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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, Mysore Un i v e r s i t y , 1964 B.E. (Met.), Indian I n s t i t u t e of Science, 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 thesis, as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA Jul y , 1971 In present ing t h i s thes is in p a r t i a l f u l f i l m e n t o f the requirements for an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L ib ra ry s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I fu r ther agree that permission for extensive copying o f t h i s thes is for s c h o l a r l y purposes may be granted by the Head of my Department or by h is representa t ives . It i s understood that copying or p u b l i c a t i o n o f th is thes is f o r f i n a n c i a l gain sha l l not be allowed without my wr i t ten permiss ion . f Department of The Un ivers i ty of B r i t i s h Columbia Vancouver 8, Canada i i ABSTRACT A study has been made of the martensitic transformations occurring in g-phase silver-cadmium and silver-zinc alloys. In silver-cadmium alloys the Mg 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 in Ag-45 at. % Cd alloy was found to have an orthorhombic structure of the 2H type. This was confirmed by X-ray diffraction and electron microscopy. 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 filing. 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. i i i 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, stress-induced and deformation martensites were found to agree well with the values obtained using phenomenological theory assuming a {110}<110> microscopic shear. The 'elastic' elongations accompanying the trans-formation could be accounted for using the theory. A mechanism suggesting the course of the transformation was developed. iv TABLE OF CONTENTS Page 1. 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 Martensite 10 1.7 Electron Microscopic Observations 14 1.8 Aim of the Present Work 14 2. 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 3.2.1 Ag-Cd Alloys ; 29 3.2.2 Ag-Zn Alloys ^ 33 3.3 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 3.4 Slip Systems in Ag-Cd and Ag-Zn Alloys 58 3.4.1 Experimental Results 58 3.4.2' Discussion of Slip Systems in CsCl Type Alloys 65 3.4.3 Discontinuous Slip in Ag-Cd Alloys 65 3.5 Modulus Determination in Ag-Cd Alloys 69 3.6 Deformation Martensite Formed by Filing ^ Ag—Cd Specimens 72 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 3.7.3 Structure of Martensite Formed on Rolling a Ag-41 at. % Zn Alloy 80 3.7.4 General Discussion .. 83 vi Page 3.7.5 Electron Microscopy-of Rolled Specimens .... 83 3.8 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 Stress-Strain 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 Discussion 130 3.9 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 .. 152 4. CONCLUSIONS 158 APPENDIX A Matrix Algebra of Martensitic transformation 161 v i i P a S e APPENDIX B Calculation of Strain Associated with the Transformation 171 REFERENCES 1 ? 7 / / i v i i i LIST OF FIGURES Figure Page 1 Schematic diagram showing the variation of chemical free energy with temperature for parent and product phases 2 2 Basic relation between the b.c.c. lattice and the essentially close-packed structures resulting from martensitic transformation 10 3 Ag-Cd phase diagram showing the alloy compositions used 16 4 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 compos-... S X S I — 0 ltxon 32 11 X-ray diffractometer trace for thermal martensite in Ag-45 at. % Cd alloy 36 12 Unit cell of orthorhombic martensite .: 39 13 Close-packed layer in f.c.c. structure 42 14 Reciprocal lattices for close-packed structures with different stacking orders 43 15 Atom positions in the basal plane of close-packed structures 45 16 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 Page 19 Electron micrograph of thermal martensite showing 'needles' 52 20 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 55 23 Stacking fault fringes in spontaneous martensite .. 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 planes in Ag-45 at % Cd alloy . . 62 28a,b 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 68 32 Tensile axes for specimens tested for modulus determination 69 33 Diffractometer traces of filed Ag-Cd alloy specimens 73 34a,b 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 X Figure Page 38 Electron micrograph of 15% cold rolled Ag-45 at. % Cd alloy 86 39 Electron micrograph of deformation martensite in 15% cold rolled material 87 40 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 temp-eratures above A^  in Ag-45 at. % Cd alloy 92 44 Micrographs of a tensile specimen showing the forma-tion of stress-induced martensite and its reversal.. 94 45 Stress-strain curve corresponding to the photographs in figure 44 . 96 46 Stress-strain curves for specimen 1, over a series of temperatures 98 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 50 Stress necessary to form martensite vs. temperature for specimen 5 105 51 Stress-strain curves showing repeated testing at -45°C 107 52. Stress-strain curves for specimens 1, 5 and 7 at (a) -60° C 109 (b) -55°C 110 (c) -45°C I l l (d) -35°C 112 (e) -10°C 113 xi Figure Page 52 (f) Stress-strain curves for #8, at RT strained twice 115 (g) Initial straining of specimen close to [001] showing plastic deformation 116 53 (a) Surface of #8, after first strain showing slip markings . 117 (b) Above specimen polished and strained to form martensite and released 117 54 Stress-strain curves for polycrystalline specimens over a range of temperatures 119 55 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 58 Typical stress-strain curve used in strain memory effect 127 59 (a) Strain'memory recovery vs. temperature for ill.. 128 (b) Strain memory recovery vs. temperature for #2.. 129 60 Photographs revealing the changes in morphology of thermal martensite brought about by stressing ...... 131 61 Habit plane normals for thermal martensite and S.I. martensite 134 62 (a) Habit plane normals for deformation martensite in Ag-45 at. % Cd alloy 136 (b) Habit plane normals for deformation martensite in Ag-41 at. % Zn alloy 136 63 Lattice correspondence between the body centred cubic i and the orthorhombic lattices 139 64 Laue back reflection photographs of $^  a n c^ S.I. martensite phases 142 65 Geometrical construction to calculate the tensile strain involved in the transformation 144 i x i i Figure Page 66 Stereographic projection showing the various angular relations involved in the calculation 148 67 Stereographic projection showing contours of calcu-lated amount of strain obtained during S.I.M. transformation for various orientation os the tensile axis 150 68 Strain values associated with oriented thermal martensite for various orientations of tensile axis. 150 69 Close-packed layer of (110) showing the atomic shuffles needed to produce tne'martensite structure. 153 70 Schematic diagram indicating the course of trans-formation 155 71 X-ray diffractometer trace of filed specimen (Ag-45 at. % Cd) at l i q . N temperature 156 x i i i LIST OF TABLES Table Page I Structures of thermal and deformation mart'ensites in Ag, Au and Cu base alloys 11 II Compositions of Ag-Cd alloys used ... 27 III List of common symbols used in identifying martensite structures in g-phase alloys 35 IV Positions of diffraction peaks for thermal martensite in Ag-45 at. % Cd alloy 37 V Calculated relative intensities of reciprocal lattice points for a 2H structure 47 VI Comparison of d values (for thermal martensite) obtained' from x-ray and electron diffraction 48 VII Slip systems in Ag-Cd and Ag-Zn alloys 61 VIII Slip vectors and ordering energy relationships of some CsCl type alloys 66 IX Young's modulus values for various orientations in Ag-Cd alloys 70 X Positions of the diffraction peaks for deformation martensite, as a function of % rolling for Ag-45 at. % Cd alloy 79 XI Positions of diffraction peaks for deformation martensite for Ag-41 at. % Zn alloy 82 XII Comparison of lattice spacings obtained from electron and x-ray diffraction for deformation martensite in Ag-45 at. % Cd alloy 90 XIII Lattice parameters of fc^ a n a orthorhombic structures of Ag-45 at. % Cd alloy used in the theoretical calculations 137 XIV Crystallographic data calculated from the theory ... 140 XV Calculated orientation relationships between g2~P n a s e and S.I. martensite 141 XVI Comparison between the calculated and experimental values of <j> 145 xiv Table Page A-1 Crystallographic data calculated from theory for different secondary shear systems for orthorhombic martensite 169 A-2 Habit plane normal for deformation martensite for Ag-Cd and Ag-Zn alloys 170 B-l Calculated values of strain for stress-induced martensite 172 B-2 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 jig-Thanks 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 is 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. > o _J ac • • i ICA UJ Z 111 1 • 1 UJLU 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 Mg temperature (i.e., the temperature at which the martensite phase first 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 Mg temperature is 180°C below T q , whilst in an 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 is generally athermal and the transformation proceeds pnly; on further cooling. The temperature at which the transformation is completed is denoted as M^ . The martensitic transformation is generally reversible so that on heating the martensite phase to a sufficient temperature, (A g), i t begins to transform to the original parent structure. If initially the parent phase is in the form of a single crystal, i t remains so after the reverse transformation. However, in cases where a diffusion controlled reaction is competing with the reversal, the martensite parent transformation may not take place. 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 its 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 the temperature will affect the amount of martensite present. The martensite is in the form of long thin p l a t e s which g e n e r a l l y grow by i n c r e a s e s i n l e n g t h w i t h l i t t l e change i n the p l a t e w i d t h . S i m i l a r growth can a l s o be brought about by the a p p l i c a t i o n o f e x t e r n a l s t r e s s a t c o n s t a n t temperature"*. B u r s t m a r t e n s i t e o c c u r s at temperatures s i g n i f i c a n t l y below the M g temperature. F e - N i a l l o y s p r e s e n t a c l a s s i c example of t h i s i n . t h a t more than 30% of the specimen volume t r a n s f o r m s a t one s p e c i f i c temperature d e s i g n a t e d as M^. The o c c u r r e n c e of t h i s type of m a r t e n s i t e i s b e l i e v e d t o have i t s o r i g i n i n the m e c h a n i c a l c o u p l i n g between c e r t a i n v a r i a n t s of the h a b i t p l a n e . The f o r m a t i o n of one p l a t e t r i g g e r s the f o r m a t i o n 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 a r e a s , 7 i . e . , the p r o c e s s i s a u t o c a t a l y t i c . T h i s b e h a v i o u r has a l s o been g observed by Pops and M a s s a l s k i i n Cu-Zn a l l o y s . 1.3 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 T r a n s f o r m a t i o n s 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 s t u d i e d i n d e t a i l by many r e s e a r c h workers . The m a r t e n s i t e h a b i t p l a n e has been found to be f a i r l y r e p r o d u c i b l e f o r a g i v e n a l l o y c o m p o s i t i o n , but has h i g h M i l l e r i n d e x v a l u e s . The W e c hsler Lieberman and Read (WLR) t h e o r y has been the most w i d e l y used to e x p l a i n the observed h a b i t p l a n e s and o r i e n t a t i o n r e l a t i o n s h i p s . The t h e o r y assumes t h a t the h a b i t p l a n e i s one of e s s e n t i a l l y z e r o d i s t o r t i o n so t h a t the m a r t e n s i t e phase can grow w i t h no a c c u m u l a t i o n of s t r a i n energy- at the i n t e r f a c e . The t r a n s f o r m a t i o n i s c o n s i d e r e d to take p l a c e i n t h r e e s t a g e s f o r m a t h e m a t i c a l c o n v e n i e n c e . (a) The change from the p a r e n t l a t t i c e t o the p r o d u c t l a t t i c e . 5. In t h i s s t e p the f i n a l p r o d u c t l a t t i c e i s d e r i v e d by d e f o r m a t i o n p f the o r i g i n a l l a t t i c e . The amount of d e f o r m a t i o n i s c o n t r o l l e d by the l a t t i c e c o rrespondence between the two l a t t i c e s and a l s o t h e i r l a t t i c e p arameters. The l a t t i c e c o rrespondence assumed i s q u i t e o b v ious i n most c a s e s . However, t h i s d e f o r m a t i o n by i t s e l f cannot produce an u n d i s t o r t e d p l a n e between the p a r e n t and the m a r t e n s i t e and hence a second d e f o r m a t i o n i s r e q u i r e d . (b) T h i s i s a l a t t i c e i n v a r i a n t d e f o r m a t i o n which l e a v e s the c r y s t a l s t r u c t u r e unchanged, but t o g e t h e r w i t h the d e f o r m a t i o n d e s c r i b e d i n (a) produces a p l a n e i n the o r i g i n a l l a t t i c e w hich remains u n d i s t o r t e d . T h i s i n v a r i a n t d e f o r m a t i o n can be c o n s i d e r e d to be a pure s l i p s h e a r or t w i n shear. The p l a n e and d i r e c t i o n o f t h i s shear have t o be i n c o r p o r a t e d i n the t h e o r e t i c a l c a l c u l a t i o n s . (c) The h a b i t p l a n e g e n e r a t e d i s r o t a t e d from i t s o r i g i n a l p o s i t i o n and hence a r i g i d body r o t a t i o n i s i n v o k e d t o make the : i n v a r i a n t p l a n e u n r o t a t e d as w e l l . The m a t r i x n o t a t i o n used i n the m a t h e m a t i c a l a n a l y s i s has the form: P 1 = R B P where P^ i s the t o t a l shape d e f o r m a t i o n m a t r i x P i s the l a t t i c e i n v a r i a n t s h e a r m a t r i x B i s the l a t t i c e v a r i a n t homogeneous d e f o r m a t i o n m a t r i x ( B a i n s t r a i n ) R i s the r o t a t i o n m a t r i x . 6. As the theory is phenomenological in nature, the order in which these three steps take place is of no consequence. In general the lattice invariant shear is treated first as i t simplifies the analysis consider-ably. The theory can be modified to allow for slight uniform strain in the habit plane. In this case the total shape deformation is 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 Mg tempera-ture lying below T q . Conversely, i f an external stress can be applied 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 will 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 is above the A^  temperature for the alloy, then on removal of stress, the martensite so formed is unstable and will 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 is completely removed upon unloading. The amount of pseudo-elasticity observed can be quite large. Busch et al."^ have observed a fully recoverable strain of 24% in Cu-Al-Ni alloys. Strains of ^15% have been observed in 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 in In-Tl alloys . The elasticity achieved during such a reversible process is termed Ferro-elasticity 3 or rubber-like behaviour , and is different from the more common pseudo-elasticity caused by reversible martensite formation at . temperatures above Mg. 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 first observed in 20 equiatomic Ni-Ti alloys but several alloys such as Ti-35 wt.% Nb , 21 5 Cu-Zn-Sn , 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 is 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 deforma-tion temperature either one or the other effect is dominant. Above A^ , the strain is recovered pseudo-elastically, whilst below M g the Strain is recovered only on heating, and between Mg 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 is 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 is 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^ is the rigidity modulus for a shear on {100} and (C^-C.^)/2' is 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 first 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 tempera-tures, 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}^  c c plane forming (001) o r t h t,(0001) h e x_ or ( l l l ) f < c > c > ( t ) , figure (2). The habit, plane in Cu-Zn alloys lies close to (155) for thermal martensite and is in agreement v/ith the WLR theory assuming a {110}<ll0> lattice invariant 10. (CD|) orthorhombic Figure 2. Basic relation between the b.c.c. lattice and the essentially close-packed structures resulting from martensite transformation. 32 33 shear. Very similar results have been obtained in Cu-Al 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 Mg, there exists another 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 Structures of Thermal and Deformation Martensites in Ag, Au and Cu Base Alloys. Alloy Structure Thermal Martensite Deformation Martensite Ag-Cd Ag-Zn Au-Cd Au-Zn Cu-Zn Cu-Al L2, Orthorhombic No transformation detected Close packed structure with 3R and 2H packing Not determined Orthorhombic with S.F. in the C direction Close packed structure with different stacking sequence h.c.p. (52 wt.% Cd) f.c.c. up to" 45 at, % Zn h.c.p, above 47 at. % Zn Not observed f.c.t. for light deformation f.c.c. on heavy deformation h.c.p. for higher Zn cone. 50 at. % Zn. ln-Tl f.c.t. (twinned) 12. transformation product on severe cold work i s a close-packed structure and i n Ag-Zn and Cu-Zn has a face centred cubic structure at lower a l l o y contents, the structure changing to close-packed hexagonal with 36 38 23 increasing Zn contents ' . Warlimont suggests that the solute concentration at which the hexagonal structure occurs could be derived from the v a r i a t i o n s i n the stacking f a u l t p r o b a b i l i t y with solute concentration i n the f.c.c. phase and i t s extrapolation to a value of 0.5. The ease with which the transformation occurs varies with the a l l o y content, i . e . , le s s transformation was found to occur at higher a l l o y contents. Martensite produced i n t h i s way reverted to the . 38 equilibrium phase on annealing by a nucleation and growth type 39 reaction . I t i s necessary to note that a considerable amount of p l a s t i c deformation i s necessary to form t h i s type of martensite , ( t y p i c a l l y > 10%) and t h i s d i f f e r e n t i a t e s i t from the martensite produced above Mg 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 . It has been suggested that p l a s t i c deformation produces a disordered l a t t i c e , r a i s i n g the free energy of the system and t h i s excess free energy i s responsible for the change to the martensitic phase. Greninger and Mooradian suggested that the deformation induced martensite i n Cu-Zn had a tetragonal structure when the amount of 40 deformation was s l i g h t . Hornbogen and coworkers c a r r i e d out experi-ments on sing l e c r y s t a l specimens of 60-40 brass and showed conclusively that the product phase i n i t i a l l y has a tetragonal structure and that on severe deformation i t changes to face centred cubic. In fac t t h i s i s i n keeping with the e a r l i e r work i n which f i l i n g was adopted as the. mode of deformation. As t h i s causes severe deformation, the product 13. 38 phase, i n d e e d , would have a c u b i c s t r u c t u r e . The m a r t e n s i t e phase thus produced i s h e a v i l y f a u l t e d . I t was a l s o found t h a t the axes of the t e t r a g o n a l c e l l c o i n c i d e d w i t h the cube axes of the 3 s t r u c t u r e , the maximum d e v i a t i o n b e i n g ^ 8 ° . The C a x i s o f the t e t r a g o n a l c e l l c o i n c i d e d w i t h t h a t a x i s o f the o r i g i n a l phase which was i n c l i n e d l e a s t t o the t e n s i l e a x i s . 41 A h l e r s and Pops found two d i f f e r e n t t y p e s o f m a r t e n s i t e produced on d e f o r m a t i o n i n Cu-Zn a l l o y s . One appeared as broad bands and • had a h a b i t p l a n e v e r y c l o s e t o {110}. The second c o n s i s t e d o f v e r y narrow bands of m a r t e n s i t e and formed on e i t h e r {110} o r {112} p l a n e s of t h e o r i g i n a l c u b i c phase. They s u c c e s s f u l l y a p p l i e d the WLR t h e o r y to the m a r t e n s i t e produced on d e f o r m a t i o n and showed t h a t the r e s o l v e d shear component o f the a p p l i e d s t r e s s on the secondary shear system {110}<110> or {110}<113> was the most i m p o r t a n t f a c t o r i n d e t e r m i n i n g the type of m a r t e n s i t e formed. 34 Masson and B a r r e t t found t h a t i n Ag-Cd the c l o s e - p a c k e d d e f o r m a t i o n s t r u c t u r e c o u l d be produced by deforming e i t h e r the phase o r the orthorhombic t h e r m a l m a r t e n s i t e produced on c o o l i n g . They proposed;a two s t a g e mechanism f o r the f o r m a t i o n of the c l o s e - p a c k e d phase. T h e i r argument was t h a t the o r t h o r h o m b i c phase was an i n t e r m e d i a t e s t r u c t u r e which formed because of i n s u f f i c i e n t d r i v i n g f o r c e ; and when the e x t r a d r i v i n g f o r c e needed was p r o v i d e d i n the form of e x t e r n a l work, the, t r a n s f o r m a t i o n r a n i t s complete c o u r s e . 14. 1.7 E l e c t r o n Microscopic Observations Transmission e l e c t r o n microscopy has proven to be e x t e n s i v e l y v a l u a b l e i n determining the nature of the l a t t i c e i n v a r i a n t shear i n the martensite transformations. 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 shear i n most systems, although a l a m e l l a r mixture of a cubic and orthorhombic s t r u c t u r e s was observed i n the case of 42 Cu-Zn-Si martensites . E l e c t r o n microscopy of non-ferrous martensites i s made more complicated i n that a spontaneous m a r t e n s i t i c t ransformation may occur at temperatures w e l l above M g due to 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 ociated w i t h the p r e p a r a t i o n of a t h i n f o i l specimen. 1.8 Aim of the Present Work ; The present i n v e s t i g a t i o n was undertaken w i t h the main aim of • studying the r e l a t i o n between thermal and deformation induced martensite 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 that martensite could be formed by deforming the fi^ phase at room tempera-44 tur e . Masson had obtained M g temperature data f o r a l l o y compositions very c l o s e to 50-50 Ag-Cd. The present i n v e s t i g a t i o n - extended t h i s to cover a wide range of a l l o y compositions w i t h much higher M^ v a l u e s . An a l l o y of 45 a t . % Cd 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 experiments. E l e c t r o n microscopy of the thermal and deformation-^ induced martensites was attempted. One of the main aims of the work was to f i n d the a p p l i c a b i l i t y of the phenomenological theory o f . m a r t e n s i t i c transformation to deformation-induced martensites. f 2. EXPERIMENTAL PROCEDURE 2.1 Alloy Preparation Alloys were prepared by melting known weights of the constituent elements i n evacuated quartz tubes. The s i l v e r and cadmium used were of purity Ag: 99.95%, Cd: 99.99%. Approximately 60 grams of the alloy was melted i n one batch. The alloys were kept molten at 800°C for approximately four hours and the molten alloy was kept well mixed by vigorously agitating the melt. The a l l o y was then rapidly cooled and the s o l i d i f i e d alloy weighed. The weight loss was approximately 0.02 gms/melt 0.03% loss) and consequently further chemical analysis was not carried out. The al l o y compositions used are 45 shown on the Ag-Cd phase diagram i n f i g . (3). The al l o y ingot was cold r o l l e d about 10% and annealed at 680°C for 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. single pass resulted i n shattering of the specimen. The s i l v e r r z i n c a l l o y was made i n a s i m i l a r manner. Figure (4) indicates the relevant phase diagram, again including the al l o y composition used. Figure 3. Ag-Cd phase diagram showing the alloy compositions used. Figure 4. Ag-Zn phase diagram showing the all 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 in fig. (5). The specimen was then O b I II 015 Figure 5. Dimensions of the tensile specimen. 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 in the Ag-Cd alloys. A 6% KCN solution was ultimately found satisfactory with the polishing solution contained in 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 in 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. Cr03 20 gms Na2S04 1.5 gms 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 t 0 P a r t s °^ NH^ OH. ' 2.5 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. distance of 3 cms was maintained between the specimen and the f i l m . 2.6 X-Ray D i f f r a c t i o n 2.6.1 Room Temperature X-Ray D i f f r a c t i o n 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 structures were c a r r i e d out with a North American P h i l i p s X-ray unit with a copper target. The operating conditions were 30 KV and 15 mA, with a scanning speed of 1 deg 29/min. 2.6.2 Low Temperature X-Ray D i f f r a c t i o n A s p e c i a l specimen holder was b u i l t for low temperature d i f f r a c t i o n experiments, F i g . (6). The apparatus consisted of a hollow brass cylinder with a recess for mounting the specimen. The specimen could be cooled by pouring l i q u i d nitrogen into the hollow cyl i n d e r . The specimen temperature was monitored using a thermocouple glued to the specimen mount. The specimen was then covered with an outer c y l i n d r i c a l s h e l l . X-rays could f a l l on the specimen through one m i l thick mylar windows. The volume insi d e the outer s h e l l was evacuated to minimise temperature gains and also to eliminate f r o s t i n g problems. A small heater c o i l was wound around the inner hollow cylinder and by c o n t r o l l i n g the heater current any desired temperature between -196° and -50?C could be maintained f or a considerable length of time. 2.7 Measurement of Transformation Temperatures The Mg, Mj, A g and A^ temperatures were determined by o p t i c a l microscopy. Test specimens were mounted on a s t e e l block supported at 22. -c- Vacuum *-A B C Hollow Cylinder Outer Cover Liquid Nitrogen Inlet D Specimen Figure 6. Specimen holder for low temperature X-ray d i f f r a c t i o n . the end of a 1/4" s t e e l rod and immersed i n ethanol or petroleum ether (for temperature.< -100°C) contained i n a double walled transparent dewar. To cool the specimen, l i q u i d nitrogen was added i n small qu a n t i t i e s , and the s o l u t i o n was kept w e l l s t i r r e d . A chromel-alumel thermocouple was f i x e d next to the specimen providing an accurate assessment of the specimen temperature. The specimen could be observed from outside through a microscope f i t t e d with a long f o c a l length objective. A selected area of the specimen was kept i n focus during cooling and the formation of martensite at the Mg temperature was e a s i l y revealed by the rumpling produced on the polished surface of the specimen. Microstructures could be recorded using a 35 mm camera attached to the microscope. 2.8 Tensile Tests Tensile tests were c a r r i e d out i n a f l o o r model Instron t e n s i l e t e s t i n g machine. Care was taken whilst mounting to prevent any bending of the specimen. A cross head speed of 0.005"/min (corresponding to a -4 -1 s t r a i n rate of ^ 1.4 x 10 sec ) was used i n a l l experiments. The test temperature was varied by surrounding the specimen with a cooling bath. C h i l l e d alcohol was used as the cooling medium. The specimen dimensions were measured with the help of a t r a v e l l i n g microscope. The specimen could be observed from outside through the double walled transparent dewar used to contain enthanol. An Instron extensometer was attached to the specimen gauge section whilst the modulus measurements were made. This enabled accurate determination of the modulus values but r e s t r i c t e d measurements: to 24. room temperature only. A special tensile jig [fig. (7)] proved very useful in observing specimens under tension. Using this, habit plane measurements could be made for the stress-induced martensite. The jig 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 filing 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 difficult. The following method of specimen preparation was 2 5 . Moving Stress Induced Martensite. Figure 7. Apparatus used f or 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. The dished specimen was then polished in a 6% KCN solution. A low voltage 1.5 volts) was used to obtain the in i t i a l performation of the disc. 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. A gold standard was used for determining the camera constant. 3. EXPERIMENTAL RESULTS AND DISCUSSION 3.1 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. 1 2 3 4 5 6 7 at.% Cd 42.3 44.3 45.0 45.5 46.0 47.7 50.9 28. Figure 8. Bainite needles in quenched 44.3 at.% Cd alloy (x 230). 29. The retained g phase is 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 Mg, M^ , Ag and A^  temperatures were optically determined for a series of alloys of Ag-Cd covering a composition range from 44.2 to 14 47.0 at.% Cd. Masson has determined the variation in the M s temperature with composition using X-ray diffraction techniques for alloys from 46.6-49.1 at.% Cd. At the Mg 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 tempera-ture 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 of t h i s c h a r a c t e r i s t i c zig-zag p a t t e r n ( f i g u r e (9)) was used to e s t a b l i s h M^. These m a r t e n s i t i c p l a t e s appeared to form i n a cooperative way; the formation of one p l a t e a s s i s t i n g i n the formation of the adjacent p l a t e . The t o t a l amount of martensite formed i n one burst was l e s s than 5%, much d i f f e r e n t from Fe-Ni a l l o y s where as much as 84% of the volume transformed at once 7. On f u r t h e r c o o l i n g the amount of martensite increased u n t i l the s t r u c t u r e had completely transformed. On warming the specimen, the reverse transformation s t a r t e d at the A g temperature and ended at A^, the burst martensite slowly r e v e r t i n g to the parent phase. The transformation temperatures d i d not vary s i g n i f i c a n t l y w i t h thermal c y c l i n g . Figure (10) gives the v a r i a t i o n of the M g, M^, A^ and A^ tempera-tures w i t h composition. The data obtained by Masson f o r a l l o y s of higher cadmium concentration i s included f o r comparison. From the f i g u r e , i t i s seen that M g decreases w i t h increase i n the cadmium concentration at the r a t e of 35°C/atom % Cd. The behaviour i s s i m i l a r to that found i n Cu-Zn a l l o y s where the M g temperature decreased r a p i d l y at the r a t e of 'W50C/atom % Zn. The values of the M temperature s 44 reported by Masson are lower than the values obtained i n the present work. This could be due to the f o l l o w i n g reasons. (a) Masson. determined the values by X-ray d i f f r a c t i o n and there-f o r e could detect the martensite peaks only a f t e r about 5% of the volume had transformed, thus g i v i n g a lower value of M . (b) 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 that M g decreases w i t h a decrease i n the g r a i n s i z e 6 , and t h i s could be p a r t l y r e s p o n s i b l e f o r a lower value of M . ; 31. Figure 9. Micrograph of thermal martensite. A: Thermo-elastic martensite and B: Burst Martensite. 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 temperature is below the M temperature. This could be s s due to the fact that the stresses associated with the i n i t i a l trans-formation assist the reverse transformation. This behaviour is not really unusual, and has been observed in Au-Zn alloys"^. The very small hysteresis might also suggest that the equilibrium T q tempera-ture is very near the Mg temperature. 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 Mg temperature, was cooled in liquid helium. 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 in 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 is 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 determina-tion very difficult. 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 is the fact that special thinning procedures are needed in order for electrons to penetrate the specimen and the behaviour of such thin foils 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 Mg temperatures found in the bulk material In the following sections the structure of the thermal martensite found in an Ag-45 at.% Cd alloy is discussed using both X-ray and electron microscopic observations. In the subsequent discussion a general survey of the structures of the martensites in g-phase alloys is made. Table III gives the common terminology used in 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 2H. y: 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 for a 47 at.% Cd alloy. 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 45 at.% data for Cd alloy Data Ag-47 at.% for Cd alloy 20 deg. d A° 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 basis using (020), (002) and (200) r e f l e c t i o n s . With these values the interplanar spacings f o r other r e f l e c t i o n s were calculated. The agreement between the observed and calculated values i s very good. The orthorhombic structure has the following l a t t i c e parameters a = 3.0904 A° b = 4.8550 A° c = 4.7433 A° There are four atoms i n a unit c e l l . Masson and Barrett gave their p o s i t i o n s as Cd: 0, 0.195, 1/4 0, .805, 3/4 Ag: 1/2, 0.695, 1/4 1/2, .305, 3/4 Shifting the o r i g i n to the f i r s t cadmium atom the atom posit i o n s could be given as Cd: 0, 0, 0 0 0.610, 1/2 Ag: 1/2, 1/2, 0 1/2, 0.110, 1/2 The structure could thus be interpreted as a layered structure i n which every second layer i s s h i f t e d along the b-axis by 0.610. The structure obtained i s very s i m i l a r to the one found i n Au-47.5 a t . % Cd by Olander^. This structure i s referred to as Olander structure and has atoms situated at positions given below: Cd: 0, Au: 1/2, or a l t e r n a t e l y Cd: 0, Au: 1/2, 5/16, 1/4 13/16, 1/4. 0, 11/16, 3/4 1/2, 3/16, 3/4. 0, 1/2, 0 0 0, 3/8, 1/2 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 cell of martensite is shown in figure (12). O Cd atoms 0 Ag atoms Figure 12. Unit cell of orthorhombic martensite. 40. 3.3.3 Martensite Structures in g-Phase Alloys There is much controversy in the literature regarding the martensite 62 structures produced from g-phase alloys. Kunze reported a transition lattice with a monoclinic unit cell and a superlattice with a triclinic 6 3 unit cell for Cu-Zn alloys. However, Masson and Govila failed to confirm these structures. 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 found two different structures in the case of Cu-Ga martensites: 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 1 (c) an internally twinned orthorhombic (ordered) martensite, y'. Wilkins and Warlimont^ later modified the tetragonal structure to a regular arrangement of a close-packed layer of atoms with regular 6 8 stacking faults. However, Sato et al. 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 2' (3R), B 2" (3R + 2H), and y ' (2H) structures 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 fig. (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 is 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. A characteristic of this splitting is that the split spots 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 Figure 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 f o r close-packed structures with d i f f e r e n t stacking order. In IR structure the twin spots are represented as open c i r c l e s . Indices are according to cubic notation (Ref. 70). 4 4 . 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 fig. (16). The atomic scattering 4 5 . a Cd atoms O Ag atoms Figure 15. Atom positions in the basal plane. 2 I 0 7 • • • «^ • • o 0 a • 2 • • • • • 2 0 2 4 Figure 16. Basal plane structures. of the reciprocal lattice of close-packed (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 is different from the Au-Cd alloy system where the superlattice spots are visible clearly. The value of F. remains the same for 3R or 2H : A 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 is 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 is 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. 4 7 . 2 Table V 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. The actual relative intensities 2 2 2 2 are given by | F | = | F | • | 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 - f | for superlattice spots (h = 0 , k = 1 ; h = k = 0 , 2 ) . Reciprocal lattice Relative point in orth. intensity coordinate ( 0 0 2 ) 4 ( 0 2 0 ) 2 . 3 7 ( 2 2 0 ) 2 . 3 7 ( 2 0 2 ) 4 ( 0 2 2 ) 2 . 3 7 ( 1 3 0 ) 2 . 9 6 ( 1 3 1 ) 1 . 0 3 ( 1 3 2 ) 2 . 9 6 ( 1 3 3 ) 1 . 0 3 ( 1 1 3 ) 3 . 5 4 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 fig. (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 d from X-ray from SAD diffraction (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 The 2H structure of the martensite is 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 is 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 in the microscope. These needles did not grow even after a prolonged delay (% 4 hrs) at the low tempera-ture. 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. Figure 19. Electron micrograph of thermal martensite showing 'needles'. (X 14K). Figure 20 . Electron micrograph of thermal martensite showing the faulted structure. (X 42K). 54. Figure 21. Spontaneous martensite in Ag-45 at.% Cd alloy. (X 30K). 5 5 . Figure 22 . S.A.D. of spontaneous martensite r e v e a l i n g s t r e a k i n g along <111> d i r e c t i o n . F i g u r e 23. S t a c k i n g f a u l t f r i n g e s i n spontaneous m a r t e n s i t e (X 75K). 4-20 °< 4 18 rr U J 4 1 6 UJ ^ 414 < a. y 412 < 410 408 — i 1— n 1 1 • X-Ray Diffraction. [ Pile d powder specimens ] A Electron Diffraction. [ Spontaneous transformations i n t h i n . f o i l ] 10 20 30 40 Cd CONCENTRATION (At.%) 50 Ln Figure 24. Variation of lattice parameter of a phase vs. 59 composition 58. meters of the a-phase extrapolated to the higher cadmium contents. The f.c.c. product produced by filing 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 is 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 Slip Systems in Ag-Cd and Ag-Zn Alloys 3.4.1 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. 6 1 . 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 is operative in both the alloys. In the case of (110)[111] slip, there are twelve possible slip systems -and only one of these will 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 is less than 0.06 eV. Table VIII shows the slip vectors of various CsCl type compounds and the corresponding ordering energy calculated from the critical ordering temperatures. Au-Zn and Au-Cd appear to violate this prediction. 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 dis-location elastic energy. From a geometrical view {112} and {110} are the only possible slip planes with a <111> slip direction"^. Higher order planes are not true slip planes. In 3 Cu-Zn alloys a {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 = critical 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, fig. (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 Cottrell^ 6, who noted that this behaviour was 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. These formed on a {110} plane of the matrix. 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. In view of the fact that the Mg temperatures for these alloys are below liquid helium temperature, i t is unlikely that strain-induced martensite could be produced with Figure 30. Coarse s l i p markings i n Ag-45 at. % Cd a l l o y (X 10). Figure 31. Interferometric pattern of the surface of a specimen after very l i g h t deformation. 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 is seen that the value of the modulus is 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 fig. (32). Sp. No. C.S. Strain for E dynes/cm — cm /dyne — Calculated Sq. mm 50 lb. load 2,, cm /dyne 12 12 x 10 x 10 1 3.092x.737 . 0 0 8 5 1 . 1 5 X 1 0 1 1 8.7 -2 3.343x.626 .0011 9.40X10 1 1 1.063 -3 3.316x.808 .00525 1.39xl01X 7.2 6.7 4 1.0 .002375 4.7 xlO 1 1 2.13 2.97 5 3.4 x.814 .00137 5 . 8 5 X 1 0 1 1 1.71 1.70 71. dependent. The values of the modulus can also be calculated using the expression 1 E • S N - 2S fU,i,n) where S 1 1 E i o o S - ( S N . - S 1 2 - 1/2 S 4 4 ) = - VS-Q> v = Poisson's Ratio S^^ = reciprocal of rigidity modulus for a shear on {100} 2 2 2 2 2 2 and f(£,m,n) = £ m +mn + 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 and E-^-QJ one can calculate the value of (S^2 + 1/2 and using this value and knowing f(£,m,n) for any orientation, the corresponding value of the modulus can be determined. The agreement is 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. Values of 30 29 10 and 18 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 is 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 predicted1 that a l l g type alloys with closed inner shells will have a high value for the 2(S^ - S.^ ) shear coefficient. Pops and Massalski'*''" compared the change in the anisotropy effected by changes in 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 5 8 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 filing the quenched structures at room temperature. The -150 mesh fraction of the filings was used in the study. The polished S „ phase has a pink colour which disappears on filing. Figure (33) + + a Figure 33. Diffractometer traces of filed Ag-Cd alloy specimens. 74. includes the diffractometer traces of a l l o y s 2 to 7. The range of 26 from 34 to 44 deg includes the most intense d i f f r a c t i o n peaks of the various structures. In a l l o y s 2-5 the structure transformed completely to a new close-packed phase, whilst i n a l l o y s 6 and 7, a progressively increasing amount of ^ phase was retained. This retention of the 3^ phase was a genuine e f f e c t and was not s i g n i f i c a n t affected by the delay between f i l i n g the specimen and taking the diffractometer trace. In a l l o y s 2 to 4 the close-packed structure obtained on deformation was face centred cubic (a +) whilst i n a l l o y s 6 and 7 a hexagonal close-packed product (? +) was obtained. In a l l o y 5, peaks for both the f.c.c. and h.c.p. structures were obtained, the structure presumably having a large number of stacking f a u l t s . This t r a n s i t i o n from f . c . c . to h.c.p. appears to be c h a r a c t e r i s t i c of deformation induced martensite since s i m i l a r s t r u c t u r a l changes occur 36 38 i n Cu-Zn and Ag-Zn a l l o y s . An attempt was made to determine the l a t t i c e parameter of the cub phase obtained during deformation, i n order to see whether or not t h i s phase has a l a t t i c e parameter that would be expected from an extrapolation of the equilibrium a-phase parameter to higher cadmium contents. In determining the l a t t i c e parameter, the (311) r e f l e c t i o n was used as t h i s i s s h i f t e d l e a s t by stacking f a u l t s present i n the 36 structure . The r e f l e c t i o n was f a i r l y d i f f u s e because of the cold worked state of the powder and the peak could only be read to an accuracy of + 0.1 deg. Figure (24) shows that the l a t t i c e parameter, of the deformation induced martensite appears to l i e on an extension of the a - s o l i d s o l u t i o n into the metastable region. 75. The behaviour of Ag-Cd a l l o y s i n the composition range between 42.3 a t . % Cd to 50.9 a t . % Cd i s very s i m i l a r to isomorphous 8^  Ag-Zn and Cu-Zn a l l o y s . In both cases t r a n s f o r m a t i o n to a close-packed s t r u c t u r e occurs on f i l i n g , being f . c . c . at low Zn contents and changing g r a d u a l l y to h.c.p. at higher Zn contents. In both cases, a l s o , there i s incomplete transformation to the deformation martensite at higher z i n c contents i n agreement w i t h the present r e s u l t s . 3.7 Nature of Martensite Produced on Cold R o l l i n g X-ray d i f f r a c t o m e t e r traces were taken a f t e r v a r i o u s d e g r e e s j O f deformation induced by cold r o l l i n g of the 8^ pbase i n both Ag-Cd and Ag-Zn a l l o y s . A f t e r r o l l i n g , the surface of the specimen was mechanically 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 to remove the 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 the specimen used was q u i t e l a r g e ('v 3 mm) , not a l l the X-ray d i f f r a c t i o n peaks could be recorded; and hence only a semi-q u a n t i t a t i v e treatment i s p o s s i b l e here. 3.7.1 O p t i c a l Microscopy of Deformation M a r t e n s i t e Figures (34a,b) shows.the martensite produced i n an Ag-41 a t . % Zn a l l o y , as seen on the r o l l e d s u rface and on a second surface at r i g h t angles. The martensite traces were u s u a l l y somewhat i r r e g u l a r on the r o l l e d s u r f a c e , w h i l s t they were very s t r a i g h t on the second surface. I t i s probable that t h i s waviness was due to the complex nature of the deformation on the surface. This was p a r t l y revealed by the very poor q u a l i t y Laue back r e f l e c t i o n photographs obtained from a s - r o l l e d m a t e r i a l . The back r e f l e c t i o n photographs became c l e a r e r as the .distorted 76. Figure 34a,b. Deformation martensite i n Ag-Zn all o y . Microstructures on the r o l l e d surface (a) and on a second surface at right angles (b) [X 290]. 77. surface layer was removed. Similar behaviour was seen in the case of the Ag-Cd alloy. 3.7.2 Structure of Martensite Formed on Rolling an Ag-45 at. % Cd . Alloy: Table X indicates the angular positions of the diffraction peaks, and figure (35) shows a schematic representation of the diffraction peaks. The peaks in most cases were ill-defined and hence this prevented accurate lattice parameter determination. The following conclusions can be derived from the X-ray diffraction results: (a) The structure is predominantly unchanged during the earlier stages of deformation; as revealed by the very weak peaks belonging to the martensite structure. (b) Above 15% deformation, the martensite formed could be visually detected. (c) The martensite peaks cannot be analysed in 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 axial ratio of 0.88. (d) There is no further change in the structure un t i l very severe deformation is effected (y 60%) when there is a very gradual change to a cubic structure. Ce) For comparison purposes, the diffraction peaks obtained from the f i l i n g s of the same alloy are included in the table. A gradual change to the face-centred cubic structure is 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% 45% 50% 65% 75% Filed Remarks , „ ' sample (26 deg.) 37.2 37.2 37.2 37.2 37.2 37.2 37.2 37.2 37.2 (ll l ) f . c . c . f.c.t. 38.3 38.3 38.3 38.3 38.3 38.3 38.3 38.3 38.4 38.4 38.4 (HO)b.c.c. 41.4 41.2 41.6 41.4 (200)f.c.t. 42.3 42.3 42.4 42.7 (200)f.c.c. 47.8 (002)f.c.t. 55.7 55.6 55.8 55.9 55.1 55.1 55.1 55 55.7 55.7 (200)b.c.c. 59.4 59.5 59.5 59.6 59.6 59 59.5 (220)f.c.t. 62.3 62.8 62.7 (220)f .cc. 64.3 64.3 (202)f.c.t. 69.2 69.6 69.6 69.0 69.1 69 69.0 69.0 69.0 69.3 69.4 69.0 69.1 (211)b.c.c. 72.5 72.4 72.5 72.3 72.3 72.7 72.4 72.5 72.3 (311)f.c.t. 75.2 (311)f.c.c. 79.3 (222)f.c.c. 82 (220)b.c.c. 95.0 (310)f.c.c. (004)f.c.t. 106.8 106.8 106.7 106.7 106.7 106.8 106.8 106.8 106.7 (331)f.c.c. (222)b.c.c. 80. to martensite even after ^ 75% of rolling. This is in contrast to the complete absence of the 3^ peaks in the filed material. This is indicative of the severity of the deformation imposed while filing 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. Table XI gives the angular positions of certain prominent peaks. 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 cell 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. is 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 filing did give an f.c.c. structure indicating that the structure does become close-packed on severe deformation. Figure 36. Diffractometer traces of deformation martensite as a function of % cold r o l l i n g f o r Ag-41 at. % Zn a l l o y . 82. Table XI Positions of diffraction peaks for deformation martensite in Ag-41 at. % Zn alloy. 2 e Remarks 31.25 (HO) f.c.t. 39.2 (111) f.c.t. 41.0 (110) h 44.7 (200) f.c.t. 50.2 (HI) h 58.0 (200) 65.2 (220) f.c.t. 79.2 (311) f.c.t. 99.3 (400) f. c.t. (310) h 114.5 (222) B 9 83. 3.7.4 General Discussion It is evident that the martensite that is formed in the early stages of deformation has a face centred tetragonal cell. 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 is formed after about 15% deforma-tion is 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 2 phase became unstable on deforming because 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 all o y revealing dislocation structure (X 65K). 85. dislocations form a cross grid pattern. In body centred cubic materials the screw dislocations are very predominant.*^ It was very difficult to observe deformation martensite in the microscope. At low amounts of deformation the amount of the matrix transformed to martensite is very small and hence the probability of observing the martensite was negligible. An increase in the amount of deformation increased the amount of martensite but this was also accompanied by an increase in the dislocation density which made i t yery difficult 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 in the dislocation structure of the 3 matrix, which would act as a strain embryo in the formation of martensite. It was difficult to produce good diffraction patterns owing to cold work. Figure (41) shows streaking indicating the presence of stacking faults, very much more evident than in 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 in the adjacent matrix, implying that the disloca-tions 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. All 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 deformation martensite 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 in 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. (hkl) d A° d A° Electron X-ray diffraction diffraction 311 1.24 1.303 331 0.932 0.99 022 1.36 1.447 313 0.91 0.942 3.8 Stress-Induced Martensite in 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 fig. (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 trans-formation is 'smooth', the growth of the martensite taking place by 92. F i g u r e 43. G e n e r a l shape o f t h e t e n s i l e c u r v e o b t a i n e d a t t e m p e r a t u r e s above Af i n Ag -45 at . % Cd a l l o y . 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 is almost negligible, i.e., the matrix transforms at a constant load. After the gauge length is 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 in the reverse order. Provided that the test temperature is 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 taken of a specimen whilst loading in the Instron machine. 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 first 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 difficult 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 its reversal (X5). 96. T 1 1 1 r STRAIN (%) Figure 45. 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 tempera-ture was used for the first test and the temperature was gradually | raised for subsequent tests. The results can be discussed with reference to transformation temperatures, (the alloy has = -98°C, M = -74°C, A =-80°C, A_ =-67°C). Figure (47) shows the level of S S 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 Mg temperature, the specimen is partially or fully 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 it is below A . s (b) Above the temperature, the specimen is fully a n ^ martensite forms on application of stress. The stress necessary to cause the transformation is a function of temperature, being higher at high temperatures. Up to approximately 50°C above Mg the stress for the formation of martensite is less than the yield stress of the specimen and so no plastic deformation takes place before the transform-ation. 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 temperatures. vo V O 101. 30 ^20 o o o CO CO rr 10 0 O Loading Cycle A Unloading Cycle -80 -60 -40 -20 0 TEMPERATURE Figure 4 7 . Variation of stress necessary to form SIM with temperature for specimen 1. 102. -60 -40 TEMPERATURE -20 0 Figure 48. Pseudo-elastic recovery vs. temperature for specimen 1 103. s u f f i c i e n t l y strong to support martensite formation and so recovery i s only p a r t i a l . At s t i l l higher temperatures (+20°C) only p l a s t i c deformation occurs and there i s no martensite formation at a l l . Figure (47) i s the s t r e s s to form martensite as a function of temperature and shows a two stage behaviour, the f i r s t stage with a steeper slope occurring at lower temperatures, and a second stage at higher temperatures. The t r a n s i t i o n from one region to the other coincides with the smoothing of the transformation curve and also witb the lowering of the hysteresis associated with the transformation. Figure C47), also includes the stress l e v e l s at which the reverse transformation i s completed on unloading. At higher temperatures (stage II) the stress during reversal i s the same as that during the formation of martensite, a feature c h a r a c t e r i s t i c of thermo-elastic transformation. The martensite formed during loading remains stable upon unloading at temperatures below A^, w h i l s t above A^ the martensite formed during the i n i t i a l loading cycles disappears completely upon unloading as revealed i n fi g u r e (46). The stress necessary to form martensite i s by d e f i n i t i o n zero at the Mg temperature. The i n i t i a l portion of the curve must, therefore, extrapolate to the Mg temperature at zero s t r e s s . The extrapolated value i s -70°C compared to the experimentally determined value of -74°C. By a s i m i l a r argument, the stress during the reverse transforma-ti o n must extrapolate to 0 at the A^ temperature. The present data did not confirm t h i s too w e l l , owing to the d i f f i c u l t y of extrapolating the curve to zero stress due to i t s r a p i d l y varying curvature. However, as shown i n figure (49), there seems l i t t l e doubt that t h i s does indeed 21 extrapolate to A f as was found by Eisenwasser 104. 3 0 dL O 8 2 0 00 00 LU rr 1-00 0 0 o A Tested at -45 c Loading Cycle Unloading Cycle - 8 0 - 6 0 4 0 - 2 0 TEMPERATURE 0 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. The following features can be generalised: (a) 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., %Mg, at 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). In this case the specimen was strained repeatedly at -45°C. It is thus felt that the procedure used was valid. 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 it is recovered in a l l three specimens (-55°C is well above the A^  temperature for the alloy, -67°C). The recovery is 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 initially deforms plastically, before the transformation takes over. The reversal of martensite is 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. It started to deform plastically with two slip systems. 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 is involved. Similar reloading of specimen IA failed to yield a transformation. A simple explanation for this behaviour would be that the yield stress is 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 is 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. 1 1 6 . Figure 52g. Initial straining of specimen close to [001] showing plastic deformation. 117. Figure 53. (a) Surface of #8, a f t e r f i r s t strain,showing s l i p markings(X 230). (b) Specimen polished and strained to form martensite and released. Note the absence of s l i p markings (X 230). 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 Mg. Region b This region covers the temperature range from -75°C to -20°C. The Mg 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 is to be expected. Region a In this region, the specimen is 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 . S t r e s s - s t r a i n curves for 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 is -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 is 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 is possible that the specimen will ultimately transform to martensite provided the stress level is 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 Ag temperature. The reversion is nearly complete in the case where the test temperature is above and is only partial in the temperature range Ag 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 -50 0 TEMPERATURE °c Figure 56. Amount of pseudo-elastic recovery vs. temperature for polycrystalline specimens. 124. This behaviour i s very s i m i l a r to the one exhibited by the sin g l e c r y s t a l specimens of the same a l l o y except that 100% recovery was never obtained i n p o l y c r y s t a l l i n e specimens; the maximum value obtained was 85% only. 3.8.3 Microscopic Observations Microscopic examination at room temperature revealed the presence of deformation martensite a, ( s i m i l a r to the martensite formed on 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. The amount of martensite formed was very small and could be observed only i n one or two grains. Figure (57) shows the martensite as revealed under the microscope. In order to check that t h i s was not a surface e f f e c t , the specimen was repolisbed and re-etched. An edge view of the specimen i s included i n the figure and t h i s reveals the p l a t e - l i k e nature of the deforma-t i o n martensite. Deformation martensite was not observed i n specimens deformed at temperatures -10°C and above. In these specimens martensite did not form during the i n i t i a l loading as can be seen from the t e n s i l e curves (figure (54)). However, the specimens work hardened during th i s i n i t i a l loading and on t e s t i n g a second time they did form stress-induced martensite during loading. On subsequent examination they were found to have deformation martensite i n i s o l a t e d grains i n the specimen. This suggests that e i t h e r severe deformation of the ft^ phase or deformation of the thermal martensite i s necessary i n order to form deformation martensite. This w i l l be discussed l a t e r . 125. Figure 5 7 . Deformation martensite in Ag-Cd polycrystalline specimen after tensile testing. Traces on two surfaces are matched (X 1 2 5 ) . 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 studied i n an Ag-45 at % Cd a l l o y . Single c r y s t a l specimens were strained to a constant value of 5% s t r a i n at various temperatures and released. This gave the amount of e l a s t i c or pseudo-elastic recovery. The specimen was then allowed to warm up to room temperature causing reverse transformation to the matrix. This resulted i n a 'buildup of stress i n the material which was l a t e r released. The s t r a i n associated with t h i s was a measure of the s t r a i n memory recovery. A t y p i c a l s t r e s s - s t r a i n curve i s given i n f i g u r e (58) This method of t e s t i n g proved e f f e c t i v e only at temperatures above M . Below t h i s temperature the small value of load (y 3 lbs) maintained while cooling the specimen was s u f f i c i e n t to cause the transformation. Figures (59a,b) show the s t r a i n memory e f f e c t obtained i n the ;. case of the two s i n g l e c r y s t a l specimens. The amount of pseudo-21 e l a s t i c i t y obtained i s also included. Eisenwasser showed that the s t r a i n memory e f f e c t and p s e u d o - e l a s t i c i t y were complementary i n nature; and the r e l a t i v e amounts depended on the temperature of: the test, iThis i s indeed true, as revealed from the f i g u r e s . At low temperatures 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 of the recovery i s by the s t r a i n memory e f f e c t . The s t r a i n memory ef f e c t drops d r a s t i c a l l y ; above A^ and at the same time there i s a s i g n i f i c a n t increase i n the p s e u d o - e l a s t i c i t y from about 15% to ^97%. 1 2 7 . Figure 58. Typical stress-strain curve used in strain memory effect. 128. 100 80 STRAIN MEMORY —A-Q -O / PSEUDO-ELASTIC O 60 oc LU o 40 o LU oc 20 — ° - o - o ' A \ -100 -80 2. -60 -40 -20 TEMPERATURE °c Figure 59a. Strain memory recovery vs. temperature for #1. 129. T 100 80 60 or LU > o u UJ cr 40 20 STRAIN MEMORY V - o - o / O — o — o — PSEUDO-ELASTIC -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. Partial transformation to ^ takes place in the range A < T < A.. However, when the specimen is heated S 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 is either partially or fully martensitic to begin with, depending upon whether the temperature is above or not. 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 micro-scope. 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 in 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 is 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 21 the relative proportion 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 is 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 is difficult 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. The poles are clustered very close to [133]. A Thermal Martensite • Stress Induced Martensite Figure 61. Habit plane poles for thermal and stress-induced martensite. Shaded symbols represent theoretically calculated values. ( • ) is obtained using the actual values of lattice para-meters at -74°C. 135. 3.9.1.2 Habit Plane Poles f o r Stress-Induced Martensite The habit plane of stress-induced martensite was determined f o r several specimens and the plane normals are given i n figure (61). The t e n s i l e apparatus was used to keep the specimen stressed at the low temperature; and the angular measurements were made as before. There i s some scatter i n the habit plane normal; nevertheless, i t can be^ ; said that the plane normals are d i f f e r e n t from those determined f o r thermal martensite. The observed habit planes made varying angles (46-70°) with the t e n s i l e axis and did not l i e on the plane of maximum shear. 3.9.1.3 Habit Plane Determination f o r Deformation Martensite The deformation martensite was produced i n coarse grained poly-c r y s t a l l i n e specimens by cold r o l l i n g ^12% for the Ag-45 at. % Cd a l l o y and ^15% for the Ag-41 at. % Zn a l l o y . A f t e r r o l l i n g , t h e specimens were mechanically polished to remove the disturbed surface layer; and a second surface was polished at r i g h t angles to the f i r s t . This permitted a two surface analysis to be made. Figures (62a,b) shows the habit plane poles of the deformation martensite i n both Ag-Cd and Ag-Zn a l l o y s . In both cases the habit plane poles clustered very near the [110] corner of the stereographic t r i a n g l e . The figure also includes the orientations of the grains i n which martensite formed f i r s t . These poles are grouped near the [111] corner of the stereographic t r i a n g l e . I t i s important to r e c a l l at Habit planes are referred to the b.c.c. axes. 136. Figure 62a. Habit plane normals for deformation martensite i n Ag-45 at. % Cd a l l o y , shaded symbol represents the t h e o r e t i c a l value. Figure 62b. Habit plane normals for deformation martensite i n Ag-41 at. % Zn a l l o y . Shaded symbol represents the t h e o r e t i c a l value. 137. t h i s stage that during t e n s i l e t e s t i n g of s i n g l e c r y s t a l s , only c r y s t a l s o r i e n t e d c l o s e to the [111] corner showed any deformation martensite. This i s , t h e r e f o r e , i n agreement w i t h the observations on col d r o l l e d 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 Habit plane poles were c a l c u l a t e d based on the a n a l y s i s of 73 • Wechsler and Otte , a m o d i f i c a t i o n of the b a s i c WLR theory to face centred orthorhombic and body centred orthorhombic martensite s t r u c t u r e s . In t h i s a n a l y s i s the input data c o n s i s t s of the l a t t i c e parameters of the parent and product phases, the l a t t i c e correspondence and the plane and d i r e c t i o n of the l a t t i c e i n v a r i a n t shear. The l a t t i c e parameters used i n the a n a l y s i s are shown i n Table X I I I . The parameter of the g Table X I I I L a t t i c e parameters of g^ a n ^ orthorhombic s t r u c t u r e s of Ag-45 at. % Cd a l l o y S t r u c t u r e L a t t i c e Parameter A° i ^ ^ , at 25°C at -74°C D . C . C . a = 3.3206 a = 3.31432 o o at -196°C at -74°C a = 3.0904 a = 3.0968 orthorhombic 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 Mg 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 will 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 41 shear in thermo-elastic martensite in Cu-Zn alloys . 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 Stress-induced Martensite Lattice invariant shear (Oil)[Oil] (110)[110] Amount of microscopic shear g 0.053894 ,0585875 Habit plane pole 0.6768947 -0.2181258 0.7030184 ,713566 .148195 ,684734 Macroscopic shear direction +0.044247 -0.959821 -0.277102 ,670421 ,139228 ,728803 Magnitude of macroscopic shear 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 is 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 2 matrix and stress-induced martensite. The two photographs are very similar, with the positions of the close-packed planes in the two photo-graphs 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 in the -matrix and martensite. Table XV Orientation relationships between the principal planes and directions in the 3 and stress-induced martensite. hkl, hkl deg. b o [ 1 1 0 ] B A [ 0 1 0 ] Q 3.4 [ 1 1 0 J B A U 0 0 J O 2.6 [001], A [001] 3.6 b o (ioo) b A ( n o ) 0 4 (010), A (110) 2.6 b o 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. a = 3.3206 A° o f.c.t. (martensite) a = 4.3792 A° c = 3.8580 A° (2) Ag-41 at. % Zn: b.c.c. a = 3.1749 A0 o f.c.t. (martensite) a = 4.0413 A° c = 3.860 A° All parameters were determined at 25°C. The formulae given by Otte .74 and Massalski were used in the calculations. A (110) [HO] shear is implied in the formulae. 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, where <)> i s the a n g l e between the t e n s i l e a x i s and the h a b i t p l a n e normal and X i s the a n g l e between the t e n s i l e a x i s and the m a c r o s c o p i c shear d i r e c t i o n . (b) t h a t such a v a r i a n t w i l l y i e l d a p o s i t i v e s t r a i n i n the d i r e c t i o n of s t r e s s . The c o n d i t i o n f o r a maximum r e s o l v e d shear s t r e s s on the secondary Q L a t t i c e i n v a r i a n t ) shear system cannot be used i n t h i s c a s e, because a l l the d i f f e r e n t o r i e n t a t i o n s o f the t e n s i l e a x i s c o n s i d e r e d a r e e q u i v a l e n t and w i l l g i v e the same r e s o l v e d s h e a r s t r e s s component. T h i s i s s u p p o r t e d by the e x p e r i m e n t a l d a t a on 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 g i v e n i n T a b l e XVI. In a l l cases, t h a t h a b i t p l a n e p o s s e s s i n g a near maximum v a l u e f o r the r e s o l v e d shear s t r e s s i s the one a s s o c i a t e d w i t h m a r t e n s i t e . 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 i s a s s o c i a t e d w i t h a m a c r o s c o p i c shear which i s c a l c u l a t e d from the WLR t h e o r y . I t i s t h i s shear, t h a t i s r e s p o n s i b l e f o r the i n c r e a s e i n l e n g t h d u r i n g the f o r m a t i o n o f m a r t e n s i t e i n t e n s i o n , thus g i v i n g p s e u d o - e l a s t i c e f f e c t . F i g u r e (65) X A B 6 Y F i g u r e 65. G e o m e t r i c a l c o n s t r u c t i o n t o c a l c u l a t e the t e n s i l e s t r a i n i n v o l v e d i n the t r a n s f o r m a t i o n . 145. Table XVI Comparison between the observed and calculated values of <f> (angle between habit plane normal and the tensile axis) Tensile <j> Possible <j> cos<j> cosA axis Observed tensile Calc. axis <^119> 42° 119 39.5° .487 40° 119 52.1° .488 119 42.4° .478 119 54.4° .470 <^265> 69° 265 69° .184 265 60.5° .090 265 44.6° .129 265 82.1° •^ <115> 55° 115 34.4° .450 115 56.6° .442 115 39.8° .460 115 60.5° .355 <^5,10,16> 65° 5,10,16 33° .290 5,10,16 64° .317 5,10,16 46° .334 5,10,16 73° .249 <^5,7,13> 62° 5,7,13 31.3° .353 5,7,13 42.1° .384 5,7,13 61.8° .364 5,7,13 69.0° .314 gives the geometrical construction involved. The i n i t i a l position of the specimen is x Y V U 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> •^ g - 2 sxnzvb tany. i.e.,strain = sin2tj> tany In this analysis, it is 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 1 4 7 . BE defines this component and is 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 restric-tion 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 : Habit Plane Normal. p Tensile Axis. s ; Normal to Plane of Shear. t Normal to Plane of Tension. S Macroscopic Shear Direction. gS = A np X = A Sp a = A ts Figure 66. 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 is possible near the 1001] corner and the minimum value is 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. Figure (68) shows the corresponding strain values. 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 in the strain associated with the transformation. This also explains why there should be a change in the microstructure as the specimen is stressed below (refer fig. (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 will not provide significant elongation (figure (68)), whereas a change to stress-induced martensite will 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 stereo-graphic triangle, with the 1111] orientation being least favourable. Specimens strained beyond the limits given in figure (67) will 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 will be reversible. The theory is in excellent qualitative agreement with the observations in figure (52), which shows that pseudo-elasticity is a maximum for orientations close to [001], is 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]. This is true in both cold rolled and tensile specimens. It is precisely this orientation that has the least pseudo-elasticity so that at small strains complete trans-formation to stress-induced martensite will occur. If i t is considered that the stress-induced martensite is 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] will have deformation martensite and other orientations will only have stress-induced martensite present. Only one section of the results cannot be completely explained with the present theory. This is the increase in pseudo-elastic elongation obtained at higher temperatures. Between and M + 30°C, martensite forms in bursts. At higher temperatures the formation is more gradual and gives pseudo-elastic strains ^50-100% higher than the burst martensite. There is, however, no change in the habit plane of the martensite, just a change in its morphology. No clear explana-41 tions for this effect can be given. Ahlers and Pops suggest that thermoelastic martensite differs from burst martensite in 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 is 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 is very similar to the one proposed by Lieberman^ for Au-Cd alloys. The (Oil), plane is distorted according to the Bain distort D • C • C • tion and a further shuffling of atoms in the intervening planes is necessary to complete the structure. On further deformation, a close-packed structure can be generated in two ways depending on the cadmium concentra-tion. (a) High Cd alloys: The (Oil) plane of the original cube lattice is 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 sit in the valleys above the close-packed plane; thus consti-tuting 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' is close-packed hexagonal. Therefore i f subsequently a disordering transformation takes place, for example, by plastic deformation then the resulting structure is 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 is the same as above. On further deformation, the shuffling is considered to take place in opposite directions in the intervening layers immediately above and below. This generates a structure of the AuCu (Ll o) type. This is a structure based on a face centred cubic lattice in which alternate C 0 0 2 ) layers contain atoms of one element. This results in some tetra-gonality in the structure. There is 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 A / r , = .97) and in Ag-Zn c/a = 0.955 (r A /r^ = 1.085) Ag Cd Ag Zn 26 and these values are quite reasonable for AuCu type structures If the order of the structure is destroyed, then i t will become true face centred cubic. This change is 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 its formation. The high dislocation density in the martensite as observed by electron microscopy confirms this yiew. The habit plane will 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 1 i i i i u 70 60 50 40 30 2 0 deg. Figure 71. X-ray diffractometer trace of f i l e d specimen (Ag-45 at. % Cd) at l i q . N 2 temperature. Planes are indexed based on f.c.c. structure. 157. Read theory should s t i l l be applicable as found experimentally. According to the above discussion, the orthorhombic lattice is only a transitional one and the final structure is 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 is insufficient for the complete transformation and external energy in the form of deformation is necessary. That the fa,ce centred cubic structure is the most stable one is 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, indicat-ing that no further transformation has taken place. Mechanical deforma-tion is not expected to lower Mg to such an extent as to prevent the thermal martensite formation. The absence of thermal martensite makes the two stage transforma-tion mechanism inapplicable in the case of Ag-Zn alloys. The reasons for the absence of a martensitic transformation in this system, which is analogous to Cu-Zn, Ag-Cd and Au-Cd systems, are not quite clear. However, i t is 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 tempera-tures. The Mg varies approximately 35°C/at. % Cd. There is 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 cell. 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 is 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. The product structure can be detected after about 15% strain. 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 close-packed 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 is 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 Mg. (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 is due to SIM formation; below M to a s s s change in the morphology of the existing martensite. This difference in structure below Mg 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 is found that the only difference between thermal and stress-induced 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 is 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 transformation d i s t o r t i o n i s given by ? 1 = RBP (1) where P = L a t t i c e i n v a r i a n t shear B = Bain d i s t o r t i o n R = Rotation The two matrices B and P can be expressed i n simple terms i n d i f f e r e n t systems of axes given below. The Bain d i s t o r t i o n B can be expressed as (diagonal ri^, r ^ ' I3) > i - n t n e system of axes, [T], along which the Bain d i s t o r t i o n takes place i . e . B I T ] -n-L 0 0 0 n 2 0 0 0 n 3 (2) The r e l a t i o n between the o r i g i n a l cubic axes [B] and the [T] system of axes can be obtained from the assumed l a t t i c e correspondence. In transformations involving a t r a n s i t i o n from b.c.c. to f.c.o. or f . c . c . to b.c.o., t h i s correspondence can be expressed as r 1 [ T / B ] = 1//2 -1//2 0 1//2 1//2 0 0 0 1 (3) as seen i n figu r e (63). The values of n^, n2» I3 c a n be calculated from 162. the lattice parameters of the two structures involved, viz. = b/»/2ao, n 2 = c/Jla , = a/a0* The shear is best represented in a coordinate system, [g], given by the shear direction IJ [U^, U2, U^], the normal to the shear plane V [V1, V2, V3] and the vector defined by U x V = W [W , Wj, Wj]. If g is the amount of shear, then the matrix representing the shear is given by P[g] = 1 g 0 0 1 0 0 0 1 (4) The original cubic system, [B], and the shear axes system are related by the following equation r 2 ( g / s ) = U 1 2 V 1 2 wn W 1 2 ( 5 ) 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 1 5 u 2 , u 3 ] V = [v 1, v 2, v 3] W = [vv w2, w 3J The [T] and [g] systems are in turn related by the expression u i U2 53 r 3[g/T] = \ 2^ 3^ (6) w2 w3 1 6 3 . The Bain distortion and the lattice invariant distortion P together generate an undistorted habit plane. This is possible i f and only i f the three eigenvectors of the matrix F = BP are such that X^  = 1, X2 > 1 and X^ < 1, where X^, X2 a n a 3^ a r e t n e eigenvalues of the matrix F. In general i t is convenient to form the symmetric matrix J = F'F (where F' is the transpose of F), and the eigenvalues of the 2 2 2 1 2 3 matrix J correspond to X^  , X2 and X^  • The eigenvectors R , R , R corresponding to the three eigenvalues form an orthogonal system of coordinates [d]. The condition that one of the eigenvalues of the matrix J is equal to one results in a quadratic equation in g: Ag2 + Bg + C = 0 (7) 2 2 - 2 - 2 where A = Er^ (n 2 v 3 - \ ) B = -21 u l v 1 ( n 1 2 + n 2 2 n 3 2 ) c = (l - n i 2 ) ( l - n 2 2 ) ( l - n 3 2 ) The solution to equation (7) gives the values g^ and g2» The remaining 2 2 eigenvalues X2 , X^  can be determined from the quadratic equation: X^4 + (1 - ty^X* + * 3 = 0, (8) a = 2, 3 2 2-2 - -where if^ = Er^ (g \]± + 2gu 1v 1 + D 2 2 2 * 3 = n l n2 n 3 164. The undistorted vectors R are given by the following expressions: £ 1 2 2 2 2 - - 3 2 - -x [g] = -£ [z(n2 n 3 + A^ n-L )u1w1 - gE n 2 n 3 v1w1l £ 1 2 2 2 2 - - 2 2--y [g] = [z(n2 n 3 + A^ ^ )v1w1 + gx£ E T ^ u ^ l z [g] = . N ~l [ Z ( n 2 2 n 3 2 + n i 2 > w i 2 - + 1], £ = 1 1 r v / 2 2 . . 2 2,- 2 .2 2 2 2, -I t E ( n2 n3 + A£ n i ) W1 " \ ~ \ n2 n3 ]> N £ = 2 , 3 (9) where is the normalisation factor. In the system [d], the matrix J takes the form J[d] = 2 0 2 0 0 A 2 0 0 0 (10) 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 = X ' X in the d system. i.e. x'Jx = x'x 0 0 0 0 0 A -x = 165. Expanding we get (X 1 2 - l ) X l 2 + (A 2 2 - l ) x 2 2 + (A 3 2 - l ) x 3 2 = 0 (11) where the vector x is expressed in the [d] system. Since A^  = 1, equation (11) becomes (1 - A/) (A2 - 1) setting x 3 = 1, x = 5 K where K = z K. (i - x / ) 1 / 2 (*o - !) 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 [0,6K ,1] [0,1,5RK] or the unit normal is given as n[d] = ( 1 + K 2 ) 1 / 2 0 1 6K K (12) This vector can be expressed in terms of the original cube axes as follows: 166. n[B] ; = r 2'[B/g] r 4'[g/d] n[d] (13) The c a l c u l a t i o n s are much s i m p l i f i e d when Wr = 1 (Wg = 0» Wt = 0) > a n d s i m p l i f i e d expressions are a v a i l a b l e to ca l c u l a t e n[B] d i r e c t l y . When W 4 1 5 the c a l c u l a t i o n s are very involved and cumbersome. Calcul a t i o n of Rotation Matrix: Consider any two vectors p and a l y i n g i n the habit plane (e.g.., take the vector product of 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' re s p e c t i v e l y (p' and a' have t h e i r magnitudes unchanged by v i r t u e of the fa c t that p and a l i e i n the habit plane). The r o t a t i o n axis and the amount of ro t a t i o n necessary to leave the habit plane unrotated are given by Euler's theorem: [Pi - pJ, X \°\ - °j - u tanCf) : (14) La - a J • Lp + p J — ^ Where _u i s the axis of r o t a t i o n , and the magnitude i s the tangent of the h a l f angle of ro t a t i o n . Knowing u j u ^ ^ . u ^ ] and 0 , the r o t a t i o n matrix, R, can be 12 calculated using the expression 167. R [ B ] = [u^ (1-cose) + cos6], [ u 1 u 2 ( l - c o s 6 ) - u sin6],-[u^u^Cl-cose) + ursine] [ u 2 u 1 ( l - c o s 8 ) + l y s i n e ] , [ u 2 (l-cos0)+ cos6], [u 2u 3(l-cos0) - ursine] [ u 3 u 1 ( l - c o s 9 ) - u 2 s i n 8 ] , [ u 3 u 2 ( l - c o s 6 ) + u^sin©], (15) [ u 3 (1-cosO) + cos9] C a l c u l a t i o n of Macroscopic Shear: The u n i t v e c t o r n.[B] normal to the h a b i t plane transforms to n_^[B] where n^B] = [RBP] n[B] (16) The d i r e c t i o n of displacement i s given by the v e c t o r n [B] - n[B] = S N n r rl 1 Habit Plane 0 168. The magnitude of the macroscopic shear angle is given by the relation tany (17) 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 : 2nn 2 . 2 . 2 2 . / . 2 2 + n 2 _ 2n1 n 2 / ~ n i •~-n2 l - n. 1 - n. } n. 2n, •2 . 2 . 2 2 n2 ~ n i n2 l - n. 1 - n J n. 1 " r)' where n [n^n^n^] represents the habit plane pole. n^ = a/a^-Jl , n „ = c/a where a is 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 Magnitude Shear System of Sec. Shear Habit Plane Normal Macroscopic Shear Direction Amount of Rotation (110)[110] .0585875 .657825 .164888 .734900 .083680 .017378 -.090967 7.11c (011)[011] .053894 1.0735 0.9315 .6768947 .2181258 .7030184 .0442469 -.9598211 -.2771021 2.26c (011)[311]* .05002 1.1172 0.8951 .428544 .513585 .743357 (112)[111] .04527 ,615107 ,406035 ,675854 .379991 .598390 -.705363 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 of ty was 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 cosa _S x n H * £ = s • t Tables B-1,2 give the calculated values of strain for various orienta-tions 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° [p] COS(j> cos<j> cosA cosa Strain 001 .685 .499 1.0 6.23 Oil .589 .246 0.516 3.06 Oil .379 .233 - -111 . 722 .082 .165 1.02 111 .069 .050 - -012 .679 ' .400 ' .803 4.99 102 .932 .328 - -012 .546 .390 .853 4.86 112 .911 .241 - -112 .790 . 299 .617 3.73 112 .328 .266 - -122 .317 .195 - -122 .793 .134 - -122 .596 .212 .442 2.64 212 .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 _ _ 173. Table B-l (Continued [p] costy c o s t } ) c o s A c o s a Strain 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 .349 2.15 334 .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 3.72 174. Table B-l (Continued) [p] COS<f> cos<J> cosX cosa Strain 265 .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 5.56 137 .589 .411 - -137 .659 .416 .830 5.13 137 .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 5.3.1 1,4,10 .644 .427 1,4,10 .754 .422 175. Table B-l (Continued) [p] COS(j) cos<)> cosA cosa Strain 1,3,15 .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. 78 176. Table B-2 Calculated values of strain for thermal martensite. Value of y = 2.26039° [p] COS(j> cos<}> cosX cosa Strain % 001 .705 .195 \ .434 0.8 Oil .345 .302 .948 1.21 Oil .652 .315 .599 1.17 110 .631 .448 .882 1.70 110 .323 .209 - -111 .671 .465 .970 1.90 II I .143 .053 - -112 .762 .458 .979 1.91 211 .750 .352 - -II2 .389 .057 - -121 .386 .339 - -113 .369 .204 - -113 ; .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 .6413 1.25 105 .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 1.29 177. REFERENCES ' ' 1. Lieberman, D.S., Phase Transformations,A.S.M. Seminar, 1970, 1-58. 2. Kaufman, L.:, Cohen, M. , Progress i n Metal Physics, Vol. 7, Ed. Chalmers, B., King, R., Pergamon Press, 1958, 179. 3. Chang, L.C., Read, T.A., Trans. 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