate of temperature change produces some interesting variations in. transformation products. Three important types of phase diagrams are encountered in the study of titanium alloys; these are the eutectoid, peritectoid and beta isomorphous types. The eutectoid-type systems offer the most interesting properties from the viewpoint of heat treatment and fundamental phase transformation studies; TI-Fe and TirNi alloys f a l l into this classification. The transformation of y6 -» o<  can proceed either by diffusion  or diffusionless means.. If a specimen is cooled quickly enough from the yt3  range the o<* phase may form from 0  by a shear process without observ-  able diffusion! i t is therefore considered to be a martensitic transformation. On the other hand, slower cooling may enable nucleation and growth reactions to occur in the manner characteristic of diffusion processes.. In the presence of alloying elements theft>I  +^  phase boundary may be raised or lowered  from 880* depending on the added elementsj however in eutectoid systems the type solute always lowers the boundary.  For example, oxygen raises this boundary  whereas Iron and nickel lower i t .  The presence of these elements has a marked  - 2 effect on the Ms temperature and the critical cooling rate necessary to effect a martensite reaction.. In some alloys of titanium the transformed products may be formed by both shear and diffusion i f cooling is not sufficiently rapid. This phenomenon is commonly observed in eutectoid systems when l•  proeutectoid phases tend to form by diffusion on cooling hypo- or hypereutectoid alloys. In some systems (e.g. Ti-Fe and.Ti-Mn) the /6 phase will tend to be retained on quenching to room temperature i f sufficient alloying element is present and i f the cooling rate is fast enough. Further, proeutectoid products may exist with retained /6  i f cooling is not rapid "enough.  It is important to note that retained formed  , martensitically trans-  , and proeutectoid constituents' are a l l non-equilibrium phases at  room temperature. The phase diagram is virtually valueless in considering these structures, because i t represents only the conditions which exist at equilibrium. Equilibrium can be achieved only by infinitely slow cooling to the prescribed temperature or ,by prolonged holding at temperature. Even when diffusion reactions appear to be complete there may be some concentration gradients and structural imperfections still'existing.  It is therefore  very important to use phase diagram.information with a great deal of caution and to realize that i t cannot t e l l how quickly or by what means equilibrium is approached. Previous work (2,3) has shown that phase transformations  in the •  various eutectoid-type titanium systems bear many similarities to one another. Some significant observations are summarized as follows: (1) With increasing amounts of alloying element there is an increasing tendency for jS y5  to be retained at least partially on rapid cooling from the  range.. At low soltite contents the j&  (hexagonal-close-packed) by shear.  may transform completely to  - 3 -  (2)  Definite orientation relationships have been observed between of.'  and retained D in several systems. (3)  The eutectoid reaction in most systems is very sluggish, presum-  ably due to the slow diffusion rates and large composition changes involved. In some cases, notably the Ti*Mn system (2), the intermetallic -phase nearest the T i end of the diagram does not form even after prolonged heat treatment .at temperatures only slightly below the eutectoid.  (h): At cooling rates slower than critical diffusion processes may'oceur which will result in formation of proeutectoid constituents, (5)  The eutectoid composition and temperature vary considerably, depend-  ing on the alloy systemj for example, in Ti-Pe alloys the eutectoid Is at 625 C and 16$ Pe, whereas in TI-Ni alloys i t is at 770°C and 5$ Ni (2). a  (6)  Both the u(' and retained  ft  phases are metastable and decompose  on tempering to approach the constitution indicated by the* phase diagram for the particular tempering temperature. The mechanisms of these processes have not been previously studied in titanium alloys. Most of the previous work In kinetics has involved quenching specimens from the p  range to a  lower temperature, holding at this temperature for various times, and" examining the resulting structures at room temperature. In the previous work phase ratios were estimated from metallographic observations and, in some cases, qualitative X-ray checks were also made.  . Iv -  PART I TITANIUM-IRON SYSTEM  - 5GENERAL The titanium-iron system was selected for an initial study in order to test newly developed experimental teohniques (Appendices I-IV) and to examine the suitability of the system for a detailed kinetic analysis. Early phase diagram work on this system was done by Wallbaum and associates (**->5*6)  w h o  u s e d  relatively impure titanium and encountered considerable con-  tamination. Subsequent work on the heat treatment and constitution of titanium-rich alloys was done by Werner (7,8) whs used Kroll sponge as the base for his alloys. Van Thyne, Kessler and Hansen (9) studied the phase diagram by using iodide titanium for alloys up to 30$ Fe and Kroll sponge for higher iron alloys; part of their diagram is shown in Figure 1.  Other work  on this system has included Ms temperature determinations on Kroll spongebase alloys by Duwez (10) and an investigation of the controversial phase TiaFe by Rostoker (11). In the present investigation the constitution of quenched powders and lumps and the decomposition'rates of quenched powders (-200 mesh*) were studied, • Further, some parts of the phase diagram were re-investigated by using high temperature X-ray diffraction methods (Appendix IV).  Most of this  work was performed on powder specimens obtained by filing alloy ingots since they are more amenable to X-ray studies and, in addition, diffusion reactions are often more rapid in powdered specimens than in lumps. It is. realized, however, that the practice-of relating phase constitutions in powders to the properties of lump specimens is questionable. Powder specimens and lumps which * Particles smaller than 7^ microns were obtained by using 200 mesh Tyler screens which have openings of 7^ microns. Tyler standard screens were used throughout this work for particle sizing.  - 6-  i8oo L  0  10  20  30  ^  ATOMIC $ IRON  Figure 1.  .Ti-Fe Phase Diagram after Van Thyne, Kessler, and Hansen (9)  50  - 7 -  have similar phase constitutions can have quite different appearances under the microscope (12). EXPERIMENTAL A series of alloys ranging in-composition from 0.2 to 49.6$* Pe were prepared by levitation melting of Iodide titanium and Johnson Matthey electrolytically prepared vacuum-melted iron. The.experimental techniques including levitation melting, heat treatment, phase ratio estimation etc. are discussed in detail In the Appendices.. Most heat treatments were performed on =200 mesh powders. X-ray studies of similarly heat treated powders revealed no difference In constitution for various particle sizes. CONSTITUTION, MICROSTRUCTURE AND HARDNESS OP QUENCHED HYPO -EUTECTOID ALLOYS Powder specimens (-200) of a series of hypoeutectoid alloys"were heated to 1000'C and quenched by a blast of cold argon (Appendix 11^ to yield martensitic o(.' and/or retained ft . The powders tended to sinter lightly at 1000°C and in order to obtain a much, faster cooling rate the specimens were agitated during heat treatment to prevent sintering. There was no difference in structure between sintered and unsintered quenched specimens and hence most powders were quenched in the sintered form since this technique was much simpler.. In order to compare the constitution of quenched powders with that of lump specimens a series of small alloy lumps was also quenched from 1000*C by a blast of cold gas. Figure 2 shows the representative microstructure of bi' in a 0.2$ Fe alloy powder quenched from 1000*C. The structure shows a Widmanstatten pattern of strain lines characteristic of'martensite"observed 1  ilt Atomic percentages are used throughout unless otherwise stated.  - 8-  Figure 2. - Photomicrograph showing 100$ oi' (martensite) i n a 0.2$ Fe alloy powder (-200 mesh) which was quenched from lOOO'C - Mag. 800X.  Figure 3> - Photomicrograph showing representative martensitic structure of a lump specimen of 0.2$ Fe alloy which was quenched from 1000'C. - A very slight trace of j3 i s also present. - Mag. 800X. Etchant: Both of the above were etched i n 1$ HF, 1$ H 0 i n H 0c 2  2  2  - 9 -  in other titanium systems (13,1*0 • Figure 3 shows the structure of oi'. in a quenched lump specimen of 0.2$ Fe content. It is evident that the structures are quite similar except that the martensite needles are slightly coarser in the lump specimen than in the small particle. Quenched powder specimens showed 100$  at iron contents less  than l$j higher alloys showed a progressively'increasing tendency to retain the l& (l).  phase, which agrees with general observations in other eutectoid systems Figure k shows the variation of oi  /  phase with iron content for alloy  powders and lumps quenched from 1000°C. The phase ratios in lump specimens had to be visually estimated from X-ray diffraction films and, hence, are only approximations. • Fairly reliable values were obtained" for the constitution of quenched powders from spectrometer intensity measurements, worrier, "in his work on heat treatment of Ti-Fe alloys (8), reported that quenched specimens containing more than 4$ iron 'appear to consist.of retained ^>  'although  they 'may not be strictly unaltered solid solutions' . In addition, he obtained a maximum hardness at a composition of about k$ iron. The small lump specimens (l/8 x l/8 x l/20) which were quenched from 1000°C in the present work yielded similar results (see Figure h) except that a higher maximum hardness was obtained than that reported by Worner. Further, at' was detected in quenched alloy powder specimens containing up to 12$ iron and . hardness values increased very gradually to a much lower value than the maximum observed for lump specimens. . The difference in. hardness between similarly treated powders and lumps appears to be a characteristic of specimen size. . The effects of specimen size on phase transformations are controversial and i t was felt that investigations on other systems than titanium alloys would be more  - 10  0  2  ~  6  Q  10  12  14  16  ATOMIC i IRON  Figure ^. - Constitution and Hardness of Ti-Fe Alloys Quenched from lOOO'C.  18  20  -  11  fruitful; therefore the subject was not pursued in the present work. CONSTITUTION OP RYPER-EUTECTOID ALLOYS Several hypereutectoid alloys were heat treated at 1000°C and examined by X-ray diffraction- and. microscopic techniques. 25$ alloys showed j& content.  Both 20$ and  + Ti Fe with larger-amount of Ti Fe at the higher iron 2  2  A 50$ Fe alloy showed FeTi + Ti Fe. No quantitative estimate could 2  be made of the amount of FeTi -because its complex structure is not accurately 2  known. Due to the controversy over the existence of Ti Fe in the absence of 2  interstitials a detailed investigation of this phase was carried out and is reported later in this thesis. Information about the phase FeTi was reported by Worner (7) and some points are given here merely to supplement his information. The lattice parameter was found to be 2.978 A + .001 as compared to Worner's value of e  2.97 A. The density, as determined from the above lattice parameter for a body-centred cubic structure and Avogadro number of 6.023 x 10^'  , should  be 6.52 gms/cm^ . The density, as measured by a water displacement method, is 6.5O gms + .03.  No ordering was observed in FeTi produced in slowly  cooled powders. EUTECTOID TEMPERATURE It is valuable to know the eutectoid temperature with reasonable accuracy since i t is the maximum temperature at which quenched structures can be safely tempered. A 12$ as-cast iron alloy containing j8 +  was studied  by high-temperature X-ray methods.. This alloy was selected because i t was near the eutectoid composition and would,therefore, yield sufficient F«T  4  for easy detection by X-ray diffraction. Reflections of FeTi were first  - 12 -  detected at about 500°C on heating and subsequent observations were made by measuring the intensity of the 110 reflection. The observed amount of FeTi increased with a corresponding decrease of intensity of &xoi  and A.io-  At  625°C an equilibrium condition was reached whereby the phase quantity did not change over a three hour period. At higher temperature the FeTi line began to disappear. The transformations of the same alloy were studied on cooling from 1000°C where the structure is initially 100$ j3 . The € range over which the FeTino would be expected was repeatedly scanned. A broad, low intensity reflection was observed after 20 minutes at 600°C which resolved into a fairly sharp peak after two hours at temperature. It is evident that 600° must be below the eutectoid temperature.  The slowness of the reaction  is a further indication of the low diffusion rates in the Ti-Fe system. BEC0MP0SITI0N OF o£' AND j8 Since diffusion reactions in the Ti-Fe system were found to be extremely slow, detailed studies of the decomposition of ct'  andj&  were  not attempted. Subsequent work on Ti-Ni alloys revealed this system to be much more satisfactory for kinetic studies.' Consequently detailed discussion of the kinetic approach in studying tempering reactions is reserved until later in the report of Ti-Ni work. Some useful information was obtained for partial decomposition,of quenched Ti-Fe powders and this is presented here. The quenched powder specimens were tempered at 570°C for various periods of time in order to study the rate of decomposition of retained j3 . The $ ^  , $ FeTi and combined $ ( oi +  ' ) as determined from X-ray  line intensities are shown; in Figure 5 for series of tempered alloys The a  e  reactions involved in tempering are as follows:  - 13 ^ The # of lines  7  oi.  1 Q 1  c* + FeTi  -»  + FeTi  at any time could not be estimated since the positions  c( 101 and  process the  -*  1 0  i are almost coincident. During the tempering  decreases in Intensity but the  to the decomposition of both  o^'and j&  ^ 101 increases due  .  It can be seen from Figure 5 that the slope of the ^  breakdown  curves Increases with increasing iron content, which can probably be attributed to the higher percentage of ft present in the quenched form.  Alloys  containing below 6$ Fe display discontinuities in their ft decomposition curves when FeTi is first detected. This is probably due to the incubation period required for the formation of FeTi nucleii during which the growth reaction is not detectable. Subsequently, the growth of these FeTi nucleii proceeds with the accompanying formation of pi  j both of these reactions  proceed at the expense of the ft phase which decomposes. Accordingly ^ the percent ft decreases more rapidly with the increase of $ ol  arid $ FeTi.  . The ratio of FeTi: o( after ,1000 hours tempering is much higher than would be expected from the phase diagram. This seems not unreasonable since the presence of ft and oi' means that the system Is out of equilibrium and, hence, further tempering would favour the formation of 0<  from these  metastable forms to produce equilibrium phase ratios. Hardness measurements made on alloys tempered for 1000 hours are plotted in Figure 6.  Note, that the hardness increases quite regularly  with Iron content and also increases consistently with % FeTi which is also shown on the graph.  1^ -  10Q, 90 80  lOOt-  ioo  0.20$ Fe 100$ <*•  79  at a l l times  60  x — «•  J 50  9 — fi Phc,st. I"  o — FeTi /?>«•«•  30 20 10 0 O ^ c v c r f  1 L©6>  2  3  1  Ti»i& I'HOURS)  100,  Qwevcv i 100,  t-ofir  2 T i « t £  3.  c HOURS)  SlltSHM \ 23 U o a T i i ^ e (HOURS)  100,  .  901  Queue*1 Uo& T i i ^ e (HOURS)  .  6.12$ Fe  'Guauai ]_  — , 100  1  100c 90  1  "<WA«* 1  2  LOG TIME.(MOUR$)  LOG,  - LOG. T I M E C tt'ou'es)  2  3  TIME ( Houes)  100 f  100*  1 2  3  8.14$ Fe  QUfMCM  U O & T I M E (HOURS)  2  3  LOG. T I M E (HOURS)  O t a * *  LoC  Figure. 5. - Constitution -of Ti-Fe .alloys tempered at 570*£.... The alloys.contained from 0.2 to 15-31$ iron. The rates of breakdown of and rates of formation of FeTi are indicated.  i . .  2  3  T i M B ifHOUR*}  - 15 -  ATOMIC <f> IRON  Figure 6. - Hardness of alloys tempered, at 570*C for 1000 hours.  - 16 -  THE PHASE Tl Pe IN Tl-Fe ALLOYS 2  .Introduction Previous work has created some controversy over the existence of the phase Ti Fe in binary. Ti-Fe alloys. 2  In early work, Wallbaum and  co-workers (4,5,6) reported a phase Ti Fe which was face-centred-cubic with 2  96 atoms per unit cell.  In later work Duwez and Taylor (15) supported Wall-  baum's results and found the lattice parameter to be 11.305  •  Worner (7)  in his investigations failed to produce the phase Ti Fe. . It is significant 2  that a l l of these investigations utilized relatively impure titanium.  In the  more recent work on the Ti-Fe system by Van Thyne.et al (9) both high purity iodide titanium and Kroll sponge were used. Ti Fe-was not produced and 2  hence, Worner's contention that the phase does not exist was supported. Rostoker (ll) has reported that the phase Ti Fe occurs only in the presence of 2  oxygen and proposes a composition range Ti4Fe 0 to TIsFesO. 2  : In a preliminary study of hypereutectoid Ti-Fe alloys the present author observed the phase Ti Fe by means of X-ray diffraction methods on heat 2  treated specimens. High temperature diffraction studies indicated that the phase occurs between the eutectoid and eutectic temperatures. Examination of an as-cast 25$ Fe alloy failed to reveal Ti Fe but the phase did appear in 2  crushed powders of the same alloy after heat treatment in purified argon, purified helium  or in vacuo at 1000*0.  identical heat treatments performed  on pure titanium indicated insignificant amounts of oxygen contamination. Rostoker determined the 1000°C Isothermal section of the Ti-Fe-0 system and maintains that at least 2$ 0 is necessary for the co-existence of Tl Fe with 2  j0> and FeTi. This contention led to a detailed study of the characteristics of the phase.  - 17 -  Experimental  i  An alloy corresponding to the composition Ti^Fe was prepared by levitation melting from pure Iodide titanium stock and pure iron. Powder specimens were prepared by crushing and the -200 mesh fractions were used in subsequent heat treatments. Heat treated powder specimens were remelted by supporting the sintered specimen in an induction field on a molybdenum wire. . The maximum amount of contamination due to heat treatment was established as 0.07$ (atomic) oxygen by hardness measurements made pn identically treated Ti-Fe filings.  Scratch hardness tests, which were performed  on numerous specimens, failed to reveal any variation of hardness from edge to centre of particles.  Any oxygen-rich surface layers would be detectable  by this test. Discussion- of Results X-ray diffraction examination of the as-cast alloy (crushed to powder) revealed FeTi and ft phases.  In spite of the brittle nature of the  alloy, diffraction peaks were very broad, implying considerable internal strain 1  in the powder. Microscopic examination of the powder showed massive primary dendritic FeTi. and a eutectic of FeTi and ft (see Figure 7). Reference to Worner's phase diagram for the system indicates that this structure would be expected In the 33«3 atomic$ Fe.alloy. . After heat treatment at 1000*0 for three hours crushed powders of the as-cast alloy showed new X-ray diffraction lines of TigFe. The phase had formed at the expense of some ft and FeTi. The quantity of the hew phase could not be measured from line intensities because of Its complex crystal structure. Microscopic examination revealed a coarse structure (Figure 8) in which only two phases were discernible. However, much of the  - 18 -  eutectic seemed to have disappeared due to coagulation and the .grain boundaries of FeTi etched heavily. It therefore appeared that although TigFe was not produced in an as-cast structure, It could be formed by heat treating a crushed powder, To check this surmise, the heat treated powder specimen (containing TigFe) was remelted, crushed and.examined. X-ray spectrometer plots showed that the phase Ti Fe had almost completely disappeared. 2  As the experimental techniques  merely allowed the material to be brought just to the fusion point and then cooled, It is not surprising that a trace of TI Fe remained, for the centre of z  the sample may not have melted. A photograph of a particle of the remelted and crushed material is shown in Figure 9« While' heat treated crushed powders (-200 mesh) produced the phase • Ti Fe, small lumps broken from the as-cast ingot did not show Ti Fe diffract2  2  ion lines after 2k hours annealing at 1000*0.  The micrestructure.(Figure  10) shows that the eutectic has disappeared, presumably due to the diffusion of FeTi to the dendrites. It is .believed that the difference in behaviour of lumps and powders can be attributed to one of two reasons: (a) The powder is susceptible to oxidation and the phase Tl.iFe 0 could 2  be formed, as suggested by Rostoker (11).  A lump sample having a smaller  surface-to-volume ratio may be less likely to react with oxygen so readily. . (b) The powder is strained and hence is in a more susceptible condition for reaction between FeTi and FeTi + ^  . . If the driving force of the reaction  '-* Ti Fe is insufficient to surmount the activation barrier It may 2  be necessary to induce the reaction by strain.  Such a mechanism Is b'elieved  * to exist for example in the system Fe-NI where metastable Y  can only be  - 19 -  Figure 7 - - Micro-structure of crushed powder of 3 3 - 3 $ Fe  Figure 8 . - Microstructure of crushed 3 3 . 3 $ Fe alloy after heat treatment for 3 hours at  a l l o y , as-cast - Mag. 800X  1000*C - Mag. 800X  Figure 9 - - Microstructure of 3 3 - 3 $ Fe alloy which was heat treated at 1000*C, remelted, and crushed.  Figure 10. - Microstructure of crushed powder taken from lump specimen which was heated 2k hrs. at 1000*C.  - Mag. 800X  - Mag. 800X.  Etchant; Etched i n 1$ HF, 1$ H 0 i n H 0. 2  2  2  -20  -  transformed to the stable o<. phase by cold work In addition to appropriate heat treatment. The first possibility of oxidation is ruled out on the following grounds: (1)  Checks made on titanium powder (see section headed 'Contamination*)  showed insignificant oxygen pick-up.  Further hardness tests shqwed that a.  small lump of titanium acquired as much oxygen as the 200 mesh powder. (2)  If the heat treated powder samples contained T i 4 F e 0 , the oxygen 2  would remain in the specimen on remelting. This remelted material was heat treated In lump form at 1000*C for one day - a treatment which is known to produce T i 4 F e 0 i f sufficient oxygen is present. Therefore, If the Ti Fe 2  2  in the original heat treated powder is, in fact, the oxygen-containing phase then no less of this phase should appear In the remelted lump, heat treated at 1000'C- However, only a small trace of the phase was produced under these circumstances and this can be attributed to incomplete fusion during the remelting operation. The cycle of operations including melting, crushing, heat treating to produce Ti Fe, remelting, and re-annealing in 2  lump form was made on several samples with similar results. • The second possibility, described in (b) above, was confirmed by stress-relieving the as-cast crushed powder Just below the eutectoid temperature for 65 hours.. Even after this period, the structure remained in some state of strain, as indicated by broad diffraction peaks. However, on subsequent heat treatment at 1000*C for three hours the relieved powder showed considerably less Ti Fe than the unrelieved powder which had been . 2  held at 1000*C for three hours. An approximate estimation Indicated that the amount of TI Fe produced in the stress-relieved powder was about"one 2  half that in the unrelieved specimen.  - 21 -  Margolin*s. Work Recent work by Margolin (l6) on lump specimens has confirmed the existence of ion.  T±zFe  in the absence of significant interstitial contaminat-  His results offer sufficient agreement with the present work to refute  the conclusions of previous investigators that TigFe exists only in the presence of greater than 2$ oxygen at 1000*C. Ti-Fe SYSTEM, SUMMARY AND CONCLUSIONS (1)  Martensitic o^.' is produced in Ti-Fe alloys containing iip to  12$ iron which have been argon-quenched from 1000*C. (2)  Retained ^  decomposes very slowly at 50*C below the eutectpid  but the rate increases with higher iron contents. The slope of the )B versus log time curve increases as the presence of'FeTi is detected. (5)  The tempering curves at 570*C indicate a very slow rate of format-  ion for FeTi. Hence complete decomposition of j& would involve extremely long heating times even at the eutectoid temperature. For this reason i t was decided not to make a more detailed kinetic analysis on the Ti-Fe alloys. It has been suggested by Jaffe (17) that the early appearance of FeTi reported by the present work (l8) may explain the brittleness encountered in commercial Ti-Fe alloys subjected to moderately high operating temperatures. (k)  The hardness of tempered alloys increases'with FeTi content.  (5)  High temperature X-ray diffraction studies have established  the eutectoid temperature at 625* + 10*C.  (6)  The density and parameter of FeTi have been determined to be  6.50 gms/cm  +0.05 and 2.978 A + 0.001.  No ordering has been found.  - 22 (7) TiaPe is produced in..sensibly oxygen-free specimens which are coldworked and heat treated.in. the .range between eutectoid .and eutectic temperatures.. Unstrained material-does...not-appear.to~produce TisFe-and  this is in  accordance with some results of previous investigators. However, TlaFe cannot be nucleated from the melt.and hence i t appears difficult to .amend the phase diagram. It appears that TigFe cannot -be distinguished microscopically from FeTi and jS when customary etching reagents are used. (8) The effect of specimen size on the-martensite.reaction has been studied. The hardness of as-quenched alloys appears dependent on particle size since worner's results for lump specimens were confirmed. The hardness maximum of powders and lumps appears at a composition where the formation of o*- ' has a l l but ceased. Appearance of the martensitic structure is essentially similar in both powders and lumps.  It is significant that the martenslte  structure in Ti-Fe alloys is not a hard phase like the martensite observed in steels. The hardness of Ti-Fe quenched structures is greater when there is a great deal of internal strain which will be the case when the "oC reaction is on the verge of occurring.. It therefore appears that these strains are relieved at least partially by the shear transformation.  - 23 -  •  PART II TTTANIUM-NICKEL SYSTEM  -  2k  -  .  GENERAL In view-of the slow decomposition rates observed in Ti-Fe alloys and the similar behaviour-reported for the Ti-Mn system (19) i t was"'decided to work on a system with a higher eutectoid temperature and lower eutectoid composition. Work by other investigators (l) suggested that metastable phases in such systems experience fairly rapid decomposition in tempering.or interrupted quenching.  The Ti=Ni system was selected for this study since  it has a eutectoid temperature of 770*C, a eutectoid composition of 5$ Ni, and, in addition, the phase diagram is known with reasonable certainty (l).. Previous investigations of Ti-NI alloys were devoted primarily to phase diagram studies; relatively little attention was given to metastable phases and tempering processes. Early work by Wallbaum (4,5,6) on alloys prepared by powder metallurgical techniques and later efforts by Long et al (20) who used Kroll sponge titanium resulted in tentative phase diagrams. However these did not represent true binary conditions since their alloys were contaminated by oxygen and nitrogen. The most recent diagram. (Figure 11) is due to Margolin et al (21) and a slight modification of the . o(. +ft /ft t-ransus (shown dotted in Fig. 11) has been proposed by McQuillan (22), Margolin et al (21) reported the formation of a martensite phase (close-packed hexagonal  ) in rapidly cooled lump specimens of  titanium-nickel alloys of low nickel content. With increasing nickel content an increasing tendency to retain the ft phase (body-centred cubic) was observed and at 7$ nickel 100$ ft was retained. McQuillan (22) has studied the effect of delay time before quenching on the microstructure of a hypo-eutectoid alloy. This delay time results in slow cooling from the ft to o*- +ft zone before rapid quenching to room temperature.. He has included a series  ~ 25 -  Figure 11. - Phase Diagram of the Ti-Ni System after Margolin et al (21).  - 26 -  of micrographs in his paper which show the formation of increasing quantities of precipitated alpha due to progressively greater delay times before quenching. McQuillan also pointed out that the o£ + ^3  transus reported by Margolin  et al is higher than i t should be due to the inherent delay involved in the quenching method used in their phase diagram investigation. . In the present work on Ti-Ni alloys similar techniques to those used in the Ti-Pe work have been used to study the formation and decomposition of metastable phases. EXPERIMENTAL Alloys ranging from .25$ Ni to l8$ Ni were prepared by levitation melting from iodide titanium and Johnson Matthey spectrographic grade nickel. Most of the subsequent work was performed on powder specimens-ranging from /r ft  +65  to -200 mesh by using techniques described in the Appendices.. X-ray  diffraction and microscopic studies of screened specimens which received a common heat treatment revealed no difference in constitution for particle sizes ranging from -48 to -200 mesh. Specimens of -200 mesh compacted quite readily during heat treatment at 1000*C unless they were continuously rotated to inhibit sintering (see Appendix II).  Filings of +65 mesh did not sinter readily and, conseq-  uently, were quenched more rapidly since individual particles were contacted by the quenching,gas.  During the course of heat treatments on each alloy  above 2$ nickel it was observed that the constitution of powders quenched in helium differed from that of powders quenched in.argon. This difference was found to be caused by the different quenching rates. Specimens of -200 mesh.and +65 mesh were quenched in the sintered'and unsintered c.onditipn~by" ft +65 mesh powder corresponds to oversize material from 65 mesh screens (openings of 208 microns).  -27 -  both argon and helium. This work revealed that the difference in constitution is definitely due to cooling rate and not due to particle size effects.. The different quenching.rates and measurement of relative rates are discussed in Appendix II. CONSTITUTION, MICROSTRUCTURE, AND HARDNESS OP QUENCHED ALLOYS A series of alloy powder specimens in the composition range up to the solid solubility limit of Ni in ft titanium (approximately 11$) were quenched from the ft range and examined by X-ray diffraction and metallographic methods. Alloys were heated to 1000*C prior to quenching with the exception of some of the hypereutectoid compositions which required slightly lower soaking temperatures to avoid Incipient melting. No differences were observed in the quenched products for a given alloy when the soaking time was increased from one minute or when the holding temperature was varied within the ft range. 4  Samples containing less than 2$ nickel showed a completely hexagonal close-packed transformed-  structure after either argon or helium  quenching. This structure is believed to be martensitic and Is designated oC' , as in other titanium systems.. Compositions greater than 2$ Ni showed differences in constitution with varying quenching rate. Argon quenched sintered specimens (i.e. the slowest quenching rate used)'produced 100$ of  in alloys up to 6$ nickel. However, the more rapid helium quench  of sintered and unsintered powders retained increasing amounts of ft in alloys containing more than 2$ nickel'(Pig. 12). 100$ ft could be retained"by helium-quenching an unsintered specimen containing 6$ nickel. . Figure 13 shows a typical Widmanstatten pattern of strain lines In a structure consisting entirely of oC' . The microstructure becomes progressively finer with increasing nickel content - an observation  - 28 -  Figure 12. - Graph, of .V..P.N'. Hardness, versus composition for as-quenched sintered alloy powders;..and percentage retained versus composition for the helium quenched '", specimens.  - 29 -  that has been made In the Ti-Cu system (23). Investigation of alloys In the vicinity of 11$ nickel (the limit of solubility of nickel in ft titanium) showed that Ti Ni precipitated in 2  powders regardless•of the quenching speed from 950*C. . Presumably the diffusion rates are quite rapid at the temperature of the  ft/  /&  + Ti Ni 2  boundary. . High temperature X-ray goniometry studies (Appendix IV) confirmed the existence of 100$ ft at 950*C in an 11$ nickel alloy. The following reactions were observed during heating and holding at 950*C.  c< + Ti Ni 2  -» ft + Ti Ni 2  -* ft  100$ ft was produced within a few seconds at 950'C and after approximately one minute at temperature the base of the ft peak broadened arid the intensity gradually decreased, suggesting that incipient melting occurred. Water quenching a lump of the 11$ alloy retained a completely ft$  structure; this suggests that the precipitation of Ti NI is more rapid 2  In powders than in lumps since the gas quenching of powders Is considerably faster than water quenching of lumps. Stabilization of the ft phase was not observed In either hypoeutectold or hyper-eutectoid alloys when cooling rates slower than the argon quench were employed.  The retained ft phase in a 6$ Ni alloy remained  untransformed on subsequent cooling to liquid oxygen temperature; nor could a martensitic transformation be induced by cold working powders at room temperature prior to sub-zero quenching. Hardness measurements were made on powder specimens quenched in argon and in helium. A Bergsman microhardness tester with 10 gm. loads was used. The variation of microhardness with composition for -200 mesh alloy powders quenched by helium and argon in the sintered condition is shown in  - 50 -  Figure 13. - Photomicrograph showing 100$ structure i n a 1$ Ni alloy powder which was quenched from 1000*0 - Mag. 800X. Etchant z Etched i n 5$ HF i n H 0 - HN0 rinse. 2  3  - 31  Figure 12. . The $ retained J@  -  in the helium quenched specimens is also  shown on the graph and i t is apparent that this more rapid quench retains more readily"and"produces higher hardness values than the argon quenched powders. . In alloy powders containing 6$ Ni and above, i t was possible to completely suppress the transformation of j&  by quenching in the unsintered  form. The results indicate that the presence of a mixed structure leads to higher hardness values at a given composition.  6<.'+/3  For example) in the  6$ alloy a helium quenched sintered specimen contains 80$ oc' and 20$/^  ;  it has a hardness of ^75 V.P.N.. The unsintered specimen^ with a correspondingly faster quenching rate, shows 100$ retained j8 390 V.P.N.  and has a hardness of only  An argon quenched sintered specimen (slowest quench) of the same  alloy contains 100$ pt' and has a hardness of U30 V.P.N. CONSTITUTION OF RETAINED j3 PHASE Sub-boundaries A photomicrograph of retained J@ reproduced in Figure lh.  in a quenched 6$ Ni alloy is  In this structure a pronounced network of subFigure 15, which was  boundaries which occurred in many grains is visible. taken at high magnification (1500 X) shows adjacent ^  grains in another  6$ quenched powder; one grain contains marked intra-crystalline boundaries and the other is completely free from any sub-structure. The sub-crystals appear to have fairly regular shapes - which suggests a regular orientation relationship among them. Tempering the retained ^ the sub-structure at an early stage of ^  structure eliminates  decomposition.  Ogden et al (19) have previously observed sub-boundaries In the ^  phase of a Ti-Mn-N alloy; but this structure was attributed to nitrogen-  r,ich OC precipitation. The nitrogen content of the Ti-Ni alloys does not  - 32 -  Figure lk. - Photomicrograph of 100$ $ i n a quenched 6 $ Ni alloy powder - Note the substructure within the & grains.- Mag. 800X  Figure 1 5 - - Photomicrograph showing two adjacent grains of 100$ retained /& i n a quenched 6 $ Ni a l l o y j one grain exhibits sub= boundaries but the other i s apparently free from any sub-structure - Mag. /fibOX Etchant: - Etched i n 5 $ HF i n H 0 - HN0 rinse 2  3  - 33 exceed .02$ and, in addition, the quenching rate was sufficiently rapid to suppress precipitation reactions. Further,. X-ray diffraction results have confirmed the absence of any second phase which might account for this phenomenon.. Therefore i t seems unlikely that this phenomenon is explicable in terms of nitrogen content. At the present time i t is possible only to conjecture an explanation for this sub-boundary phenomenon since very little work 'has been reported on sub-structures resulting from phase changes.. It is believed that the present phenomenon is due to polygonization resulting from unrelieved stresses set up during the  transformation on heating. Since some  Ti Ni is also present, the reaction on heating i s : 2  oC + Ti Ni 2  -» j&  In hypereutectpid Ti-Ni alloys the  oC  proceeds before Ti Ni starts to decompose. If the 2  fairly rapid strains may be induced in the polygonization during soaking.  reaction possibly oC  reaction is  grains which could lead to  A similar type of process is' believed to  cause the 'alpha veining' observed in ferrite (2k). Subsequently when Ti Ni decomposes, nickel atoms diffuse into the 2  phase and the vacancy  flow involved could assist in the movement of dislocations'necessary to form low angle boundaries. • The mechanism of polygonization is believed to involve climbing' of edge dislocations out of their slip planes in order to change their grouping (2.5) - a process which involves vacancy diffusion and which can only occur athigh temperatures where self diffusion is rapid. Faulting A second type of sub-structure has been observed in retained during the course of this work.. This structure has a twin-like appearance  ^  - 3k  -  F i g u r e l6. - Photomicrograph o f r e t a i n e d p showing the t w i n - l i k e s u b - s t r u c t u r e observed i n some g r a i n s and a t t r i b u t e d t o c l u s t e r s o f s t a c k i n g f a u l t s - Mag.  800X  Etchants - Etched i n  5$  HF  in  H 0 - HN03 2  rinse  - 35 I I (Figure 16) and does not occur in all specimens.  It usually appears in grains  which do not show the previous type of sub-boundaries. A similar type of structure, observed by Barrett (26) in Cu-Si alloys, has been attributed to clusters of faults separated by relatively perfect crystal layers. Such a structure indicates the presence of internal strains caused by quenching stresses.  (  The appearance of faults in a body-centred cubic structure is rather unusual but not impossible. Stacking faults in this system are believed to occur along ^112J  planes (27) and could conceivably cluster to  give the twin-like.microscopic appearance. . Faults are generally expected when a transformation is on the verge of occurring or has just started. It is pointed out in the next section of this thesis that the Burgers shear mechanism for the transformation of a hexagonal close packed structure to bodycentred cubic (28) satisfies the observed orientation relationships.'. This process involves shear'on the In the retained ^  {ll2,}  planes of the body-centred cubic.  structures examined in this investigation the martensite  reaction which produces  occurs very readily with slower quenching  rates, due to the 'inverse*' nature of  stabilization in Ti-NI alloys.  Consequently, faulting on {"112} planes might be possible in specimens in which the martensite transformation.has not been detected by X-ray methods but which may, nevertheless, have been initiated.  ORIENTATION RELATIONSHIPS . Introduction The crystallographic relationship between, martensitic retained p  c<' and  has been studied in alloys of titanium with Mn, Mo, Cr and Fe  - 36 -  (29, 30, 31).. In these studies the habit planes of the martensitic phase were determined as well as the planes parallel to each other in the two phases. The following habit planes were found: TABLE I SYSTEM  HABIT PLANE "  REFERENCE  Ti - Mo  {53^  Liu (29)  Ti - Cr  {33^  Liu (29)  Ti - Fe  f  Ti - Mn  { 4^  5  5  55  ^  L i u  b^fi  L  l  u  a  n  d  M ^ 8  0 1 1 1 1  ( ) s8  Liu has also found that orientation relations listed, in Table I I exist for the { 3 3 ^ and  h a b i t  Planes.  .TABLE. II - ORIENTATION. RELATIONSHIPS HABIT •PLANE  ORIENTATION  fa)  (110)ftII (0001) d\  $kk)p  a  SPEC. A  SPEC. B  [lll]p  :  [lllbj^i 0 - 1 / 2 -  (110j|j  :  (0001)^' approx. l 4 '  [noJ|ft  ;  (110)|3  II  [ill] £  :  [ l o T o ] * ' approx. i * (000l)«*'  (llh)oi  'approx. 1'  Liu has found that, in an alloy exhibiting two martensite habit planes> i t is the temperature of martensite formation and not the nature of any externally applied stresses or quenching stresses (i.e. compression or tension.) which determine the particular habit plane.  - 37 -  Orientations In. Ti-Ni Alloys In the present research program orientation relationships in a Ti-Ni alloy have been determined from spotty X-ray films (32). This method enables the use of polycrystalline specimens so long as their grain size is large enough to avoid continuous diffraction lines on the films.. In this method use is made of the fact that parallel diffraction spots from the two phases indicate parallel planes in these phases. Parallel spots must necessarily occur in adjacent lines on account of the similar necessary for parallelism of planes.  values  Film exposures were made in a Unicam  single crystal camera with specimen oscillations of -5*, 10* and 15*. The following parallelisms were detected on diffraction films of an 8$ Ni alloy;  JL  J?L  {on}  (0002}  {200}  £l0l2j  / m l  i 2i3o(  {211}  (10T3J  In order to check the relationships and also to determine .fairly complete orientation relationships the (Oil) stereographic projection of a body centred cube.(Figure 17) was superimposed on a standard (0001) projection of a hexagonal structure with — of I.58 (Figure 18).'. The crystallographic angles for titanium and zirconium (hexagonal close packed) have been reported by McHargue (33). The projections revealed that the observed parallelisms were possible.- The following pole projections were coincident and hence indicative of parallel planes in the two phases;  -38-  IOO  -ion  Figure 17. - Stereographic projection of a cubic cell on (Oil)  -39-  7o/o  S T A N D A R D  foooij  PfiojgcTfOhf  7~ITANIUM  foA  H E X A G O N A L  %• = f.587  Figure l 8 . - Stereographic projection of a hexagonal cell, on (0001) for c/a = I.587  - 40 -  u (211)  (1010)  (211)  (1010)  (121)  (1013)  approx. 2"  (112)  (1013)  approx. 2  (111)  (2130)  (111)  (1210)  (111)  (2130)  (111)  (1210)  (212)  (1102)  (001)  ;(0112)  %  -  -  approx.  Mechanism A shear mechanism that produces the observed orientation relationships between  and  has been proposed by Burgers (28) for zirconium. In  this mechanism transformation is proposed to occur by heterogeneous shear on the £ l l 2 J ^  planes In the  [lllj^  direction. Burgers arrived at  this me'chanism since the atomic configuration in the (112) plane of the bodycentred cubic is exactly the same as that in the (1010) of a close-packed hexagonal of the same atomic radius. d x 2 /2- d. a rectangle  ^  The pattern on both these planes is  . The hexagonal structure is formed by displacement  of (112) planes relative to each other. Since the spacings of the (112) planes and the (1010) planes to which they transform are not equal an exact hexagonal-array cannot be formed by pure shear. The observed orientation relationships are approximately attained by the proposed Burgers mechanism. Other transformation mechanisms Involving multiple shear processes have been considered for the  reaction but these are not considered  - in satisfactory or logical  since a transition structure is involved.  One  such mechanism suggested by Burgers (28) does not satisfy all the orientation relations. It is therefore believed that the single shear on in the  /3 -* Of.'  (ll2J^3  applies  transformation in Ti-Ni alloys.  EFFECT OF QUENCHING RATE The generally accepted theories of diffusionless transformations do not satisfactorily explain the fact that a more rapid quenching rate tends to retain the high temperature phase in some systems, while a slower quench produces a martensitic structure. In Ti-Ni alloys this effect is most marked in the 6$ alloy, which may produce a structure consisting entirely of retained j8  or. of oC . The retention of a high temperature phase by 1  rapid quenching (while slower quenching produces martensite) has also been observed in some iron alloys by Kurdjumov and Maksimova (3*0 • They showed that shear processes could be suppressed and that martensite tended to form isothermally on holding below the Ms temperature. Kurdjumov and Maksimova's results were subsequently confirmed by Cech and Hollomon (35)•  Of even  greater interest are some recent studies of Philibert and Crussard (36) on martensite transformation in hypereutectoid steels. They have shown that less martensite forms with more rapid cooling rates and referred to the phenomenon as 'inverse stabilization'.  In their, work they suggest that 'martensite  nucleation is not athermal but due to thermal fluctuations so that a l l the martensite can be considered as forming in isothermal increments'. In view of these very important results i t is evident that the- reaction path theory (37) and theories due to Fisher, Hollomon, and Turnbull (38) cannot be applied to a l l systems. The observation of 'inverse stabilization* is sufficient in itself to indicate the need for a unified theory since i t refutes the idea of athermal nucleation and, further, has modified our concepts of  .- k2 i  isothermal nucleation of martensite.  Although  Philibert'and Crussard studied  s t e e l specimens t h e i r o b s e r v a t i o n s are c e r t a i n l y o f no l e s s g e n e r a l  applicabil-  i t y than the e x i s t i n g t h e o r i e s . The  q u e s t i o n may  l e g i t i m a t e l y a r i s e as t o whether the  by argon quenching i s , i n f a c t , m a r t e n s i t e . r a i s e d by M a r g o l i n  (39) and J a f f e e ( 4 0 ) .  The  oi ' formed  T h i s p e r t i n e n t 'query has following observations  been support  the proposal of a m a r t e n s i t i c r e a c t i o n : (a)  The  s t r a i n e d appearance o f the s t r u c t u r e and  i t s broad  r e f l e c t i o n s are c o n s i s t e n t w i t h a s t r u c t u r e formed by a shear (b)  I f the phase were  r a t h e r than  oi'  would c o n c e i v a b l y p r e c i p i t a t e s i m u l t a n e o u s l y .  X-ray  process.  a second phase T i N i 2  T h i s might not be  by X - r a y o r m i c r o s c o p i c t e c h n i q u e s , but on subsequent tempering  t h e r e would  be no i n d u c t i o n p e r i o d p r i o r t o the growth o f T I N i p l a t e l e t s . .  Reference  2  t o F i g u r e 20 shows t h a t an i n d u c t i o n p e r i o d i s a c t u a l l y  detectable  experienced.  (c) . I f a d i f f u s i o n r e a c t i o n o c c u r r e d the h y p e r e u t e c t o i d 6$ NI would p r o b a b l y p r e c i p i t a t e T i N i r a t h e r than 2  i n quenched specimens o f t h i s (d) then j8  o<  .  ot.  formed out of" e q u i l i b r i u m ,  2  detected  alloy*  I f on the o t h e r hand, p r o e u t e c t o i d remaining  No T i N i was  alloy  a t e a r l y stages o f the quench would be o f h i g h e r  average s o l u t e content and s h o u l d be r e t a i n e d .  No  3  than  i s retained, i n the  i  6$ a l l o y u n l e s s • f a s t e r quenching speeds are used.  ISOTHERMAL DECOMPOSITION STUDIES Introduction It o f metastable  i s n e c e s s a r y t o know the mechanism and r a t e o f  decomposition  phases b e f o r e -alloys can be s e n s i b l y heat t r e a t e d o r s u b j e c t e d  t o e l e v a t e d temperatures  i n service.  The  tempering  k i n e t i c s o f some  important  - k3 ferrous alloys have been studied in detail (4l-l*5) by applying theories of diffusion"and precipitation developed by Johnson and Mehl (k6) and Zener (^7). This work included decomposition studies of retained and martensitically transformed austenite as well as graphitization in cast irons. Most of this previous research has been concerned with interstitial alloying' elements (C,N) in materials of complex commercial compositions. it was possible to retain 100$ /3  In the present work, since  or produce 100$ transformed  in the  same alloy by simply varying the cooling rate, i t was decided--to compare the decomposition mechanism of these phases without the usually inherent'complication of different composition. Hence, in this work, the composition of  d'  is believed to be identical to that of retained j& but the atomic configurations are quite different (close-packed hexagonal and body-centred cubic respectively). In studying decomposition processes i t is necessary-to emphasize that non-equilibrium conditions exist until the reaction is completed. -Deviation from equilibrium is essential to provide a driving force for the reaction and the only place where equilibrium can be assumed to exist is at a reaction interface where for the Ti-Ni system, the following relationship r  holds for the. nickel content in phases I and II: (f*m)j  =  or  y*m\j  f d F | = fdF l^CNi/j ^C^J  y/^Ni |  8 F acN1  =  ohemical potential of Ni partial molar free energy of Ni.  In the structure away from the reaction interface there-..are such metastable conditions, as concentration gradients or structural" imperfections which must be removed before equilibrium is achieved. In precipitation processes in alloys the diffusion reactions-involve concentration gradients  - 44 -  which are levelled by. transport of solute atoms to the matrix - precipitate interface.  This results in growth.-of the -precipitate by the -advance of the  interface. The diffusion equations for reactions of this type have been studied theoretically by Wagner (48). However, quantitative solution of a diffusion equation"is almost hopeless in-practice due to the irregularities in concentration gradients and complications introduced by structural imperfectionso- The directional solidification of a melt offers -ian Interesting analogy to the reaction between two solid phases. In this simpler case quantitative study is possible in some cases because a single interface can be observed and moved under carefully controlled conditions.  The solute  distribution about a solid-liquid Interface during solidification has been studied by Chalmers et al (49). It is possible in many cases to describe the intermediate stages of a solid phase reaction by a general rate equation from which an energy of activation can be determined. Precipitation reactions proceed by nucleation •and growth mechanisms which are independent of each other and either may control the overall rate of a reaction.  Consequently i f an activation energy  calculated for a particular reaction is to be compared with values obtained for other systems the processes must be similar. In many nucleation and. growth reactions either of the steps may make a negligible contribution to the activation energy in comparison to the other. This is notable In such reactions as some Isothermal martensite processes where nucleation is the dominating factor in the transformation. Also, in some precipitation and recrystallization processes the extent of transformation is determined by the growth rate of existing centres or nucleii which may be formed during the incubation period.  Some reasonable assumptions and. simplifications"'are  necessary, i f useful Information about the kinetic mechanisms is to be obtained.  - 4  -  5  Decomposition of As previously indicated, i t was possible to produce 100$ transformed ft (called c*' ) in Ti-Ni alloy powders (-200 mesh) containing up to 6$  Ni by quenching them from 1000*0 with a blast of purified argon. Specimens  of higher Ni content showed some retained ft after quenching. Metallographic examination of completely transformed ft specimens revealed pronounced strain patterns (Figure 19) which are typical of martensitic structures observed In other TI alloys (13, l 4 , l 8 ) .  No other phase was detected by  X-ray diffraction studies. The 6$ Ni alloy was particularly useful for the present study for i  the followsng reasons; (1)  It was possible to retain 100$ j3  or produce 100$ cC' by  varying the cooling rate from the ft range for the alloy. (2)  Phase ratios could be assessed more accurately than in.'alloys of  lower nickel content. The phase diagram of the TI=Ni system (Fig. l l ) shows that the approach towards equilibrium during tempering yields the phase TigNI.. During the formation of TigNI the oi' phase is depleted in nickel until Its composition conforms to that of equilibrium oi at the tempering temperature (probably less than 0.1$ Ni at 500*C). . Experimental Results for oi.' Decomposition. A sufficient quantity of argon quenched 6$ NI alloy powder was prepared for subsequent Isothermal heat treatments. X-ray diffraction checks ensured that the structure of this material was completely c*r' . The extent of the tempering reaction after heat treatment was determined by computing the amount of TigNi formed from X-ray diffraction line intensities (see Appendix VI).  - ke -  Figure 19. - Photomicrograph of 1 0 0 $ ©< i n a quenched 6$ Ni alloy powder - Mag. 2000X y  Etchant:  Etched i n 5$ HF i n Glycerin with HNO3 rinse.  The ..tempering reaction in the 6$ Ni alloy was followed at ^50*, 500*, 525*,.and 550*0.  The weight $ of Ti Ni is plotted as a function of log time 2  in Figure 20. .The curves exhibit the familiar S-shape (although the early stages are difficult to measure) and may be reasonably superimposed by translation along the log time axis. Once the reaction is initiated the-amount of TiaNi formed is approximately proportional to log time up to the concluding stages of the reaction ( ^  than l4$ TiaNi) when the rate decreases quite  markedly. Specimens were examined metallographically after various amounts of tempering at each temperature in order to detect any microstructural changes due to diffusion and precipitation. The original strained structure appeared to be transformed to a Widmanstatten precipitation type. Figure 21 shows a typical microstructure for 90$ transformation at 500*0.  The  structure appears extremely fine and needle-like. Since TiaNi is not resolvable at 2000X i t is presumably very finely dispersed. At 55Q*C the structure is a little coarser*(Figure 22) but no definite precipitation of TiaNi can be seen. Microscopic examination of a specimen heated at 750*C for 15 minutes revealed a spheroidal precipitate of TiaNi in a matrix of ;(Figure 23). Hardness measurements of o< ' at various stages of isothermal decomposition at four temperatures are shown in Figure 2k. With the depletion of nickel in the close-packed hexagonal structure and the corresponding formation of Ti Ni there is a gradual decrease in hardness values. 2  No  initial hardness increase was observed during the earliest stages of the process.  co  LOGio TIME. (mins). Figure 20. - Graph of ^"TigNi versus Logio time for decomposition of transformed ft ( c * . ' ) at 450, $00*, 525*, 559*  - 4  Figure 21. - Photomicrograph of 6$ Ni alloy powder showing Widmanstatten structure after 9 0 $ decomposition of e*' at 5 0 0 " G - Mag. 2000X  9  -  Figu^p 22. - Photomicrograph of 6$ Ni alloy powder after  9 0 $ decomposition at 5 5 0 * C -  Mag. 2000X  Figure 2 3 . - Photomicrograph showing spheroidal precipitate of T i N i i n an oi matrix after 1 0 0 $ decomposition of oi' 2  at 7 5 0 * C - Mag. 2000X  Etchant: Etched i n 5 $ HF i n Glycerin with HNO3 rinse  -50  -  Figure 2k. - Graph of hardness versus log time, during the isothermal decomposition of o^' .  = 51 -  Discussion of Tempering Results. The general shape of the curves in Figure 2 0 suggests a type of nucleation and growth reaction which was quantitatively analysed by Johnson and Mehl (46). They proposed an equation of the following form for a rate.of nucleation N -and rate of growth G which are both assumed constant for a given process: / ( t ) = 1 - exp ( ~ JT_ . N G V )  (1)  5  where  /(t) represents the fraction transformed In time 't* (2)  A more general form of equation (l) is /(t) = 1 - exp ( - kt" ) which yields  (3) a f(t).  = knt"" e-^"  = knt " (l  1  11  1  dt The coefficients 'k* and 'n' are constants for a particular process. If logarithms are taken in equation.(2): (M and  log (1 - / ( t ) )  =. ~ k t  e  (* (5) logiolog  1  k  !.jT(.t)  =  10  n  lo  S i o 2 3 + n log t  Cohen et al (4l, 4 2 ) have proposed the following equation which serves to relate the constant k in the above to the specific rate constant K for the process: (6)  l£M  = K (1 -yftflt " 1  where m = n - 1  Equation (6) is merely another form of equation ( 2 ) . Comparison of (3) and (6) reveals (7)  nk = K »  Substituting equation (7) in (5) (8) logiologio i . ^ f c ) = logio 2?%  +  n  lo  S t  - 52  -  It can be seen that i f the tempering reaction is to obey equation (8) then a plot of l o g l o g 10  10  i„  versus logiot will yield a  straight line. The experimental values for the current investigation are plotted in Figure 25 and produce reasonably straight lines, up to the late stages of the reaction. The curves for different temperatures deviate from linearity at approximately the same ordinate values, suggesting the possibility of impingement which inhibits.the growth process. Reference to equation (8) shows that the slopes of the curves LogLog Y-yr7Jtyversus log time gives 'n' for each temperature.  The values for  different temperatures are listed in Table III*whereis-sefn'that, except for the figure of 0.7 at 550*0, n is fairly constant at 0.52. TABLE III - KINETIC RESULTS -  oi' DECOMPOSITION K-  n  log 2.3n "  ^50  . 53  - 2.1V0  500  .51  -  1.-+5  525  .52  -  1.02  TEMP. -,*C.  550  0.7  Table III also shows the value of log ^  - 0.8 for each temperature.  2.3n  These were obtained from the log time = 0 intercepts of Figure 25. From basic rate theory i t is known that: (9) Kt = Ae"^*/™ where Kt is the activation energy and A is a frequency factor i f the reaction is first order. If log Kt is plotted against the reciprocal of the absolute temperature then a straight line should •Qt . result and i t will have a slope equal to ^ ^  ... (This is the standard  Arrhenius method of obtaining activation energy). From equation (7) the rate constant for a precipitation reaction  -  5  4 -  as defined by equations (6) and (8) i s ; (10)  k=  £ n  K Consequently, the values of log 2.3n in Figure 26.  1  have been plotted against T  a s  shown  An excellent linear relationship yields an activation energy  OK = ^3,500 cal/mole. From equation (8) i t can be seen that the rate constant K is expressed in units time  =n  but, according to Zener (59), the corresponding  activation energy. Qj^ must be evaluated in terms of K in units time ^ before any comparisons can be drawn with other rate processes. The conversion can 1 . K 1 be made automatically by plotting n log 2.3n versus T more simply by o r  OK using the relationship Qt = „  w h e r e  Qt  process. For this investigation Q = t  i s  the activation energy for the = 84000 cal/mole.  Alternatively the activation energy, Qt , for the tempering 1  process can be obtained from the slope of a graph of log time against  IJ  for a specific fraction of decomposition (e.g. 50$) (45) as shown in Figure 27. • This method produces the same value for Q^. The similarity between the two methods of obtaining Qt has not been clearly indicated in the literature. This relationship is discussed in Appendix VII together with a modification of the rate equation as proposed by Burke and Owen (45). . Diffusion"Model. The following experimental results and conclusions have been considered in proposing a model for the tempering of transformed j8 in Ti-Ni alloys; (l) The reaction is a growth process which can be adequately described  = 55 -  i/r x i(T  5  K Figure 26. - Graph of Log " .3 versus for determination of activation energy. 10  2  n  Figure 27. - Graph of logio time versus for 50$ decomposition of oi '  1  by the equation? =  1 - exp - k t n  where n = 0.5 at ^ 5 0 ' , 500*, 525* and n = 0.7 at 550* (2)  In the tempering treatments carried out at ^50*, 500", 525*, 550* i  the phase TiaNi is not microscopically resolvable; however at 750* the precipitate appears clearly spheroidal. It is therefore concluded that at the lower heat treating temperatures growth of many more dispersed nuclei! occurs than at higher temperatures. (5)  At the three lower tempering temperatures the coefficient n is  approximately.0.5*  Zener (^7, 50) has indicated in his theoretical treatment  of growth processes that the value of n corresponds to the advancement of planar interfaces of precipitate. Cohen (kl, k2) has indicated a similar process in his treatment.of first stage tempering in steels. The relationship between the coefficient n and the geometrical form of precipitates is discussed in Appendix VII. . (4) • The later stages of the reaction do not comply with equation (2). This is perhaps due to the impingement of adjacent TigNi precipitates. Further, i t is possible that there is a marked decrease in concentration gradient during the later stages and TiaNi particles may compete in withdrawing solute from the depleted oC' . (5)  Diffusion in this system is by substitution. Growth of a Ti Ni 2  precipitate requires that Ni atoms be transported through the 'ot' lattice to the interface. There is a great difference in nickel concentration between and TiaNi at the interface and consequently i t is to be expected that the rate of interface movement will be extremely slow. In addition, a •  i  countercurrent diffusion of Ti atoms away from the interface in the same  - 57 -  direction as the TINi growth must occur in. order to create vacancies for nickel atoms to form TI^Ni. . Actually, this situation should.create a high density of vacancies in the o*-' at the interface..so that incoming nickel atoms can assume the configuration of TiaNi and thus..enable the interface to advance. (6)  The activation energy for the overall process has. been-determined  as 84,000 cal/mole; this value is based on the intermediate., stage of the process only. The low n value of 0.5 has been attributed to a.process in which nucleation has already occurred (42) and the .reaction proceeds by growth only. This seems feasible in the present xjase .since the Incubation period has not been considered.. It"is"therefore reasonable to assume that nucleation contributes insignificantly to the activation energy .during the intermediate stage and the process is controlled by diffusion or growth. Hence the activation energy represents the~rate-ccmtr.ollihg.,diffusion process. On the basis of these observations i t is proposed that at 450r  550"C (and probably below this range) growth of TiaNi .proceeds in platelike form as shown in Pigure 28. Ti Ni is envisaged as,-adyancing into the 2  oC'  with a depletion of nickel ahead of the Interface. The;gradient of  nickel concentration in oi will be determined by the diffusion coefficient 1  of the reaction and by the maximum and minimum nickel-BOncentrations Co and Ci respectively. The 15ne *4a- represents'the centre-.llne.l>etween the midpoints of two growing TigNi plates. Towards the end of-the.decomposition proi  cess the concentration Co at line • aa will start to diminish, .resulting in ,  J  a subsequent decrease in concentration gradient. In this model the product should consist of oC regions surrounded by fine, :well.dispersed plates of Ti^Ni. At low tempering temperatures.(less than 550"C) i t is probable that the growth of many nucleii will proceed with eventual impingement  Figure 2 8 . - Proposed Model for growth of Ti Ni from transformed^ (/>(')' 2  which results in the non-linearity of the upper part of the curves log log }\ t l~jr (t)  versus log time. Thus the Widmans.tatt.en type of  precipitate  seems reasonable on-the basis of this model,-and under such circumstances TiaNi formation will be manifested-as an apparent, thickening-of oC boundaries. Calculations based on. cylindrical  o< needles and uniform distribution  of TiaNi as interface layers around o<- have shown that the thickness of the Ti2Ni layer will be in the order of 0.05 microns which would not be resolvable under the microscope. At- 500*C the increased value of n\(0.7) implies that precipitation occurs in thicker units for .as n approaches 3/2 spheroidal precipitates are expected. Although no measurements have been made at temperatures higher than 550"C the photomicrograph of a specimen treated at 750* (Figure 23) supports this view. The diffusion coefficient for the controlling-process, as calculated from; (11) where  D  N  =  L-a^exp-  ^RT  a is the interatomic spacing  ~y is the thermal oscillation frequency is in the order of 10"^^  cm"Vsec In the temperature range  450-550*C. Such  a small value implies a slow diffusion rate which will favour-the  formation  of a very fine and well-dispersed precipitate network. Since the proposed model requires countercurrent -diffusion -of Ti and Ni, the self diffusion of Ti to create vacancies for the Ni may well be the rate controlling factor.. Although no figure exists for the activation energy of self-diffusion in T i (Qs) an analysis of self diffusion data for several metals' indicates that Qs is roughly .proportional to'the melting point T^ . This is a reasonable relationship since melting involves the  -6o  -  breaking of atomic bonds or-release -of.an atom from its regular array which is actually what happens in substitutional diffusion.. In Figure 29 the available values of Q.s are plotted against T/  and a reasonably straight line is  obtained. From Figure 29- the activation energy for self-diffusion of Ti is estimated to be 77000 cal/mole. This value corresponds remarkably well with the activation energy for the rate controlling step of the tempering reaction in the Ti-Ni alloy. Decomposition .of Retained.^ . . Experimental. It has already been mentioned that i t is possible to retain 100$ j8. in the 6$ Ni alloy by gas quenching unsintered particles from .1000*0.. The variation of constitution with quenching, rate has already been considered. A sufficient quantity of quenched powder consisting of 100$ retained j3  was prepared for subsequent isothermal heat treatments. These  heat treatments were performed as described in Appendix II and phase ratios were determined from relative X-ray line intensities of y^no and  °^ioi  as outlined in Appendix VI. . Results. The isothermal decomposition of retained ^  was found to  follow a step-wise reactions (b.c.c.f ->  <*"(c.p.h.) "*  ^(c.p^h.)  + Ti Ni 2  In the above reaction 0*-' is used to designate an intermed1  iate phase which is formed before the presence of TiaNi is detected. At temperatures up to 550*0 an isothermally heat treated powder may consist of  - 6i -  Figure 29. -^Graph of Activation Energy for self-diffusion Qg versus melting temperature for several metals.  Figure 50;(a)• - .Graph:Showing:rthe..fraction-of jS transformed, hardness, and line bread'th as a'function of time during tempering.at 400*\  TIME (MINUTES) Figure 30 (b). - Graph-showliJg--1;be;--t!rac-t-±on .of j8 transformed, hardness, and: -line breadth.. as..a~funoti©n.!Of time during tempering at ^25*. v  . Figure 50 (c;).. - Graph.showing., the fraction of /S transformed, hardness, and line breadth as a-function of time during tempering at 450*0.  - 65  -  100$ o^-' . The reaction curves are shown in Figure 30 (a, b, c) with the 1  corresponding hardness values for isothermal treatments at UoO'C, U25*C and 450*C. At higher-temperatures the reaction is extremely rapid; at lower temperatures i t is extremely slow. There is no 'C-curve' behaviourThe microstructure of retained j8 was shown 'in-Figure lk for the 6$ alloy. During the j@ -* o*-" transformation there is no microscopic evidence of the reaction except that the substructure (previously noted) disappears with the formation of  (Figure 31).  Black marks on the  structure are due to an etching effect.. The metallographic appearance of the CC  structure is most misleading and adds to the argument that X-ray evid-  ence is needed to substantiate any conclusions made from the microscopic appearance of structures. The positions of the diffraction peaks of the <yL" phase correspond to those of ~~ot' formed on quenching, indicating that the — ratio is a similar in both phases. During the early stages of the reaction there is a broadening of the originally sharp ^  diffraction lines.. The  o^" reflections  appearing as a result of the reaction show an initial broadening and then become progressively sharper. Figure 30 illustrates this fact and also shows that hardness values during the reaction follow the same initial increase and subsequent decline. These effects are attributed to coherency strains produced in the mixed structures during the early stages of oi" formation. As the reaction proceeds the oc" structure becomes incoherent with respect to the jS phase and stresses set up due to coherency are at least partially relieved. Attempts were made to detect any transitional omega phase (3) which might form during the early stages of ^  decomposition.  Although the  transitional structure has been observed during the isothermal decomposition of j& in several other systems (13) none was detected In alloys of Ti-Ni.  - 66 -  Figure 31 • - Photomicrograph of 100$ structure showing original A grain boundaries - Mag.  800X  Etchanti  •  Etched i n 10$ HF i n Glycerin with HN0 rinse. 3  - 67 -  The second stage of the reaction (i.e.  c*'''-* oi + Ti2Ni) yields  very similar reaction curves (Figure 32) to the decomposition .of C*' .  How-  ever the' amount of TiaNi detected at any time is slightly-greater in °^ decomposition than in 0< decomposition! and the incubation period is ..1. shorter. Figure 33 shows the plot of logxologxq x- f'(t) versus log t for the tf K decomposition of oi . The values of n and log 2.3n obtained from the f  graph in a similar way as for the decomposition of ex TABLE TV  - KINETIC RESULTS -  are listed in Table TV.  DECOMPOSITION . K  TEMP.  n  log 2.3n  J+50  .5  -  ^9  500  .56  -  l.k  525  .55  -  0.88  550  .55  -  0.66  K The plot of log 2~5n"  i versus A is shown in Figure 5^.  The  activation energy for the reaction in terms of tirne"^- has been determined to be 71000 caL/mole from the slope of the curve. Microscopic examination of specimens during stages of the ^"decomposition revealed similar structures to those observed during the oi breakdown. Discussion - ft -»  .  Kurdjomov and Maksimova (3 *-) showed that the' retained high 1  temperature phase in their alloys decomposed to martensite on tempering at temperatures below Ms.- No Ms temperatures have yet been determined for the TI-Ni system but i t is possible that the tempering temperatures in this work are above Ms.  Consequently, at the present time i t is impossible to.be  certain whether the ft -*  transformation is a martensitic or diffusion  - 69 -  DECOMPOSITION OP o<"  LOGip TIME  Figure 33- - Plot of logiologio l - y - ( t ^ for the decomposition of ©<* .  e r s u s  l o g  t i m e  - 70 -  - 71 type.  -  The shape of the growth curves Is s i m i l a r to that of reaction curves  reported by several other investigators (51, formation. (53)  52,  53)  f o r isothermal martensite  In t h e i r analysis of isothermal martensite curves Cohen et a l  have concluded that, during the e a r l y stages, the transformation proceeds  primarily by nucleation of new plates rather than by growth of e x i s t i n g ones. Further^ they found that the rate of reaction increased considerably once . the transformation had s t a r t e d ; I.e. the reaction i s autocatalytic i n the e a r l y stages.  No reports of 100$ martensite transformation by purely isothermal  means has been found In the l i t e r a t u r e ; but the proceed to completion isothermally.  ft  -* c<  • reaction does  C-Curve behaviour has been noted i n  •* the isothermal martensite reactions but, as previously mentioned, no.C-Curve behaviour was  observed  i n the present work on T i - N i .  There is.strong evidence to support the thesis that the ft  -» oi"  reaction involves d i f f u s i o n . The formation of T l N i from  oi" i n  2  the subsequent tempering operation proceeds much more r a p i d l y than the decomposition  of  oi' as indicated by the b r i e f e r Induction period.  implies that n u c l e i i of T i N i have formed during the 2  ftl  -* oi  This •  reaction,  or that t h e i r formation during the e a r l y stages of oi" breakdown i s f a c i l i t ated by composition fluctuations set up during the ft$ -* °i reaction  oi  -*  (X  reaction.  The  + T i N i appears to occur more r e a d i l y than 2  -* o( + T i N i ; and t h i s behaviour i s consistent with the lower a c t i v a t 2  ion energy calculated f o r the growth stage of  ©c  -+  cx + TI- NI. 2  •diffraction and microscopic observations of specimens i n which the was  jiust completely deiomposed revealed' 100$  second phase.  The microstructure (Figure 31)  shows the o r i g i n a l transformed  ft  °*  X-ray ft  phase  with no evidence of a  i s very misleading'since i t  grain bpundaries but no indication that- the ^  has  except that the previously noted sub-structures have disappeared.  - 72  It is possible that crystals of  -  are extremely small and consequently not  resolvable by optical methods. The X-ray diffraction lines~of  o(. " (c.p.h.)  were cpntinuous and slightly broader than the corresponding reflections of C/C  (c.p.h.) which suggests a small crystal size of ex  . in addition  the previously noted polygonization boundaries result in sufficient discontinuity in the ^  phase to obstruct growth reactions and" promote nucleation  sites. Consequently, the formation of a fine transformation product is strongly favoured. Therefore i t does not seem unreasonable that composition fluctuations, might arise during the j& -* c<" reaction, and create some regions which are richer in nickel. This situation would be similar to the formation of 'Guinier-Preston' Zones observed in the aging of Al-Cu alloys. The establishment of such nickel-rich regions in <=<• would facilitate subsequent decomposition because the required induction period for nucleation of TiaNi would be shortened. Further, because of the structural irregularities due to a high concentration of nickel atoms in certain•regions there would probably be associated vacant lattice sites. . On the basis of the decomposition mechanism proposed for the hexagonal close-packed structure this would explain the more rapid decomposition and correspondingly lower activation energy involved in the decomposition of oi" ttian in It was observed that the 9 value of the broadened  ^  no  peak decreased 0.1* - 0.2* during the early stages of ^decomposition. This cannot be attributed to composition changes due to normal diffusion since such a process would imply that the nicker content of the j8 phase decreases and the j& peak positions would increase in angle. Moreover i t is difficult to believe that Ti Ni would not be detected by X-ray methods in 2  - 73 such a case.. This shift in line position is accompanied by line-broadening, which' in turn has been attributed to strain.  Previous observations in strain-  ed metal aggregates ( 5 M indicate that stacking faults induced by strain can cause a shift in X-ray line positions. The view that the line shift of  no  is due to stacking faults and strain is acceptable since considerable structure strain is involved during the first half of the j& -* oi" reaction as indicated by microhardness results (Figure 30). It is concluded that nucleation rather than growth by diffusion is the controlling factor during the early stages of the ^ -* °( <• reaction ;  r  (up to. 50$ transformation). During this stage the X-ray line breadths and hardness values increase to a maximum. These observations can be attributed to strain, which is probably of two types; (1)  Internal strain which will result from the formation'of many  widely distributed nucleii due to the specific volume difference between  oc"  andl&  (approx. 3$).  it (2) Coherency strains which are set up between the oi  j$  and retained  since in this type of reaction, there is a tendency for'lattice  conformity along atomic planes having similar spacings. As transformation proceeds the strain increases to a maximum after which there is" a gradual loss of coherency and corresponding relief of strain and decrease of hardness. The condition during the initial loss of coherency'is-generally designated as the 'semi-coherent state' in which some lattice registry is maintained by arrays of dislocations at the interfaces between the two phases. Coherency generally contributes much more significantly than specific volume difference to the overall strain in a nucleation and growth reaction. The decrease of hardness observed during later stages  - 7^ -  ( ^  than 50$ transformation) of the ft -» oi"  to the loss of coherency between ft and  reaction maybe attributed  <si" or possibly to strain relief  by shear. The shape of reaction curves for ft -* oi*  , when compared to  other rate curves, suggest that nucleation and growth both contribute significantly to the transformed fraction during the latter half-of the- process. The temperatures and holding times are such that a significant amount of diffusion is inevitable. On the other hand, the reaction is not retarded even at above 90$ transformation.. This implies that-new nucleii must be forming at all times In the unreacted j&  since growth control would probably result  in'impingement effects, which in turn suppress the reaction in the late stages. Decomposition of oi" . The decomposition of the transition-phase oi similar process to the breakdown of oi'  .  appears to be a  Microstructural-observations  and hardness measurements together with X-ray diffraction studies indicate that a similar mechanism operates in both processes. An explanation of the more rapid nucleation and growth process has been given on page 72. SUMMARY OF CONCLUSIONS (1)  The constitution of quenched Ti-Ni alloy powders is dependent on  both composition and cooling rate from the jft  range. An 'inverse stabil-  ization of the ft phase has been observed.- The 1  oi  1  structure •' (martensite)  becomes progressively finer with increasing nickel content. (2)  The 100$ retained ft phase in quenched powder specimens has  exhibited two types of sub-structures.  - 75 (a) Sub^boundaries believed due to polygonization resulting from transformation stresses (b) stacking faults created by quenching stresses. (3)' Hardness of the as-quenched alloys Increases with nickel content and is higher in alloys containing mixed structures of ot' and /6 is believed to be due to coherency strains at the (h)  and ^  . This  interfaces.  Orientation relationships between the ot' and f% phases after  quenching have been studied in an 8$ alloy. The relationship (OOOl)ot' // (Oil) j$ ~ (observed from parallel adjacent diffraction spots) was used as the basis for stereograms from which other observed parallelisms were confirmed. The Burgers shear mechanism for Zr has been proposed as the likely crystallographic process for the ^  -» et' martensite reaction In Ti-Ni  alloys, i (5) | Decomposition studied of the ot' phase have shown that decomposes by a growth-controlled process similar to that described by Johnson and Mehl.. An activation energy of 84000 cal. per mole has been, determined and a growth model has been proposed which involves plane interfaces of TiaNi advancing into at' regions to produce a Widmanstatten-type microstructure. The self-diffusiori of titanium is believed to -be the growthcontrolling factor. (6)  Retained f$  decomposes on tempering by a two-stage process:  -> ot" -»  ex  + Ti Ni 2  X-ray diffraction data Indicate that ot" ot. . .  The p -» <=*  Y<ns  the same crystal-structure as  reaction curves are similar-to those observed for  t  Isothermal martensitic formation. However, the oi" formation appears to involve diffusion since: (a) Formation of TI N1 during subsequent tempering is facilitated, 2  - 76 -  as indicated by the brief induction period, suggesting that regions relatively rich in nickel are set up during ft -* oi  reaction.  H  (b) The tempering temperatures and times were such that diffusion processes are inevitable. The reaction  oi" -* oi. + Ti Ni proceeds in a similar way to 2  the decomposition of o< j however, there is a shorter-induction period for /  Ti Ni formation in the oi" decomposition, as already mentioned. . Further, the 2  activation energy for the  oi"  -»  oi  + Ti Ni growth process (71000 cal/mole) 2  is lower than that for oi ' decomposition suggesting that regions which are rich in nickel exist in the oi" phase. (7)  During the tempering of oi'  the hardness of quenched powders  decreases with heating time - the rate of hardness decrease being greater for higher tempering temperatures. This is In contrast to observations in the Ti=Fe system where the hardness increased with the forma'tipn of FeTi . during tempering. The difference in behaviour is probably due to the stoichiometric and crystallographic differences of the intermetallic phases In thei two cases. However, the Ti-Ni observations show a similar trend to results in the Ti-Cu system (23) where Ti Cu Is precipitated during temper2  ing. (8)  During the reaction ft -» oi" the hardness initially shows a  sharp Increase probably due to lattice coherency strains between oi ' and f  ft  j as decomposition-exceeds 50$ the hardness decreases. The magnitude  of-X-ray line breadth follows the hardness curves.  - 77 -  • REFERENCES  1.  A. D. McQuillan, Journal Inst, of Metals (1950)., l 8 , p. 2^9-  2.  R. I. Jaffee, Journal of Metals-, Feb. 1955, p. 2kf.  3.  L. D. Jaffe, Metal .Progress, Feb. 1955, P« 101.  4.  H*Witte and H. J. Wallbaum, Z. Metallkunde (1938), 30, p. 100.  5«  H. J. Wallbaum, Archiv Eisenhuttenwesen-, (1938), 12, p. 33.  =  i ' 6.  F. Laves and H. J. Wallbaum, Naturwissen Schaften (1939), 2J_, p. 674.  7. • H. W. Worner,. Journal. Inst, of Metals (1951), 79, 3, p. 173.  8.  H. W. Worner, Journal Inst, of Metals,(1951), 80, No. 5, P. 213.  9.  R. J. Van Thyne, H. D. Kessler and M. Hansen, Trans. A. S. M. (1952), p. 97k. P. Duwez, Trans. A. S. M., (1953), ^£5, P« 93^.  10.  1  kk,  11.  W. Rostoker, Trans. A. I. M« E. (1952), 19^, P. 209; Journal of Metals, Feb. 1952. ,  12.  J. G. Parr, Journal Inst, of Metals.(1952), 8 l / p. 2l4. i  13.  •'  P. D. Frost, W. M. Parris, L. L. Hirsch, J. R. Doig and 6. M. Schwartz, -. Trans. A.. S. M., (195*0, M> P« ' » 2  lk..  1  P. Duwez, Trans. A. I. M. E,. (.1951), 191, -P- 7^5.  15.  P. Duwez and J. Taylor-, Trans. A. I. M. E. (1950), 188, p. 1173.J Journal of Metals, Sept. 1950.  16.  H. Margolin, private communication.  17.  L. D. Jaffe, Discussion to paper by D. H. Polonis and J. G. Parr, (Ref. 18), Journal of Metals Supplement-, May, 1955, P-« 7l8•  18. - D. H. Polonis and J. G. Parr, Trans. A. I. M. E., "(195^), 200, p. Il48;  Journal of Metals, Oct. 195^.  19.  H. R. Ogden, F. C. Holden, R. I. Jaffee, Trans. A.I.M.E. (1955), 203, p. 105.  20.  J. R. Long, E. T. Hayes, D. R. Root, C. E. Armentroutj Bureau of Mines, .. R.I. U 6 3 . (19^9).  - 78 21.  H. Margolin-, E. Ence and J. P. Nielsen, Trans. A. I. M. E. (1953), 197. P- 2^3j Journal of Metals, Feb. 1953, Supplement.  22.  A. D. McQuillan, Journal Inst, of Metals, 1953 , 82-, No. 1, p. 47.  23.  F. C. Holden, A. A. Watts, H. R. Ogden, R. I. Jaffee, Trans. A. I. M. E., (1955), 2Q3, P. 117.  24.  A. Guinler-, Substructures•In Crystals, Imperfections, in'Nearly Perfect Crystals, Wiley, 1952, 402, New York.  25.  N. F. Mott, Proc. Phys. Soc, (1954), B  26.  C. S. Barrett/Transformations, and Deformation. Imperfections in Nearly Perfect.Crystals, Wiley (1952). p. 97. New York.  27.  A. H. Cottrell, Dislocations and Plastic Flow In Crystals, Oxford, 1953, p. 76, London.  28.  W. G. Burgers, Phys ica, 1_, 561 (1934).  29.  Y. C. Liu and H. Margolin-, Trans. A. I. M. E. (1953), 197, p. 667; Journal of Metals-, May, 1953.  30.  Y. C. Liu--, Research to be published, obtained through private communication with H. Margolin.  31.  S. Weinig and E. S. Macklin, Trans. A. I. M. E. (1954), 200, p. 1280.  32.  J. G. Parr, Acta Crystallographica, Nov. 1952 (5), p. 842.  33.  C..J. McHargue, Trans. A. I. M. E. (1952), 19^, P- 660.  3k.  G. P. Kurdjumov and 0. P. Maksimova, Doklady Akad. Nauk, S.S.S.R. 6 l ,  35.  R. E. Cech and J,, H. Hollomon-, Trans. A. I. M. E. (1953), 197, P« 685, Journal of Metals, May, 1953.  !  i  6k,  p. 729,.  (1948), 83, 73 (1950), 95.  •  36.. J. Philibert and C. Crussard, Journal Iron and Steel Institute•,May, 1955, 180, p. 39. 37» • M. Cohen, E. S. Machlln and V. G.. Paranjpe, Thermodynamics of'the . '• Martensitic Transformation, Thermodynamics in Physical Metallurgy, A. S. M. (1950), p. 242, Cleveland. \ 3.8.  J. C. Fisher, J. H. Hollomon, and D. Turnbull, Journal of Applied Physics, Aug.. 1948, Vol. 19, p. 775.  59.  H, Margolin, private communication to J. G. Parr.  4o.  R, I. Jaffee, private communication to J. G. Parr.  - 79 -  41. B. L. Averbacb and M. Cohen, Trans. A. S. M. (19^9), i£l, pp. 1024-1060. 42.  C. S. Roberts, B. L. Averbach, and M. Cohen-, Trans. A. S. M. (1953), PP. 576.  43.  C. A. Wert,,. Journ. of Applied Physics (19^9), 20, p. 9^3.  44.. W. S. Owen-, Trans. A. S. M. (195M, 46, p. 8l2. 45.  J. Burke and W. S. Owen, Journ. of Iron and Steel Inst"., Feb. 195**-, 176, p. 147.  46.  W. A. Johnson, and. R. F. Mehl, Trans. A. I. M. E. (1939), 135. p. 4l6.  47.  C. Zener, Journ.. of. Applied Physics (1949), 20, p. 950.  48.  W. Jost, Diffusion, Academic Press, (1952), p. 69.  New York.  49... W-. Tiller, K. A. Jackson,- J. W. Rutter, and. B. Chalmers, Acta Metallurgica. 50... C. Wert, Thermodynamics in Physical. Metallurgy. A. S.'M.  Cleveland.  (1950), p. 178,  51.  S. C. Das Gupta and B. S. Lement, Trans. A. I. M. E. (1951), 191. P« 727, Journal of Metals (Sept. 1951).  52.  S. A. Kulin and'G. R. Speieh* Trans. A. I. M. E. (1.952), 1<&, P- 258, Journal of Metals .(March, 1952).  .53.  C. H. Shih, B.. L. Averbach, and'M. Cohen-, Trans. A. I. M. E. (.1955), 205, p.. l83| Journal of Metals, Supplement (Jan.. 1955).  54.  G. B. Greenough,.-Quantitative X°Ray...Diffractlpn-^Observati-ons in- Strained . Metal Aggregatesj Progress.in Metal Physi6s, 4, Pergamon, 1952, p. 176, . London.  = 80 -  ACKNOWLEDGEMENT  The author wishes to express his gratitude to Dr. J. G. Parr under whose capable direction the research i  in this thesis was performed. Thanks are also extended to Professors W. M. Armstrong and P. A. Forward for their cooperation and encouragement and for providing the facilities for the research.- Many stimulating discussions held with various members of the Department of Mining and Metallurgy are gratefully acknowledged. The author would also like to place on record his thanks to Mr. R. G. Butters and the workshop personnel for their generous assistance and advice on many occasions. .' Finally, the financial assistance provided by the Defence Research Board of Canada (7510-18) and fellowships awarded by the International Nickel Company of Canada Ltd. are acknowledged with thanks.  - 81 -  APPENDICES  - 82  -  •APPENDIX I  LEVTTATION MELTING  Titanium is-a highly reactive metal which is particularly susceptible to interstitial contamination by ."Og'.Na-and Ha-at elevated temperf  atures.- The effect-of oxygen contamination.~on the hardness of pure titanium is illustrated in Appendix V.  As a result i t is necessary to prepare titan-  ium alloys in either a vacuum or a purified inert gas atmosphere. This extreme reactivity of titanium at temperatures over 700*C forbids contact with nearly a l l refractory materials both during heat treatment -and melting. The customary method of preparing titanium alloys for research purposes is arc-melting in a water-cooler copper hearth. This process is carried out by using either a tungsten-tipped or titanium-tipped electrode in an Inert gas atmosphere (argon or helium).. Arc furnaces are commonly used for producing commercial alloys since they are readily adaptable to large scale operations. In arc-melting, the entire charge'cannot be completely molten because of the chilling effect of the mold.- Therefore i t is necessary to remelt the alloy to ensure homogeneity.- Margolin (l) has reported that even after several re-meltings significant heterogeneity exists in an alloy button.  An additional disadvantage of arc-melting "is the  rather large cost of equipment, auxiliary Installation, and operation. Levitation melting is a possible alternative to arc melting for producing small quantities of alloys.• This method was first suggested for metals by Muck ( 2 ) .  It was more recently considered by Comeiietz and assoc-  iates ( 3 , 4 ) , who reported that they had 'almost completely melted a lump of  - 83 -  titanium bylevitation in a high frequency field'.  However, it was believed  that if- complete fusion were achieved the metal would be unstable in the field and would tend to drip. Subsequent experiments were performed in the U. B. C. laboratories (5),  to develop a levitation process by which titanium and its alloys might  be melted and cast. After experimenting with induction coils of many shapes a final design comprising a conical-shaped coil of seven parallel turns with an additional upper reversed turn proved successful. The upper reversed turn was necessary to stabilize the field in the coil. Without it metal levitated higher but moved around the periphery of the coil.  It was necessary  to have a large enough opening in the bottom of the coil to-allow the molten metal to drop through into a cold copper mold. The melting operation was performed under a positive pressure of purified argon and the system was enclosed by-a lucite cylinder and brass end plates.  In order to. ensure that any traces .of- oxygen and nitrogen  were completely removed 'the "system was evacuated -and flushed several times with purified argon before each specimen was.melted-. Positive' argon pressure of 5 lbs./in were necessary, to prevent arcing between the coil and specimen. 2  The levitation unit is illustrated iri. Figure. Land shown in "operation in Figure 2. The power source was a -Lepel. spark-gap»oscillatbr with a rated output of 3.75 kw, and a frequency of 200 to 500 kc/sec. With this equipment up to six grams of titanium can be successfully levitated-, melted and. cast. The specimens melted within 30 seconds, remained stably supported without dripping after melting and were cast by cutting the power. Solidification and subsequent cooling were very rapid. There was'.no alloying between the metal and the mold; and a bright, clean ingot was -produced. Titanium alloys were successfully prepared from Iodide titanium  = 84 bar stock by Inserting the.alloying element (lump form) in a hole drilled in the titanium. Subsequent checks revealed that homogeneous Ingots were consistently produced by the technique. CONTAMINATION Hardness measurements are accepted as a parameter^for oxygen and nitrogen contamination in-pure titanium. Values obtained after repeated melting and "re-melting 'ofrpure titanium showed, that no appreciable contaminat= ion occurred In levItation melting. Hardness figures are listed in Appendix V.  REFERENCES 1.  H. Margolin, E. Ence and J. P. Nielsen, Trans. A. I. M; E. (1953), p. 247.  2.  0. Muck, German Patent>_ No-. 422,004.  3.  E. C. Okress, D. M i Wroughton, G. Comenetz, P. H* Brace, J. C. R. Kelly, J. Applied Physics (1952), 23, p. 5^5.  ,  4. . E..C. Okress, D. Mi Wroughton, G. Comenetz, P. H. Brace, J. C. R. Kelly, J. Electrochem. Soc, (1952), 99, P« 205. '5.  D. H. Polonis, R. G. Butters, J. G. Parr, Research, London, (195*0> 7, 512.  - 8 5 -  APPENDIX I Free machining brass end plate  '$in.*Sin.* Vrein.thick  'Lucite 'cylinder - V in. O.D. - in. thick 7 in. long~  ofa/a.  • 1 to. rubber Q ring gasket (set in groove in brass p/ate) 'Ve xn.diam. steel rods  Induction coil Va in. O.D copper tubing 0032in? wall Copper mould- O.D. A in. I.D. V*  in.  3  Tubing to pipe connector  '1 m diam. rubber Oring gasket Loiver brass plate $in,.x$in. Vie in. thick  Power  leads ^  To pressure gouge. and vacuum pump  ^Wooden platform  Argon inlet Scale Vu- xn.= 1 in.  Figure 1. - Levitation Melting Unit  Figure 2. - Levitation Melting Unit in Operation  - 86 -  APPENDIX II  HEAT TREATMENT AND QUENCHING  Quenching Treatments Precautions against contamination were particularly important In the present work because most heat treatments were performed on powder specimens which, due to their large surface area, are more reactive than lump samples. Even minute traces of oxygen and nitrogen In an 'inert* atmosphere will cause sufficient contamination to affeoi; the properties of titanium alloys. Therefore the argon that was used for inert atmospheres was purified by^passing it through two calcium trains at 500*C (to remove nitrogen and oxygen), copper mesh at 500°C (to remove oxygen) and a  P2O5  trap (to remove water vapour). Developing a technique for quenching powder specimens from 1000'C created some initial difficulties. . In preliminary work specimens were heated In 1 l / 2 inch diameter vitreosil tube furnaces followed by water quenching under a pressure head. Fears that the specimens would be severely oxidized by the water at 1000*C were immediately substantiated. Additionally, the long heating times involved In bringing the'furnace and specimens to temperature gave further opportunity for contamination to occur. Subsequent work, was done in smaller tube furnaces of 3/8 inch diameter which were wound with chromel ribbon and could be heated to 1000*C in one to three minutes. In addition, a gas quenching method was devised. The following requirements dictated heat treatment technique:  - 87 -  (1) . Furnace must be gas tight and vacuum tight. (2)  A protective atmosphere is needed during heat treatment.  (3) Furnace must be capable of rapid heating to soaking temperature. (k) Ti=alloy specimens must, not-be in direct contact with refractory materials, including S1O2, at temperatures above 60O-700*C. (5)  Some non-contaminating quenching medium must be used.. Since specimens are very small-,- inert gas quenching is the best available method. The experimental arrangement for heating and quenching is  shown in Figure 1.  The specimen is contained in a small-molybdenum boat  in an atmosphere of purified argon for the required soaking time. - Then the system is evacuated, and immediately argon is passed into the furnace tube. The specimen is propelled from the furnace to the end of the tube where i t is cooled by combined radiation and forced convection.• This arrangement complied with the above requirements and produced consistently clean heat treated powders. As a check against contamination standard runs were made on pure titanium and hardness values indicated less than .03$ oxygen '+ nitrogen pick-up during heating and quenching (see Appendix V). Holding times at 1000*0 prior to quenching were standardized at one and two minutes. Longer soaking times produced no difference in structure in Ti-Fe and TI-Ni alloys. Titanium  ppwdeKS  finer than 65 mesh sinter quite readily during  heat treatment at temperatures above 800=900*C.  in some cases "it was  desirable to prevent sintering and the powders were continuously agitated during heating. This was done by using an arrangement shown it} Figure 2. When unsintered powders are quenched the maximum possible cooling rate Is expected since particles are individually exposed to the cooling medium.  88 lf»  acnfro/Al/'  S**b6er Seat  'A  /•fe/ttir?}  Cfirotne/ - A tome/ Ccup/c  W r  A7e> iybcrertuw b cet-tfMi/>o/ef •Specimen'-'  Figure 1. - Sketch of Heat Treating Furnace equipped for gas quenching.  Figure 2. - Arrangement for preventing sintering of powders during heat treatment by rotation of specimen.  - 89 Both argon and helium were used' for quenching, particularly in the Ti-NI system where quenching rate affected the constitution-of the product. In order to make an approximate determination of the relative quenching rates argon and helium cooling curves were observed on a cathode ray oscilloscope screen. The set-up involved connecting a thermocouple through an amplifier to a cathode ray oscilloscope. Measurements were made by observing the thermocouple potential change on the scope screen and showed that helium quenching from 1000*C is about five times faster than argon quenching. The measurements could not be made directly on alloy specimens since a thermocouple could not be maintained in contact with powders during quenching. It was possible to obtain the•following quenching rates by using i •• -  both argon and helium: (1)  helium quench  unsintered  (fastest)  (2) helium quench  sintered  (intermediate)  03)  sintered  (slowest)  argon quench  The absolute quenching rates could not be determined with the apparatus available. Isothermal Heat Treatments Isothermal heat treatments were performed on specimens sealed in evacuated vitreosil tubing. For heat-treatments above 700*C the tubing was lined With molybdenum so that the titanium powder would'not react with the Silica.  A^l silica capsules were pumped for one half to one.hour before  being sealed. Temperature control during isothermal heat treatment at k0O*  r  600*C was + 3*C. Wherever heat treatments were of less than 15  minutes duration a thermocouple was attached to the specimen tube and time was measured from the instant that the thermocouple reached temperature.  - 90 -  1 APPENDIX III  MICRO-HARDNESS TESTING  Metallographic specimens of alloy powders were mounted and polished in transoptic mounting compound in the customary way but with low mounting pressures. After specimens were suitably etched -(HF solutions) hardness measurements were made on +65 to =200 mesh powders by means of a Bergsman micro-hardness tester. Loads of 10 grams and 2-5 grams were commonly used. At least 10 hardness tests were made on each specimen and after rejecting the highest and lowest value the variation was not more than 10$. Additional specimens were mounted in cold setting resin to see i f mounting under pressure at 150*C affected the-micro-hardness. No differences in micro-hardness were detected, implying that in the case of retained j3  structures precipitation did not occur to any extent during  customary mounting procedures.  - 91 -  APPENDIX IV  HIGH- TEMPERATURE X-RAY GONIOMETRY  The constitution of alloys at elevated temperature is frequently studied by examining specimens which have been quenched to room temperature. In such studies i t Is possible that transformations may occur by shear or diffusion during cooling. Consequently in-order to determine the true phase constitution of alloys at a high temperature (say up to 1000'C) i t is necessary to actually make observations or measurements at the temperature. Recent progress has been made In developing hot-stage microscopy and high-temperature X-ray techniques.  .  A high temperature X-ray camera was used in con-junction with a Phillips X-ray goniometer to study phase transformations in titanium alloys. This camera has been described in detail elsewhere (I) and is shown in Figures 1-and 2. It is not proposed to elaborately-describe the camera construction here but the following essentials are mentioned for clarity. The alloy powder specimen is-placed.on a molybdenum "sheet which, in turn, rests on a fused quartz plate. The specimen-and-holder are enclosed by a water-cooled, brass case into which a platinum wound heating element is semi-permanently fitted. The winding of the heating"element is parallel to the axis of the quartz plate specimen holder in order to minimize the temperature gradients in the specimen. The entire assembly,  - 92 -  including brass can  and -speclinen-holder-, is fitted to a head which is  attached "to the -goniometer axis by-a shaft. During operation of the goniometer the specimen rotates at.one half the angular velocity-of the-geiger tube. The specimen temperature is-measured by means of a thermocouple which is touching the specimen. The. brass can h??s a slit or window of sufficient length about its circumference to-allow the X-ray beam to -enter and leave over a reasonable scanning range. This window- is-covered"by aluminum f o i l . The entire heating chamber is-vacuum., tight i f the window' seals, O-ring connection between the can and head and other minor connections are carefully made. When the camera-was. used ,to„,study the structure-of "titanium alloys up to 1000*C extreme caution._was.«observed..in *order -to minimize contamination by "oxygen "and nitrogen. ..A continuous. flow of he litmrrwas" passed through the camera prior to heating .in.-.order to ensure that ^any residual oxygen and nitrogen remaining after pumping-would be.diluted-. Further, the helium gas was purified "by passing it.through activated silica gel at liquid oxygen temperature- to-remove 0 and N. Zirconium powder was mixed with the titanium in: some runs at 1000*0-to act as a 'getter' for any traces Of 0 and N which might be present.  However, this was merely an  additional precaution which produced no difference in results in most cases.  REFERENCES 1.  R. G. Butters and J. G. Parr, Canadian Journ. of Technology (1955), 55, P. 117.  -93-  APPENDIX IV 3 Mo supports bound to furnace 8 shield  furnace terminal  binding wire  jaH  Mo radiation shield  moveable O-ring seal  Alfoil window  Y gas outlet  aligning adjustment  furnace |  brass can  I  Mo  I  3 en  t_  pi ate  p*» rOnt«  quartz plate  »—^gas inlet -thermocouple brass end-plate  IPS •4V-  Figure 1. - High temperature attachment for the X-ray spectrometer (Furnace winding and water-cooling are not shown)  Figure 2 . - Photograph of the High Temperature Attachment i n position i n the spectrometer.  - 9k =  APPENDIX V  CONTAMINATION OP ALLOYS  The magnitude of the effects of interstitial contamination on the properties of titanium "is described in almost every introductory paper on titanium. Hardness measurements are generally used to estimate the degree of contamination due to oxygen and nitrogen in pure titanium. . Accordingly, periodic heat treatments identical to those given to the alloys" used in this work were performed on pure iodide titanium. The degree of contamination Incurred in heat treatment could then be estimated. The heat treating techniques used in the present research were effective in restricting contamination to a very safe level. Typical results of hardness checks are summarized in the following, with estimated oxygen pick-up in parenthesis: 1.  Iodide Titanium Bar Stock - 75 VPN (Rp 72)  2.  Iodide Titanium Bar Stock Micro-Hardness .110 VPN  5.  Ti after levitation melting - Rp  80 to 90. No increase with successive  remelting. 4.  T i Filings - heat treated at 1000* in evacuated silica capsules, held 1 hour - VPN 120 (.03$ 0) . 3 hrs. - VPN 130 (.04$  0)  5.  Ti Lump -heat treated 3hours at 1000' - VPN 130 (.04$ 0)  6.  Ti Pilings in Argon Atmosphere - in heat treat furnace - 1 hour at 1000* - 120 VPN. (.03$  0) I  7.  T i Filings - heated to 1000* in high temperature camera, 1 l / 2 hours VPN - 150 (.20$  0)  - 95  -  The difference-between hardness and micro-hardness values for iodide bar stock is not surprising since micro-hardness values tend to be higher. • Effects of the polished surface together with the-very light loads (10 gm., 25 gm-) used in microhardness testing appear to account for this difference. The hardness, of titanium after melting and chill casting is expected to increase slightly because of internal stresses due to rapid solidification and cooling, and also due to the extremely fine grain structure produced. Accordingly, there is a slight Increase of hardness (5 to 10 points VPN).  - 96 -  APPENDIX VI  PHASE RATIO 'DETERMINATIONS  Throughout the work on titanium alloys phase ratios were determined from the relative intensities of X-ray diffraction spectra measured on a Phillips Geiger counter spectrometer. Introductory calibration studies showed that relative intensity measurements determined by pulse counting produced similar values to those obtained by measuring areas underneath the peaks on the recorder plots. It is well knpwn that the intensity of the diffraction lines of a particular phase depends on the number of reflecting planes and, therefore, on the quantity of phase present. The diffraction intensities for a series of lines of one phase should bear constant ratios to one another.  By calculating the structure factor and applying several corrections as  outlined by Barrett (T) and illustrated by Parr (2) the relative intensities of lines in two phases can be calculated from a knowledge of the structure cells and then used to assess phase ratios. The relative intensity of diffraction for a particular family of planes in a phase is calculated from the following equation i f the structure cell is known:  _L  oc  X  »  - 97 where  1 + cos^28 P sin^e  = Lorentz - Polarization factor  |F|*"  = Structure Factor  /AlC©)  =  •f(X)  Absorption Factor  ~ Variation of photographic effect with wave length  The quantity, I.represents the-relative intensity per atom for 100$ of one phase and when this calculated intensity is compared with that estimated for a particular set of planes in another, phase then the ratio of the two values Is the amount expected when equal amounts of the two phases are present. It is then possible to determine the phase ratios corresponding'to any other measured ratio of intensities,•as for example: For a 6 Atomic $ Ni alloy containing  oC + |6  Calculated relative scattering intensity/atom  c* i = 62100 1 Q  P no = 89300 , Therefore ratio Of intensities & * For a measured ratio r  for equal amounts of = 89300 = 62100  oi and ^  1.435  = x,  X  1^35  1  Therefore $ oc'  ~<x' 100  = x  $ 6 + 1  =100 - $ «  '  The percentages of o^' and j& in specimens of both Ti-Fe and Ti-Ni were determined by calculating the expected relative Intensities of ' oC  and  ^110 for equal quantities of the two structures.  In  - 98 -  this determination it-was-.necessary-.to-assume-a  random solute distribution  and to calculate a mean-atomic.scattering, factor. . In the Ti-Fe system the Intensity of the 11Q diffraction line of FeTi (body-centred cubic) was calculated on the basis that each structure cell consists of one atom of T i and one of Fe. The $FeTi was then determined from the measured intensity ratio of FeTi(110) . oi  101  Several complications arise in determining phase ratios on the basis of theoretical intensity calculations: (1) . Absorption effects are difficult to compensate and hence i t Is necessary to use neighbouring diffraction lines since their absorption characteristics are similar and may be ignored. This Is no serious problem in Tl-a-lloys because the 110 P  •, 002 °*  occur over a range 19* to 22*9 with Cu Koi  , 101 Oi  2  radiation.  (2) Some difficulty arises since the 101 oi However the 002 oi  , TlFeno and Ti Nl3as  and 110 ji> lines overlap.  line-at 19*9 can be accuratelymeasured and from the 101 oi  calculated and measured intensity ratio  002~oT~  the 101 line intensity. The intensity of 110 j&  * possible to determine s  can then be estimated by  difference. (3) At low 9 values the X-ray diffraction lines of the oi' (martensitic) and oi structures are coincident (both are close-packed hexagonal structures). Consequently, determination of the hexagonal phase includes--both oi and oi'  .  For the low alloys there is no marked difference between fihe mean atomic scattering factors of pi and  oi.' .  PHASE RATIOS FROM STANDARD CURVES In the Ti-Ni work i t was necessary to determine the percentage T12NI formed during heat treatment.  Thr structure-of this phase is complex  - 99 face-centred cubic with-96-atoms-per structure cell (3).  The--positions of the  atoms are "not yet known and hence, i t is impossible to calculate the intensity of reflections from this phase. The alternate method adopted and described is, in any case, probably more accurate than the method involving,calculation of intensity. A series of Ti-Ni alloy powders were heat treated' slightly below the eutectoid temperature to produce equilibrium phase ratios. The 511  ratios of intensities TiaNisss ;  .  '  ioi were measured from spectrometer  plots and the corresponding phase ratio for each alloy was calculated from the phase diagram by using the lever law. A plot was made of percentage TiaNi i  '  511  versus the ratio TigNisss oc i o i  for the range of compositions (Figure!) and this  was used as a standard in subsequent work to convert observed intensity ratios to percentage TiaNi.  '  The effect of the isothermal heat treatments-on the microstructure of the 6$ Ni alloy is shown in Figures 2. and 3.  Note that holding for  prolonged periods causes agglomeration of TiaNi.  REFERENCES 1.  C. S. Barrett, Structure of Metals, McGraw-Hill, 1952, New York.  2.  J. G. Parr, Research, (1953), p. 373.  3.  P.Duwez and J. Taylor, T-rans. A. I. M. E., (1950), 188, p. 1173; Journal of Metals (September, 1950).  Figure 1. - Standard Curve for Phase Ratio Determinations from measured, ratio of intensities TigNi .  -  101  -  Figure 2 . - Microstructure of 6 $ Ni alloy powder which was slowly cooled from the temperature range. Note pro-eutectoid T i N i formation and eutectoid of o£ and T I N i - Mag. 8 0 0 X 2  2  Figure 3 - - Photomicrograph of 6 $ alloy heated 1 7 hours at 7 5 0 * C to agglomerate T i N i i n &C matrix - Mag. 8 0 0 X 2  Etchant:  Etched i n  5$  HF In  H 0 - HN0 2  3  rinse  0  - 102  APPENDIX VII  RELATIONSHIP BETWEEN ALTERNATIVE METHODS OF. DETERMINING ACTIVATION• ENERGY - SIGNIFICANCE'OF THE COEFFICIENT 'n'.  (1)  The Cohen equation is  - K (l -/) t  m  dt where m = n - 1  (2)  After integration and taking logarithms• 1 K• loglog ~iZ~f = (m+l) log t + log .3(m+l) 2  METHODS OF DETERMINING ACTIVATION ENERGY Arrhenius Plot A plot of log K versus 1 yields QX 1  e  T  equal to the slope of  2.3R  the line. However i f the value Qt Is to be compared with-other rate processesK must be expressed in units of time ' . -  -  From equation (2) i t is seen that K  will have units time . As a result, obtaining Q directly from a plot of log K versus 1 will actually yield: 2.3(m+l) T (3)  Qp^ = (m+l) Q^_ where Q^. is the true energy of activatiqn. For this reason i t is necessary to plot 1 log K versus 1. m+l 2,3(m+l) T  and obtain Q directly or to apply equation (3) after plotting log +  versus 1 . T:  K . 2.3(m+l)  The value of Q^ can also be obtained by considering the relationship between log time a-nd 1 for a specific amount transformed (e.g. 50$). T  -103-  It is known that (k)  K = A  e'^™  Integrated form of equation (l) can be expressed as (5)  K =  - 2.3(m+l)log,(l4 ) m-+l :  t  Consequently by substituting (5) in (h) for K (6)  - 2,5(m-H)log(l-/) , m+l  = Ae  ~  Q  K  ^  t  Taking logs, numerator is a constant i f m is assumed constant ft for a particular reaction. Therefore: (7) B - 2.3(m+l)log t * A'- QK RT A is assumed constant and is a frequency factor for a first order reaction where K = time"^ . Rearranging equation (7), gather constants: (.8) log t  = ? +  Q« 2.3(m+l)RT  Consequently, a plot of log t versus 1 should yield a straight T* line of slope ( .3)(m+l)R 2  Qj^ bears no actual significance for comparison -purposes unless it is converted to QK m+1  units tlme~^ ^  . since i t corresponds to a specific rate constant in .  or time"".  m+  Zener (i,2) has shown that precipitation reactions which are growth controlled obey the following equation in the absence of impingement.  ft m is constant until a late stage in reaction as indicated -by similar slopes 1  of loglog  curves.  -104$ (t) = const X " t  n  £ (t) = fraction transformed t  = time  The coefficient n corresponds to m+1 of Cohen's equation as before. Zener has related the values of n to precipitate shapes as follows; n = 5/2 discs n =2  rods  n = 3/2 spheres n = 1 pearlitic type of growth. It is interesting to follow Zener's.argument-fey which he relates the.growth coefficient to precipitate shape. (a) In his theory of spherical precipitate growth,- Zener has shown that the radius of a growing sphere increases with time as follows: •A f~  l/2  = (t = t )-' x const. Q  3  Therefore the volume increases as  / %3/ or (t-t )  2  0  (b) For a long thin rod the length Increases uniformly with time  (c) For.a thin flat disc; l/2  thickness increases as (t - t )• radius increases as (t - to) Consequently ^ vol = const, x (t - to) /?(t - t ) = (t - t ) 5 / 1  2  0  0  2 x  constant  (d) For.a plane interface growth proceeds in one direction and hence & vol = const.,x (t - t ) 0  ALTERNATIVE EQUATION It should be pointed out that an alternative equation proposed  =105-  by Burke and Owen (3) for first stage graphltization in Fe-O-Si alloys can be applied equally well to the experimental results of this investigation.  This 'equation-differs from Cohen's..equationonly in the definition of the rate constant K. . Iff the Burke-and Owen equation.  is initially def-  ined in terms of units of. time and hence subsequent determination of Q K I yields the value Q,^ obtained from the previous treatment. . Comparison of equations (l) and (10) reveals the following relationship between Ki and K;  Therefore:  Since  is obtained from the earlier method by plotting  1 log K versus 1^ i t is seen that the same value will~be obtained by n 2;3n T plotting - log Kj  2?y  versus 1^ by the Burke and Owen method. T  REFERENCES 1.  C. Zener, Journ. of Applied Physics (19^9), 20, P« 950.  2.  C. Wert, Thermodynamics in Physical Metallurgy, A. S. M-. (1950), p. 178, Cleveland.  3«  J» Burke and W. S. Owen, Journ. of Iron and Steel Institute, Feb. 195**, 176, p. 1^7.  106'  APPENDIX VIII  SUMMARY OF SIGNIFICANT EXPERIMENTAL DATA  Ti-Fe SYSTEM and Ti-Ni SYSTEM  Ti°Fe ALLOY CONSTITUTIONS AS"QUENCHED SPECIMENS .(SINTERED) Spec-^ • £Fe 002 oi imen Atomic F 5 4  5 6 7 8 8A  9 10 11A 12  54 58 4o 59  .20 • 71 1.26 2.21 3.25 4.66 6.12 8.14 11.97 14.23 15.51  101 <* 110 4 ' 110  $  oi'  $ FeTi  FeTi  124 155 128 155 152 71 62 20  tr. tr.  tr. 42  55 85 95 106 127 100$ 100$ 100$  AND "TEMPERED 10 HRS. AT 570*C  002 oi  10l<*  110/3 $ c*  <  100 89 80 76 65  21  Qmnn  •49 40  17  tr.  . tr.  57 27 •  11 20  24 .  24  50.54 25 16 17. 10 9 11  55 51 60 85 100$ 100$ 100$  150 112-100 108 122 75 - 58 58-  36  32 59  $  $ FeTi  1  . 100  18 28 42 52 79 -97 .102 94 8l 60  90  85 77 66 55 44 59 51 28 54  . 10 17 25 .54 45 56 6i 6l 55 42  tr. 8 19  24  o "-  Qirihn AND. TEMPERED^.100..HRS. AT 5 7 0 ' F 5  4 5  6'  7 8  8A 9 10 11A  12  .20 .71 1.26 2.21 5.25  4.66  6.12  8.14  11.97 14.25 15.51  '  51 25 22 50 27. 24  i4 14  10  ll  12  115 110 69 99 97 86 50 50 56 59 45  tr. tr. 5(est)  14 52 54 45 54 43  58 56  tr. 6  15 11 17 29 4o 45  100 100 95 89 76 71 56 49 41 46  45  Qmoo AND TEMPERED 1000 HRS. AT 5 7 0 ' 74  tr. 5 11 19 21 57 4o 56 50 24 f  tr. 5 8 9  ll  25 30  51  .  240  17 16  60  21  76  18 18 16' •• ••  IP  15 12 14  59  65  65 58 56  .47 44 52-  5 7 12  • 19 25' 25 17  -18 . 15 8  100 100  tr.  96  2 10  86 75  67 65 55 57 5456  16 .  tr. tr. 2  4 9  20 21  26 17  15 16 19 . 26  15 10  55 54  I  108-  CONSTlTUTION AND: HARDNESS OF QUENCHED Ti-Fe ALLOY POWDERS AND LUMP SPECIMENS  ALLOY  H> IRON  . % c*'  F 3  0.20  100  4  0.71  90  5  1.26  80  6  2.21  75  7  3.25  65  8  4.66  50  8A  6.12  9  POWDERS LUMPS HARDNESS ft i o i ' HARDNESS 170  237 ft  195  257  Line of  254 454  ^o,  260  versus <f> Fe estd. approx. from film lines.  8.14  18  280  311  10  11.97  0  307  446  11A  14.23  12  15.31  Hi  13  19.62  458  14  25.32  580  1  600 493 366  503  Ti-Ni ALLOY (6f> Ni-} - DATA "Fftfr-DFJSOl^ 1  at 450*0 - 550*0 for Figures ,20, 25. 26.and 27 TEMP.- TOTE min. ~  450* 300  l44o  3000  4320 6000  30000 50000 500*  5 15  20 30 kl 6o 120 . 180 300 600 3000 525*  .75  1.0  1.25 1.5  3.0 5.0  8.0 15  "30 85  130  •  ' . - . " LOOi-o AREA RATIO. f T-ipNi ^ f r a c t .Time • from ion trans - x 100 l - / ( t ) . Ti NI Standard formedxlOO Plot  LOGib 1-'' • l-/(t)  :  i  2  2.4^8.  3V; 58 -J 3,4783.-636 3.778 4.478 4;. 700 r  0.7  1.176 1.303 1.478 I.671 1.778 -2.08 2.255 2.478 2.778 3,478 1,87  0  0.095 O.178 0.478 0.70 0.904 1.178 1.4"78  1.930  2.114.  .0512  ..08l4 .11  -.1475 .169 .198 .240 .0379 .0435 .08  .1024 .123 .126 .157 . .176 .1-96 .211  A*  6.3 9.2 10.912.0 14.7 16.3  3.0 3.4 6.1  7.8  9.25 9.5  11.6  .222  12.75 l4.25 15.4 16.3  ..0148 .0231 .060  1.2 2.0 4.5  .077 .093 .119 .139 .184 .207  6.0  .247  7.5 9.0  10.5  .13.4. 15.1 16..7  21.2-.. 33.3  48.6 57*9 65.O  77-7  86.4  78.8  1.285  66.7  1.5. 1.-95.-  42.1....  35.0 22.3  13.6  15.9 18.0 32.3  84.1  . 49.0 50.2 60.4 67.5 75.-4 81,5 86.0  51 ..49.8 39*6 32.5  4i.3  82.0 67.7  59.7  24.6 18.5  l4.o  2.37_ 2.85. 4.48  .292 .303 ^402 .498 .609 .732 . .854  1.465  l.4f 1.67 1*96  -. 2-*01 -2.52 - -3-08 . 4,06 5.^  7.I5  .1.47  44.3  1.90 . 2.25 3-44  84.7  ld.3-  1.12  1.33  1.66.  5.02 6.L4  .222  - .963  - .75-+  1.658  5.875 2*934  68.2  .29-. 119.9  1.8l4  -0.075 0.086 .167  31.8  70,9 . "80.1  .652  • .455  1.19  1.22.  24.8  60.4 52.5  1.037 1.246 . 1.462 1.57*  .866  1.07  39.6 W.5 55.7  •  .176, >i290 .375  7.3^  93.65 89.4 75-2  6.35  10.6  .0vl09  LOGioLOGio LOG.LOG .1- " l-/r(t)  1.938  1.222 1.346  -  .538 .426 .542 .186 .062  -  1.125 -1.066 0.778 O.656  - 0.535 - 0.519 - 0.396 - 0.303  l,48l  l,6o4 1.697  1.784  - 0.216 - 0.135 - O.069  1.865 1.931  - 1.538  0.029 -.0.649  5.462 2.690  1.094  - 0.906  . - O.167 .. - 0.220  1.222  -  0.124  . 0.278 -0.352 —OU-536 0.701 JO.788  - .1.310  1.343 1.444  l»5*6  1.730  1.846  1.896  -  0.778 0.657 0.556 0.454 O.270 - O.156 --0.104  (continued next page....)  "TEMP. TIME, .min.  550*  .25 .5 • 75 1.0 1.5 2.0 3.0 4.0 6.0 9-0 15*0 30.0  6o.O  LOCrjo Time  1.398 T.'7 T.8Y5 . 0 0.178 0.303 0.478 0.6 0.778 0.955 1.179 1.478 1.778  AREA. RATIO j> TigNi #k fract- 11TigNi from ion trans- X 100 l-/"(t) Standard formed X100 Plot .0194 .0594 .062 .071 .095 .109 .129 .171 .19 .195 .203 .201 .23  1.7 4.2 4.8 •5-5 7.4 8.3 9-75 12.2 13.^9. l4,25 14.8 15.8 16.8  9-0 22.2 . 25.4 29.1 • 39.1 43.7 . 51.6 64.5 -73.5 75.7 78.3 83.6 88.8  LOGio LOGJQLOGI n LOG LOG .1 ' • --1 _JL l-y;(t) l-./(t)  -i<)4i ..1..191 . -1.28 77.8 .107 .127 74.6 ...L.34 1.4i . .149 70.9 1,64 . -..21-5 -.60.-9 .248 ..1...77 -56.3 48.4 . .2.1.1 .325 2.B2 .45 - 35.5 .576 ..-26.5. . 3.77 . i6l4 4.11 24.3 4.6 ' .663 21.7 16.4 6.1 .785 U.2 • 950 8.91  2.613 . 1.029 1.104 1.173 •T.332 .1.394 1.512 1.653 T.761 .1.788 . 1.822 T.895 1.978  - 1.387 - 0.971 - O.896 - 0.827 -  0.668 O.606 0.488 0.347 .0.239 .0.212 ,0.178 0.105 0.022 I M  oI  - I l l -  DATA FOR FIRST 3rAtffi.:-3^0MPOSa'Jtt6^-^ ^All^>A  >  FOR FIGURE 30:(a. b and•-c)  Ratio of" Intensities . ,,#110, = mi  10".Gm. . load . V.P.N." Hardness  Temp.  •Time min.  400*C  30 60 120 240 360 480 900 1380 1680 2400 2880  3.95 2.04 1.49 1.24 1.14 1.03 .58 .48 .29 .07 .00  26.6 4i.3 49.2 54.0 56.0 58:4 71.5 75.2 83.O 95-0 100  73.4 58.7 , 50.8 46.0 44.0 4i.6 28.5 24.8 17.0 5.0  580 570 .^24  4 15 30 60 90 120 150 240  4.96 3.31 2.0 1.53 • 73 .77 . .33  22.4 30.2 4i.7 48.4 39-9 65.4 81.2 100  77.6 69.8 58.3 51.6 60.1 34.6 18.8  600 '577 ' 570 482  1 2 5 10 15 20  3-50 2.11 1.35 .69 • .31  29.O 4o.4 51.5 67.6 82.2 100  71.0 59-6 49.5 32.4 17.8  425*  450*  NOTE:  x  1  560 465 450 •425  - 444 "  420 570 520 500 472 425 420  hardness. listed representsi the average of at least 10 values.  I  DATA FOR ISOTHERMAL-DECOMPOSITION OF. <*" IN Si Ni - ALLOY FOR FIGURES 52.55 AND 54  -/fcl •  TEMP. TIME • min.  LOG jo Time  AREA.RATIO TiaNi  450*  V?  .045 .060 .106 .150 .20 , .215  5.4 4.5 8.0 11.2 14.6 15.7  ,l80 .258 .422 .595 • 772 .852  .820 .762 • 578 .407 .228 .168  .04 . .065 .095 .14 .20 .25  5.2 5.0 7.5 10.5 14.7 16.7  .170 .265 .586 .556 .778 .884  .850 .755 ' .6i4 .444. .222 .116  : 1.20 1.56 I..65 2.25 4.50 8.60  500*  50  100 400 1000 3150 7280  2.0 2.6 5-0 5-5 3U9  % TigNi from Standard Plot  fraction transformed. X 100  1  x 100  1.22 1.51 ... 1.75 2.45 4.-58  i  LOGio .-••1, >/(*.)  LOGioLOGm • 1 l-/(t)  LOG LOG  0.086 0.118 0.258  2.-954  - 1.066 - 0.928 - 0.624 - O.4io - 0.192 --0.111  0.080 -0.135 0.212 0.352 -0.653 0.934  15.90 1.124 T.526 1.815 1.970  -. 1.1. . - 0.876 - 0.674 - -0.454 - 0.185 - 0*05  "2.875 1.000 l.44i 1.696 T.894 T.982  - 1.125 - 1.000 - 0.559 - 0.504 - 0.106 -- 0.018  2V968 1.124 1.504 1.596 l.8l4. 1.910 .0.124  - 1.052 - 0.876 - 0.696 - 0.4o4 - O.186 - O.090 0.124  •Ov390  0.642 0.775  4 10 25 . 50 100 600  0.6 1.0 i.4 1.7 - 2.0 .£.8  525'  0.5 1.0 4.0 10 50 100  1.7 0 0.6 1.0 1.7 2.0  .04 .05 .117 .175 .217 .250  5.0 4.0 8.8 12.9 15.8 16.8  .159 . .211 .471 .682 .856 .890  .841 .789 .529 .518 .164 .110  1.19 -1.26 1.89 5.14 6.09 9rl0  0.075 0.100 0.276 0^97 0.784 0.960  550'  .3 .5 .1 3 6 10 55  1.48 1.7 '0 0.48 0:78 1.0  .045 .065 .090 .155 .200 .220 .245  5.7 5.0 7.0 11.5 l4.7 16.0 18.O  .195 .265 •570 •598 .778 .846 • 955  .805 .755 .650 .402 .222 .154 .047  -1.24 1.56 1-59 2.48 4.50 6.50 21.5  0.093 -0.155 0.201 0.595 0.655 0.815 I.529  1.54  1  1.072 I.576 1-.-590 1.808 1.889  1.546  -113-  Ti-Ni ALLOYS. -• CONSTITUTION AND HARDNESS - OF QUENCHED POWDERS  Alloy N 1  2 3 4 5  6 7  Atomic % Ni  10 ,gm. V.P-.N. Hardness Argon Q • He Q  0.25 0.5 1.0 2.0  l43 197 225 254 3*5 44o  4.o  6.0  159 207 229 297 429 475 500  46o .  7.0  % Retained HeQ  12 20 44  N 6 - , 6ja .Ni - , MlcrorHardness of Tempered Structures , (10 gm. Load) Temp.  Time  Hardness  Temp.  Time  Hardness  1 l/2 6 l/2 15 180  369 330 320 318  15 45 4 9 60  362 320 310 290 275  450*  60 l44o 4320 30120  387 365 320 309  525*  500*  5 45 120 600  400  550'  357 329 313  .  -11*-  APPENDIX IX  PUBLICATIONS RELATED TO THE PRESENT THESIS  1.  Levitation Melting Titanium and Titanium Alloys, Research (195*), y i i , 2, S 12.  2.  Some Techniques for Melting Reactive Metals, Research (195*), VII, p. 272 1  Three basic melting methods are reviewed that may be applied to metals which, on account of their reactivity, cannot be melted in 1  refractory crucibles. Levitation melting is- considered in most detail, as the technique Is felt to warrant more- attention than i t has received in the past.  3.  Phase Transformations in Titanium-Rich Alloys of Iron and Titanium, Journal of Metals, Oct. 195*J Trans. A. I. M. E. (195*), 200, p.11*8. High purity alloys of titanium and iron, made by a technique of levitation melting have been investigated with particular reference to martensite formation and decomposition in the hypoeut'ectoid range. A preliminary study has been made of the phase corresponding to the structure TisFe.  4.  Martensite Formation in Powders and Lump Specimens of Ti-Fe Alloys, Journal of Metals, January, 1955*  5.  Non-Equilibrium Structures In Ti-Alloys, Letter to.the. Editor, Journal of the Institute of Metals, Oct., 195*.  6.  Isothermal Decomposition Kinetics of Transformed-^ Ti-Ni Alloy, Acta Metallurgica, in press. '  Phase in a  

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