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Martensitic transformations in Ag-Cd and Ag-Zn alloys Kirshnan, R.V. 1971

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MARTENSITIC TRANSFORMATIONS  IN Ag-Cd and Ag-Zn ALLOYS  BY  R.V. KRISHNAN  B.Sc, B.E.  Mysore U n i v e r s i t y ,  1964  (Met.), I n d i a n I n s t i t u t e o f S c i e n c e , Bangalore, 1967  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  i n the Department of  METALLURGY  We accept t h i s t h e s i s , as conforming required  THE  to the  standard  UNIVERSITY OF BRITISH COLUMBIA J u l y , 1971  ;  In p r e s e n t i n g t h i s  thesis  an advanced degree at  further  for  agree  of  the  requirements  freely  available  for  this  this  thesis for  written permission.  Department  financial  i s understood that gain s h a l l f  of  The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada  not  that  thesis  s c h o l a r l y purposes may be granted by the Head of my Department It  for  r e f e r e n c e and s t u d y .  t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f  by h i s r e p r e s e n t a t i v e s . of  fulfilment  the U n i v e r s i t y of B r i t i s h Columbia, I agree  the L i b r a r y s h a l l make i t I  in p a r t i a l  or  copying or p u b l i c a t i o n  be allowed without my  ii ABSTRACT A study has been made of the martensitic transformations occurring in g-phase silver-cadmium and silver-zinc alloys. alloys the M  g  In silver-cadmium  temperature was found to change from -44°C to -137°C  as the cadmium content changed from 44.2 at. % Cd to 47.0 at. % Cd. Alloys of silver-zinc did not show any martensitic transformation; even on cooling to liquid helium temperature. The thermal martensite i n Ag-45 at. % Cd alloy was found to have an orthorhombic structure of the 2H type. X-ray diffraction and electron microscopy.  This was confirmed by A spontaneous martensite with  a face centred cubic structure was found to occur along the thin edges of perforated specimens used for electron microscopy, because of the relaxation of volume constraints during thinning. In both Ag-45 at. % Cd and Ag-41 at.% Zn alloys a <111> slip direction was found.  Also i t was shown that Ag-45 at. % Cd alloy was  elastically anisotropic, a characteristic very common to g-phase alloys. In both Ag-Cd and Ag-Zn alloys a face centred tetragonal structure could be formed on deforming the specimens by rolling or by tensile deformation.  The structure changed to close-packed on severe deformation  e.g. by f i l i n g .  At lower Cd and Zn contents this close-packed structure  was face centred cubic, whilst at higher alloy concentrations, this structure was close-packed hexagonal. Pseudo-elasticity was found to occur by stress-induced martensitic transformation.  Maximum pseudo-elasticity occurred at temperatures just  above A^ and the actual amount of pseudo-elasticity was found to be dependent on the orientation of the tensile axis.  iii The strain memory effect was studied by deforming specimens below  and then heating.  At temperatures below M^,  deformation  of the martensite takes place and i t is suggested that there is a change in the martensite structure, involving a change from thermal martensite to stress-induced martensite. The experimentally determined habit planes for thermal, stressinduced and deformation martensites were found to agree well with the values obtained using phenomenological theory assuming a microscopic shear.  {110}<110>  The 'elastic' elongations accompanying the trans-  formation could be accounted for using the theory. suggesting the course of the transformation was  A mechanism  developed.  iv TABLE OF CONTENTS Page 1.  2.  INTRODUCTION  1  1.1  General Review  1  1.2  Morphology of Thermal Martensite  3  1.3  Crystallography of Martensitic Transformations ....  4  1.4  Stress-Induced Martensite  6  1.5  Martensites in Cu and Ag Base Alloys  8  1.6  Deformation-Induced  1.7  Electron Microscopic Observations  14  1.8  Aim of the Present Work  14  Martensite  10  EXPERIMENTAL PROCEDURE  15  2.1  Alloy Preparation  15  2.2  Preparation of Tensile Specimens  18  2.2.1  Polycrystalline Specimens  18  2.2.2  Single Crystal Specimens  19  2.3  Metallography  20,  2.4  Preparation of Ag-Zn Crystals  20  2.5  Orientation Determination  20  2.6  X-Ray Diffraction  21  2.6.1  Room Temperature X-Ray Diffraction  21  2.6.2  Low Temperature X-Ray Diffraction  21  2.7  Measurement of Transformation Temperatures  21  2.8  Tensile Tests  23  2.9  Habit Plane Determination  24  2.10 Deformation Martensite  24  2.11 Electron Microscopy  24  V  Page 3.  EXPERIMENTAL RESULTS AND DISCUSSION  27  3.1  Quenched Structures in Ag-Cd Alloys  ,  27  3.2  Determination of Transformation Temperatures  29  3.3  3.4  3.2.1  Ag-Cd Alloys  3.2.2  Ag-Zn Alloys  ;  ^  29 33  Structure of Thermal Martensite  34  3.3.1  Introduction  34  3.3.2  X-Ray Diffraction Results  35  3.3.3  Martensite Structures in g-Phase Alloys ....  40  3.3.4  Structure Analysis  41  3.3.5  Electron Microscopy of Thermal Martensite in Ag-45 at. % Alloy  / 48  3.3.6  Spontaneous Martensite Obtained at Room Temperature  51  Slip Systems in Ag-Cd and Ag-Zn Alloys  58  3.4.1  58  Experimental Results  3.4.2' Discussion of Slip Systems in CsCl Type Alloys  65  Discontinuous Slip i n Ag-Cd Alloys  65  3.5 3.6  Modulus Determination in Ag-Cd Alloys Deformation Martensite Formed by Filing ^ Ag—Cd Specimens  69  3.7  Nature of Martensite Produced on Cold Rolling  75  3.7.1  Optical Microscopy of Deformation Martensite  75  3.7.2  Structure of Martensite Formed on Rolling a Ag-45 at. % Cd Alloy  77  Structure of Martensite Formed on Rolling a Ag-41 at. % Zn Alloy  80  General Discussion  83  3.4.3  3.7.3 3.7.4  72  ..  vi Page 3.7.5 3.8  3.9  4.  Electron Microscopy-of Rolled Specimens ....  83  Stress-Induced Martensite in Ag-45 at. % Alloy  90  3.8.1  Single Crystal Specimens  90  3.8.1.1  General Shape of Tensile Curve ....  91  3.8.1.2  Effect of Temperature  97  3.8.1.3  Effect of Orientation on the StressStrain Curves  108  3.8.2  Polycrystalline Specimens  118  3.8.3  Microscopic Observations  124  3.8.4  Strain Memory Effect  126  3.8.4.1 Experimental  126  3.8.4.2  130  Discussion  Habit Plane Determination  134  3.9.1  Experimental Results  134  3.9.1.1  Thermal Martensite  134  3.9.1.2  Stress-Induced Martensite  135  3.9.1.3  Deformation Martensite  135  3.9.2  Theoretical Calculations of Habit Plane Poles  137  3.9.3  Discussion  143  3.9.4  Course of the Transformation  CONCLUSIONS  ..  152  158  APPENDIX A Matrix Algebra of Martensitic transformation  161  vii  P  a  S  e  APPENDIX B  Calculation of Strain Associated with the Transformation  REFERENCES  171  1 ? 7  i  / /  viii LIST OF FIGURES Figure 1  2  3 4  Page Schematic diagram showing the variation of chemical free energy with temperature for parent and product phases  2  Basic relation between the b.c.c. lattice and the essentially close-packed structures resulting from martensitic transformation  10  Ag-Cd phase diagram showing the alloy compositions used  16  Ag-Zn phase diagram showing the alloy compositions used  17  5  Dimensions of the tensile specimen . ..'  18  6  Specimen holder for low temperature x-ray diffraction  22  7  Apparatus used for stressing specimens .. .  25  8  Bainite needles in quenched 44.3 at. % Cd alloy ....  28  9  Micrograph of thermal -martensite  31  10  Variation of M , M,, A , A. temperature with compos32  11  ltxon X-ray diffractometer trace for thermal martensite in Ag-45 at. % Cd alloy  36  ...  S  X  S  I  —  0  12  Unit c e l l of orthorhombic martensite .  39  13 14  Close-packed layer in f.c.c. structure Reciprocal lattices for close-packed structures with different stacking orders Atom positions in the basal plane of close-packed structures  42  15 16  :  43 45  Basal plane of the reciprocal lattice of close-packed s tructures  ;  45  17  S.A.D. of thermal martensite  49  18  S.A.D. of thermal martensite; 0G intersection  50  ix Figure 19 20  Page Electron micrograph of thermal martensite showing 'needles'  52  Electron micrograph of thermal martensite showing the faulted structure  ,  53  21  Spontaneous martensite in Ag-45 at. % Cd alloy .....  ; 54  22  S.A.D. of spontaneous martensite revealing streaking along 111 direction Stacking fault fringes in spontaneous martensite ..  55 56  24  Variation of lattice parameter of g-phase vs. composition  57  25  Spontaneous martensite showing striations along different directions in different regions  59  26  S.A.D. of twinned area in spontaneous martensite...  60  27  Location of tensile axes and corresponding slip  23  planes in Ag-45 at % Cd alloy . . 28a,b  62  Slip traces in Ag-45 at. % alloy  63  29  Slip traces in Ag-41 at % Zn alloy  64  30  Coarse slip markings in Ag-45 at. % Cd alloy  68  31  Interferometric pattern of the surface of a specimen after very light deformation Tensile axes for specimens tested for modulus determination  69  Diffractometer traces of filed Ag-Cd alloy specimens  73  Deformation martensite in Ag-Zn alloy. Microstructures on the rolled surface and on a second surface at right angles  76  35  Diffractometer traces of deformation martensite as a function of % deformation for Ag-45 at. % Cd alloy..  78  36  Diffractometer traces of deformation martensite as a function of % cold rolling for Ag-41 at. % Zn alloy .  81  37  Electron micrograph of an as-quenched Ag-45 at. % Cd alloy revealing dislocation structure  ' 84  32 33 34a,b  68  X  Figure 38  Page Electron micrograph of 15% cold rolled Ag-45 at. % Cd alloy  86  Electron micrograph of deformation martensite in 15% cold rolled material  87  Electron micrograph of deformation martensite in 40% cold rolled material  88  41  S.A.D. of deformation martensite  89  42  Orientation of tensile axes of specimens used in stress-induced transformations  91  43  General shape of the tensile curve obtained at temperatures above A^ in Ag-45 at. % Cd alloy  92  44  Micrographs of a tensile specimen showing the formation of stress-induced martensite and i t s reversal..  94  45  Stress-strain curve corresponding to the photographs in figure 44 .  96  Stress-strain curves for specimen 1, over a series of temperatures  98  39 40  46 47  Variation of stress necessary to form SIM with temperature for specimen 1  101  48  Pseudo-elastic recovery vs. temperature for specimen 1  102  49  Stress necessary to form martensite vs. temperature for specimen 4  104  Stress necessary to form martensite vs. temperature for specimen 5  105  Stress-strain curves showing repeated testing at -45°C  107  50 51 52.  Stress-strain curves for specimens 1, 5 and 7 at (a)  -60° C  109  (b)  -55°C  110  (c)  -45°C  Ill  (d)  -35°C  112  (e)  -10°C  113  xi Figure 52  Page (f) Stress-strain curves for #8, at RT strained twice (g)  53  (a) (b)  54  115  I n i t i a l straining of specimen close to [001] showing plastic deformation  116  Surface of #8, after f i r s t strain showing slip markings .  117  Above specimen polished and strained to form martensite and released  117  Stress-strain curves for polycrystalline specimens over a range of temperatures  119  Stress necessary to form martensite vs. temperature for polycrystalline specimens  121  56  Amount of pseudo-elastic recovery vs. temperature for polycrystalline specimens  123  57  Deformation martensite in Ag-Cd polycrystal after tensile testing. Traces on two surfaces  125  55  58  Typical stress-strain curve used in strain memory effect  59  60 61 62  127  (a)  Strain'memory recovery vs. temperature for ill..  128  (b)  Strain memory recovery vs. temperature for #2..  129  Photographs revealing the changes in morphology of thermal martensite brought about by stressing ...... Habit plane normals for thermal martensite and S.I. martensite (a) Habit plane normals for deformation martensite in Ag-45 at. % Cd alloy (b)  Habit plane normals for deformation martensite in Ag-41 at. % Zn alloy  63  Lattice correspondence between the body centred cubic and the orthorhombic lattices  64  Laue back reflection photographs of $^ martensite phases  65  Geometrical construction to calculate the tensile strain involved in the transformation  anc  131 134 136 136 i 139  ^ S.I.  142  i  144  xii Figure  Page  66  Stereographic projection showing the various angular relations involved in the calculation  148  67  Stereographic projection showing contours of calculated amount of strain obtained during S.I.M. transformation for various orientation os the tensile axis  150  Strain values associated with oriented thermal martensite for various orientations of tensile axis.  150  Close-packed layer of (110) showing the atomic shuffles needed to produce tne'martensite structure.  153  70  Schematic diagram indicating the course of transformation  155  71  X-ray diffractometer trace of filed specimen (Ag-45 at. % Cd) at l i q . N temperature  156  68 69  xiii LIST OF TABLES Table I  Page Structures of thermal and deformation mart'ensites in Ag, Au and Cu base alloys  II III IV V VI  VII VIII IX X  XI XII  XIII  XIV XV XVI  Compositions of Ag-Cd alloys used  11 ...  List of common symbols used in identifying martensite structures in g-phase alloys Positions of diffraction peaks for thermal martensite in Ag-45 at. % Cd alloy Calculated relative intensities of reciprocal lattice points for a 2H structure  27 35 37 47  Comparison of d values (for thermal martensite) obtained' from x-ray and electron diffraction  48  Slip systems in Ag-Cd and Ag-Zn alloys  61  Slip vectors and ordering energy relationships of some CsCl type alloys Young's modulus values for various orientations in Ag-Cd alloys  66 70  Positions of the diffraction peaks for deformation martensite, as a function of % rolling for Ag-45 at. % Cd alloy  79  Positions of diffraction peaks for deformation martensite for Ag-41 at. % Zn alloy  82  Comparison of lattice spacings obtained from electron and x-ray diffraction for deformation martensite in Ag-45 at. % Cd alloy  90  Lattice parameters of fc^ orthorhombic structures of Ag-45 at. % Cd alloy used in the theoretical calculations  137  Crystallographic data calculated from the theory ...  140  Calculated orientation relationships between g 2 ~ P and S.I. martensite  141  a n a  Comparison between the calculated and experimental values of <j>  nase  145  xiv Table A-1  A-2 B-l B-2  Page Crystallographic data calculated from theory for different secondary shear systems for orthorhombic martensite  169  Habit plane normal for deformation martensite for Ag-Cd and Ag-Zn alloys  170  Calculated values of strain for stress-induced martensite  172  Calculated values of strain for thermal martensite .  176  XV  ACKNOWLEDGEMENT The author wishes to express his sincere gratitude to Dr. L.C. Brown, for his advice and assistance during the course of this investigation.  It is a pleasure to thank Dr. E.B. Hawbolt and Dr. D.  Tromans for their helpful comments and criticism.  I would also like  to thank Professor R.G. Butters for his help in the construction of the specimen holder for low temperature X-ray diffraction and the tensile jigThanks are also extended to the members of the faculty and fellow graduate students for helpful discussion.  The assistance of  the technical staff is greatly appreciated. Financial assistance provided by the National Research Council under grant number A2549, and the graduate fellowship awarded by the University of British Columbia are gratefully acknowledged.  INTRODUCTION 1.1  General Review Martensitic transformations are known to occur in a number of  ferrous and non-ferrous systems. A martensitic transformation is one in which there is no change in composition and the product phase is produced by the coordinated movements of atoms of the parent phase. The transformation results in a shape deformation which gives rise to a t i l t on a prepolished surface.  The interface between the martensite  phase and the parent phase i s essentially undistorted and unrotated and the Miller indices of the habit plane are characteristic of that alloy.  The principal directions and planes in both lattices are  related by means of an orientation relationship''".  The transformation  may be considered quite analogous to twinning. Much of the work in martensitic transformations has been based on ferrous alloys because of their industrial Importance. However, non-ferrous martensites have been investigated quite extensively during the last twenty years. The thermodynamics of the martensitic transformation can bestjbe understood from a plot of chemical free energy vs temperature of the parent and martensite phases, Figure (1). At temperature T ,  the.  ICA  > o _J ac •• i UJ Z 111 UJ  1• 1  LU  X UJ CJ UJ £T  TEMPERATURE  Figure 1.  Schematic diagram showing the variation of chemical free energy with temperature for parent and product phases.  chemical free energies of the parent and martensitic phase are equal. Below this temperature the transformation from matrix to martensite is accompanied by a decrease in the chemical free energy.  The trans-  formation might be expected to occur at the temperatures below T ; Q  however, the formation of martensite is associated with the production of new interfaces and the concomitant increase in surface energy.  There  is also strain energy associated with the formation of the new phase. The decrease in chemical free energy has to compensate for these factors and as a consequence the M  g  temperature (i.e., the temperature at which  the martensite phase f i r s t appears) is below the equilibrium T  value,  3. the difference between the two temperatures reflecting the relative magnitudes of the surface and strain energy terms. In the case of an 2 Fe-30% Ni alloy , the M temperature is 180°C below T , whilst in an g  q  3  Au-Cd (50-50) alloy  i t is only 8°C, the difference being due to the  much larger strain energy contribution in Fe-Ni.  The martensite;  produced i s generally athermal and the transformation proceeds pnly on further cooling.  ;  The temperature at which the transformation is  completed i s denoted as M^. The martensitic transformation is generally reversible so that on heating the martensite phase to a sufficient temperature, (A ), i t g  begins to transform to the original parent structure.  If i n i t i a l l y the  parent phase i s in the form of a single crystal, i t remains so after the reverse transformation. However, in cases where a diffusion controlled reaction i s competing with the reversal, the martensite transformation may not take place.  parent  On heating the martensite in Fe-C  alloys diffusion controlled carbide precipitation occurs. 1.2  ,  Morphology of Thermal Martensite There are two types of thermal martensite depending upon the nature  of i t s formation: (a)  thermo-elastic martensite and  (b)  burst martensite.  Thermo-elastic martensite forms at temperatures just below'M. In this case the martensite and the parent phase are in thermo-elastic 4 equilibrium  and any change in  of martensite present.  the temperature w i l l affect the amount  The martensite is in the form of long thin  p l a t e s which in  the p l a t e w i d t h .  application Burst M  g  of  Similar  martensite  more t h a n  temperature  30%  of  the  at  at  alloys the  designated  v a r i a n t s of  triggers  growth  occurs  Fe-Ni  b e l i e v e d t o have  certain  increases i n length with  external stress  temperature.  that  is  g e n e r a l l y grow b y  can  constant  The  brought  example  transforms of  i n the mechanical The  about by  significantly  occurrence  the h a b i t p l a n e .  change the  temperature"*.  a classic  specimen volume  as M^.  be  temperatures present  i t s origin  formation  also  little  below  the  of  this in.  a t one  specific  this  type  of  martensite  c o u p l i n g between  formation  of  one  of o t h e r p l a t e s i n the n e i g h b o u r i n g  plate areas,  7 i.e.,  the process  observed  1.3  by  is autocatalytic  P o p s and  .  This behaviour g M a s s a l s k i i n Cu-Zn a l l o y s .  has  also  been  C r y s t a l l o g r a p h y of M a r t e n s i t i c Transformations The  c r y s t a l l o g r a p h y of  the m a r t e n s i t i c t r a n s f o r m a t i o n has  been  9-14 studied plane  in detail  has  been  composition, and  Read  observed assumes so  found  but  (WLR)  by  has  many r e s e a r c h w o r k e r s t o be  high M i l l e r  t h e o r y has  habit planes that  the  and  The  the  index  values.  The  t h e most w i d e l y  used  orientation  phase  The  The  i s one can  martensite  reproducible for a given  grow w i t h no  Lieberman  to e x p l a i n The  zero  habit  alloy  Wechsler  relationships.  of e s s e n t i a l l y  the  theory  distortion  accumulation  of  strain  interface.  transformation i s considered  mathematical (a)  been  habit plane  t h a t the m a r t e n s i t e  energy- a t  fairly  .  to  take  place i n three  stages  for  to the  lattice.  convenience. change  from  the  parent  lattice  product  5. In  this  step  the  the o r i g i n a l lattice  final  product  lattice.  The  correspondence The  most  However, t h i s  undistorted second  crystal in  or  This  invariant  incorporated  position  and  invariant The  invariant  unchanged, but  a plane  The  i n the  plane  i s controlled and  assumed  deformation  also  itself  cannot  w h e r e P^  direction  of  this  i s rotated  body r o t a t i o n  u n r o t a t e d as  lattice  leaves  which remains a pure  R B  used  shear have t o  from  i s invoked  i n the mathematical  P  i s the  lattice  invariant  B  i s the  lattice  variant  i s the  deformation  strain) rotation  undistorted.  slip  shear be  i t s original t o make t h e  analysis  has  P  shape  described  :  well.  total  R  a  the  calculations.  i s the  (Bain  an  hence  the deformation  c o n s i d e r e d t o be  generated  hence a r i g i d  =  in  produce  form:  1  the  lattice  obvious  t h e m a r t e n s i t e and  together with  c a n be and  plane  matrix notation  P  pf  by  their  i s quite  deformation which  original  theoretical  habit  plane  and  by  i s required.  i n the  The  lattices  d e f o r m a t i o n by  deformation  twin shear.  (c)  two  correspondence  is a lattice  structure  i s derived  of deformation  p l a n e between the p a r e n t  (a) p r o d u c e s  This  lattice  deformation  (b)  amount  between the  parameters. cases.  lattice  matrix.  shear  matrix matrix  homogeneous d e f o r m a t i o n  matrix  the  6. As the theory i s phenomenological i n nature, the order in which these three steps take place is of no consequence.  In general the lattice  invariant shear i s treated f i r s t as i t simplifies the analysis considerably.  The theory can be modified to allow for slight uniform strain  in the habit plane.  In this case the total shape deformation i s  given by  P  1  =  6R B P -  where 6 = dilation in the habit plane, generally less than 1%.  1.4  Stress-Induced Martensite It was mentioned earlier that the strain energy associated with  the formation of martensite was partly responsible for the M  g  tempera-  ture lying below T . Conversely, i f an external stress can be applied q  which assists the transformation strain, the transformation should occur at temperatures above M  Provided that the stress necessary  to form the martensite is lower than that necessary for plastic yielding, martensite w i l l form elastically.  As the temperature is raised  above M , the stress level at which martensite forms is also raised s' until a point is reached at which plastic deformation of the matrix 16 precedes the martensitic transformation  .  If the temperature at  which the matrix is deformed i s above the A^ temperature for the alloy, then on removal of stress, the martensite so formed i s unstable and w i l l revert back to the parent phase.  Thus the deformation can be  considered to be pseudo-elastic in that the transformation strain  7.  associated with the deformation process i s completely removed upon unloading. The amount of pseudo-elasticity observed can be quite large. Busch et a l . " ^ have observed a fully recoverable strain of 24% in Cu-Al-Ni alloys.  Strains of ^15% have been observed i n the case of  Cu-Zn-Sn and Cu-Zn-Si"^ alloys. 3 In the gold-cadmium system Chang and Read  found that deformation  of the martensitic phase (i.e., below M^) gave a significant amount of pseudo-elasticity.  The behaviour was explained on the basis that  favourably oriented twins within the martensite plates increased in size upon application of external load, i.e. the pseudo-elasticity was due to a reversible change in the relative twin thickness. A 18 similar effect has been observed i n In-Tl alloys . The elasticity achieved during such a reversible process is termed Ferro-elasticity 3 or rubber-like behaviour , and i s different from the more common pseudo-elasticity caused by reversible martensite formation at . temperatures above M . g  Another form of recoverable deformation has been termed the 19 shape memory effect  . This is the recovery of deformation carried out  in the martensitic phase as the specimen warms up and reverts back to the original parent structure.  The effect was f i r s t observed i n 20  equiatomic Ni-Ti alloys but several alloys such as Ti-35 wt.% Nb , 21 Cu-Zn-Sn  5 , Cu-Al-Ni  have since been shown to exhibit the effect.  Provided that the deformation is not severe, the recovery is 100%.  The  deformation of the martensite causes a reorientation of the martensite 22 plates and the reverse transformation annihilates this deformation  8. The shape memory effect i s closely related to pseudo-elasticity. 21 Eisenwasser  has looked at both pseudo-elasticity and the shape memory  effect in a Cu-Zn-Sn alloy, and has shown that depending on the deformation temperature either one or the other effect is dominant. Above A^, the strain is recovered pseudo-elastically, whilst below M Strain i s recovered only on heating, and between M  g  g  the  and A^ part of the  strain is recovered elastically and part on heating. 1.5  ;  Martensites in Cu and Ag Base Alloys The structures of the martensites forming in Cu-base alloys have 23 24  been investigated extensively  '  . The parent g-phase i s an electron  compound of the 3:2 type and occurs in the 50-50 composition range in Cu-Zn and at 75:25 in Cu-Al and Cu-Ga alloys.  The silver base alloys  Ag-Zn and Ag-Cd are very similar to Cu-Zn alloys as is evident from  :  their phase diagrams, in these the g-phase occurs around the 50-50 / composition range.  The g-phase is disordered at high temperatures and  undergoes an ordering transformation to a CsCl type structure on cooling to room temperature.  The stability of the g-phase decreases rapidly  as the temperature decreases.  However, the g-phase can generally be, re-  tained to room temperature as a metastable ordered structure over a wide composition range by rapid quenching.  At lower Zn or Cd contents, 27 a massive type 3—transformation takes place on cooling . This is a composition invariant transformation that occurs by the movement of 28 atoms across a relatively high energy interface  . Zener has calculated  the extent of the g-phase field from theoretical considerations and concludes that the disordered g-phase is unstable below 100°C in the case  9. of Cu-Zn alloys and that the ordering transformation i s necessary to 29 stabilize the g-phase Another characteristic feature of the g-phase in Cu and Ag base alloys is their elastic anisotropy - the elastic constants are very 30 different along different crystallographic directions  .  Elastic  anisotropy is best expressed in terms of the ratio ^C^/C^-C^ where C^ i s the rigidity modulus for a shear on {100} and (C^-C.^)/2' i s that for a shear on (110)[110].  This ratio has a very high value for  Cu-Zn alloys. Zener has noted that a (110)[110] shear in the body centred cubic lattice leaves the distance between the nearest neighbours unchanged to a f i r s t approximation and therefore should take place unimpeded in the 29 b.c.c. packing of hard spheres  . Because of the low value of this  shear constant the vibrational entropy contribution is large and this becomes responsible for stabilizing the structure at high temperatures, whilst at low temperatures the increase in the free energy is quite rapid.  This would tend to make the b.c.c. structure relatively  unstable at low temperatures, giving rise to the low temperature martensitic transformations. The martensite in g-phase alloys generally has an orthorhombic, face centred cubic or close-packed hexagonal structure (Table I ) . . 23 Warlimont  has shown that a l l these structures can be derived from  the b.c.c. matrix by a {110}<llO> shear, the {110}^ (001)  ortht  ,(0001) _ hex  or ( l l l )  f < c > c > ( t )  ,  c  c  plane forming  figure (2). The habit, plane  in Cu-Zn alloys lies close to (155) for thermal martensite and i s in agreement v/ith the WLR theory assuming a {110}<ll0> lattice invariant  10.  ( ) orthorhombic CD|  Figure 2.  Basic relation between the b.c.c. lattice and the essentially close-packed structures resulting from martensite transformation.  32 shear.  Very similar results have been obtained i n Cu-Al  33 and Au-Cd  alloys. 1.6  Deformation-Induced Martensite In addition to the martensite forming on cooling to a low temperature  or by stressing at temperatures not far above M , there exists another g  type of martensite produced by severe plastic deformation of the retained &2 phase.- Such deformation-induced martensitic transformations occur in Ag-Cd,  34  Ag-Zn,  35  Cu-Zn,  36  Cu-Pd,  37  Cu-Sn,  31  etc. The  Table I  Alloy  Structures of Thermal and Deformation Martensites i n Ag, Au and Cu Base Alloys.  Structure  Thermal Martensite  Deformation Martensite  Ag-Cd  Orthorhombic  h.c.p. (52 wt.%  Ag-Zn  No transformation detected  f.c.c. up to" 45 at, % Zn h.c.p, above 47 at. % Zn  Au-Cd  Close packed structure with 3R and 2H packing  Au-Zn  Not determined  Not observed  Cu-Zn  Orthorhombic with S.F. in the C direction  f.c.t. for light deformation f.c.c. on heavy deformation h.c.p. for higher Zn cone. 50 at. % Zn.  Cu-Al ln-Tl  L2,  Close packed structure with different stacking sequence f.c.t. (twinned)  Cd)  12.  t r a n s f o r m a t i o n product on s e v e r e c o l d work i s a c l o s e - p a c k e d  structure  and i n Ag-Zn and Cu-Zn has a f a c e c e n t r e d c u b i c s t r u c t u r e a t lower c o n t e n t s , the s t r u c t u r e changing i n c r e a s i n g Zn c o n t e n t s  36 38 ' .  to c l o s e - p a c k e d hexagonal  Warlimont  c o n c e n t r a t i o n a t which the hexagonal  23  alloy  with  suggests t h a t the s o l u t e  s t r u c t u r e o c c u r s c o u l d be d e r i v e d  from the v a r i a t i o n s i n the s t a c k i n g f a u l t p r o b a b i l i t y w i t h  solute  c o n c e n t r a t i o n i n the f . c . c . phase and i t s e x t r a p o l a t i o n t o a v a l u e of 0.5.  The ease w i t h which the t r a n s f o r m a t i o n o c c u r s v a r i e s w i t h the  a l l o y content, i . e . , l e s s t r a n s f o r m a t i o n was found a l l o y contents.  M a r t e n s i t e produced  to occur a t h i g h e r  i n t h i s way r e v e r t e d to the .  38 e q u i l i b r i u m phase on a n n e a l i n g  by a n u c l e a t i o n and growth type  39 reaction  .  I t i s n e c e s s a r y t o note t h a t a c o n s i d e r a b l e amount o f  p l a s t i c d e f o r m a t i o n i s n e c e s s a r y to form t h i s type of m a r t e n s i t e (typically above M  g  > 10%) and t h i s d i f f e r e n t i a t e s i t from the m a r t e n s i t e  by the a p p l i c a t i o n of e l a s t i c s t r e s s .  that p l a s t i c d e f o r m a t i o n produces f r e e energy for  of the system  I t has been  a disordered l a t t i c e ,  and t h i s excess f r e e energy  , produced  suggested  r a i s i n g the  i s responsible  the change to the m a r t e n s i t i c phase. Greninger and Mooradian suggested  t h a t the d e f o r m a t i o n  induced  m a r t e n s i t e i n Cu-Zn had a t e t r a g o n a l s t r u c t u r e when the amount of 40 deformation was s l i g h t .  Hornbogen and coworkers  c a r r i e d out e x p e r i -  ments on s i n g l e c r y s t a l specimens of 60-40 b r a s s and showed t h a t the product phase i n i t i a l l y  has a t e t r a g o n a l s t r u c t u r e and t h a t on  s e v e r e d e f o r m a t i o n i t changes to f a c e c e n t r e d c u b i c .  In f a c t t h i s i s  i n keeping w i t h the e a r l i e r work i n which f i l i n g was adopted mode of d e f o r m a t i o n .  conclusively  As t h i s causes  as the.  s e v e r e d e f o r m a t i o n , the product  13.  phase, thus the  i n d e e d , would have a c u b i c s t r u c t u r e  produced  i s heavily  tetragonal  cell  faulted.  coincided  with  maximum d e v i a t i o n  being ^8°.  with  the o r i g i n a l  the  that  axis  tensile  of  I t was  The  the  38  .  The  also  martensite  found  cube axes o f  C axis  of  the  that  the axes  the 3  of  structure,  tetragonal  p h a s e w h i c h was  phase  inclined  cell  the  coincided  least  to  axis. 41  Ahlers on had  and  deformation a habit  Pops in  found  two  Cu-Zn a l l o y s .  plane very  close  to  narrow bands o f m a r t e n s i t e and of  the o r i g i n a l  to  the m a r t e n s i t e produced  shear  component  {110}<110> the  or  structure  of  {110}<113> was  and  on  t h e most  on  which  because  f o r the  by  that  either  and the  {110}  or  applied  showed  of  very  {112}  planes  t h e WLR  theory  that  the  shear  factor  produced  bands and •  consisted  secondary  i n Ag-Cd  deforming  of  on  resolved system  i n determining  driving  p r o v i d e d i n the  ran i t s complete  course.  close-packed  the  cooling.  p h a s e was  insufficient  the  either  formation of the  the orthorhombic  f o r c e n e e d e d was  transformation  as b r o a d  second  important  thermal m a r t e n s i t e produced  that  driving  The  successfully  stress  of martensite  appeared  deformation  found  produced  a r g u m e n t was  types  formed. 34  Barrett  s t a g e mechanism  formed  {110}.  They  on  One  formed  the a p p l i e d  c o u l d be  orthorhombic two  c u b i c phase.  type of m a r t e n s i t e  Masson  different  form  deformation  phase or They  proposed;a  c l o s e - p a c k e d phase. an  intermediate  force;  and  the  Their  structure  when t h e  of e x t e r n a l work,  extra the,  14.  1.7  E l e c t r o n Microscopic Observations T r a n s m i s s i o n e l e c t r o n m i c r o s c o p y has proven t o be  extensively  v a l u a b l e i n d e t e r m i n i n g the n a t u r e of the l a t t i c e i n v a r i a n t shear i n the m a r t e n s i t e t r a n s f o r m a t i o n s .  Twinning i s found to be the mode of  l a t t i c e i n v a r i a n t s h e a r i n most systems, a l t h o u g h a l a m e l l a r m i x t u r e of a c u b i c and o r t h o r h o m b i c  s t r u c t u r e s was  observed i n the case of  42 Cu-Zn-Si m a r t e n s i t e s  .  E l e c t r o n microscopy of non-ferrous martensites  i s made more c o m p l i c a t e d i n may  t h a t a spontaneous m a r t e n s i t i c t r a n s f o r m a t i o n  o c c u r at temperatures w e l l above M  g  due t o the r e l a x a t i o n of volume  c o n s t r a i n t s a s s o c i a t e d w i t h the p r e p a r a t i o n o f a t h i n f o i l 1.8  specimen.  Aim of the P r e s e n t Work  ;  The p r e s e n t i n v e s t i g a t i o n was  undertaken w i t h the main aim of •  s t u d y i n g the r e l a t i o n between t h e r m a l and d e f o r m a t i o n i n d u c e d m a r t e n s i t e i n the Ag-Cd and Ag-Zn systems.  E a r l i e r i n v e s t i g a t i o n s had shown t h a t  m a r t e n s i t e c o u l d be formed by deforming the fi^ phase a t room tempera44 ture.  Masson  had o b t a i n e d M  v e r y c l o s e t o 50-50 Ag-Cd.  g  temperature d a t a f o r a l l o y  compositions  The p r e s e n t i n v e s t i g a t i o n - extended  t h i s to  cover a wide range o f a l l o y c o m p o s i t i o n s w i t h much h i g h e r M^ v a l u e s . An a l l o y of 45 a t . % Cd was experiments.  E l e c t r o n m i c r o s c o p y of the t h e r m a l and deformation-^  induced m a r t e n s i t e s was was  used f o r p s e u d o - e l a s t i c i t y and s t r a i n memory  attempted.  One  of the main aims of t h e work  t o f i n d the a p p l i c a b i l i t y o f the phenomenological  transformation to deformation-induced martensites.  theory o f . m a r t e n s i t i c f  2. 2.1  EXPERIMENTAL PROCEDURE  A l l o y Preparation A l l o y s were prepared by melting known weights of the c o n s t i t u e n t  elements i n evacuated quartz tubes.  The s i l v e r and cadmium used were  of p u r i t y Ag:  Approximately 60 grams of the  99.95%, Cd:  99.99%.  a l l o y was melted i n one batch.  The a l l o y s were kept molten at 800°C  for approximately four hours and the molten a l l o y was kept w e l l mixed by v i g o r o u s l y a g i t a t i n g the melt.  The a l l o y was then r a p i d l y cooled  and the s o l i d i f i e d a l l o y weighed.  The weight loss was approximately  0.02 gms/melt  0.03% loss) and consequently f u r t h e r chemical  analysis was not c a r r i e d out.  The a l l o y compositions used are 45  shown on the Ag-Cd phase diagram  i n f i g . (3). The a l l o y ingot was  cold r o l l e d about 10% and annealed at 680°C f o r 48 hours i n an evacuated quartz tube.  These ingots were heated to 650°C and subsequently r o l l e d  while s t i l l hot to the desired thickness. Extreme care had to be taken i n the i n i t i a l stages of r o l l i n g as excessive reduction i n a. s i n g l e pass r e s u l t e d i n s h a t t e r i n g of the specimen. a l l o y was made i n a s i m i l a r manner.  The  silver zinc r  Figure (4) i n d i c a t e s the relevant  phase diagram, again i n c l u d i n g the a l l o y composition used.  Figure 3.  Ag-Cd phase diagram showing the alloy compositions used.  Figure 4.  Ag-Zn phase diagram showing the a l l o y composition used.  18.  2.2  Preparation of Tensile Specimens  2.2.1  Polycrystalline Specimens Polycrystal specimens for tensile tests were prepared from 0.030"  thick rolled material by cutting thin strips of dimensions 1 1/2" x 1/4" using a jeweller's saw.  Gauge lengths were prepared by spark machining  the specimen to the dimensions given i n fig. (5).  I  The specimen was then  015  Ob  Figure 5.  Dimensions of the tensile specimen.  II  19.  mechanically polished to 3/0 emery and was then heat treated to retain the $2 phase at room temperature.  This treatment consisted of  heating the specimen in molten salt at 680°C for two minutes and quenching in iced caustic solution (10%). A neutral salt, Houghton 300, was used for the heat treatment.  A final mechanical polish on the 3/0  paper removed any surface contamination and this was then followed by electropolishing.  This proved very difficult i n the Ag-Cd alloys.  A  6% KCN solution was ultimately found satisfactory with the polishing solution contained i n a water cooled stainless steel beaker which acted as the cathode.  A polishing voltage of 2 volts (D.C.) was found to  yield optimum polishing conditions.  2.2.2  Preparation of Single Crystal Tensile Specimens Single crystals were produced by a modified strain anneal method.  Strips 2" x 1/4" were cut from 0.045" thick rolled material using a jeweller's saw and these were annealed and quenched to give the high temperature cubic structure.  These specimens were then strained  approximately 5% using an Instron tensile testing machine. Following this the specimen was slowly lowered into a molten salt bath held at 680°C at a rate of 10 cm/hour, so that a crystal of the (3 phase was grown from one end of the specimen.  Following this the specimen was  quenched into iced caustic solution to retain the ^ phase single, crystal. The surfaces were then mechanically cleaned to remove any contaminated layers.  The gauge section was spark machined and.finally the specimen  was further mechanically and electrolytically polished. The crystals produced i n this manner had random orientations.. <  20. Attempts were made to obtain Ag-Cd alloy single crystals of controlled orientation using the Bridgeman technique.  However, these crystals  a l l recrystallized on subsequent heat treatment and hence did not prove useful.  2.3 Metallography Specimens for metallography were cut from the rolled strips.  These  were heat treated and polished both mechanically and electrolytically. The following etchant proved useful in identifying the deformation martensite. Cr0  20 gms  3  Na S0 2  1.5 gms  4  water  100 ml  2.4 Preparation of Ag-Zn Alloy Crystals Crystals of Ag-Zn alloy were prepared in the same way as the Ag-Cd alloy except that the prestraining for producing single crystals was carried out by rolling.  This was necessary since tensile deforma-  tion produced nonuniform strain in the specimens.  Electropolishing of  Ag-Zn alloys proved relatively easy and fast with a freshly made electrolyte of 1 part of  2.5  t 0  P  a r t s  °^ NH^OH.  '  Orientation Determination The orientations of the single crystal specimens were determined  using the Laue back reflection technique.  A molybdenum tube operated  at 35 KV, 15 mA for 15 minutes gave spots of optimum intensity.  A  21.  d i s t a n c e of 3 cms was m a i n t a i n e d between the specimen and the f i l m .  2.6  X-Ray  2.6.1  Diffraction Room Temperature  X-Ray  Diffraction  X-ray d i f f r a c t i o n experiments to i d e n t i f y the c r y s t a l were c a r r i e d target.  structures  out w i t h a North American P h i l i p s X-ray u n i t w i t h a copper  The o p e r a t i n g c o n d i t i o n s were 30 KV and 15 mA, w i t h a s c a n n i n g  speed of 1 deg 29/min.  2.6.2  Low Temperature A special  X-Ray  Diffraction  specimen h o l d e r was b u i l t f o r low temperature  diffraction  experiments, F i g . ( 6 ) . The apparatus c o n s i s t e d of a h o l l o w b r a s s cylinder  w i t h a r e c e s s f o r mounting  the specimen.  be c o o l e d by p o u r i n g l i q u i d n i t r o g e n i n t o specimen  windows.  the h o l l o w c y l i n d e r .  The  The specimen was then covered w i t h an o u t e r c y l i n d r i c a l  X-rays c o u l d f a l l on the specimen The volume i n s i d e  through one m i l t h i c k  mylar  the o u t e r s h e l l was evacuated to minimise  temperature g a i n s and a l s o to e l i m i n a t e f r o s t i n g problems. h e a t e r c o i l was wound around the i n n e r h o l l o w c y l i n d e r the  could  temperature was monitored u s i n g a thermocouple g l u e d t o the  specimen mount. shell.  The specimen  A small  and by  controlling  h e a t e r c u r r e n t any d e s i r e d temperature between -196° and -50?C  c o u l d be m a i n t a i n e d f o r a c o n s i d e r a b l e l e n g t h of time.  2.7  Measurement of T r a n s f o r m a t i o n Temperatures The M , g  microscopy.  Mj, A  g  and A^ temperatures were determined by o p t i c a l  Test specimens were mounted on a s t e e l b l o c k supported at  22.  Vacuum *-  -c-  F i g u r e 6.  A  Hollow Cylinder  B  Outer  C  Liquid Nitrogen Inlet  D  Specimen  Specimen h o l d e r  Cover  f o r low temperature X-ray  diffraction.  the end of a 1/4"  s t e e l rod and immersed i n e t h a n o l or p e t r o l e u m e t h e r  ( f o r temperature.< dewar.  -100°C)  c o n t a i n e d i n a double w a l l e d t r a n s p a r e n t  To c o o l the specimen, l i q u i d n i t r o g e n was  q u a n t i t i e s , and the s o l u t i o n was thermocouple was assessment  added  kept w e l l s t i r r e d .  A  i n small chromel-alumel  f i x e d next to the specimen p r o v i d i n g an a c c u r a t e  of the specimen  temperature.  The specimen  c o u l d be observed  from o u t s i d e through a microscope f i t t e d w i t h a l o n g f o c a l objective.  A s e l e c t e d a r e a of the specimen was  c o o l i n g and the f o r m a t i o n o f m a r t e n s i t e at the M  length  kept i n f o c u s d u r i n g g  temperature was  easily  r e v e a l e d by the rumpling produced on the p o l i s h e d s u r f a c e of the specimen.  M i c r o s t r u c t u r e s c o u l d be r e c o r d e d u s i n g a 35 mm  camera  a t t a c h e d to the microscope.  2.8  Tensile Tests T e n s i l e t e s t s were c a r r i e d out i n a f l o o r model I n s t r o n taken w h i l s t mounting  tensile  t e s t i n g machine.  Care was  of the specimen.  A c r o s s head speed of 0.005"/min ( c o r r e s p o n d i n g t o a -4  s t r a i n r a t e of ^ 1.4  x 10  to p r e v e n t any bending  -1 sec  ) was  used i n a l l experiments.  The  t e s t temperature was v a r i e d by s u r r o u n d i n g the specimen w i t h a c o o l i n g bath.  C h i l l e d a l c o h o l was  used as the c o o l i n g medium.  The  specimen  dimensions were measured w i t h the h e l p o f a t r a v e l l i n g m i c r o s c o p e . specimen  The  c o u l d be observed from o u t s i d e through the double w a l l e d  t r a n s p a r e n t dewar used to c o n t a i n e n t h a n o l . An I n s t r o n extensometer was whilst  a t t a c h e d t o the specimen  the modulus measurements were made.  gauge s e c t i o n  T h i s enabled a c c u r a t e  d e t e r m i n a t i o n o f the modulus v a l u e s but r e s t r i c t e d measurements: to  24. room temperature only. A special tensile j i g [fig. (7)] proved very useful in observing specimens under tension.  Using this, habit plane measurements could  be made for the stress-induced martensite. The j i g also proved very useful while taking X-ray back reflection pictures of the stress-induced martensite.  2.9  Habit Plane Determinations  46 A two surface analysis  was carried out to determine the habit  plane of the various martensite structures produced.  The angle between  the trace of the martensite plate and the reference edge was measured through a Zeiss optical goniometer. 2.10 Deformation Martensite  >  Deformation martensite was produced by cold rolling or f i l i n g the heat treated specimens.  Attempts were made to produce deformation  martensite in normal tensile specimens.  The specimens invariably  fractured before any significant amount of martensite was produced. The presence of deformation martensite in the rolled specimens was confirmed both by metallography and by X-ray diffraction.  However, in  the early stages of transformation optical microscopy was easier to use.  X-ray diffraction could be used only after a significant fraction  of the $2 pbase had transformed.  2.11 Electron Microscopy Preparation of specimens for electron microscopic observation proved extremely d i f f i c u l t .  The following method of specimen preparation was  25.  Moving  Stress Induced Martensite.  F i g u r e 7.  Apparatus used f o r s t r e s s i n g  specimens.  26. ultimately employed.  Discs 3 mm in diameter were spark machined from  the specimen after the necessary mechanical and thermal treatment. These were then surface ground to a thickness of 0.025".  Both sides  of the disc were dished using electrolytic jet polishing with 50% phosphoric acid solution. 6% KCN solution.  The dished specimen was then polished in a  A low voltage  i n i t i a l performation of the disc.  1.5 volts) was used to obtain the The area adjacent to the perforation  proved quite transparent to the electron beam. This method of specimen preparation has the advantage that no additional straining of the  •  specimen is involved. A Hitachi HU 11 microscope operated at 100 KV was used to examine the specimens.  A high resolution stage was employed.  A study of the  thermal martensite was carried out using the standard cold stage in the microscope. constant.  A gold standard was used for determining the camera  3. 3.1  EXPERIMENTAL RESULTS AND DISCUSSION  Quenched Structures in Ag-Cd Alloys Table II indicates the compositions of Ag-Cd alloys used in this  series of experiments.  They cover a large portion of the range of  the high temperature 3phase.  In alloys 3-7, the body centred cubic  phase was retained on quenching to room temperature whilst in alloys 1 and 2 partial transformation to massive a occurred. Similar massive transformations have been reported in low cadmium 3 alloys by Ayers 27 and Massalski In alloy 2, an apparent bainitic product appeared when the quenching rate was insufficient, (fig. (8)). This had a needle-like appearance and appeared to form on certain planes of the parent lattice.  Most of the needles are; bent in a very characteristic manner  and are usually referred to as "chevrons".  Ayers observed similar  chevron markings in a quenched Ag-44.7 at.% Cd alloy and in a pulse 47 heated 3^ Ag-38.5 at.% Zn alloy . Table II. Compositions of Ag-Cd alloys used in experiments. Alloy No. at.% Cd  1 42.3  2 44.3  3 45.0  4 45.5  5 46.0  6 47.7  7 50.9  28.  Figure 8. Bainite needles in quenched 44.3 at.% Cd alloy (x 230).  29. The retained g phase i s fully ordered.  It was not possible  to confirm this by means of conventional X-ray diffraction, because both Ag and Cd have nearly equal scattering factors.  However, the  temperature dependence of the elastic modulus of the g Ag-Cd did 48 confirm the order in the structure  . Hence i t is believed that on  quenching, ordering of the g phase takes place similar to that occurring in Cu-Zn and Ag-Zn alloys. 3.2  Determination of Transformation Temperatures  3.2.1  Ag-Cd Alloys M , M^, A g  g  and A^ temperatures were optically determined for a  series of alloys of Ag-Cd covering a composition range from 44.2 to 14 Masson has determined the variation in the M  47.0 at.% Cd.  s  temperature with composition using X-ray diffraction techniques for alloys from 46.6-49.1 at.% Cd. At the M  g  temperature very fine plates of martensite appeared,  most often near the edges of the specimen.  As the temperature  was  lowered further, additional martensitic plates formed, mainly parallel to the original ones; growth of the existing needles also occurred. These needles disappeared with very l i t t l e hysteresis as the temperature was increased indicating that this was thermoelastic martensite. Martensite plates forming in adjacent areas merged to form a characteristic V-shape. As the temperature was lowered further, burst martensite formed.  The plate-like nature of the martensite was confirmed by matching the traces along two surfaces.  30. The  appearance o f t h i s c h a r a c t e r i s t i c z i g - z a g p a t t e r n ( f i g u r e  was  used t o e s t a b l i s h M^.  i n a c o o p e r a t i v e way;  These m a r t e n s i t i c p l a t e s appeared to form  the f o r m a t i o n of one p l a t e a s s i s t i n g i n the  f o r m a t i o n of the a d j a c e n t p l a t e . i n one b u r s t was  The  t o t a l amount of m a r t e n s i t e  at o n c e . 7  On f u r t h e r c o o l i n g  the amount of m a r t e n s i t e i n c r e a s e d u n t i l the s t r u c t u r e had On warming the specimen, the r e v e r s e  s t a r t e d a t the A  temperature and ended a t A^,  g  r e v e r t i n g to the p a r e n t phase.  The  not v a r y s i g n i f i c a n t l y w i t h t h e r m a l  The  transformation  the b u r s t m a r t e n s i t e  M^,  A^ and A^  g  tempera-  d a t a o b t a i n e d by Masson f o r a l l o y s of  h i g h e r cadmium c o n c e n t r a t i o n i s i n c l u d e d f o r comparison. f i g u r e , i t i s seen t h a t M  slowly  cycling. g  tures w i t h composition.  completely  t r a n s f o r m a t i o n temperatures d i d  F i g u r e (10) g i v e s the v a r i a t i o n of the M ,  decreases w i t h i n c r e a s e i n  c o n c e n t r a t i o n at the r a t e of 35°C/atom % Cd. to t h a t found i n Cu-Zn a l l o y s where the M at the r a t e of  formed  l e s s than 5%, much d i f f e r e n t from F e - N i a l l o y s where  as much as 84% of the volume t r a n s f o r m e d  transformed.  (9))  'W5 C/atom % Zn. 0  g  From the  the cadmium  The b e h a v i o u r  i s similar  temperature decreased r a p i d l y  The v a l u e s o f the M  temperature s  44 r e p o r t e d by Masson work.  are lower  T h i s c o u l d be due (a)  than the v a l u e s o b t a i n e d i n the  present  to the f o l l o w i n g r e a s o n s .  Masson. determined the v a l u e s by X-ray d i f f r a c t i o n and  there-  f o r e c o u l d d e t e c t the m a r t e n s i t e peaks o n l y a f t e r about 5% o f the volume had  transformed, (b)  thus g i v i n g a lower v a l u e of M .  Masson used 300 mesh powder i n h i s i n v e s t i g a t i o n . However,  i t has been shown t h a t M  d e c r e a s e s w i t h a d e c r e a s e i n the g r a i n s i z e , 6  g  and t h i s c o u l d be p a r t l y r e s p o n s i b l e f o r a lower v a l u e o f M .  ;  31.  F i g u r e 9.  Micrograph  of thermal  A: T h e r m o - e l a s t i c  martensite.  m a r t e n s i t e and  B: B u r s t M a r t e n s i t e .  33. It has been well established that the burst phenomenon is the manifestation of the autocatalytic effect associated with the formation of martensite.  The stress that produces the autocatalysis is induced  in the matrix by the formation of a plate of martensite and the situation can be compared with one where external stresses assist the martensite formation.  The negligible change in the volume due to  transformation is perhaps responsible for the small amount of martensite formed in bursts.  This is in direct contrast to the 3% volume change 49  in the Fe-31 Ni alloy The A  s  .  temperature i s below the M  s  temperature.  This could be  due to the fact that the stresses associated with the i n i t i a l transformation assist the reverse transformation.  This behaviour i s not  really unusual, and has been observed in Au-Zn alloys"^.  The very  small hysteresis might also suggest that the equilibrium T ture is very near the M  g  temperature.  q  tempera-  The small degree of supercooling  required is again a reflection of the very small volume change involved in the transformation.  3.2.2  Ag-Zn Alloys Ag-Zn alloys have not been known to undergo martensitic transforma-  tion on cooling to low temperatures"'"''.  However, to ascertain this,  an alloy low in zinc (41 at.% Zn), which in analogy with the Ag-Cd and Cu-Zn systems might be expected to have the highest M  g  was cooled in liquid helium.  temperature,  Subsequent examination failed to reveal  any occurrence of transformation.  This behaviour goes contrary to the  general behaviour of Cu-Zn and Ag-Cd alloys.  34.  3.3  Structure of Thermal Martensite  3.3.1  Introduction  The structures of martensite developed on cooling from the B phase region of non-ferrous alloys have been the subject of intense investigation i n recent years.  In spite of this, the crystal structures  in a number of alloys are s t i l l unidentified or, at most, remain at a controversial stage.  The main difficulty i s the inhomogeneity of  the martensite which prevents the unambiguous determination of the crystal structure.  The strains accompanying the transformation and  the faulted product structure result in extreme diffuseness and shifts in the X-ray diffraction peaks and this makes crystal structure determination very d i f f i c u l t .  Electron microscopy has proven to be a very  useful means of identifying the crystal structures of these phases. The main argument against such a techniques i s the fact that special thinning procedures are needed i n order for electrons to penetrate the specimen and the behaviour of such thin f o i l s of material may not be characteristic of the bulk material.  This argument carries further  weight in view of the fact that thin foils of Cu-Zn alloy have been; found to transform to martensite spontaneously at temperatures much 43  above the M  g  temperatures found in the bulk material  In the following sections the structure of the thermal martensite found in an Ag-45 at.% Cd alloy i s discussed using both X-ray and electron microscopic observations.  In the subsequent discussion a  general survey of the structures of the martensites i n g-phase alloys is made.  Table III gives the common terminology used i n the  literature.  35. Table III  List of common symbols used in identifying martensite structures in $ phase alloys.  a:  b.c.c.-f.c.c. (lR) transition  8:  b.c.c.-stacking variants of close packed structures other than IR and  y:  2H.  b.c.c.-h.c.p. (2H) transition :  no subscript; derived from disordered b.c.c.  ^:  derived from Fe^Al (L2^) type superlattice  ^:  derived from CsCl (B^) type superlattice  ':  indicates a single phase transformation product; can be either faulted or twinned  it  :  lamellar composite of two structures  :  transformation induced by deformation  3.3.2  X-Ray Diffraction Results Figure (11) shows a typical diffractometer trace obtained from a  flat polycrystalline specimen cooled to -196°C; and Table IV indicates the peak positions obtained from several experiments.  The table  34 includes the results obtained by Masson and Barrett alloy.  for a 47 at.% Cd  The lattice parameters of the unit cell were calculated on an  36.  Figure 1 1 .  X-Ray diffractometer trace for thermal martensite in Ag-45  at.% Cd alloy.  Table IV Positions of diffraction peaks obtained for low temperature martensite  hkl  Present data for 45 at.% Cd alloy 20 deg.  d A°  Data for Ag-47 at.% Cd alloy 20 deg.  d A°  (110)  34.4  2.604  34.28  2.614  (020)  37.0  2.4275  36.96  2.431  (002)  37.9  2.3719  37.77  2.381  (111)  39.4  2.285  39.2  2.296  (021)  41.8  2.1591  41.6  2.169  (112)  51.8  1.7634  51.68  1.767  (022)  53.6  1.7083  53.64  1.707  (200)  59.8  1.5452  59.3  1.557  (130)  64.6  1.4415  64.58  1.442  (131)  67.8  1.381  67.84  1.380  (113)  69.0  1.3599  68.88  1.362  (023)  70.6  1.3329 .  70.54  1.334  (202)  72.5  1.3026  72.34  1.305  CO 04)  80.9  1.1872  80.34  1.194  (222)  84.5  1.1456  84.00  1.151  38.  orthorhombic b a s i s u s i n g  these v a l u e s the i n t e r p l a n a r calculated.  With  (020), (002) and (200) r e f l e c t i o n s . spacings f o r other  r e f l e c t i o n s were  The agreement between the observed and c a l c u l a t e d  i s v e r y good.  The orthorhombic s t r u c t u r e has the f o l l o w i n g  values  lattice  parameters a  =  3.0904 A°  b  =  4.8550 A°  c  =  4.7433 A°  There a r e f o u r atoms i n a u n i t c e l l . positions  Masson and Barrett gave their  as Cd:  0,  Ag: 1/2,  0.195,  1/4  0,  .805,  3/4  0.695,  1/4  1/2,  .305,  3/4  Shifting the o r i g i n t o the f i r s t cadmium atom the atom p o s i t i o n s could  be g i v e n as Cd:  0,  0,  0  A:  1/2,  1/2,  0  g  The s t r u c t u r e  could  thus be i n t e r p r e t e d  0  0.610,  1/2  1/2, 0.110,  1/2  as a l a y e r e d  structure i n  which every second l a y e r i s s h i f t e d along the b - a x i s by 0.610. The s t r u c t u r e  o b t a i n e d i s v e r y s i m i l a r to the one found i n Au-  47.5 a t . %  Cd by O l a n d e r ^ .  structure  and has atoms s i t u a t e d a t p o s i t i o n s g i v e n below:  Cd:  0,  Au: 1/2,  This s t r u c t u r e i s r e f e r r e d t o as Olander  5/16,  1/4  0,  13/16,  1/4.  1/2,  11/16,  3/4  3/16,  3/4.  or a l t e r n a t e l y  Cd:  0,  Au: 1/2,  0,  0  0,  3/8,  1/2  1/2,  0  1/2,  1/8,  1/2  39.  The positions of the atoms are very nearly the same as calculated by 3^  Masson and Barrett  . The unit c e l l of martensite i s shown i n figure  (12).  O  Cd  atoms  0  Ag  atoms  Figure 12. Unit c e l l of orthorhombic martensite.  40.  3.3.3  Martensite Structures in g-Phase Alloys There is much controversy in the literature regarding the martensite  structures produced from g-phase alloys.  62 Kunze reported a transition  lattice with a monoclinic unit c e l l and a superlattice with a t r i c l i n i c 63 unit c e l l for Cu-Zn alloys. confirm these structures.  However, Masson and Govila  failed to  It was further suggested that a variable  structure should be assigned to the martensite in view of the various 64 possible intermediate structures. Saburi and Wayman structures in the case of Cu-Ga martensites:  found two different  a disordered face-centred  cubic lattice g' and an ordered face centred cubic structure g^' with stacking faults.  Delaey and Warlimont^ found two different martensite  structures in a Cu-23 at.% Ga alloy; g^" martensite, which is a lamellar mixture of two different structures and y ' martensite.  Pops and  42 Delaey  later observed a lamellar mixture of an orthorhombic structure  ( ABC BCA CAB) and a face centred cubic structure (ABC) in the case of Cu-Zn-Si martensites. Several studies of Cu-Al martensites have been carried out., 66 Swann and Warlimont observed three different structures, viz. (a) an internally faulted f.c.c. martensite (b)  an internally faulted tetragonal martensite,g  (c)  an internally twinned orthorhombic  1  (ordered) martensite, y'.  Wilkins and Warlimont^ later modified the tetragonal structure to a regular arrangement of a close-packed layer of atoms with regular 68 stacking faults.  However, Sato  et a l . found only two different  structures, one with a 3R (orthorhombic) stacking sequence and one with a 2H stacking sequence.  41. In the Au-Cd system, martensites with different structures have 69  been seen with changes in the cadmium content.  Toth and Sato  observed a' (IR), 3 ' (3R), B " (3R + 2H), and y ' (2H) structures 2  2  with increase in cadmium contents.  Thus far there have been no  electron microscopic observations on the martensite in Ag-Cd alloys. The following section describes the theoretical analysis used in structure determination in quasi-close packed structures.  The electron  diffraction patterns of Ag-Cd martensite are then discussed in the light of this analysis. 3.3.4  Structure Analysis Many of the martensite structures are derived from the regular  stacking of a close packed layer of atoms.  The different structures  are a result of the introduction of faults in the stacking sequence in a regular manner. A close-packed structure is specified by a stacking order of the close packed hexagonal layers which occupy one of the three possible positions A, B, C as shown in f i g . (13). Assume that the stacking order ABC ABC ABC is the fundamental unit. As stacking faults are introduced the basic structure changes and gives an extra degree of periodicity in the direction of stacking. These changes are easily seen in the reciprocal lattice of these structures as described below. (a)  IR Structure:  Stacking fault boundaries are introduced at every layer: the resulting structure is ACBACBACB which i s twin related to the former structure and hence the reciprocal lattice consists of twin spots along  42.  Figure 13. Close-packed layer in f.c.c. structure.  with cubic spots, figure (14). (b)  2H Structure:  If the stacking fault boundaries are introduced at every other layer, the resulting structure is ABABAB..., which is hexagonal. The original reciprocal lattice points are split into two in the direction of modulation. spots  A characteristic of this splitting i s that the split  are at the same level. (c)  3R Structure:  When stacking faults are introduced every third layer, the; resulting structure is ABCBCACAB, and can be thought of as three series of three layers which are each related by a unit stacking shift — <112>. This 6 type of modulation has a rhombohedral symmetry, and the spots are split  43.  2 H  F i g u r e 14.  Mutual r e l a t i o n s of the r e c i p r o c a l l a t t i c e  for close-  packed s t r u c t u r e s w i t h d i f f e r e n t s t a c k i n g o r d e r . In IR s t r u c t u r e the twin spots are r e p r e s e n t e d as open circles. (Ref. 70).  I n d i c e s are a c c o r d i n g to c u b i c n o t a t i o n  44.  into three along the stacking direction.  The split spots are displaced  and are not at the same level in adjacent layers. This kind of variation in stacking sequence can be extended further to include complex arrangements.  If one considers an ordered structure,  then further changes have to be incorporated to take into account the superlattice reflections. In the case of martensite structures derived from a caesium chloride type lattice, one may consider the CHO)  type plane of the CsCl lattice  as the basal plane (this is equivalent to the (111) plane of the f.c.c. version of the CsCl structure). The intensity of spots in the electron diffraction pattern depends on the magnitude of the structure factor for the various diffracting planes.  The structure factor for such a structure made up of close  packed layers can be expressed as ^ 7  where F^ represents the structure factor for the basal plane and F  represents the stacking arrangement, since each layer is  derived from the basal plane by a suitable shift of the layer.  Figure  (15) gives the atom positions in the basal layer.  F  A  =  f^.  +  f ^ exp[2,i (|  +  |)]  The intensity distribution in the basal plane of the reciprocal lattice based on the above equation is given in f i g . (16).  The atomic scattering  45.  a  Cd atoms O  Ag atoms  Figure 15. Atom positions in the basal plane.  2  • • ^« •  •  I  •  0  o  a  •  •  •  •  •  2  0  2  4  7 2  Figure 16.  •  0  Basal plane of the reciprocal lattice of close-packed structures.  (Indexed according to orthorhombic notation).  46. factors of Ag and Cd are very nearly the same and this gives rise to negligible intensity for the superlattice spots.  This situation i s  different from the Au-Cd alloy system where the superlattice spots are The value of F. remains the same for 3R or 2H A  visible clearly. :  structures, because they are formed by a difference in the stacking sequence of the same close-packed plane of atoms. F^  on the other hand, describes the stacking sequence and hence  is different for different structures.  For a 2H structure F  i s given  by F  » I I + exp 2*1' <| + j)l  £  i.e., the atoms in the second layer are displaced along the k direction by  The expression for the structure factor then becomes  F  =  F  • F„  a  A  '  =  (  f c d  + f  A  g  exp[2TTi (| + !>]}{1 + exp 2 * i (| + |) }  The above equation is valid only in the ideal case where the atoms in every second layer are displaced by 2 / 3 .  In the case of Ag-Cd  alloy where this displacement i s only 0.61, assuming the Masson and Barrett structure, the structure factor equation modifies to  F  = [f  c d  + f  exp 2iri (| + j ) ] [ l + exp 2TTiC.61k + 0.5*)]  The calculated intensity values for a few reflecting planes are given in Table V.  47.  Table V  2  Calculated relative intensities, | F | , for the 2H modulation of the close-packed structure; for h = 0 , 1 and k = 0 , 1 , 2 in orthorhombic coordinates. 2  are given by | F | = | F |  2  The actual relative intensities 2  2  • | F | where | F | is equal to  2  |f  A  + f  c d  |  for normal spots ( h = 0 , k = 0 , 2 ; h = 1 ,  k=l)  2 1  and to |f k = 0, 2).  - f  | for superlattice spots (h = 0 , k = 1 ; h =  Reciprocal lattice point in orth. coordinate (002)  Relative intensity  4  (020)  2.37  (220)  2.37  (202)  4  (022)  2.37  (130)  2.96  (131)  1.03  (132)  2.96  (133)  1.03  (113)  3.54  48. 3.3.5  Electron Microscopy of Thermal Martensite in an Ag-45 at.% Cd Alloy: Figures (17,18) give the selected area diffraction patterns of  thermal martensite taken at low temperatures.  Figure (18) represents  the OG intersection (refer to f i g . (16)) normal to the basal plane.; The d-spacings calculated from electron diffraction patterns and the values obtained from X-ray diffraction are given in Table VI.  These  values compare very'well and this confirms the structure as a genuine one.  Table VI  Comparison of d values obtained from electron and X-ray diffraction (values in A°).  hkl  d from SAD  (131)  1.40  1.381  (133)  1.04  1.06  (202)  1.28  1.302  (130)  1.46  1.44  (002)  2.50  2.37  d from X-ray diffraction  The 2H structure of the martensite i s clearly revealed from the diffraction patterns.  The calculated and observed intensities agree.*,*,.....  very well, indicating the correctness of the assumed atom positions. For example, the calculated intensity of (131) spot, assuming a shift of 2/3, is zero; whereas the (131) spot i s observed in diffraction ,  i  Figure 17.  S.A.D. of thermal martensite.  50.  patterns.  The presence of an (001) spot in the diffraction pattern  (figure (18)) can be explained on the basis of double diffraction from the (130) and (131) planes. Figures (19,20) show the electron micrographs of thermal martensite taken at low temperature.  Figure (19) represents martensitic 'needles'  formed as the specimen was cooled i n the microscope.  These needles  did not grow even after a prolonged delay (% 4 hrs) at the low temperature.  This might be due to the fact that the temperature was not low  enough for the transformation to be completed.  The edges of martensite  needles are a l l parallel, implying a definite habit plane.  Some  stacking faults (random) can be seen in the micrographs.  3.3.6  Spontaneous Martensite Obtained at Room Temperature Several specimens observed at room temperature showed a different  kind of martensitic structure.  It occurred only on thinning and was  more prevalent in specimens which were slightly deformed before polishing or in specimens which were accidentally deformed during thinning.  The martensite was present only in the thinnest areas of  the f o i l .  Figure (21) shows a typical area as seen in the microscope.  The region is heavily striated.  The corresponding selected area  diffraction pattern shows very prominent streaking along the <111> direction, figure (22), which is indicative of a faulted structure. A high magnification photograph of the same area, figure (23), shows the fringed contrast from the striations.  The diffraction pattern  corresponds to a face centred cubic structure. The value of the lattice parameter is plotted in figure (24), and is seen to agree with the para-  52.  F i g u r e 19.  E l e c t r o n micrograph of thermal m a r t e n s i t e 'needles'.  (X  14K).  showing  Figure 2 0 .  E l e c t r o n micrograph of thermal m a r t e n s i t e showing faulted structure.  (X 42K).  the  54.  Figure 21.  Spontaneous martensite in Ag-45 at.% Cd alloy. (X 30K).  55.  Figure 22.  S.A.D. of spontaneous m a r t e n s i t e r e v e a l i n g s t r e a k i n g <111>  direction.  along  Figure  23.  Stacking  fault  fringes  i n spontaneous  martensite  (X  75K).  — i  4-20  •  1—  n  1  1  X-Ray Diffraction. [ P i l e d powder specimens ]  °< 4 18  A  Electron Diffraction. [ Spontaneous transformations i n t h i n . f o i l ]  rr UJ  416  UJ  ^< 414 a.  y 412 <  410 408 20  10 Cd Figure 24.  30  CONCENTRATION  40 (At.%)  Variation of lattice parameter of a phase vs. composition  59  50 Ln  58. meters of the a-phase extrapolated to the higher cadmium contents. The f.c.c. product produced by f i l i n g shows a similar characteristic (see Section 3.6). The striations run along different directions in different areas and the boundary connecting these areas is rather irregular, figure (25).  This i s to be compared with the rather discrete boundary obtained  in the thermal martensite fig.(19).  In some cases the diffraction  patterns obtained from selected areas show twinned spots besides streaking.  For example, the pattern shown in figure (26) can be  analysed on the basis of twin related spots.  The twin plane contains  the beam direction and hence the twin spots can be derived by a rotation of 180° about the twin axis. A twinned f.c.c. structure has been observed in many alloys.  In  69 Au-Cd  alloys with low Cd content, such a structure has been observed.  In Cu-Zn alloys such a structure was seen to form spontaneously along 43 the thin edges of a perforated specimen  .. It was concluded that the  relaxation of the external constraints during the thinning process caused this.transformation even though the specimen was well above the transformation temperature.  This spontaneous martensite was found to  have no specific habit plane as observed in the present work. 3.4 3.4.1  Slip Systems in Ag-Cd and Ag-Zn Alloys Experimental Results The slip systems operating in Ag-Cd and Ag-Zn alloys were determined  as follows. The slip plane was determined using the standard two 46 surface analysis  . The slip direction was found by noting the movement  59.  Figure 25.  Spontaneous martensite showing striations along different directions in different regions (X 40K).  Figure 26.  S.A.D. of twinned area i n spontaneous  martensite.  61.  of the tensile axis in the stereogram after successive amounts of strain.  The results are given in Table VII.  Table VII  Slip systems in Ag-Cd and Ag-Zn alloys.  Alloy  Slip plane  Slip direction  Ag-45 at.% Cd  {112}  <111>  Ag-41 at.% Zn  {110}  <111>  Figure (27) indicates the location of the tensile axis and the corresponding habit plane poles.  The slip lines were short and wavy in  some cases but quite straight in others as shown in figures 28a,b and 29. Deformation bands occurred in some tensile specimens but a detailed analysis of these bands was not attempted. The [111] slip direction i s operative in both the alloys.  In  the case of (110)[111] slip, there are twelve possible slip systems and only one of these w i l l be operative in each unit triangle.  The  experimentally determined slip systems are in keeping with this. A (112)[111] slip also offers twelve possible slip systems, but more than one slip system is possible within the unit triangle, unlike the previous case.  Figure (27) shows the two most highly stressed  slip systems within the primary unit triangle.  The experimentally  determined systems are indeed the most highly stressed ones.  Figure 27.  Location of tensile axes ( O ) and corresponding slip planes ( A  ) in Ag-45 at. % Cd alloy.  Figure 28a,b.  Slip traces in Ag-45 at.% Cd alloy (X 230).  Figure 29.  Slip traces in Ag-41  at.% Zn alloy (X 230).  65. 3.4.2  Discussion of Slip Systems in CsCl Type Alloys In general materials with a caesium chloride structure exhibit  either <001>  type ionic slip or <111>  type metallic slip.  <111>  slip causes a change in the nearest neighbour relation, whereas a <100> slip leaves them unaltered. Therefore, the deciding factor which determines the nature of slip is the relative magnitudes of the bonding energy between A-A, B-B and A-B type atoms.  Rachinger and  52 Cottrell  calculated that i f the bond energy of the material is  greater than 0.06 eV, then ionic slip is favoured, whilst metallic slip is favoured i f i t i s less than 0.06 eV.  Table VIII shows the slip  vectors of various CsCl type compounds and the corresponding ordering energy  calculated from the c r i t i c a l ordering temperatures.  and Au-Cd appear to violate this prediction.  Au-Zn  However, this is  attributed to the incorrectness of their ordering temperatures, since order persists up to the melting point. However, in subsequent literature this problem is reconsidered in terms of the total dislocation elastic energy. From a geometrical view slip planes with a  <111>  not true slip planes.  {112}  and {110}  slip direction"^.  In 3 Cu-Zn alloys a  are the only possible  Higher order planes are {110} type slip plane  was operative in tension, whilst both {110} and {112} were found under compression. 3.4.3  Discontinuous Slip in Ag-Cd  ;  In some specimens of Ag-Cd discontinuous slip bands were observed. These formed in the very early stages of plastic deformation, their  66.  Table VIII  Slip vectors and ordering energy relationships of some CsCl type alloys.  Alloy  Observed slip vector  T °K c  Bond strength eV  Cu-Zn  <111>  738  0.0159  Ag-Mg  <111>  1093 (mp)  0.0236  TlBr , TlCl  <001>  ionic compounds  Au-Zn  <001>  998 (mp)  0.0215  Au-Cd  <001>  900 (mp)  0.0194  Ag-Zn  <111>  543  0.0117  Ag-Cd  <111>  693  0.0149  T  c  = c r i t i c a l temperature of ordering  kT Bond strength = —^— Ordering temperature data taken from refs. 53 and 54.  -  •  67.  formation corresponding with a stress relaxation on the stress-strain curve.  The bands formed randomly along the crystal until the whole  gauge length was covered with them, f i g . (30). These were found to form on a {112} type plane.  Laue back reflection photographs taken  after deformation did not reveal any new spots. Therefore, formation of a new structure on deformation had to be ruled out.  Also the bands  did not reappear on etching after they were removed by polishing. Hence they could only be slip bands forming in a cluster.  Figure (31)  shows the interferogram on the specimen, which shows surface rumpling; and seems to suggest some kind of phase transformation.. However, electron reflection experiments failed to yield any conclusive proof for the existence of a new structure at the surface.  Hence i t seems  most likely that the markings are indeed slip bands. Similar discontinuous slip has been previously observed in  Cu-Zn  alloys by Ardley and C o t t r e l l ^ , who noted that this behaviour was 6  an indication of the yield point behaviour commonly observed in mild steel caused by traces of impurity elements present. 41 Ahlers and Pops  observed broad strain markings in Cu-45 and  48 at.% Zn alloys in the very early stages of plastic deformation. formed on a {110} plane of the matrix.  These  They attributed this to  deformation martensite and interpreted the habit plane using the WLR theory of martensitic crystallography.  However, they do not present  any X-ray evidence to indicate the presence of a new structure nor consider the possibility of a surface effect. the M  g  In view of the fact that  temperatures for these alloys are below liquid helium temperature,  i t is unlikely that strain-induced martensite could be produced with  F i g u r e 30.  Coarse s l i p markings i n Ag-45 at. % Cd a l l o y  F i g u r e 31.  I n t e r f e r o m e t r i c p a t t e r n of the s u r f a c e of a specimen a f t e r very l i g h t  deformation.  (X 10).  69. such ease at room temperature.  Hence i t does seem likely that the  broad bands observed by Ahlers and Pops were simply slip bands and not martensite.  3.3  Modulus Determination Table IX gives the values of Young's modulus obtained for various  orientations of the tensile axis as given in the unit triangle (figure (32)).  It i s seen that the value of the modulus i s very much orientation  [Ml]  Figure 32. Tensile axes for specimens tested for modulus determination.  70.  Table IX Values of Young's modulus obtained for various specimen orientations given in f i g . (32).  Sp. No.  C.S. Sq. mm  Strain for E dynes/cm 50 lb. load  — cm /dyne — Calculated 2,, cm /dyne 12 12 x 10 x 10  1  3.092x.737  .0085  1.15X10  2  3.343x.626  .0011  9.40X10  1 1  3  3.316x.808  .00525  1.39xl0  1X  7.2  6.7  .002375  4.7 x l O  1 1  2.13  2.97  .00137  5.85X10  1.71  1.70  1.0  4 5  3.4  x.814  1 1  1 1  8.7  -  1.063  -  71.  dependent.  The values of the modulus can also be calculated using the  expression  1  • S  E  N  - 2S fU,i,n)  where S 1 1  S  E  =  S^^  ioo ( S  -  =  V  N  . -  S-Q>  v  - 1/2  12  =  S  4 4  )  Poisson's Ratio  reciprocal of rigidity modulus for a shear on { 1 0 0 } 2 2  and  S  f(£,m,n) = £ m  2 2  +mn  2 2  + n I ; £,m,n being the direction  cosines of the tensile axis with respect to'.the three axes. This function has a value equal to 1/3 for an orientation of the tensile axis close to [ 1 1 1 ] .  Using the value of  can calculate the value of (S^  + 2  1/2  and E-^-QJ one  and using this value and  knowing f(£,m,n) for any orientation, the corresponding value of the modulus can be determined.  The agreement i s fairly good as can be  seen from Table IX. Though the anisotropy can be seen very clearly, i t would be convenient to express i t in the conventional manner, i.e., 2 ( S ^ -  ^il^^h^'  However, i t is not possible to determine the values of S..„ and S.. 12  44  from the above relationships; and so one has to assume a value for the Poisson's ratio in order to calculate the anisotropy. Assuming a value of 0.4, the value of the anisotropy factor comes as 16.9. 30  10  Values of  29  and 1 8  have been reported for the anisotropy factor in Cu-Zn  alloys, whilst in 0 Au-Cd the value has been given as 14.1  . A high  value of the shear constant 2(S^ - S^) has been reported in 3-Au-Cu-Zn 25 alloys  . The result obtained in the present work thus seems to be  reasonable.  However, the value of the anisotropy factor obtained i s  very sensitive to the assumed value of the Poisson's ratio and hence, the agreement might just be fortuitous. The elastic anisotropy is in part due to the interaction between the various constituent species and Zener predicted that a l l g type 1  alloys with closed inner shells w i l l have a high value for the 2(S^ - S.^) shear coefficient.  Pops and Massalski'*''" compared the  change i n the anisotropy effected by changes i n composition with the corresponding absence of the occurrence of thermal martensite in 50-50 Cu-Zn. However, an extension of this argument to imply the absence of thermal martensite with a corresponding low value of the anisotropy 58 ratio fails in the case of Au-Zn alloys  . They thus suggest that  perhaps a very high value for the 2(S^ - S.^) coefficient rather than the anisotropy ratio is the deciding factor, i.e., the {110}<110> shear is the deciding factor for martensite formation.  Thus the very  high value for the anisotropy factor in Ag-Cd indicates the ease of {110}<ll0> shear. 3.6  Deformation Martensite Formed by Filing ^  Ag-Cd Specimens  Diffractometer traces were obtained approximately ten minutes after f i l i n g the quenched  structures at room temperature.  -150 mesh fraction of the filings was used in the study. S „ phase has a pink colour which disappears on f i l i n g .  The  The polished Figure (33)  +  Figure 33. Diffractometer traces of filed Ag-Cd alloy specimens.  + a  74.  i n c l u d e s the d i f f r a c t o m e t e r t r a c e s o f a l l o y s 2 to 7. from 34 to 44 deg  i n c l u d e s the most i n t e n s e  the v a r i o u s s t r u c t u r e s . c o m p l e t e l y to a new  In a l l o y s 2-5  range of  r e t e n t i o n of the 3^ phase was  the s t r u c t u r e transformed  diffractometer trace.  phase was  retained.  a genuine e f f e c t and was  a f f e c t e d by the d e l a y between f i l i n g  the specimen and  7, a  This  not  significant  t a k i n g the  In a l l o y s 2 to 4 the c l o s e - p a c k e d s t r u c t u r e  o b t a i n e d on d e f o r m a t i o n was  face centred cubic (a ) w h i l s t i n a l l o y s +  7 a hexagonal c l o s e - p a c k e d product  ( ? ) was +  obtained.  In  alloy  5, peaks f o r b o t h the f . c . c . and h.c.p. s t r u c t u r e s were o b t a i n e d , s t r u c t u r e presumably having a l a r g e number of s t a c k i n g f a u l t s . t r a n s i t i o n from f . c . c . to h.c.p. appears deformation i n Cu-Zn  36  26  d i f f r a c t i o n peaks of  c l o s e - p a c k e d phase, w h i l s t i n a l l o y s 6 and  p r o g r e s s i v e l y i n c r e a s i n g amount of ^  6 and  The  the  This  to be c h a r a c t e r i s t i c of  induced m a r t e n s i t e s i n c e s i m i l a r s t r u c t u r a l changes o c c u r and Ag-Zn  An attempt  was  38  alloys.  made to determine  phase o b t a i n e d d u r i n g d e f o r m a t i o n , t h i s phase has  the l a t t i c e parameter of the  cub  i n o r d e r t o see whether o r not  a l a t t i c e parameter t h a t would be expected  from  an  e x t r a p o l a t i o n of the e q u i l i b r i u m a-phase parameter to h i g h e r cadmium contents. was  used  In d e t e r m i n i n g  the l a t t i c e parameter, the  (311)  reflection  as t h i s i s s h i f t e d l e a s t by s t a c k i n g f a u l t s p r e s e n t i n the 36  structure  .  The  r e f l e c t i o n was  worked s t a t e of the powder and accuracy of + 0.1 of the d e f o r m a t i o n  deg.  fairly  d i f f u s e because of the  cold  the peak c o u l d o n l y be read to an  F i g u r e (24) shows t h a t the l a t t i c e  induced m a r t e n s i t e appears  of the a - s o l i d s o l u t i o n i n t o the m e t a s t a b l e  parameter,  to l i e on an e x t e n s i o n  region.  75. The b e h a v i o u r o f Ag-Cd a l l o y s i n t h e c o m p o s i t i o n range between 42.3 t . % a  Cd t o 50.9 a t . % Cd i s v e r y s i m i l a r t o isomorphous 8^ Ag-Zn  and Cu-Zn a l l o y s .  I n b o t h cases t r a n s f o r m a t i o n t o a c l o s e - p a c k e d  s t r u c t u r e o c c u r s on f i l i n g , b e i n g f . c . c . a t low Zn c o n t e n t s and changing g r a d u a l l y t o h.c.p. a t h i g h e r Zn c o n t e n t s .  I n both cases, a l s o ,  there  i s incomplete transformation to the deformation martensite at higher z i n c c o n t e n t s i n agreement w i t h t h e p r e s e n t  3.7  N a t u r e of M a r t e n s i t e Produced  results.  on C o l d R o l l i n g  X-ray d i f f r a c t o m e t e r t r a c e s were t a k e n a f t e r v a r i o u s d e g r e e s j O f d e f o r m a t i o n i n d u c e d by c o l d r o l l i n g of t h e 8^ pbase i n b o t h Ag-Cd and Ag-Zn a l l o y s .  A f t e r r o l l i n g , the s u r f a c e of t h e specimen was m e c h a n i c a l l y  and e l e c t r o l y t i c a l l y p o l i s h e d t o remove t h e top d i s t u r b e d l a y e r .  As  the g r a i n s i z e of t h e specimen used was q u i t e l a r g e ('v 3 mm) , n o t a l l the X-ray d i f f r a c t i o n peaks c o u l d be r e c o r d e d ; and hence o n l y a semiq u a n t i t a t i v e treatment i s p o s s i b l e h e r e .  3.7.1  O p t i c a l Microscopy o f Deformation M a r t e n s i t e F i g u r e s (34a,b) shows.the m a r t e n s i t e produced  i n an Ag-41 a t . % Zn  a l l o y , as seen on t h e r o l l e d s u r f a c e and on a second angles.  surface at r i g h t  The m a r t e n s i t e t r a c e s were u s u a l l y somewhat i r r e g u l a r on t h e  r o l l e d s u r f a c e , w h i l s t they were v e r y s t r a i g h t on t h e second s u r f a c e . I t i s p r o b a b l e t h a t t h i s waviness was due t o t h e complex n a t u r e o f t h e d e f o r m a t i o n on t h e s u r f a c e .  T h i s was p a r t l y r e v e a l e d by t h e v e r y poor  q u a l i t y Laue back r e f l e c t i o n photographs material.  o b t a i n e d from  The back r e f l e c t i o n photographs  as-rolled  became c l e a r e r as t h e . d i s t o r t e d  76.  Figure 34a,b.  Deformation martensite i n Ag-Zn a l l o y .  Microstructures  on the r o l l e d surface (a) and on a second surface at r i g h t angles (b) [X 290].  77.  surface layer was removed.  Similar behaviour was seen i n the case of  the Ag-Cd a l l o y .  3.7.2  Structure of Martensite Formed on Rolling an Ag-45 at. % Cd . Alloy: Table X indicates the angular positions of the d i f f r a c t i o n peaks,  and figure (35) shows a schematic peaks.  representation of the d i f f r a c t i o n  The peaks i n most cases were i l l - d e f i n e d and hence this  prevented accurate l a t t i c e parameter determination.  The following  conclusions can be derived from the X-ray d i f f r a c t i o n r e s u l t s : (a)  The structure i s predominantly unchanged during the e a r l i e r  stages of deformation; as revealed by the very weak peaks belonging to the martensite structure. (b)  Above 15% deformation, the martensite formed could be  v i s u a l l y detected. (c)  The martensite peaks cannot be analysed i n terms of a face-  centred cubic l a t t i c e , but do agree well with a face centred tetragonal c e l l with a = 4.379 A° and having an a x i a l r a t i o of (d)  0.88.  There i s no further change i n the structure u n t i l very severe  deformation i s effected (y 60%) when there i s a very gradual change to a cubic structure. Ce)  For comparison purposes, the d i f f r a c t i o n peaks obtained from  the f i l i n g s of the same a l l o y are included i n the table.  A gradual  change to the face-centred cubic structure i s apparent. Cf)  Even after severe deformation induced by r o l l i n g , the $^ peaks  are s t i l l present.  Therefore, the structure cannot be f u l l y  transformed  Table X  Positions of the diffraction peaks as a function of amount of deformation for Ag-45 at. % Cd alloys  15%  27%  36%  37.2  45%  37.2  50% , „ ' (26 deg.) 37.2  37.2  37.2  65%  75%  37.2  37.2  37.2  Filed Remarks sample 37.2  (lll)f.c.c. f.c.t.  38.3  38.3  38.3  38.3  38.3  38.3  41.4  41.2  38.3  38.3  38.4 41.6  38.4  38.4  (HO)b.c.c.  41.4 42.3  (200)f.c.t. 42.3  42.4  42.7  47.8 55.7  55.6  59.4  55.8  55.9  59.5  59.5  (002)f.c.t. 55.1  55.1  55.1  59.6  55  55.7  55.7  (200)b.c.c.  59.6  59  59.5  (220)f.c.t.  62.3 64.3 69.2  69.6  69.6  69.0  69.1  69  69.0  72.5  72.4  72.5  72.3  72.3  72.7  72.4  69.0  62.8  62.7  64.3 69.0  69.3  69.4  72.5  72.3  69.0  69.1  (211)b.c.c. (311)f.c.t. 75.2  (311)f.c.c.  79.3  (222)f.c.c. (220)b.c.c.  95.0 106.8  (220)f . c c . (202)f.c.t.  82  106.8  (200)f.c.c.  106.7  106.7  106.7  106.8  106.8  106.8  106.7  (310)f.c.c. (004)f.c.t. (331)f.c.c. (222)b.c.c.  80.  to martensite even after ^ 75% of rolling.  This i s i n contrast to  the complete absence of the 3^ peaks in the filed material.  This is  indicative of the severity of the deformation imposed while f i l i n g the specimen.  3.7.3  Structure of Martensite Obtained on Rolling Ag-41 at.% Zn alloy: Figure (36) shows the diffractometer peaks obtained after various  degrees of cold rolling of the ft^ phase.  The analysis is made a  l i t t l e complicated by the presence of superlattice peaks. gives the angular positions of certain prominent peaks.  Table XI The  following conclusions can be drawn from the X-ray diffraction results. (a)  The martensite diffraction peaks can be analysed in terms  of a face centred tetragonal c e l l with a = 4.041 A° and an axial ratio of 0.955. (b)  The relative intensities of (200) 3  2  and (220) f.c.t. peaks  change considerably as the percent deformation increased. (c)  The superlattice peak (110) f.c.t. i s visible until the  very last stage of deformation (^ 70%) indicating the preservation of order in the 3^ structure. (d)  It was not possible to extend the deformation further,  because of cracking of the specimen.  This prevented the identification  of the cubic structure at later stages of deformation.  However,  38 f i l i n g did give an f.c.c. structure  indicating that the structure  does become close-packed on severe deformation.  F i g u r e 36.  D i f f r a c t o m e t e r t r a c e s of deformation  martensite  f u n c t i o n of % c o l d r o l l i n g  at. % Zn  f o r Ag-41  as a  alloy.  82.  Table XI  Positions of diffraction peaks for deformation martensite in Ag-41 at. % Zn alloy.  2e  Remarks  31.25  (HO) f.c.t.  39.2  (111) f.c.t. (110)  h  50.2  (HI)  h  58.0  (200)  41.0 44.7  (200) f.c.t.  65.2  (220) f.c.t.  79.2  (311) f.c.t.  99.3  (400) f. c.t.  114.5  (310)  h  (222) B  9  83.  3.7.4  General Discussion It is evident that the martensite that i s formed in the early  stages of deformation has a face centred tetragonal c e l l .  The present 40  observations are in agreement with the results obtained by Hornbogen and coworkers for the Cu-Zn system.  In the case of 8  2  Cu-Zn alloys  they observed that (a)  the deformation martensite i s formed after about 15% deforma-  tion i s given (b)  the structure of the martensite formed is face centred  ;  tetragonal with c/a = 0.94 and this structure remains unchanged until about 70% deformation Cc)  beyond 70% deformation a gradual change to the face centred  cubic structure takes place. The fact that the structure remains ordered until the very last 44 stages of deformation is contradictory to the earlier view  ,  according to which the B phase became unstable on deforming because 2  of disruption of order.  It thus appears that interpretation of the  martensite structures on the basis of the state of ordering of the matrix  is not useful.  Rather i t is necessary to look at details of  the deformation process. 3.7.5  Electron Microscopy of Rolled Specimens Figures (37,38) give the electron micrographs of quenched and  cold rolled specimens of an Ag-45 at.% Cd alloy.  The dislocations  are fairly straight in as-quenched alloy figure (37).  In the cold  rolled material, the dislocation density is naturally higher and the  84.  Figure 37.  Electron micrograph of an as-quenched Ag-45 at. % Cd a l l o y revealing  d i s l o c a t i o n structure  (X 65K).  85. dislocations form a cross grid pattern. In body centred cubic materials the screw dislocations are very predominant.*^ It was very d i f f i c u l t to observe deformation martensite in the microscope.  At low amounts of deformation the amount of the matrix  transformed to martensite i s very small and hence the probability of observing the martensite was negligible.  An increase i n the amount of  deformation increased the amount of martensite but this was also accompanied by an increase i n the dislocation density which made i t yery d i f f i c u l t to delineate the martensite from the matrix.  Figures  C39,40) show the martensitic plates produced during cold rolling. It was not possible to detect any gradual change i n the dislocation structure of the 3 matrix, which would act as a strain embryo in the formation of martensite. It was d i f f i c u l t to produce good diffraction patterns owing to cold work.  Figure (41) shows streaking indicating the presence of  stacking faults, very much more evident than i n the case of thermal> martensite (see figures (19,20)).  The spots could be interpreted on  the basis of a face centred tetragonal cell in agreement with X-ray diffraction data.  Table XII gives the d values for some of the  planes obtained by the two methods. The electron micrographs showed a high degree of dislocation density, higher, than i n the adjacent matrix, implying that the dislocations are concentrated in the martensite.  No trace of twinning was  ever seen. Thin foils suitable for observation could not be obtained from Ag-Zn alloys.  A l l the different methods , tried proved unsuccessful. (  Figure 38.  Electron micrograph of 15% cold rolled Ag-45 alloy (X 50K).  87.  Figure 3 9 .  E l e c t r o n micrograph of d e f o r m a t i o n m a r t e n s i t e i n 15% c o l d r o l l e d m a t e r i a l (X 50K).  88.  Figure 40.  Electron micrograph of deformation martensite i n 40% cold rolled material (30K).  89.  Figure 41.  S.A.D. of deformation martensite.  90. Table XII Comparison of lattice spacings obtained from electron and X-ray diffraction for deformation martensite in Ag-45 at. % alloy.  3.8  d A° X-ray diffraction  (hkl)  d A° Electron diffraction  311  1.24  1.303  331  0.932  0.99  022  1.36  1.447  313  0.91  0.942  Stress-Induced Martensite i n Ag-45 at. % Cd alloy  3.8.1  Single Crystal Specimens  Single crystal specimens of several orientations (figure (42)) were tested over a range of temperatures from -90°C to 0°C. In this temperature region the stress needed to form martensite increased with increasing temperature.  91.  3.8.1.1  General Shape of the Tensile Curve  The loading portion of the curve is made up of three distinct parts as seen from f i g . (43).  There is an i n i t i a l elastic region a,  where the stress is proportional to the strain.  The slope of this  i n i t i a l region gives the elastic modulus of the specimen (a correction has to be applied to account for the softness of the machine).  The  specimen deforms elastically until the point p is reached, when the applied stress causes the transformation to initiate.  At lower  temperatures martensite forms in sudden bursts with associated stress relaxation whilst at relatively high temperatures (-40°C) the transformation is 'smooth', the growth of the martensite taking place by  92.  Figure  43.  General  shape  temperatures  of  the  above  A  tensile  f  curve  i n Ag-45  obtained  a t . % Cd  at  alloy.  the formation of fine plates ahead of the martensite-32 interface which merge with the bulk of the martensite.  In this region (b) of  growth of martensite the slope of the curve i s almost negligible, i.e., the matrix transforms at a constant load. After the gauge length i s fully transformed, the load increases gradually (region cj) • This region corresponds to the elastic deformation of the martensite; and continues until  the point when plastic deformation ensues.  On unloading these changes take place i n the reverse order. Provided that the test temperature i s above A^, the martensite completely reverts to the b.c.c. matrix.  The region e, which corresponds to the  reverse transformation is either serrated or smooth, depending on the temperature, a behaviour very similar to that exhibited in region b. Figure (44) shows a series of photographs whilst loading in the Instron machine.  taken of a specimen  The corresponding stress-  strain curve is given in figure (45), the numbers on the curve corresponding to the photographs in figure (44).  The photographs  show clearly that in the plateau portion of the load-elongation curve a band of martensite develops along the specimen until the entire gauge length has transformed.  On relase of the load the martensite  shrinks in the reverse sequence such that the final area to disappear is the same as the f i r s t area to form.  There appears to be a sharp  interface delineating the transformed region from the untransformed and in this temperature range there is no trace of fine plates appearing prior to the formation of the martensite band, .t.  It was very d i f f i c u l t to obtain high quality photographs of the specimen. The main problem was to get good focussing through the coolant and the double walled transparent dewar, v/hich contained the coolant.  Figure 44.  (continued)  Micrographs of a tensile specimen showing the formation of  stress-induced martensite and i t s reversal (X5).  96.  T  1  STRAIN  Figure 45.  1  1  r  (%)  Stress-strain curve corresponding to the photographs in Figure 44.  3.8.1.2  Effect of Temperature: j  Figure (46) shows a series of stress-strain curves obtained at various temperatures for a single crystal specimen.  In a l l cases, the  specimen was extended t i l l the gauge length was fully transformed. The specimen was then unloaded gradually. The lowest test temperature was used for the f i r s t test and the temperature was gradually raised for subsequent tests.  The results can be discussed with  reference to transformation temperatures, (the alloy has M  = -74°C, A S  =-80°C, A_ =-67°C). S  |  = -98°C,  Figure (47) shows the level of  j_  stress associated with the end of the true elastic portion of the curve as a function of the test temperature.  Figure (48) shows the  % recovery as a function of test temperature. (a)  Below the M  temperature, the specimen is partially or fully  g  martensitic to start with and the application of external stress causes two things: formation of new martensite and deformation of existing martensite.  The martensite thus formed is stable upon unloading  because i t is below A . s (b)  Above the  temperature, the specimen is fully  martensite forms on application of stress.  a n  ^  The stress necessary to  cause the transformation i s a function of temperature, being higher at high temperatures.  Up to approximately 50°C above M  g  the stress  for the formation of martensite i s less than the yield stress of the specimen and so no plastic deformation takes place before the transformation.  The recovery is complete on removing the load, figure (46),;  provided the test temperature is above A^.  At higher temperatures,  (e.g., -10°C) there is plastic deformation before the matrix is  Figure 46.  Stress-strain curves for specimen 1, over a series of temperatures.  STRAIN % Figure 46.  (Continued) Stress-strain curves for specimen 1, over a series of vo  temperatures.  VO  101.  30  O  Loading  A  Unloading  Cycle Cycle  ^20 o o o CO CO  rr  10  0  -80  -60  -40  -20  0  TEMPERATURE Figure 4 7 . Variation of stress necessary to form SIM with temperature for specimen 1 .  102.  -60  -40  -20  0  TEMPERATURE Figure 48.  Pseudo-elastic recovery vs. temperature for specimen 1  103.  s u f f i c i e n t l y s t r o n g to support m a r t e n s i t e is  only p a r t i a l .  deformation Figure  At s t i l l  occurs and (47)  temperature and  f o r m a t i o n and  h i g h e r temperatures  t h e r e i s no m a r t e n s i t e  so  recovery  (+20°C) o n l y p l a s t i c f o r m a t i o n at a l l .  i s the s t r e s s to form m a r t e n s i t e as a f u n c t i o n of shows a two  stage b e h a v i o u r ,  s t e e p e r s l o p e o c c u r r i n g at lower h i g h e r temperatures.  The  the f i r s t  temperatures, and  t r a n s i t i o n from one  stage w i t h  a  a second stage a t  r e g i o n to the  other  c o i n c i d e s w i t h the smoothing of the t r a n s f o r m a t i o n curve and  also  w i t b the l o w e r i n g of the h y s t e r e s i s a s s o c i a t e d w i t h the t r a n s f o r m a t i o n . Figure  C47),  a l s o i n c l u d e s the s t r e s s l e v e l s a t which the r e v e r s e  t r a n s f o r m a t i o n i s completed on u n l o a d i n g .  At h i g h e r  temperatures  (stage I I ) the s t r e s s d u r i n g r e v e r s a l i s the same as t h a t d u r i n g  the  f o r m a t i o n of m a r t e n s i t e , a f e a t u r e c h a r a c t e r i s t i c of t h e r m o - e l a s t i c transformation.  The m a r t e n s i t e formed d u r i n g l o a d i n g remains s t a b l e  upon u n l o a d i n g a t temperatures formed d u r i n g the i n i t i a l unloading The the M  g  below  loading cycles disappears  as r e v e a l e d i n f i g u r e s t r e s s necessary  temperature.  The  e x t r a p o l a t e to the M  g  A^, w h i l s t above A^  upon  (46).  to form m a r t e n s i t e i s by d e f i n i t i o n zero at initial  p o r t i o n of the curve must, t h e r e f o r e ,  temperature a t zero s t r e s s .  The  extrapolated v a l u e of  By a s i m i l a r argument, the s t r e s s d u r i n g the r e v e r s e  t i o n must e x t r a p o l a t e to 0 at the A^ did  martensite  completely  v a l u e i s -70°C compared to the e x p e r i m e n t a l l y determined -74°C.  the  temperature.  transforma-  The p r e s e n t  data  not c o n f i r m t h i s too w e l l , owing to the d i f f i c u l t y of e x t r a p o l a t i n g  the curve to zero s t r e s s due as shown i n f i g u r e e x t r a p o l a t e to A  f  to i t s r a p i d l y v a r y i n g c u r v a t u r e .  (49), t h e r e seems l i t t l e doubt t h a t t h i s does as was  found by  Eisenwasser  21  However, indeed  104.  Tested at -45 c  30  o  Loading  A  Unloading  Cycle Cycle  dL  O  820  00 00 LU  rr  100  0  0  -80  -60  40  -20  0  TEMPERATURE Figure 49.  Stress necessary to form martensite vs. temperature for specimen 4.  Fig  50.  Stress necessary to form martensite vs. temperature for specimen 5.  1  106. Figures (49,50) give similar data for crystals of different orientations. (a)  The following features can be generalised:  the stress-temperature  relation for the loading cycle  follows a two stage behaviour in a l l orientations. (b)  the curves a l l extrapolate to -70 + 2°C, i.e., %M ,  at  g  zero stress. (c)  the relative value of the stress for the reverse transforma-  tion is a function of the orientation; viz. in certain orientations reverse transformation takes place at a much lower stress than the stress required for the i n i t i a l transformation.  This is clearly  evident in specimens having their tensile axes away from the  [001]  corner of the unit stereographic triangle. The stress values obtained at various temperatures using the same specimen might seem questionable.  To ensure that these values were not  spurious, a specimen was tested at -45°C and the stress value thus obtained was compared with the corresponding value taken from a specimen of almost identical orientation.which was tested over a series of temperatures.  Figure (49) shows very good agreement between  the two values. Also repeated-testing of a specimen at one particular temperature was found to have very l i t t l e effect on the magnitude of stress required to cause the transformation as shown in figure (51). this case the specimen was strained repeatedly at -45°C. felt that the procedure used was valid.  In  It is thus  108. 3.8.1.3  Effect of Orientation on the Stress-Strain Curves  Figures (52a-g) show the load-elongation curves obtained at different temperatures for three orientations. At -60°C, a l l specimens exhibit a serrated stress-strain curve, indicating that martensite was formed in bursts, figure (52a). Specimen 1 shows f u l l recovery, whilst 5 and 7 do not show any recovery other than the true elastic recovery. At -55°C, the martensitic formation is s t i l l of the burst type, but now i t i s recovered in a l l three specimens (-55°C i s well above the A^ temperature for the alloy, -67°C).  The recovery i s close to  100% for specimen 1, whereas for 5 and 7 i t is  90%, figure (52b).  At -40°C, specimen 1 transforms at a constant load (thermo-elastic ) whilst specimens 5 and 7 s t i l l show serrated transformation curves. Again the recovery is complete for specimen 1, whilst specimens 5 and 7 have recovery values of ^95% and 85% respectively, figure (52c). At -35°C specimens 1 .and 5 behave as before, but specimen 7 shows a considerable amount of permanent set after unloading; recovery is only 75% for this specimen, figure (52d).  No further  [  tests at higher temperatures were carried out on this specimen owing to the plastic deformation. ; At -10°C, specimen 1 i n i t i a l l y deforms plastically, before the transformation takes over.  The reversal of martensite i s complete,  but the i n i t i a l plastic deformation gives a permanent set to the specimen.  Specimen 5 transforms on application of stress and recovers  almost 95%, figure (52e). At room temperature two other specimens, one oriented close to  Figure 52a.  Stress-strain curves for. specimens 1, 5 and 7 at -60°C.  o VO  Figure 52b.  Stress-strain curves for specimens 1, 5 and 7 at -55°C.  t—* o  Figure 52c.  Stress-strain cuves for specimens 1, 5 and 7 at -45°C.  Figure 52d.  Stress-strain curves for specimens 1, 5 and 7 at -35°C.  114. specimen 1 (IA) and another at orientation 8 were deformed.  Specimen  IA deformed plastically and continued to deform likewise on increasing the stress.  Specimen 8 showed a peculiar behaviour.  deform plastically with two slip systems.  It started to  The deformation became  non-uniform with the development of a neck in the gauge length. At this stage, the specimen started to transform to martensite in the necked area.  On releasing the load the martensite disappeared, as  revealed by the kink in the unloading portion.  Figure (53a) shows the  surface of the specimen, revealing profound slip markings.  The specimen  was then polished to remove the deformation marks and then reloaded. No evidence of plastic deformation was observed.  This is confirmed by  the figure (53b), which shows the surface of the same specimen after the second loading cycle.  The absence of any profound slip markings  suggests that no plastic deformation i s involved.  Similar reloading  of specimen IA failed to yield a transformation. A simple explanation for this behaviour would be that the yield stress i s increased by prior deformation to a point that i t exceeds the value needed for, the transformation.  The increased hardening is perhaps more prevalent  near the JOIT] corner because of the two slip systems that are favoured. Occurrence of deformation martensite was observed in specimen 7 only.  The tensile axis in this case i s located close to the [111] corner.  Only a few observations of deformation martensite were carried out on single crystal specimens, since once they had been plastically deformed, they were useless for any further work.  116.  Figure 52g.  I n i t i a l straining of specimen close to [001] showing plastic deformation.  117.  F i g u r e 53.  (a)  Surface of #8, a f t e r f i r s t  strain,showing  slip  markings(X 230). (b)  Specimen p o l i s h e d and s t r a i n e d and r e l e a s e d . (X 230).  to form m a r t e n s i t e  Note the absence of s l i p markings  118. 3.8.2  Polycrystalline Specimens Polycrystalline specimens were tested over a range of temperature  from -196°C to +20°C.  The specimens were given a constant value  of strain (5%) and were then unloaded.  The resulting stress-strain  curves are given in figure (54). The values of the stress at which the curves deviated from linearity are plotted as a function of temperature in figure (55). The figure can be divided into three different regions, depending on the temperature relative to M . g  Region b This region covers the temperature range from -75°C to -20°C. The M  g  temperature for the alloy is -74°C and so in this region the  specimen is fully g  t o  start with (except at -75°C where a l i t t l e  martensite had appeared prior to the start of the test).  On loading  the specimen in this temperature region the matrix deforms elastically up to a certain value of the stress, which is a function of the temperature, and above this stress the matrix transforms to martensite. This is usually accompanied by a stress relaxation, as seen from the serrations in the load-elongation curve.  [The formation of thermal  martensite could easily be detected because of the accompanying colour change in the specimen.]  The stress needed for the formation  of martensite increases with increase in the temperature of testing, as i s to be expected. Region a In this region, the specimen i s fully or partly martensitic to. start with. The increase in the applied stress causes a reorientation and deformation of the existing martensitic plates.  The stress varies  I  Figure 54.  Stress-strain  curves f o r p o l y c r y s t a l l i n e  specimens  over a range of  temperatures.  •031  Figure 55.  Stress necessary to form martensite vs. temperature for polycrystalline specimens.  122. drastically only in the temperature range where the specimen is not fully martensitic to start with (M^ temperature for this alloy i s -99°C).  Between -196°C and -100°C the stress level necessary to  cause a reorientation of the existing martensitic plates does not change significantly. Region c In this temperature range the stress necessary to cause the transformation is so high that plastic deformation of the specimen precedes the transformation.  The stress corresponding to the point of  deviation in the tensile curves then corresponds to the yield stress of the material at that temperature.  The drop in the yield stress with  temperature i s in keeping with the behaviour of b.c.c. materials. Even though the material deforms plastically in the i n i t i a l stages, i t i s possible that the specimen w i l l ultimately transform to martensite provided the stress level i s high enough to cause the transformation. The martensite so formed reverts back to the (^phase upon unloading provided that the test temperature is above the A  g  temperature.  The reversion is nearly complete in the case where the test temperature is above  and is only partial in the temperature range A  g  to A^.  This reversion is easily revealed in the unloading portion of the curves.  (Note the curves for tests conducted at -70°C and -50°C.)  Figure (56) gives the % recovery obtained as a function of test temperature.  The recovery obtained below -75°C and above -10°C is -  purely elastic in nature whilst in the temperature range -75°C to -10°C the recovery is both elastic and that due to the reverse transformation.  -200  -150  -100 TEMPERATURE  Figure 56.  -50 °c  Amount of pseudo-elastic recovery vs. temperature for polycrystalline specimens.  0  124.  This behaviour i s very s i m i l a r  t o the one e x h i b i t e d by the  c r y s t a l specimens of the same a l l o y except never o b t a i n e d i n p o l y c r y s t a l l i n e o b t a i n e d was  3.8.3  t h a t 100%  specimens;  recovery  was  the maximum v a l u e  85% o n l y .  Microscopic Observations M i c r o s c o p i c examination a t room temperature  of d e f o r m a t i o n m a r t e n s i t e a,  formed was Figure  r e v e a l e d the presence  ( s i m i l a r t o the m a r t e n s i t e formed  r o l l i n g ) i n the p o l y c r y s t a l l i n e  specimens.  on  The amount of m a r t e n s i t e  v e r y s m a l l and c o u l d be observed o n l y i n one o r two  grains.  (57) shows the m a r t e n s i t e as r e v e a l e d under the microscope.  order to check t h a t t h i s was r e p o l i s b e d and r e - e t c h e d . in  single  the f i g u r e  and  not a s u r f a c e e f f e c t , the specimen  An edge view of the specimen  In  was  i s included  t h i s r e v e a l s the p l a t e - l i k e n a t u r e of the deforma-  tion martensite. Deformation m a r t e n s i t e was at temperatures  -10°C  and above.  not form d u r i n g the i n i t i a l curves  (figure  this i n i t i a l  (54)).  not observed i n specimens deformed In these specimens m a r t e n s i t e d i d  l o a d i n g as can be seen from the  However, the specimens work hardened  l o a d i n g and on t e s t i n g  a second  stress-induced martensite during loading.  tensile during  time they d i d form  On subsequent  examination  they were found to have d e f o r m a t i o n m a r t e n s i t e i n i s o l a t e d g r a i n s i n the specimen.  T h i s suggests t h a t e i t h e r  severe d e f o r m a t i o n of the ft^  phase or d e f o r m a t i o n of the thermal m a r t e n s i t e i s n e c e s s a r y i n o r d e r to form d e f o r m a t i o n m a r t e n s i t e .  T h i s w i l l be d i s c u s s e d l a t e r .  125.  Figure 5 7 . Deformation martensite in Ag-Cd polycrystalline specimen after tensile testing. (X  125).  Traces on two surfaces are matched  126.  3.8.4  S t r a i n Memory E f f e c t  3.8.4.1  Experimental  The  s t r a i n memory e f f e c t was  s t u d i e d i n an Ag-45 at % Cd  alloy.  S i n g l e c r y s t a l specimens were s t r a i n e d to a constant v a l u e of 5% at v a r i o u s temperatures  and r e l e a s e d .  o r p s e u d o - e l a s t i c r e c o v e r y . The  strain  T h i s gave the amount of e l a s t i c  specimen was  then allowed  to warm up  to room temperature c a u s i n g r e v e r s e t r a n s f o r m a t i o n to the  matrix.  T h i s r e s u l t e d i n a 'buildup of s t r e s s i n the m a t e r i a l which was released.  The  s t r a i n a s s o c i a t e d w i t h t h i s was  memory r e c o v e r y .  A typical stress-strain  T h i s method of t e s t i n g  proved  effective  a measure of the  Figures  o n l y at temperatures  (58)  above M .  maintained  s u f f i c i e n t to cause the t r a n s f o r m a t i o n .  (59a,b) show the s t r a i n memory e f f e c t  case of the two  strain  curve i s g i v e n i n f i g u r e  Below t h i s temperature the s m a l l v a l u e of l o a d (y 3 l b s ) w h i l e c o o l i n g the specimen was  later  s i n g l e c r y s t a l specimens.  The  o b t a i n e d i n the ;.  amount of pseudo21  e l a s t i c i t y obtained i s also included. s t r a i n memory e f f e c t n a t u r e ; and test,  temperatures of  amounts depended on the temperature of: the  t r u e , as r e v e a l e d from the f i g u r e s .  drops d r a s t i c a l l y ; above A^ and  significant  At  low  there i s r e l a t i v e l y l i t t l e p s e u d o - e l a s t i c i t y and most  the r e c o v e r y i s by the s t r a i n memory e f f e c t .  effect  showed t h a t the  and p s e u d o - e l a s t i c i t y were complementary i n  the r e l a t i v e  i T h i s i s indeed  Eisenwasser  The  s t r a i n memory  at the same time  there i s a  i n c r e a s e i n the p s e u d o - e l a s t i c i t y from about 15%  to  ^97%.  127.  Figure 58.  Typical stress-strain curve used in strain memory effect.  128.  100  STRAIN  /  MEMORY  Q  -O  PSEUDO-ELASTIC  O  —A-  80  60 oc LU  o o  40  LU  oc  20  — ° - o - o '  -100  -80  A  \ 2. -60  TEMPERATURE  Figure 59a.  -40 °c  Strain memory recovery vs. temperature for #1.  -20  129.  T  100  STRAIN MEMORY  /O  — o—o— PSEUDO-ELASTIC  V 80  60 or LU  >  o u  40  UJ  cr 20 -o-o  -100  80  -60  40  -20  TEMPERATURE Figure 59b.  Strain memory recovery vs. temperature for #2.  130. 3.8.4.2  Discussion  On straining specimens below the  temperature, two things can  happen: (a)  at T > M , martensite forms on straining the specimen and  this forms in an oriented manner so as to give an elongation in the direction of stress.  On removal of the load, martensite that is formed  does not revert back completely. place in the range A  < T < A.. S  Partial transformation to ^  takes  However, when the specimen is heated  I  above the A^ temperature, any remaining martensite also disappears. The reverse transformation is accompanied by a strain recovery.  This  can be seen from the load elongation curves for specimens tested above M  temperature. (b)  T <  M  s In this range, the specimen i s either partially or fully martensitic to begin with, depending upon whether the temperature is above not.  or  The martensite needles form in a l l possible orientations.  However, when the specimen is strained there is a rearrangement of these needles so as to give rise to an oriented martensite.  The  strain induced in the martensite is' taken up by this rearrangement and on heating the specimen above A^, the reverse transformation takes place and once again the strain is fully recovered. A specimen was deformed below the  temperature, and the changes  in the microstructure of the specimen were observed through a microscope.  Figure (60) shows a series of photographs of the specimen  surface, with increasing amount of deformation.  The change in the  disposition of martensite needles is clearly revealed. Whether there  133. is a change i n the structure of the martensite associated with this reorientation is not known, since i t was not practical to obtain single crystal diffraction patterns at low temperatures. 22 deLange and Zijderveld  explained the strain memory effect on  the basis of a preferential growth of twins oriented in a favourable manner. This description i s considered adequate in cases where the thermal martensite has a twinned internal structure but cannot be used here since electron microscopy showed the martensite to have a 42 faulted structure. In the case of Cu-Zn-Sn alloys, the martensite is considered to be a lamellar mixture of orthorhombic and face centred cubic structures; and the elongation obtained is due to a change in the relative proportion  21 of these two structures . In the present  system, the martensite occurring at the composition of interest is found to have a unique structure and hence this argument is not valid. 71 72 Wasilewski  '  suggests that below  there i s a reverse transformation  of the martensite to g under stress and this being unstable, immediately transforms to the favourably oriented martensite.  This change results  in an elongation without plastic deformation of the martensite. It is very difficult to explain thermodynamically  the reversion to fc^  and in the absence of any metallographic evidence, i t i s d i f f i c u l t to accept Wasilewski's argument.  In a later section, the probable  cause of the elastic strain in Ag-Cd alloys is presented in some detail.  134. 3.9  Habit Plane Determination  3.9.1  Experimental Results  3.9.1.1  Habit Plane Poles for Thermal Martensite  Figure (61) shows the habit plane poles obtained for thermal martensite.  Angular measurements of the traces were made at -85°C  corresponding to a temperature just below M^.  The traces on two  surfaces were matched and the habit plane pole was determined by a two surface analysis.  Figure 61.  The poles are clustered very close to [133].  A  Thermal Martensite  •  Stress Induced Martensite  Habit plane poles for thermal and stress-induced martensite. Shaded symbols represent theoretically calculated values. ( • ) is obtained using the actual values of lattice parameters at -74°C.  135.  3.9.1.2  H a b i t Plane P o l e s f o r S t r e s s - I n d u c e d M a r t e n s i t e  The h a b i t p l a n e of s t r e s s - i n d u c e d m a r t e n s i t e was determined f o r s e v e r a l specimens and the p l a n e normals are g i v e n i n f i g u r e (61). The  t e n s i l e apparatus was used to keep the specimen s t r e s s e d a t the  low temperature; There  and the angular measurements were made as b e f o r e .  i s some s c a t t e r i n the h a b i t p l a n e normal; n e v e r t h e l e s s , i t can  be^; s a i d that the p l a n e normals are d i f f e r e n t thermal m a r t e n s i t e . 70°)  from those determined f o r  The observed h a b i t p l a n e s made v a r y i n g angles (46-  w i t h the t e n s i l e a x i s and d i d not l i e on the p l a n e of  maximum shear.  3.9.1.3  H a b i t Plane D e t e r m i n a t i o n f o r Deformation  The d e f o r m a t i o n m a r t e n s i t e was produced  Martensite  i n coarse g r a i n e d p o l y -  c r y s t a l l i n e specimens by c o l d r o l l i n g  ^12% f o r the Ag-45 at. % Cd a l l o y  and ^15% f o r the Ag-41 at. % Zn a l l o y .  After rolling,the  specimens  were m e c h a n i c a l l y p o l i s h e d to remove the d i s t u r b e d s u r f a c e l a y e r ; and a second  s u r f a c e was p o l i s h e d a t r i g h t angles t o the f i r s t .  This  p e r m i t t e d a two s u r f a c e a n a l y s i s to be made. Figures  (62a,b) shows the h a b i t p l a n e p o l e s of the d e f o r m a t i o n  m a r t e n s i t e i n both Ag-Cd and Ag-Zn a l l o y s . plane p o l e s c l u s t e r e d v e r y near triangle.  In both cases the h a b i t  the [110] c o r n e r of the s t e r e o g r a p h i c  The f i g u r e a l s o i n c l u d e s the o r i e n t a t i o n s of the g r a i n s i n  which m a r t e n s i t e formed f i r s t .  These p o l e s are grouped  corner of the s t e r e o g r a p h i c t r i a n g l e .  H a b i t planes are r e f e r r e d to the b . c . c .  I t i s important  axes.  near  the [111]  to r e c a l l a t  136.  F i g u r e 62a.  H a b i t plane normals f o r deformation Ag-45 at. % Cd a l l o y ,  martensite i n  shaded symbol r e p r e s e n t s the  t h e o r e t i c a l value.  F i g u r e 62b.  H a b i t plane normals f o r deformation m a r t e n s i t e i n Ag-41  at. % Zn a l l o y .  theoretical value.  Shaded  symbol r e p r e s e n t s the  137. t h i s stage t h a t d u r i n g t e n s i l e t e s t i n g o f s i n g l e c r y s t a l s , o n l y c r y s t a l s o r i e n t e d c l o s e t o t h e [111] c o r n e r showed any d e f o r m a t i o n m a r t e n s i t e . T h i s i s , t h e r e f o r e , i n agreement w i t h t h e o b s e r v a t i o n s on c o l d  rolled  specimens.  3.9.2  T h e o r e t i c a l C a l c u l a t i o n s of Habit Plane Poles H a b i t p l a n e p o l e s were c a l c u l a t e d based on t h e a n a l y s i s o f  73 • Wechsler  and O t t e  , a m o d i f i c a t i o n o f t h e b a s i c WLR t h e o r y t o f a c e  c e n t r e d orthorhombic and body c e n t r e d o r t h o r h o m b i c m a r t e n s i t e s t r u c t u r e s . In t h i s a n a l y s i s t h e i n p u t d a t a c o n s i s t s o f t h e l a t t i c e parameters o f the p a r e n t and p r o d u c t phases, t h e l a t t i c e correspondence  and t h e p l a n e  and d i r e c t i o n o f t h e l a t t i c e i n v a r i a n t s h e a r .  The l a t t i c e  used i n the a n a l y s i s a r e shown i n Table X I I I .  The parameter  Table X I I I  L a t t i c e parameters  parameters  o f g^ ^ o r t h o r h o m b i c s t r u c t u r e s o f a n  Ag-45 at. % Cd a l l o y Structure i  ^  L a t t i c e Parameter  ^,  D.C.C.  a  at 25°C = 3.3206 o  a  A°  a t -74°C = 3.31432 o  at -196°C  orthorhombic  of the g  at -74°C  a  = 3.0904  a  = 3.0968  b  = 4.8550  b  = 4.86505  c  = 4.7438  c  = 4.75362  138.  phase at -74°C (M ) was found from the diffractometer trace at 25°C, applying a thermal contraction correction of 18 x 10 *V°C. The lattice parameter of the thermal martensite was measured at -196°C and also corrected to the M  g  temperature in the same way.  It was found, however, that using these values, there was a calculated volume change of 1.64% associated with the transformation. Dilatometer experiments gave a maximum volume change of only 0.2%. It was therefore decided to carry out two sets of calculations, one using the actual lattice parameters at -60°C and one in which a value of 6 = 1.005 was applied so as to give no volume change in the transformation.  In fact, there was only a very  slight difference in the results of the analysis fpr the two cases with the calculated habit plane being within 3° in the two calculations (see figure (61)).  Only the results for the  second calculation w i l l be given in detail.  The lattice correspondence  as given in figure (63) was assumed in the calculations. In this the two lattices are connected by a rotation of 45° about the [001] axis of the parent structure. Several choices for the lattice invariant shears were considered and the habit plane normal was calculated in each case. A {110}<110>  shear was considered because of the ease with which  a stacking fault shear can take place in b.c.c. materials. A {112}<111> shear was chosen because i t is the observed slip system in the b.c.c. phase. The choice of {011}<311> was made because i t has been suggested that this might be the lattice invariant shear in thermo-elastic martensite in Cu-Zn alloys  41  . The  139.  b  ure 63.  Lattice correspondence between the body centred cubic and the orthorhombic lattices.  calculations are given in Appendix A. Figure (61) gives a comparison between the habit plane normals found experimentally and those computed by theory.  The  habit plane pole resulting from a (Oil)[Oil] lattice invariant shear agreed with the plane normals obtained for thermal martensite whilst a (110)[110] shear system resulted in a habit plane that agreed well with the plane normals obtained in the case of stress-induced martensite.  Habit planes computed using the  (112)[111] and CLIO)[113] shear system did not yield habit planes that agreed with experimental results; and hence were discarded.  140.  Table XIV  Crystallographic  data calculated from the theory  (Appendix A).  Thermal Martensite Lattice invariant shear Amount of microscopic shear g  Habit plane pole  Macroscopic shear direction  Magnitude of macroscopic shear  (Oil)[Oil]  Stress-induced Martensite (110)[110]  0.053894  ,0585875  0.6768947 -0.2181258 0.7030184  ,713566 .148195 ,684734  +0.044247 -0.959821 -0.277102  ,670421 ,139228 ,728803  2.26°  7.11°  141. It is necessary to investigate the reason for the difference in the habit planes of thermal and stress-induced martensite.  From the  table i t is seen that the amount of macroscopic shear needed in the two cases is widely different, 2.26 deg. for thermal martensite and 7.11 deg. for stress-induced martensite.  Therefore, i t i s concluded  that in the absence of external stress, a lower value of overall shear governs the choice of particular lattice invariant shear selected and hence the habit plane. Figure (64) shows the Laue back reflection photographs of the; 3 matrix and stress-induced martensite.  2  The two photographs are very  similar, with the positions of the close-packed planes in the two photographs being very close, suggesting that the close-packed planes in the two structures are almost parallel.  In fact,as shown in Table XV, the  theory predicts a maximum deviation of 4 deg. for the close-packed planes i n the -matrix and martensite. Table XV  Orientation relationships between the principal planes and directions in the 3 and stress-induced martensite. hkl, b  hkl o  deg.  [110]  B  A  [010]  Q  3.4  [110J  B  A  U00J  O  2.6  [001], A  [001]  (ioo) A  (no)  (010), A  (110)  b b  b  o  3.6  4  0  o  2.6  143. In the case of deformation martensite, the product structure is face centred tetragonal and this made the calculations simpler.  The  lattice parameters used were (1)  Ag-45 at.% Cd: b.c.c.  f.c.t.  a  a = 4.3792 A°  = 3.3206 A°  o  (martensite)  c = 3.8580 A° (2)  Ag-41  at. % Zn:  b.c.c. a  f.c.t.  = 3.1749 A  o  (martensite)  a = 4.0413 A°  0  c = 3.860 A° A l l parameters were determined at 25°C.  The formulae given by Otte  .74 and Massalski  were used in the calculations. A (110) [HO]  implied in the formulae.  shear is  The calculated habit plane normals are  included in figures (62a,b).  It can be seen that the agreement is very  good for the Ag-Cd case but only moderate for Ag-Zn. 3.9.3  Discussion The formation of stress-induced martensite is accompanied by a  positive change in length of the specimen in the direction of the stress. This condition further restricts the possible habit plane variants that are permissible for a given tensile axis.  Hence the general condi-  tion for the choice of the habit plane can be stated as follows: (a)  that the resolved shear stress on the potential habit plane,  in the direction of macroscopic shear be near maximum, i.e. cos<J> cosX  144. be  a maximum, w h e r e  habit the  macroscopic that  QLattice  such a v a r i a n t w i l l  i n v a r i a n t ) shear  a x i s and  a positive strain  system  cannot  shear  be used  the d i f f e r e n t orientations of the tensile and w i l l  supported  possessing  give  with  i n the d i r e c t i o n  65.  f o r the increase  axis  shear  case,  considered  stress  f o r the resolved  plane  shear  because are  component.  This  of s t r e s s -  I n a l l cases, t h a t  i s associated  t h e WLR  theory.  habit  stress  i n length  during  plane  i s the  construction  i n the  a macroscopic shear, t h a t  the formation effect.  of  Figure  (65)  Y  B 6  Geometrical  with  I t i s this  thus g i v i n g p s e u d o - e l a s t i c  A  involved  on t h e s e c o n d a r y  i n this  on t h e h a b i t  XVI.  transformation  i n tension,  X  stress  martensite.  i s c a l c u l a t e d from  responsible  data  i n Table  a n e a r maximum v a l u e  shear which  Figure  given  martensitic  martensite  t h e same r e s o l v e d  by t h e e x p e r i m e n t a l  associated The  is  yield  f o r a maximum r e s o l v e d  induced martensite  one  the t e n s i l e  and t h e  shear d i r e c t i o n .  condition  equivalent is  axis  stress. The  all  the tensile  p l a n e n o r m a l and X i s t h e a n g l e between  (b) of  < ) > i s t h e a n g l e between  to c a l c u l a t e the t e n s i l e  transformation.  strain  145.  Table XVI  Comparison between the observed and calculated values of < f > (angle between habit plane normal and the tensile axis) <> j Observed  Tensile axis ^<119>  ^<265>  Possible tensile axis  <> j Calc.  cos<j> cosA  42°  119  39.5°  .487  40°  119  52.1°  .488  119  42.4°  .478  119  54.4°  .470  265  69°  .184  265  60.5°  .090  265  44.6°  .129  265  82.1°  115  34.4°  .450  115  56.6°  .442  115  39.8°  .460  115  60.5°  .355  5,10,16  33°  .290  5,10,16  64°  .317  5,10,16  46°  .334  5,10,16  73°  .249  5,7,13  31.3°  .353  5,7,13  42.1°  .384  5,7,13  61.8°  .364  5,7,13  69.0°  .314  69°  •^<115>  55°  ^<5,10,16>  65°  ^<5,7,13>  62°  gives the geometrical construction involved. specimen is x  Y  VU  The i n i t i a l position of the  and after the region ABCD has transformed to  martensite, the specimen takes the form  XZWU.  146.  In the diagram y  =  Macroscopic shear angle obtained by WLR analysis.  ct  =  Angle between habit plane normal and the tensile axis.  BE  =  Macroscopic shear direction.  This is approximated to a  simple shear because of near zero volume change in the transformation. OB  =  Habit plane normal.  BG  =  Elongation in the direction of applied stress.  =  BE cos(90-<|>)  =  BE sin<j>  BE  =  OB tany  OB  =  AB cosct  BG  =  (OB tany) sintb  =  AB coscj> tany sin<j>  -  2 sxnzvb tany.  •^g  i.e.,strain =  sin2tj> tany  In this analysis, i t i s assumed that the tensile axis, habit plane normal and the macroscopic shear direction are coplanar. For the general case the component of shear direction in the plane defined by the tensile axis and the habit plane normal should be used.  Then  147.  BE defines this component and i s given by  BE  = BE' cosa  where BE' is the macroscopic shear in the plane of shear (plane containing the habit plane normal and macroscopic shear direction) and a  is the angle between the plane of shear and the plane of tension  (plane containing the habit plane normal and the tensile axis). Figure (66) indicates the various planes and angles involved in the construction.  The general relation for the strain involved in the  transformation is given as  strain  = — sin2<() tany cosa  Therefore the particular choice of habit plane and macroscopic shear direction determines the strain possible for a given orientation of the tensile axis.  However, to make calculations easier, for a given  habit plane and direction, various possible orientations of the tensile axis that would result in an elongation were considered. This restriction placed the positions of the tensile axis within the two great circles N and P in figure (66). For each orientation of the tensile axis <hkl>, various combinations were considered [hkl], [hkl], [hkl] and in each case the value of cos<J> cosA was calculated to determine which variant of the tensile axis would result in maximum shear stress on the habit plane in the macroscopic shear direction.  The strain was  This plane of shear should be distinguished from the shear plane,which in this case is the habit plane.  148.  n  :  p s  gS =  Figure 66.  Habit Plane Normal. Tensile  ;  Axis.  Normal to Plane of  t  Normal to Plane  S  Macroscopic Shear  A np  X = A Sp  Shear.  of Tension. Direction. a  = A ts  Stereographic projection showing the various angular relations involved in the calculation.  149. then calculated for this particular tensile axis.  Appendix B shows  the detailed calculations and the results are summarised in figure (67). The strain associated with the formation of stress-induced martensite is very much dependent on the orientation of the tensile axis, maximum elongation i s possible near the 1001] corner and the minimum value i s near the 1111] corner.  The magnitudes of the strain calculated are in  fair agreement with those found experimentally.  However, an accurate  determination of the pseudo-elastic strain was not possible. A similar calculation was carried out in the case of thermal •martensite to determine the possible elongations. the corresponding strain values.  Figure (68) shows  It is seen that very l i t t l e elongation  is possible during the formation of thermal martensite.  Therefore the  change in the habit plane in the case of stress-induced martensite is due to the fact that such a change provides an increase i n the strain associated with the transformation.  This also explains why there should  be a change in the microstructure as the specimen i s stressed below (refer f i g . (60)).  The martensite that forms at zero stress is  thermal martensite, but on stressing it, a mere change to an oriented form of thermal martensite w i l l not provide significant elongation (figure (68)), whereas a change to stress-induced martensite w i l l provide strain of up to ^6%.  Thus the martensite changes from thermal  martensite to stress-induced martensite, with the accompanying elongation. Figure (67) shows that pseudo-elasticity decreases progressively as the tensile axis deviates from the 1001] corner of the stereographic triangle, with the 1111] orientation being least favourable. Specimens strained beyond the limits given in figure (67) w i l l have  Figure 67.  Stereographic projection showing contours of calculated amount of strain obtained during S.I.M. transformation for various orientations of the tensile axis.  Figure 68.  Strains that can be obtained during the formation of oriented thermal martensite for various orientations of tensile axis.  151. either deformation martensite or deformed stress-induced martensite neither of which w i l l be reversible.  The theory i s i n excellent  qualitative agreement with the observations i n figure (52), which shows that pseudo-elasticity is a maximum for orientations close to [001], i s less near 1011] and is very restricted indeed near [111]. It was found that deformation martensite formed preferentially when the tensile axis was close to [111]. rolled and tensile specimens.  This i s true in both cold  It i s precisely this orientation that has  the least pseudo-elasticity so that at small strains complete transformation to stress-induced martensite w i l l occur.  If i t is considered  that the stress-induced martensite i s a necessary structure before the formation of deformation martensite, (see next section) i t can be seen that at a given strain, orientations close to [111] w i l l have deformation martensite and other orientations w i l l only have stressinduced martensite present. Only one section of the results cannot be completely explained with the present theory.  This i s the increase in pseudo-elastic  elongation obtained at higher temperatures.  Between  and M + 30°C,  martensite forms in bursts. At higher temperatures the formation i s more gradual and gives pseudo-elastic strains ^50-100% higher than the burst martensite.  There i s , however, no change i n the habit plane  of the martensite, just a change in i t s morphology.  No clear explana41  tions for this effect can be given.  Ahlers and Pops  suggest that  thermoelastic martensite differs from burst martensite i n the choice of lattice invariant shear viz. {110}<ll3> shear for thermoelastic , and {110}<ll0> for burst martensite.  Calculations based on a {110}<ll3>  152. shear failed to yield a habit plane pole which was in agreement with the experimental results. Probably the only technique that might be successful in giving an explanation for the effect would be electron microscopy and the observation of martensite under stress at carefully controlled temperatures in the electron microscope would not be easy.  3.9.4  Course of the Transformation  ;  Masson proposed•that the orthorhombic lattice was only a transition structure between the parent b.c.c. lattice and the final close-packed structure.  The idea i s developed further in the following discussion.  Figure (69) shows a close-packed layer of the b.c.c. lattice. After the Bain strain some of the atoms are not in their final positions in the product lattice; and atomic shuffles are needed to complete the a,tom movements. The picture i s very similar to the one proposed by Lieberman^ for Au-Cd alloys. The (Oil),  plane i s distorted according to the Bain distort  D • C • C •  tion and a further shuffling of atoms in the intervening planes i s necessary to complete the structure.  On further deformation, a close-packed  structure can be generated in two ways depending on the cadmium concentration. (a)  High Cd alloys:  The (Oil) plane of the original cube lattice i s deformed further so that i t forms a close-packed plane of atoms.  The atoms in the  intervening planes move further along the same direction as before so that they s i t in the valleys above the close-packed plane; thus constituting an ABAB type of packing.  The structure s t i l l has to be referred  154.  to as an orthorhombic lattice because of the existing order though the 'Unterstruktur' i s close-packed hexagonal.  Therefore i f subsequently  a disordering transformation takes place, for example, by plastic deformation then the resulting structure i s truly hexagonal.  Figure  (70) shows the atom movements involved, (b)  At low Cd contents:  The i n i t i a l stage forming thermal martensite i s the same as above. On further deformation, the shuffling i s considered to take place in opposite directions in the intervening layers immediately above and below.  This generates a structure of the AuCu ( L l ) type. o  This i s a  structure based on a face centred cubic lattice in which alternate layers contain atoms of one element.  C002)  gonality in the structure.  This results in some tetra-  There i s no direct correlation between  the relative atom sizes and the axial ratio of the ordered tetragonal structure.  In the present case the f.c.t. martensite in Ag-Cd has  c/a = 0.88 ( r / r , = .97) and in Ag-Zn c/a = 0.955 (r /r^ = 1.085) Ag Cd Ag Zn A  A  26 and these values are quite reasonable for AuCu type structures If the order of the structure is destroyed, then i t w i l l become true face centred cubic. This change i s considered to be brought about by severe deformation.  The change in the direction of shuffle can  be considered as a manifestation of a low stacking fault energy in the lattice.  ,  This martensite is non-reversible, because of the severe plastic deformation associated with i t s formation.  The high dislocation density  in the martensite as observed by electron microscopy confirms this yiew.  The habit plane w i l l however s t i l l tend to be one of minimum  distortion as the martensite forms, so the Wechsler,biebermann and  Figure 70.  Schematic diagram indicating the course of transformation.  156.  *  "  1  1  70  F i g u r e 71.  60  1  2 0  X-ray d i f f r a c t o m e t e r at l i q . N f.c.c.  2  50 deg.  t r a c e of f i l e d  temperature.  structure.  i  i  i  i  40  specimen  u 30  (Ag-45 at. %  P l a n e s are indexed based on  Cd)  157.  Read theory should s t i l l be applicable as found experimentally. According to the above discussion, the orthorhombic lattice i s only a transitional one and the final structure i s close-packed, being face centred cubic at lower Cd contents and close-packed hexagonal at higher Cd concentrations.  The thermal energy provided during the  transformation i s insufficient for the complete transformation and external energy i n the form of deformation i s necessary.  That the  fa,ce centred cubic structure i s the most stable one i s demonstrated in figure (71).  The figure shows the diffractometer trace of a filed  specimen at liquid nitrogen temperature.  Only face centred cubic  peaks are present, the same as those seen at room temperature, indicating that no further transformation has taken place. tion i s not expected to lower M  g  Mechanical deforma-  to such an extent as to prevent the  thermal martensite formation. The absence of thermal martensite makes the two stage transformation mechanism inapplicable i n the case of Ag-Zn alloys.  The  reasons for the absence of a martensitic transformation in this system, which i s analogous to Cu-Zn, Ag-Cd and Au-Cd systems, are not quite clear.  However, i t i s assumed that the change to the face centred  tetragonal structure takes place in one step directly without the intermediate orthorhombic structure. Further deformation causes: the atoms to become disordered thus giving the face centred cubic structure.  158. CONCLUSIONS (1)  Alloys of silver-cadmium in the composition range 44.2 at. %-  47 at. % Cd transform to thermal martensite on cooling to low temperatures.  The M  g  varies approximately 35°C/at. % Cd.  There i s no  martensitic transformation in an Ag-41 at.% Zn alloy, even at liquid helium temperature.  C2)  X-Ray diffraction experiments indicate the thermal martensite  in Ag-45 at. % Cd alloy to have an orthorhombic unit c e l l .  Selected  area diffraction experiments performed in the electron microscope agree very well with this finding.  (3)  The thin edges of some specimens used for electron microscopy are  found to transform to a spontaneous martensite with an f.c.c. structure. This is believed to be due to the relaxation of volume constraints accompanying the thinning process.  (4)  An Ag-45 at. % Cd alloy is found to deform on a {112} plane with  a <111>  slip direction.  {110}<lll> slip i s found to be operative  in an Ag-41 at. % Zn alloy.  C5)  Ag-45 at. % Cd alloy exhibits a very high degree of elastic aniso-  tropy.  The values of Young's modulus along the three directions [100],  1110] and 1111] are in the ratio of 1:4:9. A rough calculation shows the value of the elastic anisotropy factor 2CS.,, - S „)/S.. to be 17.  159. (6)  Deformation martensite can be produced in Ag-45 at % Cd and  Ag-41 at.% Zn alloys by cold rolling. detected after about 15% strain.  The product structure can be  The deformation martensite has a  face-centred tetragonal structure with an axial ratio of 0.88 for the silyer-cadmium alloy and 0.95 for the silver-zinc alloy.  X-ray  diffraction results indicate that this structure changes to a closepacked one on severe deformation.  In silver-cadmium alloys i t is  found that this structure is f.c.c. up to 45.5 at.% Cd, h.c.p. above 47.7 at.% Cd and a mixture of f.c.c. and h.c.p. at 46.0 at.% Cd.  (7)  Stress-induced martensite i s found to occur in Ag-45 at. % Cd alloys  at temperatures above M . The stress needed to form martensite varies s almost linearly with temperature for temperatures up to 30°C above M . g  (8)  Reversible strains of ^12% can be obtained by deforming single  crystal specimens at temperatures above A^.  (9) A strain memory effect is found on deformation at temperatures close to M . Above M , i t i s due to SIM formation; below M to a s s s change in the morphology of the existing martensite. This difference in structure below M  g  is due to a change from thermal to stress-  induced martensite.  (101 The experimentally determined habit plane normals for thermal, stress^-induced and deformation martensite are found to be close to [133]  , [144]  and [177]  respectively.  These habit planes are  160. found to be in agreement with the theoretical predictions assuming a {110}<110> microscopic shear.  (11) It i s found that the only difference between thermal and stressinduced martensite lies in the variant of the microscopic shear chosen viz. C011)[Oil] for thermal martensite and (110)[llo] for stress-induced martensite.  (12) The elongations that result from the transformation can be calculated from a knowledge of the relative dispostions of habit plane normal, macroscopic shear direction and tensile axis. This gives the condition that the habit plane associated with SIM is determined by the maximum stress condition.  (13) The orthorhombic martensite i s considered to be an intermediate structure between b.c.c. and f.c.c. or h.c.p.  The face centred  tetragonal structure can be considered to arise from an ordered f.c.c. structure possessing AuCu (Ll ) type order.  1  161.  APPENDIX A MATRIX ALGEBRA OF MARTENSITIC TRANSFORMATIONS  The  t o t a l t r a n s f o r m a t i o n d i s t o r t i o n i s g i v e n by  ?  1  = RBP  (1)  where  The  P  = Lattice invariant  B  = Bain  R  = Rotation  distortion  two m a t r i c e s B and P can be expressed  systems o f axes g i v e n below. as  shear  ( d i a g o n a l r i ^ , r ^ ' I3) > i -  n  i n simple  terms i n d i f f e r e n t  The B a i n d i s t o r t i o n B can be expressed t  n  system o f axes,  e  [ T ] , along which the  B a i n d i s t o r t i o n takes p l a c e n-L 0 BIT]  i.e.  The of  -  0  n  0  0  0 0  2  n  (2)  3  r e l a t i o n between the o r i g i n a l c u b i c axes [B] and the [T] system axes can be o b t a i n e d from the assumed l a t t i c e In t r a n s f o r m a t i o n s i n v o l v i n g  or f . c . c .  a t r a n s i t i o n from b . c . c .  to b.c.o., t h i s correspondence  r [T/B] 1  as seen i n f i g u r e  =  (63).  correspondence.  1//2  -1//2  0  1//2  1//2  0  0  0  1  to f . c . o .  can be expressed as  The v a l u e s o f n^, n2» I3  (3)  c  a  n  be c a l c u l a t e d  from  162. the lattice parameters of the two structures involved, v i z . b/»/2a , n o  c/Jla  = 2  ,  =  / *  =  a  a  0  The shear is best represented in a coordinate system, [g], given by the shear direction IJ [U^, U , U^], the normal to the shear plane 2  V  [V , V , V ] and the vector defined by U x V = W [W , Wj, Wj]. 1  2  If  3  g i s the amount of shear, then the matrix representing the shear is given by 1 P[g]  0  g  0  =  1 0  0  0  (4)  1  The original cubic system, [B], and the shear axes system are related by the following equation  r (g/s)  1  2  1  2  n  2  =  2  w  1  U V  (5)  W  The three vectors IJ, V and W can be expressed in terms of the [T] system of axes, and in this system they take the form  U  = [u  V  =  W =  1 5  u ,u ] 2  3  [v , v , v ] 1  2  [v  3  w,  v  wJ  2  3  The [T] and [g] systems are in turn related by the expression u  r [g/T] 3  =  i  \  U  2  5  3  ^2  ^3  w  w  2  3  (6)  163.  The Bain distortion and the lattice invariant distortion P together generate an undistorted habit plane.  of the matrix F = BP are such that X^ = 1,  the three eigenvectors X  2  > 1 and X^ < 1, where X^, X  matrix F.  This i s possible i f and only i f  a n a 2  ^3  a r e  t n e  eigenvalues of the  In general i t i s convenient to form the symmetric matrix  J = F'F (where F' i s the transpose of F), and the eigenvalues of the  2  matrix J correspond to X^ , X  2  2 and X^ 2• The eigenvectors R1 , R2, R 3  corresponding to the three eigenvalues form an orthogonal system of coordinates [d]. The condition that one of the eigenvalues of the matrix J i s equal to one results in a quadratic equation in g:  Ag where  +  2  Bg  +  2  C =  =  Er^ (n  B  =  -21 u l v ( n  c  =  (l -  v  2  2 n i  \ )  -  3  1  (7)  -2  2-2  A  0  + n22  2 1  n32)  ) ( l - n ) ( l - n32) 2  2  The solution to equation (7) gives the values g^ and g » 2  2 eigenvalues X  X^  +  4  where  2 , X^  2  can be determined from the quadratic equation:  (1 -  ty^X*  2 2-2  if^ =  Er^ (g \]  2 2 2  *3  =  The remaining  n  ln 2  n  3  ±  + *  3  =  a = 2, 3 - -  0,  + 2gu 1 v 1 + D  (8)  164.  The undistorted vectors R  x  y  £  £  -1  =  [g]  [g] =  £  1  are given by the following expressions:  22  [z(n  2  [z(n  2  ~l  [ Z ( n  .N  n  3  22  2  n  3  2 n  3  +  A^  +  A^  2  +  n  22-n-L  )uw 1  1  22--  )v w  ^  1  i > i 2  w  2  1  -  gE  +  gx 2  -  n  £  32--  n  2  vwl 1  3  1  2--  u^l  ET^  + 1],  (9)  £ = 1 z [g]  = 1 -I  r v / t E ( n  2 2 . . 2 2,- 2 2 3 £ i 1 " \ n  +  A  n  )W  N where  .2 ~ \  n  2 2 2 3 > n  2,  ]  £=2,3  is the normalisation factor.  In the system [d], the matrix J takes the form 2 J[d]  =  0 0  0 A  0 2  2  (10)  0  0  The habit plane normal can be derived from the condition that vectors in the habit plane do not change in length during the transformation. This condition is expressed as follows: x'F'Fx i.e.  x'Jx  =  =  X'X  in the d system.  x'x 0  0 0  0 0  A-  x  =  165. Expanding we get  (X  2 1  - l)  + (A  2 X l  2 2  - l)x  2 2  + (A  2 3  - l)x  2 3  = 0  (11)  where the vector x is expressed in the [d] system. Since A^ = 1, equation (11) becomes (1 (A setting x x  A/) - 1)  2  = 1,  3  z  =  5 K K.  where K =  x / ) /  (i -  1  -  (*o  !)  2  1/2  The undistorted vectors from equation (11) are [0, 6„.K,1]. Further, equation (11) is satisfied for any value of x^ since A-^ = 1.  Therefore [1,0,0] is an undistorted vector also.  The habit  plane is then defined by the two vectors [1,0,0] and [o,6„K,l],  and  the cross product of the two vectors defines the habit plane normal.  n[dj  =  [1,0,0] x [0,6 K,1] K  [0,1,5 K] R  or the unit normal is given as 0 n[d]  = (1 K ) 2  1  (12)  1 / 2  +  6  K  K  This vector can be expressed in terms of the original cube axes as follows:  166.  n[B]  ;=  r '[B/g] 2  r ' [ g / d ] n[d]  (13)  4  The c a l c u l a t i o n s a r e much s i m p l i f i e d when W  r  = 1 (W  g  =  0» W  =  t  0) >  a n  d  s i m p l i f i e d e x p r e s s i o n s a r e a v a i l a b l e to c a l c u l a t e n[B] d i r e c t l y . When W  4 1  5  Calculation  the c a l c u l a t i o n s  are v e r y i n v o l v e d  and cumbersome.  of R o t a t i o n M a t r i x :  C o n s i d e r any two v e c t o r s p and a l y i n g i n the h a b i t  plane  take the v e c t o r product o f n[B] and [ 1 , 0 , 0 ] and [ 0 , 1 , 0 ] ) .  A f t e r the  a p p l i c a t i o n of B and P, l e t them become p' and a' r e s p e c t i v e l y and  a' have t h e i r magnitudes unchanged by v i r t u e of the f a c t  p and a l i e i n the h a b i t  plane).  (p' that  The r o t a t i o n a x i s and the amount of  r o t a t i o n n e c e s s a r y t o l e a v e the h a b i t Euler's  (e.g..,  p l a n e u n r o t a t e d are g i v e n by  theorem:  [Pi - , pJ  La  X  - aJ  Where _u i s the a x i s  \°\  • Lp  - °j +  pJ  -  u tanCf) —  ^  of r o t a t i o n , and the magnitude i s the tangent of  the h a l f angle o f r o t a t i o n . Knowing u j u ^ ^ . u ^ ] and 0 , the r o t a t i o n m a t r i x , R, can be calculated  : (14)  u s i n g the e x p r e s s i o n  12  167.  [u^  (1-cose) + c o s 6 ] , [ u u ( l - c o s 6 ) - u s i n 6 ] , 1  2  [u^u^Cl-cose) + ursine]  [ u u ( l - c o s 8 ) + l y s i n e ] , [ u (l-cos0)+ cos6], 2  R[B]  1  2  =  [ u u ( l - c o s 0 ) - ursine] 2  3  (15)  [ u u ( l - c o s 9 ) - u s i n 8 ] , [ u u ( l - c o s 6 ) + u^sin©], 3  1  2  3  2  [u  3  (1-cosO) + cos9]  C a l c u l a t i o n of M a c r o s c o p i c Shear: The  u n i t v e c t o r n.[B] normal t o t h e h a b i t p l a n e t r a n s f o r m s t o  n_^[B] where  n^B]  The  =  [RBP] n [ B ]  (16)  d i r e c t i o n o f d i s p l a c e m e n t i s g i v e n by t h e v e c t o r n [B] - n [ B ] =  S  N n  r rl 1 0  Habit Plane  168. The magnitude of the macroscopic shear angle i s given by the relation  (17)  tany  In the case of deformation martensite with a face centred tetragonal structure the habit plane normals can be calculated by using the 74 :  simplified formulae  }  2 . 2 . 2 2 . / . 2 2 + n 2n n / ~ i •~-2 _  n  2  2n  •2  n.  2n,  .  n  2  2  ~  n  2  1 - n.  l - n.  n  n.  1  . 2 2 i2 n  n  l - n.  1 - n  J  1 " r)'  where n [n^n^n^] represents the habit plane pole.  n^ = a/a^-Jl  ,  n„ = c/a where a i s the lattice parameter of b.c.c. structure, and 2 o o c and a that of the f.c.t. structure.  The results are given in Table A-2.  Table A-1  Crystallographic data calculated from theory for different secondary shear systems for orthorhombic martensite  Secondary Shear System  Magnitude of Sec. Shear  (110)[110]  .0585875  (011)[011]  .053894  1.0735  0.9315  .6768947 .2181258 .7030184  (011)[311]*  .05002  1.1172  0.8951  .428544 .513585 .743357  (112)[111]  .04527  Habit Plane Normal  .657825 .164888 .734900  ,615107 ,406035 ,675854  Macroscopic Shear Direction  .083680 .017378 -.090967 .0442469 -.9598211 -.2771021  .379991 .598390 -.705363  Amount of Rotation  7.11  c  2.26  c  4.;  Other shear systems of the form {011}<311> and {112}<111> did not give undistorted habit planes.  Table A-2  Habit plane normal for deformation martensite for Ag-Cd and Ag-Zn alloys. Material  Habit Plane Normal  Ag-45 at.% Cd alloy  -0.1000 0.7493 0.6546  Ag-41 at.% Zn alloy  -0.1690 0.6936 0.7002  171. APPENDIX B CALCULATION OF STRAIN ASSOCIATED WITH THE TRANSFORMATION It was shown earlier that the linear strain associated with the transformation could be expressed as  strain  = — sin 2ty tany cosa.  The value oftywas determined for several orientations of the tensile axis and y was obtained from the theoretical analysis (Table A-l). Determination of a was a l i t t l e involved and was calculated in the following way. The normal to the plane of tension and the plane of shear were found by taking vector products  s_  t_ = and  = _S x n  H *£  cosa = s • t  Tables B-1,2 give the calculated values of strain for various orientations of the tensile axis, in the case of both stress-induced and thermal martensites.  0  172. Table B-l  Calculated values of strain for stress-induced martensi Value of y =  7.114703° cos<j>  cosA  cosa  Strain  [p]  COS(j>  001  .685  .499  1.0  6.23  Oil  .589  .246  0.516  3.06  Oil  .379  .233  -  111  . 722  .082  .165  111  .069  .050  -  012  .679 '  .400 '  .803  102  .932  .328  -  012  .546  .390  .853  112  .911  .241  -  112  .790  . 299  .617  112  .328  .266  -  -  122  .317  .195  -  -  122  .793  .134  -  -  122  .596  .212  .442  212  .883  .075  -  -  103  .875  .419  -  -  013  .696  .451  .902  5.63  013  .603  .443  . .922  5.53  103  .424  .383  113  .879  .365  113  .449  .368  113  .790 '  .394  .814  4.92  213  .970  .183  .777  2.29  133  .737  .186  313  .928  .067  133  .410  .229  .613  2.86  133  .533  .236  .524  2.95  115  .768  .460  .935  5.74  115  .825  .450  .964  5.61  115  .550  .442  .963  5.52  151  .137  .019  _  -  1.02 4.99 4.86 3.73  2.64  -  _  173. Table B-l (Continued Strain  [p]  costy  135  .774  .334  .686  4.17  135  .624  .358  .779  4.38  315  .916  .274  -  -  135  .533  . 351  -.  -  355  .263  .170  -  -  355  .821  .100  -  -  355  .628  .190  .390  2.38  117  .750 .  .480  .968  5.99  117  .792  .476  .984  5.94  335  .781  .244  .500  3.04  335  .916  .170  015  .701  .482  .963  6.01  015  .642  .476  .968  5.95  023  .652  .345  .698  4.31  023  .488  .334  .783  4.16  203  .174  .170  -  -  023  .488  .334  -  -  126  .799  .427  .890  5.33  126  .707  .440  .879  5.48  126  .576  .429  .911  5.35  124  .818  .351  .746  4.38  124  .689  .379  .760  4.37  124  .507  .366  334  .761  .172  334  .179  .138  119  .771  .487  .991  6.07  119  .738  .488  .981  6.1  119  .614  .478  146  .548  .338  .7366  4.21  146  .581  .340  .7188  4.24  146  .744  .321  145  .510  .296  .674  3.69  145  .547  .298  .651  3.72  cost})  ,  c o s A  c o s a  -  .349 -  -  -  -  2.15 -  -  -  174. Table B-l (Continued) cos<J> cosX  cosa  Strain  .358  .184  .551  2.30  265  .491  .090  -  147  .575  .369  .785  4.61  147  .605  .371  .771  4.64  147  .751  .358  -  034  .637  .318  .648  3.97  034  .459  .306  .750  3.82  304  .120.  .118  -  155  .483  .245  .579  3.06  155  .476  .245  .584  3.05  155  .683  .218  -  177  .514  .248  .562  3.09  177  .449  .244  .608  3.05  177  .658  .229  -  144  .456  .240  .568  2.88  144  .498  .243  .563  3.03  159  .598  .378  .788  4.72  159  .593  .377  .791  4.71  159  .736  .369  139  .618  .441  -  139  .674  .446  .895  137  .589  .411  -  137  .659  .416  .830  137  .775  .405  1,2,10  .628  .471  -  1,2,10  .709  .477  .954  5.96  1,2,10  .767  .474  .964  5.92  1,4,12  .638  .445  .907  5.89  1,4,12  .657  .447  1,4,12  .751  .445  -  1,4,10  .622  .426  .874  1,4,10  .644  .427  1,4,10  .754  .422  [p]  COS<f>  265  -  -  5.56  5.13  -  5.3.1  175. Table B-l (Continued) cos<)> cosA  cosa  Strain  .652  .476  .963  5.94  1,3,15  .688  .479  1,3,15  .746  .479  1,5,15  .650  .447  1,5,15  .647  .447  1,5,15  .740  .447  .898  5.58  1,5,13  .639  .432  .88  5.40  1,5,13  .635.  .432  1,6,16  .650  .437  1,6,16  .630  .435  1,6,16  .734  .435  .873  5.43  0,1,7  .699  .491  .9811  6.12  0,1,7  .657  .487  1,6,9  .715  .333  1,6,9  .551  .341  .742  4.26  1,6,9  .583  .343  1,6,11  .727  .377  .754  4.7  1,6,11  .613  .383  .791  4. 78  [p]  COS(j)  1,3,15  176. Table B-2  Calculated values of strain for thermal martensite. Value of y  = 2.26039°  [p]  COS(j>  cos<}> cosX  001  .705  .195  Oil  .345  Oil  cosa  Strain %  .434  0.8  .302  .948  1.21  .652  .315  .599  1.17  110  .631  .448  .882  1.70  110  .323  .209  -  -  111  .671  .465  .970  1.90  III  .143  .053  -  -  112  .762  .458  .979  1.91  211  .750  .352  -  -  II2  .389  .057  -  -  121  .386  .339  -  -  .369  .204  -  -  .776  .409  .888  1.72  131  .219  .206  -  -  313  .900  .342  .964  1.49  122  .550  .446  .999  1.81  132  .383  .347  -  -  231  .375  .309  -  -  213  .868  .395  .992  1.69  123  .269  .201  -  -  013  .600  .340  .741  1.40  012  .534  . 361  .828  1.47  103  .456  .126  -  -  102  .329  .088  -  -  114  .454  .226  -  -  Il5  .507  .233  -  -'  015  .649  .298  105  .559  .157  -  -  017  .794  .325  .589  1.16  107  .603  .169  -  -  115  .765  .339  .741  1.44  114  .771  .368  .804  1.56  117  .753  .301  .660  1.29  113 113  ;  \  .6413  1.25  177. REFERENCES  '  '  1.  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