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Morphology, structure and growth kinetics of bainite plates in the β' phase of A Ag-45 AT. PCT Cd Alloy Kostić, Miodrag Miloš 1977

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MORPHOLOGY, STRUCTURE AND GROWTH KINETICS OF BAINITE PLATES IN THE 3' PHASE OF A Ag-45 AT. PCT Cd ALLOY  by MIODRAG MILOS KOSTIC D i p l . Ing./ U n i v e r s i t y o f Belgrade, 1963  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  i n the Department of METALLURGY  We accept t h i s t h e s i s as conforming t o the r e q u i r e d standard  THE UNIVERSITY OF BRITISH COLUMBIA JULY, 1977 ©  Miodrag Miloa Kosti& 1977  In  presenting  this  an a d v a n c e d  degree  the  shall  I  Library  f u r t h e r agree  for  scholarly  by h i s of  this  written  at  thesis  make  it  freely  that permission  purposes  for  may It  is  University  British  July 8/77  British  by  for  gain  Columbia  shall  the  that  not  requirements  Columbia,  I agree  r e f e r e n c e and copying  t h e Head o f  understood  Metallurgy of  of  for extensive  permission.  of  fulfilment of  available  be g r a n t e d  financial  2075 Wesbrook Place Vancouver, Canada V6T 1W5  D a t e  in p a r t i a l  the U n i v e r s i t y  representatives.  Department  The  thesis  of  or  that  study.  this  thesis  my D e p a r t m e n t  copying  for  or  publication  be a l l o w e d w i t h o u t  my  ABSTRACT The  morphology of b a i n i t e p l a t e s and  needles formed i n ordered bcc  6* phase o f a Ag-45 a t .  pet Cd a l l o y at temperatures 160-320° C was o p t i c a l and  widmanstatten  scanning e l e c t r o n microscopy.  studied  by  Both p r e c i p i t a t e  forms were s i m i l a r i n appearance t o p r e c i p i t a t e s r e p o r t e d f o r Cu-Zn a l l o y s . various  The  s t r u c t u r e o f the b a i n i t e p l a t e s i n the  stages of t h e i r growth was  and by t r a n s m i s s i o n  s t u d i e d by X-ray  e l e c t r o n microscopy. I n i t i a l l y ,  diffraction the  formed w i t h a 3R s t a c k i n g f a u l t modulation of the fee and  contained  The  s t a c k i n g f a u l t s annealed out d u r i n g a prolonged  treatment and fee.  The  a high d e n s i t y of random s t a c k i n g  b  1.1°  as f o l l o w s :  from [100]f and [lll] . f  p l a t e s , determined by two (144) . b  The  The  [lll]  [011]  The  isothermal  b  b  4.3°  0.7°  from the  surface r e l i e f  of the p l a t e s was I t was  f e a t u r e s of the t r a n s f o r m a t i o n  of the Bowles-Mackenzie theory  and  [0ll] , f  stacking  h a b i t plane of the b a i n i t e close  observed by  i n the form of a simple  i n d i c a t i n g an i n v a r i a n t plane s t r a i n  The  from  s u r f a c e t r a c e a n a l y s i s , was  the i n t e r f e r e n c e microscopy. tilt  faults.  o r i e n t a t i o n r e l a t i o n s h i p between the bcc m a t r i x  f a u l t plane pole  to  structure  the s t r u c t u r e g r a d u a l l y changed to a r e g u l a r  the fee b a i n i t e was [110]  plates  transformation.  agreed w i t h the  o f martensite  predictions  formation.  growth k i n e t i c s o f both b a i n i t e p l a t e s  widmanstatten needles were measured by i n t e r r u p t e d  and annealing  and scanning e l e c t r o n microscopy.  Using the b a i n i t e  t h i c k e n i n g k i n e t i c s measured a t 160, Frank-Zener  200  and 240°C, the  model f o r growth o f p l a n a r p r e c i p i t a t e s ,  and  s u p e r s a t u r a t i o n data o b t a i n e d from the Ag-Cd metastable phase diagram D e  enabled the e f f e c t i v e chemical  diffusivities,  f f # t o be c a l c u l a t e d f o r the t h r e e t r a n s f o r m a t i o n temper-  atures.  The r e s u l t s were i n good agreement w i t h the expected  diffusivities. at  The l e n g t h e n i n g k i n e t i c s of b a i n i t e p l a t e s  160°C and o f widmanstatten  needles a t 240°C were analyzed  u s i n g T r i v e d i ' s model f o r d i f f u s i o n - c o n t r o l l e d growth. D f f e  o b t a i n e d from the l e n g t h e n i n g k i n e t i c s o f the needles was good agreement with the D  er f  value o b t a i n e d from the  ening k i n e t i c s o f the p l a t e s , i n d i c a t i n g t h a t  in  thick-  widmanstatten  needles lengthened and b a i n i t e p l a t e s t h i c k e n e d a t r a t e s c o n t r o l l e d by volume d i f f u s i o n .  Bainite plates  only i n the e a r l y stage of growth and a t a r a t e  lengthened approximately  180 times l a r g e r than t h a t p e r m i t t e d by volume d i f f u s i o n . I t was  concluded t h a t the morphology, s t r u c t u r e and o t h e r  c h a r a c t e r i s t i c s of the f r e s h l y formed b a i n i t e p l a t e s were c o n s i s t e n t with t h e i r f o r m a t i o n by a t h e r m a l l y a c t i v a t e d m a r t e n s i t i c process.  iii  TABLE OF CONTENTS CHAPTER 1  PAGE THE INTRODUCTION 1.1.  3  ...... .  1  N u c l e a t i o n and Growth Transformations and M a r t e n s i t i c Transformations  1  1.2.  B a i n i t i c Transformations  5  1.3.  M a r t e n s i t e and B a i n i t e i n Cu- and Ag-Based Alloys  1.4. 2  .....  Aim o f the Present Work  8  11  EXPERIMENTAL . . .  13  2.1.  Preparation of A l l o y s  13  2.2.  Quenching  15  2.3.  E l e c t r o l y t i c P o l i s h i n g and T h i n n i n g . . . .  I  2.4.  X-Ray A n a l y s i s  1  8  2.5.  Surface R e l i e f  1  9  2.6.  H a b i t Plane Measurements  19  2.7.  E l e c t r o n Microscopy  21  2.8.  Growth K i n e t i c s Measurements  22  »  . RESULTS AND DISCUSSION 3.1. 3.2.  Morphology o f P r e c i p i t a t e s Formed d u r i n g Quenching  8  25 25  Morphology o f P r e c i p i t a t e s Formed d u r i n g Isothermal A n n e a l i n g  27  3.3.  X-Ray S t r u c t u r e A n a l y s i s  35  3.4.  Surface R e l i e f  4  1  3.5.  B a i n i t e H a b i t Plane Measurements ......  4  4  iv  CHAPTER  PAGE 3.6.  3.7.  3.8.  3.9.  T r a n s m i s s i o n E l e c t r o n Microscopy R e s u l t s . . 3.6.1.  Morphology and S t r u c t u r e  o f B a i n i t e 46  3.6.2.  Orientation Relationship  61  A p p l i c a t i o n o f the Phenomenological M a r t e n s i t e Theory t o the Formation o f Bainite  67  Comparison w i t h the M a r t e n s i t i c Products Observed i n Ag-Cd, Ag-Zn and Cu-Zn Alloys  73  O r i g i n and S t a b i l i t y o f the 3R Structure  of Bainite  75  3.10. Growth K i n e t i c s 3.10.1. 3.10.2.  78  A n a l y s i s o f B a i n i t e Thickening Data A n a l y s i s o f B a i n i t e Lengthening Data  3.10.3.  A n a l y s i s o f Widmanstatten Lengthening Data  3.10.4.  Discussion  3.10.5. 4  44  79 96 102  o f the Growth  K i n e t i c s Results  105  General D i s c u s s i o n  108  CONCLUSIONS  110  SUGGESTIONS FOR FUTURE WORK  112  APPENDIX A - S t r u c t u r e A n a l y s i s  113  A.l.  A. 2.  D i s t o r t i o n o f the FCC R e c i p r o c a l L a t t i c e due t o a High D e n s i t y o f Random S t a c k i n g F a u l t s  117  Long P e r i o d S t a c k i n g Order Modulation o f the FCC L a t t i c e .... 118  v  CHAPTER  PAGE  APPENDIX B <* A n a l y t i c a l Treatment o f M a r t e n s i t i c Transformations  125  APPENDIX C - Theory o f the Volume D i f f u s i o n C o n t r o l l e d P r e c i p i t a t e Growth  139  Cl.  139  Thickening of Plates  C.2. Lengthening o f P l a t e s and Needles APPENDIX D - An estimate o f the Chemical D i f f u s i v i t y i n the g ' Phase o f Ag-Cd A l l o y s on the B a s i s of a Comparison between the Cu-Zn and Ag-Cd Systems  144  APPENDIX E - The E q u i l i b r i u m and the Metastable Ag-Cd Phase Diagram  148  REFERENCES  151  vi  140  LIST OF TABLES  vii  TABLE A-1  PAGE . Calculated Relative Intensities,  • •2 |F| , f o r  the 3R Modulation o f the CuAu I-type S t r u c t u r e Based on Equations • f o r k - 0, 1, -1. B-I  (A-3) and (A-4) ..  123  A p p l i c a t i o n f o r t h e Bowles-Mackenzie M a r t e n s i t e Theory t o t h e 3' t o a T r a n s f o r m a t i o n i n the Ag-45 A t . P e t Cd A l l o y - Summary o f the Used Data and R e s u l t s  viii  I  3  6  LIST OF FIGURES FIGURE 1.  PAGE The Relevant P o r t i o n o f the Ag-Cd E q u i l i b r i u m • Phase Diagram. Dotted L i n e s I n d i c a t e Compos i t i o n o f the A l l o y s Used  2.  14  Schematic Diagram o f the I n d u c t i o n Heating and Quenching Apparatus.  3.  16  B a i n i t e P l a t e s and Massive ot i n the B' m a t r i x m  of  a Ag-46 a t . Pet Cd A l l o y Quenched from  600°C.  The Quenching Rate was  I n s u f f i c i e n t to  R e t a i n the Untransformed 0' Phase, R e s u l t i n g i n Formation o f B a i n i t e the  4.  Quenching Rate,  ( a ) . Upon Decreasing  F i r s t Formed on G r a i n  Boundaries  (b), and Then i n the I n t e r i o r o f  the  (c) .  Grains  26  A Scanning E l e c t r o n Micrograph o f the Edge (Included Angle o f Approximately 90°) o f a s e v e r e l y Etched Specimen o f Ag-45 a t . Pet Cd A l l o y Annealed f o r 1,225  Seconds a t 200°C.  Both Widmanstatten Needles and B a i n i t e P l a t e s are V i s i b l e . 5.  Bainite Plates  28  (a) and a Mixture o f B a i n i t e  P l a t e s and Widmanstatten Needles (b)formed i n a Ag-45 a t . Pet Cd A l l o y During A n n e a l i n g at for  160°C f o r 57,600 Seconds 1,225  Seconds  (b).  ix  (a) and a t 200°C 3 0  A Mixture of B a i n i t e Plates  and Widmanstatten  Needles Formed i n a Ag-46 a t . Pet Cd A l l o y During A n n e a l i n g a t 200°C f o r 25,600 Seconds. Most P l a t e s Degenerated t o Needles Isomorphous w i t h the Widmanstatten Needles.The Broad Faces o f the P a i r o f P l a t e s  i n the  Centre are Approximately P a r a l l e l t o the , Plane o f P o l i s h Bainite Plates  i n Ag-45 a t . Pet Cd A l l o y  Formed A f t e r Approximately 2 s a t 280°C. .. The V a r i a t i o n o f B a i n i t e P l a t e Morphology i n D i f f e r e n t M a t r i x Grains A n n e a l i n g Temperature 160°C; A n n e a l i n g Time 12,600 s ( a ) , 25,600 s (b), and 57,600 s ( c ) . A n n e a l i n g Temperature 200°C; A n n e a l i n g Time 529 s ( a ) , 900 a (b), and 2,116  s (c)  A n n e a l i n g Temperature 240°C; A n n e a l i n g Time 25 s ( a ) , 64 s (b), and 144 s ( c ) . Interference  Micrographs o f the S u r f a c e R e l i e f  Caused by. Formation o f B a i n i t e P l a t e s Interference Caused  Micrographs o f Surface R e l i e f  by Formation o f Widmanstatten  Needles  x  PAGE  FIGURE 14.  P o r t i o n o f the Standard  [001]^ S t e r e o g r a p h i c  P r o j e c t i o n o f the M a t r i x Showing the Measured H a b i t Plane P o l e s o f B a i n i t e P l a t e s During A n n e a l i n g a t 240°C. Below the [011]^ Pole  Measurements.  The C i r c l e  (radius  3.5°) Encompasses Two T h i r d s  Formed  approximately of A l l  The C i r c l e Above the  [011]j  3  P o l e Has the Same S i z e and i s Centered i n the C r y s t a l l o g r a p h i c a l l y Equivalent Respect t o the [ 0 1 1 ]  b  Pole.  P o s i t i o n With  The Poles Marked  With Numbers Belong t o I n d i v i d u a l P l a t e s i n P a i r s , e.g., 31 and 31a.  Joined  The Open T r i a n g l e  Represents the T h e o r e t i c a l H a b i t Plane P o l e [0.180747; 0.667566; 0.722279] 15.  Bainite Plates  16.  (See S e c t i o n  3.7).  45  i n a Ag-45 a t . Pet Cd A l l o y  A f t e r 15,900 s a t 160°C (Dark F i e l d )  b  (a,b) and 36 s a t 240°C T . 47  (c)  S e l e c t e d Area D i f f r a c t i o n P a t t e r n  of a Bainite  P l a t e A f t e r 15,900 s a t 160°C. The s t r u c t u r e i s 3R 17.  4  8  B a i n i t e i n a Ag-45 a t . Pet Cd A l l o y A f t e r 19,800 s (a) and 25,600 s (b) a t 160°C  xi  50  FIGURE 18.  PAGE S e l e c t e d Area D i f f r a c t i o n P a t t e r n s o f B a i n i t e i n a Ag-45 a t . Pet Cd A l l o y A f t e r 19,800 s (a) and 25,600 Note the Appearance  s (b) a t 160°C.  o f f e e Spots and  Dissapearance o f 3R Spots 19.  Changes i n the D i f f r a c t i o n P a t t e r n s Due t o the 3R t o f e e S t r u c t u r e T r a n s f o r m a t i o n  20.  52  54  Micrographs o f a B a i n i t e P l a t e A f t e r 900 s a t 240°C.  Note That the S t a c k i n g F a u l t i n the  Upper Righthand Corner i n (a) Disappeared in  (b) L e a v i n g a D i s l o c a t i o n Resolved i n t o  Two P a r t i a l s 21.  (A)  56  Micrograph o f a B a i n i t e P l a t e A f t e r 900 s a t 240°C  22.  57  Micrograph o f a B a i n i t e P l a t e A f t e r 900 s at 240°C  23.  5  8  6  0  Micrographs o f B a i n i t e P l a t e s A f t e r 900 s a t 240°C.  The P o r t i o n s w i t h Zero S t a c k i n g F a u l t  D e n s i t y Thickened F a s t e r Than the Rest o f the P l a t e s 24.  S e l e c t e d Area D i f f r a c t i o n P a t t e r n Composed of  (111)^ and ( 0 1 1 )  f  Reciprocal Lattice  Planes  62  xii  Schematic S t e r e o g r a p h i c P r o j e c t i o n Diagram o f the O r i e n t a t i o n the  3' Parent and  Relationship Bainite.  Between  The  Bainite  L a t t i c e i s Indexed i n Cubic N o t a t i o n ; Although the  [lllJ  and  b  Here Shown to C o i n c i d e , Approximately 0.7° The  [Qll]  f  P-oles are  They Are  Actually  Appart  Composite M a t r i x - B a i n i t e D i f f r a c t i o n  Patterns  (a,b)  Obtained from the  Branches  of the Chevron Shown i n ( c ) . Orientation  Relationship  Bainite Plates The  (I and  Between the II) and  I 1  Matrix.  Normal t o the P r o j e c t i o n i s P a r a l l e l  the O p t i c a l A x i s i n F i g . 26. p  the  Two  and P ^  1  1  and P !  11  =  P o l e s Marked  are the T h e o r e t i c a l H a b i t Plane  Boles of the P l a t e s are p ^  to  I and  I I . Their  Indices  [-0.667566; -0.180774; 0.722279] =  b  [0.722279; -0.180747; -0.667566] . b  O p t i c a l Micrographs o f L i g h t l y Etched S u r f a c e o f a Ag-45 a t . Pet Cd Specimen Annealed a t 200°C. (a) A f t e r 625  s: a Number o f Chevron  Shaped B a i n i t e Traces Appeared w i t h O c c a s i o n a l Widmanstatten Needle (A). A f t e r 900  an (b)  s: : B a i n i t e Traces Present i n  (a)  Have E i t h e r Maintained t h e i r O r i g i n a l Length  xiii  o r Have Lengthened  S l i g h t l y , but A l l Have  Increased T h e i r T h i c k n e s s .  The T i p s o f Some  o f the P l a t e s A p p a r e n t l y A c t e d as N u c l e a t i o n S i t e s f o r Widmanstatten  Needles(B).Widmanstatten  Needles Continued t o Lengthen. B a i n i t e Traces Appeared  (C) .  A Number o f  New  (c) A F t e r l,225:;s:  The Same Behavior i s Continued; O l d B a i n i t e Traces Thicken and New While Widmanstatten Impinged Upon  Ones Keep Appearing,  Needles Which Have Not  other P r e c i p i t a t e s Continue  t o Lengthen Scanning E l e c t r o n Micrographs o f the  Unetched  Surface o f a Ag-45 a t . pet Cd Specimen Annealed a t 240°C.  (a) A f t e r 16 s: A B a i n i t e  Chevron  Appeared.  (b) A f e r 36 s: The Lower Arm o f the  Chevron Erom (a) Dad Not Lengthen Although i t Thickened A p p r e c i a b l y , While Traces o f P l a t e s Appeared  New  from the L e f t , the Lower  One  Stopping Before Impinging Upon the O r i g i n a l Plate,  (c) A f t e r 49 s: T h i c k e n i n g Continued  Without Lengthening Scanning E l e c t r o n Micrographs o f a P a i r o f B a i n i t e P l a t e s i n a Ag-45 a t . P e t Cd A l l o y Showing T h e i r E a r l y Growth a t 160°C.  Both Lengthening  T h i c k e n i n g are V i s i b l e .  xiv  and  FIGURE 31.  Scanning E l e c t r o n Micrographs Showing Thickening  o f the Trace o f a B a i n i t e  P l a t e a t 240°C i n a Ag-45 a t . p e t Cd Alloy.  ....................................  32.  Thickening  Kinetics of a Bainite  Plate  33.  Trace a t 200°C i n a Ag-45 a t . p e t Cd A l l o y . . 2 The X U 6 v - . t p l o t f o r the B a i n i t e P l a t e a  Trace From F i g . 3 2 * 34.  Schematic R e p r e s e n t a t i o n o f the Dependence o f the P l a t e Trace Width, 2X , on the Angle fc  Between the P l a t e and the Specimen  Surface,  a, and on the P l a t e T h i c k n e s s , T^ ( s i n a =  V t>--  •  2x  35.  Thickness o f P l a t e Traces a t a Given Growth Time P l o t t e d As a F u n c t i o n  o f the Angle  Between the P l a t e and the Specimen  Surface,  a. § Angle a C a l c u l a t e d Assuming That the Growth Rate was the Same f o r A l l P l a t e s and That P l a t e No.6 was P e r p e n d i c u l a r Surface o f the Specimen. •  t o the  Angle a  Measured by S e r i a l D i s s o l u t i o n . The Numbers Refer t o the 240°C B a i n i t e P l a t e s i n Table V 36.  L o g D £ £ V6. 1/T f o r a Ag-45 a t . p e t Cd A l l o y . . e  xv  PAGE  FIGURE 37.  Schematic  Diagram o f a P a i r o f B a i n i t e P l a t e s  Which Nucleated i n the I n t e r i o r o f t h e Specimen a t P o i n t N, Emerged on the S u r f a c e of O b s e r v a t i o n a t P o i n t E and Formed t h e Trace ABC a t Time t ( a ) , and Lengthening K i n e t i c s o f t h e Trace EC (b) 38.  Lengthening  9  K i n e t i c s a t 160°C o f B a i n i t e 99  P l a t e Traces i n a Ag-45 a t . p e t Cd A l l o y . . . 39.  7  Scanning E l e c t r o n Micrographs  Showing t h e  Growth o f a Widmanstatten Needle (a) and l e n g t h e n i n g K i n e t i c s o f Widmanstatten Needles  (b) i n a Ag-45 a t . p e t Gd A l l o y  a t 240°C. A-1  103  S t a c k i n g Sequence o f C l o s e Packed  [111]^  L a y e r s i n the f e e Lattice.Atoms A a r e i n the Plane o f the Drawing; the Layer Beneath Has Atoms i n C P o s i t i o n s , the Layer Above in B Positions.  The Shear V e c t o r s R o f a  S t a c k i n g F a u l t are I n d i c a t e d i n t h e Diagram. A-2  (101)  f  H4  R e c i p r o c a l L a t t i c e Plane w i t h Twinned  L a t t i c e Spots.  The Plane C o n s i s t s o f Rows  o f R e f l e c t i o n s w i t h S u c c e s s i v e Phase S h i f t s 0, 2ir/3 and - 2 T T / 3 ,  Every T h i r d Layer  Having  the Same Phase S h i f t . S t a c k i n g F a u l t s on (111)^ Plane Cause Broadening  and D i s p l a c e -  ment o r S p l i t t i n g o f Spots w i t h $=±2u^3 i n the D i r e c t i o n P a r a l l e l t o [ l l l ] f  H  6  PAGE  FIGURE A-3.  I n t e n s i t y D i s t r i b u t i o n i n the 3R R e c i p r o c a l L a t t i c e Plane (110)  i n the Orthorhombic o  N o t a t i o n o r (101)£ i n the C u b i c Notation.„. A-4.  120  (a) The L a t t i c e Correspondence Between the FCC  (CuAu I-Type) and Orthorhombic  Lattice,  (b) The U n i t C e l l o f the B a s a l Plane o f the Orthorhombic L a t t i c e . The  Orthorhombic  C o o r d i n a t e s o f Atoms i n the Plane a r e : Ag - 0, 0; Cd - h,  h-  (c) The  Distribution  of Atoms i n the \ B a s a l Plane i n the A,B C Layers.  and  The Orthorhombic C o o r d i n a t e s o f  the Ag Atoms i n the L a y e r s a r e ; A - 0, 0, B - 0, 1/3, B-1.  1/9; C - 0, 2/3;  2/9  121  Schematic R e p r e s e n t a t i o n o f the Correspondence Between the P a r e n t CsCl-Type L a t t i c e and the Product CuAu I-Type L a t t i c e  B-2.  0;  (b B a s i s ) (f B a s i s ) .  126  S t e r e o g r a p h i c P r o j e c t i o n Showing Some o f the Operations i n the D e t e r m i n a t i o n o f I n v a r i a n t L i n e S t r a i n s Compatible w i t h the Shear System  D-l.  (011)  [011] . b  Comparison o f the D i f f u s i v i t y Data f o r a-Cu-Zn and a-Ag-Cd Phase.  D-2.  130  I  4  5  Comparison o f the, D i f f u s i v i t y Data f o r g'-Cu-Zn and B'-Ag-Cd Phase  147  xvii  FIGURE E-l.  PAGE The Relevant P o r t i o n o f the Ag-Cd E q u l i b r i u m Phase Diagram (Thin L i n e s ) and the Ag-Cd Metastable Phase Diagram (Thick L i n e s ) .  In the Metastable Phase  Diagram the Formation o f the r, Phase i s Suppressed by Rapid Quenching from the B Phase t o the B  1  phase  xviii  149  ACKNOWLEDGMENTS  I am very g r a t e f u l t o Dr. E.B. Hawbolt, Dr. L.C. Brown and Dr. D. Tromans, as w e l l as t o my c o l l e a g u e s , f o r t h e i r help. My work on t h i s t h e s i s has been made p o s s i b l e by the NRC r e s e a r c h a s s i s t a n t s h i p .  xix  1.  INTRODUCTION  When a s y s t e m i n e q u i l i b r i u m phases  a t d i f f e r e n t temperatures, cooling  temperature The  consists  i n t e r v a l may g i v e  driving force  rise  f o r the transformation  final  state  does n o t n e c e s s a r i l y  s t a t e , but the requirement i s that lower than t h e t o t a l  1.1.  Nucleation  transformation.  i s the difference and f i n a l  h a v e t o be an  i t s total  states. equilibrium  f r e e e n e r g y be  f r e e energy o f the i n i t i a l  state.  a n d Growth T r a n s f o r m a t i o n s a n d  Martensitic  The  different  through a  t o a phase  between t h e f r e e e n e r g i e s o f t h e i n i t i a l The  of  phase  two m a i n g r o u p s :  Transformations.  transformations nactzation  are usually  growth  and  divided  into  t r a n s f o r m a t i o n s and  mah.t<Ln&4.t<Lc. t r a n s f o r m a t i o n s . A t y p i c a l t r a n s f o r m a t i o n o f t h e first  group i s p r e c i p i t a t i o n from a s u p e r s a t u r a t e d  solution.  The p r e c i p i t a t e p h a s e  m a t r i x phase by t h e r e l a t i v e l y i n t e r p h a s e boundary, the  boundary.  phases  grows a t t h e e x p e n s e  slow m i g r a t i o n  energy  r e s u l t i n g f r o m atom b y at6m t r a n s f e r  across  Compositions o f t h e m a t r i x and p r e c i p i t a t e  o f atoms o f d i f f e r e n t s p e c i e s  interface.  of the  of the high  a r e d i f f e r e n t and t h e m o t i o n o f t h e i n t e r f a c e  diffusion the  solid  The t r a n s p o r t  towards  o f atoms i s a  1  requires  o r away f r o m  thermally  2  a c t i v a t e d process and t r a n s f o r m a t i o n proceeds i s o t h e r m a l l y at  a r a t e which i s a f u n c t i o n of  temperature.  Transformations o f the second group, 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 , occur by the c o - o p e r a t i v e movements o f many atoms over s m a l l d i s t a n c e s o f the o r d e r of the atom size.  A u n i t c e l l o f the parent phase i s homogeneously  deformed i n t o u n i t c e l l o f the product phase.  Such a  t r a n s f o r m a t i o n mechanism causes the transformed r e g i o n s t o change t h e i r shape, g i v i n g r i s e t o a s u r f a c e r e l i e f originally flat  surface.  The boundary between the parent  and the product i s coherent and g l i s s i l e s i t i o n s o f the phases are i d e n t i c a l . of  and the compo-  Thus, d i s c r e t e r e g i o n s  the parent can t r a n s f o r m w i t h a h i g h v e l o c i t y  independent mations,  on an  o f temperature.  almost  In most m a r t e n s i t i c t r a n s f o r -  the amount o f t r a n s f o r m a t i o n i s c h a r a c t e r i s t i c o f  the temperature temperature,  and does not i n c r e a s e w i t h time; a t any  the product i s i n a t h e r m o e l a s t i c e q u i l i b r i u m  w i t h the parent, the number and the s i z e of the i n d i v i d u a l m a r t e n s i t e p l a t e s r e f l e c t i n g the e q u i l i b r i u m between the d r i v i n g f o r c e £or the t r a n s f o r m a t i o n and the e l a s t i c c r e a t e d by the t r a n s f o r m a t i o n .  stresses  However, some m a r t e n s i t i c  r e a c t i o n s are t h e r m a l l y a c t i v a t e d and hence occur i s o t h e r m a l l y . In  the case of athermal m a r t e n s i t e , the t r a n s f o r m a t i o n on  c o o l i n g begins spontaneously a t a f i x e d (M_  temperature  temperature), but deformation and e x t e r n a l e l a s t i c  can p l a y an important r o l e i n a s s i s t i n g or i n h i b i t i n g  stresses the  3  transformation. The m a r t e n s i t i c product  i s u s u a l l y i n the form o f  p l a t e s l y i n g p a r a l l e l to a u n i q u e l y d e f i n e d parent  plane  the habit pt&ne. Formation o f the p l a t e s i s accompanied by a shape deformation, which, as mentioned, causes a s u r f a c e relief,  i . e . , a t i l t i n g o f the specimen s u r f a c e about i t s  l i n e o f i n t e r s e c t i o n with the p l a t e - m a t r i x i n t e r f a c e . e f f e c t of the t r a n s f o r m a t i o n on s u r f a c e s c r a t c h e s and nature  of the s u r f a c e r e l i e f  shape deformation  d i s t o r t i o n , an i n v a r i a n t plane  parent  and product  uniquely defined.  the  i n d i c a t e t h a t the m a r t e n s i t i c  i s , a p a r t from a p o s s i b l e s m a l l and  being the i n v a r i a n t p l a n e .  The  s t r a i n , w i t h the h a b i t  The  l a t t i c e s , or  uniform plane  r e l a t i v e o r i e n t a t i o n of  the  orientation, relationship, i s a l s o  Another c h a r a c t e r i s t i c o f 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 , which can sometimes be d i r e c t l y observed u s i n g a microscope, i s the inhomogeneous shear twinning) o f the product,  (slip  or  or tattixie invariant shear. In most  cases, the h a b i t plane, amount of shape deformation,  amount  o f shear and o r i e n t a t i o n r e l a t i o n s h i p f o r a g i v e n 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 can be e x p e r i m e n t a l l y  determined.  These c h a r a c t e r i s t i c s o f m a r t e n s i t i c  transformations  have been d e s c r i b e d mathematically  i n terms o f the pheno-  menological  formation.  theories of martensite  The  b e s t known  are the t h e o r i e s o f Wechsler, Lieberman and Read (1) Bowles and Mackenzie  (2-4).  The  and  t h e o r i e s enable a p r e d i c t i o n  4  of the h a b i t p l a n e , shape deformation  and  orientation  r e l a t i o n s h i p by assuming a shear system i n the product a l a t t i c e correspondence between the parent and  and  product,  p r o v i d i n g t h a t the l a t t i c e parameters and c r y s t a l s t r u c t u r e s of the parent and product phases are known.  +  A d e s c r i p t i o n o f the Bowles and Mackenzie theory i s g i v e n i n Appendix B.  Since t h e i r f o r m u l a t i o n , the t h e o r i e s have demonst r a t e d a remarkable agreement with the experimental vations  obser-  (5) and thus p r o v i d e a p l a u s i b l e r a t i o n a l e f o r the  r a t h e r complex c r y s t a l l o g r a p h i c f e a t u r e s o f d i f f e r e n t martensitic transformations. During r a p i d c o o l i n g o f the h i g h temperature phase, massive, t/utrU) formation  may  occur i n the absence of c o m p e t i t i v e  n u c l e a t i o n and growth o r 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 . Massive t r a n s f o r m a t i o n i s a s p e c i a l k i n d o f  composition  i n v a r i a n t phase t r a n s f o r m a t i o n which becomes p o s s i b l e as soon as s u f f i c i e n t f r e e energy d r i v i n g f o r c e i s generated below the temperature a t which the f r e e energy o f the h i g h temperature,  matrix phase becomes equal t o the f r e e energy  of the low temperature,  product phase.  The  transformation  occurs by a s h o r t range d i f f u s i o n a l process t h a t i n v o l v e s a r a p i d non-cooperative  t r a n s f e r o f atoms a c c r o s s a r e l a t i v e l y  5  h i g h energy i n t e r f a c e , but does not i n v o l v e any change o f the o v e r a l l composition.  A l s o , u n l e s s the changes o f  c r y s t a l s t r u c t u r e i n v o l v e c o n s i d e r a b l e changes i n the volume, the product phase o f the massive t r a n s f o r m a t i o n i s expected t o develop without  accompanying d i s t o r t i o n of the f r e e s u r f a c e  o f the specimen. 1.2.  Bainitic  Transformations  M a r t e n s i t i c transformations generally require a l a r g e r d r i v i n g f o r c e and hence occur a t lower temperatures than n u c l e a t i o n and growth t r a n s f o r m a t i o n s .  The  do  t r a n s i t i o n from  n u c l e a t i o n and growth t r a n s f o r m a t i o n s t o 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 as the r e a c t i o n temperature i s lowered i s not s h a r p l y d e f i n e d ; baZnltic  t r a n s f o r m a t i o n s occur  before  the onset 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 .  The  t r a n s f o r m a t i o n i s g e n e r a l l y regarded  intermediate  as b e i n g  bainitic  between a t r u e n u c l e a t i o n and growth t r a n s f o r m a t i o n and martensitic transformation  (6).  a  U n l i k e many n u c l e a t i o n  and growth t r a n s f o r m a t i o n s , b a i n i t i c r e a c t i o n s are accompanied by changes o f shape o f the transformed i n t e r p r e t a t i o n , Ko and C o t t r e l l  (7)  r e g i o n s . In an e a r l y  suggested  t h a t the  s t r u c t u r e change d u r i n g a b a i n i t i c t r a n s f o r m a t i o n i s e s s e n t i a l l y m a r t e n s i t i c , but t h a t due  t o the reduced  f o r c e a v a i l a b l e a t temperatures above the M  s  driving  temperature,  growth i s o n l y p o s s i b l e i f the f r e e energy i s f u r t h e r decreased  by d i f f u s i o n a l composition  change, d i f f u s i o n  6  r a t e l i m i t i n g the r a t e o f the m a r t e n s i t i c s t r u c t u r e change. The b a i n i t e i n i r o n - c a r b o n allows c o n s i s t s of a n o n - l a m e l l a r aggregate  o f f e r r i t e and c a r b i d e s .  balnito,, which forms a t temperatures  below  Inlowoji  approximately  350°C, f e r r i t e i s plate-shaped w i t h c a r b i d e s p r e c i p i t a t e d w i t h i n the p l a t e s , the o v e r a l l s t r u c t u r e resembling of tempered m a r t e n s i t e .  that  The p l a t e s form on a d e f i n i t e  h a b i t plane and produce an i n v a r i a n t plane s t r a i n type o f surface r e l i e f .  The growing t i p s o f the p l a t e s have  sharp  r a d i i o f c u r v a t u r e and are f r e e of c a r b i d e (8). The b a i n i t e forms i s o t h e r m a l l y , i t s TTT curves C-shaped, as expected mation.  being  f o r a n u c l e a t i o n and growth t r a n s f o r -  However, the t r a n s f o r m a t i o n s t a r t s o n l y below a  w e l l d e f i n e d temperature  (B  temperature),  with the  fraction  o f a u s t e n i t e t r a n s f o r m i n g t o b a i n i t e being a f u n c t i o n o f the temperature o f i s o t h e r m a l a n n e a l i n g . I t was  s t a t e d t h a t the b a i n i t i c  transformations  were o r i g i n a l l y i n t e r p r e t e d as b e i n g a m a r t e n s i t i c formation o f s u p e r s a t u r a t e d f e r r i t e w i t h a secondary  precipitation  o f c a r b i d e s w i t h i n the f e r r i t e , the l a t t e r p r e c i p i t a t i o n being necessary t o s t a b i l i z e f e r r i t e by d e c r e a s i n g i t s f r e e energy  (Ko and C o t t r e l l ) . N e v e r t h e l e s s , some r e s u l t s  (9,10)  i n d i c a t e d t h a t a c e r t a i n amount o f r e d i s t r i b u t i o n o f  carbon  occurs a t the f e r r i t e - a u s t e n i t e i n t e r f a c e , and thus  the  7 l e n g t h e n i n g o f p l a t e s c o u l d be c o n t r o l l e d by d i f f u s i o n o f carbon i n t o a u s t e n i t e . evidence  Supported by the  experimental  o f a l i n e a r dependence o f l e n g t h e n i n g on time,  the Z e n e r - H i l l e r b model (for d i f f u s i o n c o n t r o l l e d was a p p l i e d t o the b a i n i t e growth k i n e t i c s  lengthening  (11,12). The  agreement w i t h the theory was d i f f i c u l t t o a s c e r t a i n due t o u n c e r t a i n t i e s o f c o n c e n t r a t i o n f a c t o r s and the dependence of  carbon d i f f u s i v i t y on c o n c e n t r a t i o n . The theory o f Ko and C o t t r e l l has the advantage o f  e x p l a i n i n g the s i m i l a r i t y between b a i n i t e and m a r t e n s i t e crystallographies  (13).  I t does not n e c e s s a r i l y c o n f l i c t  with the assumption t h a t a c e r t a i n amount o f d i f f u s i v e r e d i s t r i b u t i o n o f components occurs i n f r o n t o f the moving m a r t e n s i t i c boundary, as long as the a l l o y c o n t a i n s of w i d e l y d i f f e r e n t m o b i l i t i e s .  components  T h i s i s the case f o r f e r r o u s  a l l o y s c o n t a i n i n g i n t e r s t i t i a l carbon, where the m a r t e n s i t i c correspondence o f l a t t i c e s can be p r e s e r v e d by the slowly moving i r o n component. the composition component  But i n the case o f a l l o y s i n which  change occurs by d i f f u s i o n o f a s u b s t i t u t i o n a l  (e.g., Cu-Zn), i t seems necessary  t o assume t h a t  b a i n i t e i n h e r i t s the unchanged composition  o f the p a r e n t .  In s p i t e o f the c o n s i d e r a b l e a t t e n t i o n which has been g i v e n t o the b a i n i t i c t r a n s f o r m a t i o n over the l a s t f i f t e e n y e a r s , c o n t r o v e r s y concerning  the growth mechanism  s t i l l e x i s t s and w i d e l y d i f f e r i n g views are encountered i n  8  the l i t e r a t u r e 1.3.  (14) .  M a r t e n s i t e and B a i n i t e i n Cu- and Ag-Based A l l o y s M a r t e n s i t e s forming from the B-phase o f  (15-24) and Ag-based extensively.  Cu-based  (25-28) a l l o y s have been i n v e s t i g a t e d  The B-phase i n these a l l o y s i s an e l e c t r o n  compound w i t h the e l e c t r o h - t o - a t o m - r a t i o o f approximately 1.5.  In the Cu-Zn, Ag-Zn and Ag-Cd a l l o y s , i t occurs i n  the 50 a t . pet range, but i t can g e n e r a l l y be r e t a i n e d t o room temperature over a wider composition range by quenching.  rapid  On c o o l i n g t o room temperature, i t undergoes  an o r d e r i n g t r a n s f o r m a t i o n t o a B" C s C l - type s t r u c t u r e . At lower z i n c o r cadmium c o n t e n t s , a massive type t r a n s f o r mation o f B t o a  m  takes p l a c e on c o o l i n g ( 2 9 ) .  In the absence o f e x t e r n a l s t r e s s e s , the metastable B' phase transforms t o t h e r m o e l a s t i c m a r t e n s i t e o n l y on c o o l i n g below the M  g  temperature.  However, an i n t e r e s t i n g  mode o f 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 observed by Ayers  (27) i n a Ag-37.8 a t . p e t Zn a l l o y ; l a r g e p l a t e s of  m a r t e n s i t e formed i n quenched  B' phase when i t was reheated  t o approximately 280°C f o r a p e r i o d o f one second o r l e s s . The t r a n s f o r m a t i o n was  apparently thermally activated.  Longer times a t the temperature caused the f o r m a t i o n of much s m a l l e r , chevron shaped p r e c i p i t a t e s , which c o u l d p r o b a b l y be c l a s s i f i e d as b a i n i t e  (see below).  9  The  s t r u c t u r e of the t h e r m o e l a s t i c  g e n e r a l l y be d e s c r i b e d  martensite  as being e i t h e r fee o r a c l o s e packed  s t a c k i n g v a r i a n t o f the fee s t r u c t u r e , such as 3R sequence ABCBCACAB), 2H mixture o f these.  (AB),  11H  In b u r s t type  s i t e i n Cu-Zn a l l o y s (24) i n the Ag-Zn a l l o y  can  and  (stacking  (ABCBCACABAB), o r a l a m e l l a r (bulk)thermoelestic  i n thermally  (27), the m a r t e n s i t e  marten-  activated  martensite  plates consisted  of  f i n e twin l a m e l l a e having a s l i g h t l y d i s t o r t e d fee s t r u c t u r e . A p p l i c a t i o n o f the phenomenological theory martensite  r e s u l t e d i n a good agreement between/the  experimental and (24, 27,  of  t h e o r e t i c a l f e a t u r e s o f the  martensites  28). P l a t e s o f the a phase e x h i b i t i n g chevron-shaped  s u r f a c e t r a c e s were found t o form i s o t h e r m a l l y above room temperature i n the (2 8-35).  The  3 V phase o f some Cu-  and Ag-based a l l o y s  p l a t e s have been c o n s i d e r e d  analogy to the b a i n i t e i n f e r r o u s a l l o y s . found t h a t the b a i n i t e p l a t e s i n 3  1  temperatures up t o 350°C; a t h i g h e r needle shaped  t o be b a i n i t e by Garwood  Cu-Zn phase formed a t temperatures o n l y  (widmanstatten) p r e c i p i t a t e formed.  gave r i s e t o an i n v a r i a n t plane s t r a i n type o f relief.  T h e i r h a b i t plane was  temperature martensite  (35)  The  low  Garwood con-  cluded t h a t the p l a t e s formed by a shear t r a n s f o r m a t i o n , t h a t t h e i r growth was  plates  surface  i d e n t i c a l to that of  i n the same a l l o y .  a  c o n t r o l l e d by d i f f u s i o n .  but  10  Later research observations  (31-33,36) confirmed Garwood's  and s u p p l i e d new data s u p p o r t i n g  t h a t the b a i n i t e p l a t e s formed by shear.  his  conclusion  Hornbogen and  Warlimont (31) s t u d i e d t h e s t r u c t u r e o f b a i n i t e p l a t e s by e l e c t r o n d i f f r a c t i o n and found t h a t the s t a c k i n g o r d e r o f the c l o s e packed planes i n f r e s h l y formed p l a t e s was 3R, s i m i l a r t o t h a t found i n &  1  where  i t was e x p l a i n e d  i n v a r i a n t shear destroyed  (17).  martensite  i n copper a l l o y s ,  as o r i g i n a t i n g from a l a t t i c e Prolonged annealing  gradually  t h a t s t r u c t u r e and transformed the p l a t e s t o  almost e q u i l i b r i u m a phase w i t h a random d i s t r i b u t i o n o f stacking f a u l t s .  Srinavasan and Hepworth (33) found t h a t  the c r y s t a l l o g r a p h i c c h a r a c t e r i s t i c s o f b a i n i t e p l a t e s were c o n s i s t e n t w i t h the phenomenological theory s i t e formation.  o f marten-  C o r n e l l s and Wayman (24,36) performed a  r i g o r o u s c r y s t a l l o g r a p h i c study on sub-zero m a r t e n s i t e and i s o t h e r m a l l y formed a p l a t e s .  They confirmed the r e s u l t s  o f Srinavasan and Hepworth and e s t a b l i s h e d t h a t the l a t t i c e o r i e n t a t i o n r e l a t i o n s h i p , h a b i t plane and magnitude o f shape deformation f o r martensite  p l a t e s were i d e n t i c a l t o the  respective c h a r a c t e r i s t i c s f o r the a p l a t e s . found t h a t t h e m a r t e n s i t e  However, they  was i n t e r n a l l y twinned, n o t f a u l t e d .  P l e w i t t and Towner (32) and C o r n e l l s and Wayman (37) observed t h a t t h e b a i n i t e p l a t e s formed i n i t i a l l y without change i n composition, and t h a t p a r t i t i o n i n g o f copper and z i n c atoms o c c u r r e d  o n l y a f t e r the p l a t e s had formed.  11 Lorimer Z,t a.l.:.  (38) d i s p u t e d the v a l i d i t y o f t h e  r e s u l t s o f C o r n e l l s and Wayman and, F l e w i t t and Towner.  Lorimer ctaZ.  i m p l i c i t l y , those o f repeated the experiment  of C o r n e l l s and Wayman and found t h a t the composition o f the a p l a t e s ( b a i n i t e ) d i f f e r e d from the bulk composition i n the i n i t i a l Hawbolt Lorimer  stages o f t h e t r a n s f o r m a t i o n .  even  K o s t i c and  (39) c r i t i c i z e d the method o f a n a l y s i s used by zt ft£.and suggested  t h a t t h e i r c o n c l u s i o n s were n o t  c o n v i n c i n g s i n c e they r e p o r t e d an abnormally  low z i n c  c o n c e n t r a t i o n f o r the a p l a t e s . In t h e i r s t u d i e s o f massive  (29) and m a r t e n s i t i c (28)  t r a n s f o r m a t i o n s i n Ag-Cd and Ag-Zn a l l o y s , Ayers (29) and Krishnan  (28) observed  formed d u r i n g quenching region.  a p l a t e shaped a p r e c i p i t a t e which  from the h i g h temperature  3-phase  In both i n s t a n c e s t h e p r e c i p i t a t e was d e s i g n a t e d  as b a i n i t e due t o i t s m o r p h o l o g i c a l s i m i l a r i t i e s t o b a i n i t e i n the 3' phase i n Cu-Zn a l l o y s .  The nature o f t h e p r e -  c i p i t a t e was n o t i n v e s t i g a t e d i n more d e t a i l . 1.4.  Aim o f the Present Work Results i n the l i t e r a t u r e i n d i c a t e that m a r t e n s i t i c  shear may p l a y a prominent, r o l e i n the formation o f b a i n i t e i n Cu-Zn- a l l o y s .  The b a i n i t i c t r a n s f o r m a t i o n i n Ag-based  a l l o y s has been examined much l e s s e x t e n s i v e l y .  In the  p r e s e n t work, the morphology, c r y s t a l l o g r a p h i c f e a t u r e s and  growth k i n e t i c s o f b a i n i t e i n Ag-Cd a l l o y s are examined i n o r d e r t o a s c e r t a i n which mechanisms c o n t r o l b a i n i t e  formation.  2. EXPERIMENTAL 2.1.  P r e p a r a t i o n of A l l o y s The a l l o y s were prepared by m e l t i n g measured amounts  of  s i l v e r and cadmium o f 99.999 pet p u r i t y i n  s i l i c a capsules.  The c a p s u l e s were heated  hour, and the l i q u i d metal was mixing.  evacuated  to 850°C f o r one  shaken t o ensure adequate  The a l l o y s were then s o l i d i f i e d by d i p p i n g one  end  o f the c a p s u l e s i n t o c o l d water i n o r d e r t o prevent p i p i n g . The  s o l i d i f i e d i n g o t s were hot r o l l e d  a t 650°C t o a p p r o x i -  mately 50 pet r e d u c t i o n i n c r o s s - s e c t i o n a l area, s e a l e d again i n s i l i c a c a p s u l e s and homogenized f o r 48 hours a t approximatly  15°C below the s o l i d u s temperature.  i n g o t s were then hot r o l l e d  Homogenized  (450°C) and f i n a l l y c o l d  to sheets of the d e s i r e d t h i c k n e s s  (0.38  rolled  mm).  P r e l i m i n a r y experiments were c a r r i e d out u s i n g Ag-Cd a l l o y s o f t h r e e nominal compositions: Cd.  44,45 and 46 a t . p e t  These are marked i n the e q u i l i b r i u m Ag-Cd phase diagram  i n F i g . 1. The  a l l o y s were analyzed f o r s i l v e r u s i n g a s i l v e r  c h l o r i d e g r a v i m e t r i c method (43) i n o r d e r t o determine the t o t a l l o s s e s o f cadmium a s s o c i a t e d with the sample p r e p a r a t i o n procedures.  I t was  found t h a t the m e l t i n g , subsequent heat  t r e a t i n g and hot forming r e s u l t e d i n a cadmium l o s s o f approximately  0.1  a t . pet  Cd.  13  14  SILVER, AT. PCT 55  50  700 b  CADMIUM, AT. PCT FIGURE 1 The r e l e v a n t p o r t i o n o f t h e Ag~Cd e q u i l i b r i u m phase diagram. Dotted l i n e s i n d i c a t e composition o f t h e a l l o y s used.  15 2.2.  Quenching • The growth k i n e t i c s experiments r e q u i r e d t h a t  specimens be quenched  from the high-temperature  r e g i o n i n o r d e r t o r e t a i n the untransformed 3 * _ _______ . . _ _______  3-phase phased.  I t i s assumed t h a t quenching; cannot p r e s e r v e the h i g h temperature d i s o r d e r e d 3 phase (26, 31, 40). Some p r e l i m i n a r y t e s t s were c a r r i e d out by quenching evacuated pyrex c a p s u l e s c o n t a i n i n g the specimen i n t o brine.  In g e n e r a l , the quenching r a t e was  iced  not s u f f i c i e n t l y  f a s t t o prevent the f o r m a t i o n o f b a i n i t e or o t h e r t r a n s formation' p r o d u c t s . R a p i d l y t r a n s f e r r i n g the bare from the s a l t pot t o i c e d b r i n e was  also  specimen  unsatisfactory;  l a r g e cadmium l o s s e s r e s u l t e d from the n e c e s s i t y o f u s i n g h i g h quenching temperatures t o ensure t h a t the  specimen  remained untransformed d u r i n g t r a n s f e r t o the quenching b a t h . The composition change due t o the cadmium l o s s induced formation o f a phase which consumed s u b s t a n t i a l p o r t i o n s m of  the p a r e n t 3-phase g r a i n s .  to  use a method which would enable r a p i d h e a t i n g t o the  T h e r e f o r e , i t was necessary  quenching temperature,< a v i r t u a l l y i n s t a n t a n e o u s t r a n s f e r to  the quenching medium and a v i g o r o u s s t i r r i n g i n the  quenching medium.  Such a method was  frequency i n d u c t i o n h e a t i n g .  devised u t i l i z i n g high  The apparatus c o n s i s t e d o f a  s i l i c a g l a s s tube connected t o an i c e d b r i n e r e s e r v o i r  (Fig.2).  The tube .was p l a c e d i n a w a t e r - c o o l e d i n d u c t i o n c o i l .  Specimens  ARGONj THERMOCOUPLE  SILICA  GRAPHITE  FIGURE 2 Schematic diagram o f the i n d u c t i o n h e a t i n g and quenching apparatus.  17  (15 x 3 x 0.38 mm) were p l a c e d i n a groove i n a s m a l l g r a p h i t e core i n s i d e the tube. argon b e f o r e h e a t i n g .  The tube was f i l l e d  with  The temperature was monitored u s i n g  a chrome1-alumel thermocouple  having i t s h o t j u n c t i o n on  t h e s u r f a c e s u p p o r t i n g the specimens. heated t o the d e s i r e d temperature  The specimens were  i n approximately 3 seconds,  h e l d f o r another 17 seconds, and then quenched by f l u s h i n g the b r i n e through the s i l i c a tube.  T h i s method u s u a l l y  ensured the r e t e n t i o n o f the B * phase, although some a  m  phase developed i n the t h i n cadmium-depleted s u r f a c e l a y e r . T h i s l a y e r was removed by e l e c t r o l y t i c t h i n n i n g after  immediately  quenching. The average  B ' g r a i n diameter produced by the h e a t i n g  and quenching was approximately 0.25-0.5 mm.  F o r the h a b i t  plane measurements i t was necessary t o have l a r g e r g r a i n s of  a t l e a s t 2 mm i n diameter.  F o r t h a t purpose,  quenched  s t r i p s c o n s i s t i n g e n t i r e l y o f the B' phase were s t r a i n e d approximately 5 p e t and then lowered i n t o a 630°C s a l t bath at  a r a t e o f approximately 10 mm/min.  manually  Large B  into iced brine.  over 10 mm l o n g were produced. c o n t a i n e d l a r g e areas o f a  m  1  They were then quenched  g r a i n s 2-4 mm wide and  Although most o f the g r a i n s  and b a i n i t e , some were completely  f r e e from any t r a n s f o r m a t i o n product and thus were u s e f u l f o r h a b i t plane a n a l y s i s .  18 2.3  E l e c t r o l y t i c P o l i s h i n g and Thinning The  specimens f o r the o p t i c a l and scanning  electron  microscopy had t o be p o l i s h e d e l e c t r o l y t i c a l l y i n order t o remove the cadmium d e p l e t e d surface. B  1  l a y e r and o b t a i n a c l e a n , smooth  Mechanical p o l i s h i n g c o u l d n o t be used s i n c e the  phase transforms m a r t e n s i t i c a l l y when deformed a t room  temperature  (28). E l e c t r o l y t i c p o l i s h i n g o f specimens was  accomplished u s i n g a 10 p e t KCN-water s o l u t i o n w i t h nating current.  alter-  A s t a i n l e s s s t e e l water-cooled beaker was  used as the other e l e c t r o d e , a v o l t a g e o f 13.5 V and a s p e c i men c u r r e n t d e n s i t y o f 0.06 A/mm being maintained. 2  p o l i s h e d B' g r a i n s , and l i g h t l y etched transformation The etched  g r a i n boundaries and  products were r e v e a l e d by t h i s procedure.  specimens f o r the o p t i c a l microscope were a l s o  u s i n g a s o l u t i o n o f lOg CrOg and 1 g N a S 0 2  ml o f water.  Smoothly  4  i n 100  T h i s was necessary t o enhance the c o n t r a s t o f  the g r a i n and p r e c i p i t a t e boundaries. Specimens f o r t r a n s m i s s i o n  e l e c t r o n microscopy, i n  the form o f 3 mm diameter d i s c s , were c u t out o f the s t r i p s by spark machining. The centre o f the d i s k was thinned  using  a j e t e l e c t r o l y t i c procedure a t a v o l t a g e of 15 V a.c. and u s i n g the same e l e c t r o l y t e as f o r e l e c t r o l y t i c p o l i s h i n g . 2.4.  X-Ray A n a l y s i s A 57.4 mm diameter Straumanis-type l o a d i n g  Debye-Scherrer camera w i t h a r e v o l v i n g r e c t a n g u l a r  (2 x 0.4  s l i t diaphragm and CuK„ r a d i a t i o n was used f o r . t h e c r y s t a l structure analysis.  The specimen, i n the form o f a t h i n  p o l y c r y s t a l l i n e w i r e , was c u t from the sheet by spark machining and then e l e c t r o l y t i c a l l y t h i n n e d t o 0.3 mm diameter.  approximately  A v o l t a g e o f 26kV and long exposures o f  15-100 hours were used t o minimize the background i n t e n s i t y and  t o enable d e t e c t i o n o f weak p r e c i p i t a t e l i n e s i n the  h i g h angle r e g i o n o f the p a t t e r n .  The specimen was a l s o  moved a x i a l l y i n increments o f approximately exposure t o i n c o r p o r a t e as many matrix The 0.05  background  1 mm d u r i n g t h e  g r a i n s as p o s s i b l e .  i n t e n s i t y was f u r t h e r reduced by p l a c i n g a  mm aluminum f i l t e r i n f r o n t o f the f i l m .  2.5.  Surface The  Relief  surface r e l i e f e f f e c t s associated with  p r e c i p i t a t i o n were observed on the p r e p o l i s h e d specimen s u r f a c e s f o l l o w i n g the p r e c i p i t a t i o n treatment. They were examined u s i n g the Z e i s s i n t e r f e r e n c e microscope and a monochromatic t h a l l i u m - v a p o r  light.  The f r i n g e p a t t e r n s  c h a r a c t e r i s t i c o f the s u r f a c e r e l i e f were photographed and e n l a r g e d t o allow measurements o f the f r i n g e d i s p l a c e ments . 2.6.  Habit Plane Measurements Habit planes o f  b a i n i t e p l a t e s were determined  u s i n g a m o d i f i c a t i o n o f the two-surface t r a c e a n a l y s i s .  20  Quenched and p o l i s h e d  l a r g e - g r a i n specimens were f i r s t c u t  by spark machining t o o b t a i n a sharp edge.  The samples were  then annealed a t 240°C u n t i l a f a i r l y l a r g e number o f i s o l a t e d !  b a i n i t e - p l a t e t r a c e s appeared on the s u r f a c e .  Before  measurement, the specimens were l i g h t l y r e p o l i s h e d  i n order  to remove the t h i n o x i d i z e d l a y e r , and were etched. were then fastened of the specimen meter was  They  onto a goniometer which allowed r o t a t i o n  around the a x i s of i t s sharp edge.  The  gonio-  f i r s t a t t a c h e d t o the stage of the X-ray machine  and a b a c k - r e f l e c t i o n Laue photograph  was  taken to determine  the o r i e n t a t i o n o f the m a t r i x g r a i n . The goniometer was stage and photographs  then a t t a c h e d t o the microscope  of the two  surfaces  of the edge were  taken. The edge of the specimen  was  always s l i g h t l y  rounded  and the t r a c e s q u i t e s h o r t , thus i t r a r e l y o c c u r r e d t h a t a t r a c e extended  f a r enough beyond the edge on both s i d e s t o  allow a r e l i a b l e measurement o f i t s p o s i t i o n t o be made. In most cases, i t was  necessary t o attempt to i d e n t i f y o t h e r  t r a c e s which seemed t o belong to the p l a t e s o f the same h a b i t plane v a r i a n t but which d i d not extend a l l the way the edge.  to  T h i s proved p o s s i b l e , although, as the r e s u l t s  w i l l show, a l a r g e s c a t t e r r e s u l t e d , probably due t o e r r o r s i n the matching variants.  of t r a c e s b e l o n g i n g t o d i f f e r e n t p l a t e  2.7.  Electron The  Microscopy  morphology and s t r u c t u r e  o f p r e c i p i t a t e s as  w e l l as the o r i e n t a t i o n r e l a t i o n s h i p between the m a t r i x and  p r e c i p i t a t e l a t t i c e s was examined u s i n g the H i t a c h i  HU-11A 100 kV e l e c t r o n microscope. tilting  (±30°)  stage was employed f o r the o r i e n t a t i o n r e l a t i o n -  ship measurements and the s t r u c t u r e The and  A wide-angle  a n a l y s i s o f the b a i n i t e .  o r i e n t a t i o n r e l a t i o n s h i p between the b a i n i t e  the m a t r i x was determined from composite  d i f f r a c t i o n patterns containing  the { 0 1 1 }  electron reciprocal  + f  _ In t h i s work, the s u b s c r i p t s f and b are a s s i g n e d t o symbols r e f e r r i n g t o the f e e and bee s t r u c t u r e s r e s p e c t i v e l y . l a t t i c e planes o f the b a i n i t e and the {111}^ planes o f the m a t r i x .  These p a t t e r n s were o b t a i n e d u s i n g s e l e c t e d  d i f f r a c t i o n from an area s t r a d d l i n g p o r t i o n s b a i n i t e p l a t e and the surrounding m a t r i x . area s u f f i c i e n t l y small possible  t o avoid  o f both the  By making t h i s  (maximum 0.5 um square) i t was  any v a r i a t i o n o f the i n t e n s i t y o f the  spots due t o b u c k l i n g the  area  o f the f o i l .  Under these  conditions  r e l a t i v e i n t e n s i t y d i s t r i b u t i o n o f the e q u i v a l e n t  spots was s o l e l y and d i r e c t l y r e l a t e d t o the angle between the  zone a x i s o f a p a t t e r n  microscope.  This  and the o p t i c a l a x i s o f the  angle was determined t o an accuracy o f  b e t t e r than ±0.5° by u s i n g an experimental procedure  d e v e l o p e d by  The the  R y d e r and  f  relationship  Bainite  plates  which caused s t r e a k i n g ^111^ ^ d i r e c t i o n . coincide in  the  with  the  the  foil  d i r e c t i o n was  direct  ^Oll^^  from a s i n g l e  2.8.  Growth K i n e t i c s  a preliminary  matrix to  an  capabilities  of  the  optical  axis. having  the the  growth k i n e t i c s measurements,  magnification  a hot  and  Therefore,  the  stage  optical  resolution  o p t i c a l microscope d i d not  an  rotate  relationship with  c r u d e s t k i n e t i c measurements o f  incorporating  pattern  streaking  enabling  the  make  possible  precipitates  plan to d i r e c t l y  o b s e r v e i s o t h e r m a l p r e c i p i t a t e g r o w t h had one  the  orientation  research plan proposed using  B ' Ag-Cd a l l o y .  show  necessary to  the  not  Measurements  precipitate  an  did  of  the  a  photograph.  However, t h e  a  p a r a l l e l to  i t s orientation  microscope.  in  interpretation  reflecting position,  bainite  the  along  i . e . , when i t d i d n o t  therefore,  t h i s brought the  zone i n t h e  faults  reflecting position, i.e., u n t i l  determination of  even the  the  for  following  streaking  zone c o n t a i n i n g  f a u l t s were n e a r l y  For  d i r e c t i o n of  I t was,  i n the  Fortunately, a ^lll^k  the  f o r the  reciprocal lattice  Ewald sphere,  very d i f f i c u l t . until  p a t t e r n s were s u i t a b l e  determination  i n the  When t h e  was  42).  c o n t a i n e d random s t a c k i n g  d i f f r a c t i o n pattern,  stacking  (41,  (Oil) -zone b a i n i t e  orientation  reason;  Pitsch  a n n e a l i n g method t h a t  t o be  replaced  separated  by  growth  from the o b s e r v a t i o n  and measurement o f growth and so  allowed the use o f a scanning e l e c t r o n microscope. were i n i t i a l l y  Specimens  annealed i n a s i l i c o n o i l bath, maintained  to w i t h i n ±1°C o f the d e s i r e d temperature, u n t i l t r a c e s o f p r e c i p i t a t e s , v i s i b l e due t o t h e i r s u r f a c e r e l i e f , on the e l e c t r o p o l i s h e d s u r f a c e .  appeared  The t r a c e s were immediately  photographed u s i n g an ETEC scanning e l e c t r o n microscope operated i n the secondary e l e c t r o n image mode.  Specimens  were then annealed f o r an a d d i t i o n a l increment o f time, and  the t r a c e s o f the same p r e c i p i t a t e s were photographed  again. The procedure was repeated t o monitor the e n t i r e growth o f the p r e c i p i t a t e .  S t a b i l i t y o f the m a g n i f i c a t i o n  was f r e q u e n t l y t e s t e d by comparing the d i s t a n c e between unchanging d e t a i l s on t h e . s u r f a c e The  o f the specimen.  t h i c k n e s s o f the b a i n i t e p l a t e t r a c e s was  measured d i r e c t l y on the negatives  u s i n g a microdensitometer.  Measurements o f each t r a c e were repeated t e n times t o minimize any measurement error.for  A l l magnifications  were c o r r e c t e d  t i l t i n g o f t h e specimen r e l a t i v e t o the e l e c t r o n beam. An attempt was made t o determine the angle a between  the b a i n i t e p l a t e s and the specimen s u r f a c e .  Thin  layers  of the specimen were e l e c t r o l y t i c a l l y removed and a measurement o f the displacements o f the p l a t e t r a c e s r e l a t i v e t o s e v e r a l a r t i f i c i a l r e f e r e n c e marks was made.  The e r r o r o f these  measurements was l a r g e due t o d i f f i c u l t i e s i n e s t i m a t i n g  24  the  thickness  of the e l e c t r o l y t i c a l l y  due t o t h e s m a l l  s i z e of the p l a t e s .  removed l a y e r s was before  removed l a y e r s The t h i c k n e s s  u n i f o r m o v e r t h e whole s u r f a c e .  f a s t e r thereby  calculated length that  thickness  o f t h e removed  of the p l a t e s being  layers of only  The r e s u l t i n g s m a l l measure. by  introducing  layer.  approximately  The  5-15  t r a c e d i s p l a c e m e n t was  showed  this that  detailed  required  be  was  of the matrix-plate  removed. to  further  reduced  boundaries from t h e  l a r g e e r r o r , the data from these  and  surface.  measurements  t h e v a r i a t i o n o f t h e measured t h i c k e n i n g  d i s c u s s i o n of the r e s u l t s i s given  The w i d t h o f t h e s u r f a c e p l a t e s were  rates  were  traces  i n Section  of several  3.10.1.  large  c a r e f u l l y measured a f t e r t h e e l e c t r o l y t i c  the surface  level  the  um  p r e d o m i n a n t l y due t o t h e v a r i a t i o n o f t h e a n g l e a . A  was  of  average  difficult  consequent rounding o f the p l a t e p r o t r u d i n g Despite  o f the p l a t e s  a few m i c r o n s i n t h i c k n e s s  etching  the  an e r r o r i n t h e  The p r e c i s i o n o f t h e measurement  electrolytic  the d i s s o l u -  However,  s p e c i m e n e d g e s and t h e m a t r i x i n t h e v i c i n i t y dissolved  of the  e s t i m a t e d by w e i g h i n g t h e specimen  and a f t e r d i s s o l u t i o n and a s s u m i n g t h a t  t i o n was  and  removal  l a y e r and a l i g h t m e c h a n i c a l p o l i s h i n g t o  the protruding  portions  of the p l a t e s .  The w i d t h s  f o u n d t o be e q u a l t o t h e w i d t h s o f t r a c e s m e a s u r e d on original  surfaces  a f t e r annealing.  This  showed  that the  t r a c e w i d t h o f t h e p l a t e s u s e d f o r k i n e t i c measurements ponded t o t h e a c t u a l t h i c k n e s  o f t h e p l a t e s below the  corres-  surface.  3. RESULTS AND 3.1.  DISCUSSION  Morphology of P r e c i p i t a t e s Formed during  Quenching  In some specimens which were encapsulated and  quenched  manually from the s a l t bath, a spectrum of c o o l i n g r a t e s achieved due  to uneven contact  a f t e r the capsule was not  w i t h the quenching medium  broken.  When the c o o l i n g r a t e s were  f a s t enough t o completely r e t a i n the  transformed s t r u c t u r e s  was  resulted.  The  0  1  phase, p a r t i a l l y  d e t a i l s o f the  trans-  formation products were noted. Large, r e g u l a r t r a c e s o f b a i n i t e p l a t e s f i r s t With d e c r e a s i n g c o o l i n g r a t e of a  m  on the g r a i n boundaries  of the g r a i n s c o o l i n g rate, a ( F i g . 3c).  ( F i g . 3a),  appeared  then patches  w i t h b a i n i t e i n the  ( F i g . 3b). With a f u r t h e r decrease i n m  spread i n t o the  i n t e r i o r of the  interior the  grains  Slower c o o l i n g a l s o produced t h i c k e r b a i n i t e  plates with i r r e g u l a r sides h a b i t plane d e f i n e d  by  which d e v i a t e d  locally  the t h i n r e g u l a r p l a t e s .  at very slow quenching r a t e s , i t was phase spread over the e n t i r e  from  the  Finally,  observed t h a t the  a  m  surface.  In the micrograph i n F i g . 3c, t h e r e i s evidence of a  m  adapting to the  shape of b a i n i t e .  This i n d i c a t e s that  b a i n i t e p l a t e s were present p r i o r t o the development o f massive product and m-  a  a c t e d as a boundary t o the growth of  the  the the  26  FIGURE 3 B a i n i t e p l a t e s and m a s s i v e a i n t h e B' m a t r i x o f a Ag-46 a t . p e t Cd a l l o y q u e n c h e d f r o m 600°C. The q u e n c h i n g r a t e was i n s u f f i c i e n t t o r e t a i n t h e u n t r a n s f o r m e d 3• p h a s e , r e s u l t i n g i n f o r m a t i o n o f b a i n i t e ( a ) . Upon d e c r e a s i n g t h e q u e n c h i n g , r a t e , a f i r s t f o r m e d on g r a i n b o u n d a r i e s ( b ) , and t h e n i n t h e i n t e r i o r o f t h e g r a i n s ( c ) . m  m  27 S i m i l a r o b s e r v a t i o n s o f p r e c i p i t a t e s formed  during  quenching i n Ag-Cd, Ag-Zn and Cu-Zn a l l o y s were made by o t h e r researchers  (28,29).  The  r a p i d quenching d e v i c e produced specimens w i t h  r e g u l a r p o l y g o n a l 6' g r a i n s , successful.  Occasionally,  i n d i c a t i n g t h a t quenching was  the g r a i n boundaries showed  of a , and, l e s s f r e q u e n t l y ,  portions  s e v e r a l long, narrow b a i n i t e p l a t e s The 3.2.  o f the specimen c o n t a i n e d  formed during  quenching.  average & - g r a i n diameter was approximately 0.25-0.5mm. 1  Morphology o f P r e c i p i t a t e s Formed during Annealing The  isothermal 46 a t . p e t the  traces  Isothermal  morphology o f the p r e c i p i t a t e s d e v e l o p i n g  during  treatment a t 160-320°C i n a l l o y s w i t h 44,45 and Cd was examined u s i n g  the o p t i c a l microscope,  scanning and the t r a n s m i s s i o n  transmission  e l e c t r o n microscope.  The  e l e c t r o n microscope s t u d i e s w i l l be presented  i n S e c t i o n 3.6. A two-surface a n a l y s i s o f specimens w i t h v a r i e d amounts o f p r e c i p i t a t e showed t h a t two kinds o f p r e c i p i t a t e s formed; a n e e d l e - l i k e widmanstatten p r e c i p i t a t e and a p l a t e like bainite.  The b a i n i t e p l a t e s u s u a l l y formed i n p a i r s ,  j o i n e d a t an obtuse angle, g i v i n g r i s e t o a chevron-shaped t r a c e on the specimen surface.  F i g . 4 shows a scanning-  e l e c t r o n micrograph o f the edge o f a s e v e r e l y containing  both kinds o f p r e c i p i t a t e s .  etched specimen  28  FIGURE 4 A s c a n n i n g e l e c t r o n m i c r o g r a p h o f t h e edge ( i n c l u d e d a n g l e o f a p p r o x i m a t e l y 90°) o f ' a s e v e r e l y e t c h e d s p e c i m e n o f Ag-45 a t . p e t _Cd a l l o y a n n e a l e d f o r 1,225 s e c o n d s a t 2 0 0 ° C . B o t h w i d m a n s t a t t e n n e e d l e s and b a i n i t e p l a t e s a r e v i s i b l e .  29  A examination o f the e f f e c t o f p r e c i p i t a t i o n temperature on the type and amount o f p r e c i p i t a t e formed produced the f o l l o w i n g r e s u l t s .  Widmanstatten needles  formed both a t the g r a i n boundaries and i n the i n t e r i o r o f the  3 ' g r a i n s , w i t h g r a i n boundary needles n u c l e a t i n g a t  an e a r l i e r stage.  B a i n i t e plates u s u a l l y nucleated  i n t e r i o r o f the g r a i n s .  i n the  Judging by the r e l a t i v e area  f r a c t i o n o f each type o f p r e c i p i t a t e , the b a i n i t e p l a t e s were predominant a t the lower temperatures. p l a t e s both formed a t the; intermediate  Needles and  temperatures.  B a i n i t e p l a t e s i n these mixed s t r u c t u r e s nucleated Fig.5  always  b e f o r e i n t r a g r a n u l a r widmanstatten n e e d l e s .  shows o p t i c a l photomicrographs o f two p o l i s h e d and  etched Ag-45 a t . p e t Cd specimens.  F i g . 5a shows o n l y  the p l a t e - l i k e b a i n i t e product formed a t 160°C, w h i l e F i g . 5b c o n t a i n s  a mixture o f b a i n i t e p l a t e s and widman-  s t a t t e n needles formed a t 200°C. The  r e l a t i v e area f r a c t i o n s o f the two k i n d s o f  p r e c i p i t a t e s i n the mixed s t r u c t u r e s a l s o depended on the amount o f cadmium i n the a l l o y .  In the 44 a t . p e t Cd a l l o y ,  i n t r a g r a n u l a r needles d i d not form below 300°C, w h i l e i n the 45 a t . p e t Cd a l l o y they d i d not form below 200°C. Increasing  the cadmium content o f the a l l o y (44 t o  46 a t . pet) i n c r e a s e d plates.  the t h i c k n e s s - t o - l e n g t h  r a t i o o f the  The t h i c k e r , s h o r t e r p r e c i p i t a t e s e x h i b i t e d  30  FIGURE 5 B a i n i t e p l a t e s (a) and a mixture o f b a i n i t e p l a t e s and widmanstatten needles (b) formed i n a Ag-45 a t . p e t Cd a l l o y d u r i n g annealing a t 160°C f o r 57,600 seconds (a) and a t 200°C f o r 1,225 seconds (b).  31  h-30um-H  FIGURE 6 A m i x t u r e o f b a i n i t e p l a t e s and w i d m a n s t a t t e n needles f o r m e d i n a Ag-46 a t . p e t Cd a l l o y d u r i n g a n n e a l i n g a t 200°C f o r 25,600 s e c o n d s . Most p l a t e s d e g e n e r a t e d t o needles isomorphous w i t h the widmanstatten needles. The b r o a d f a c e s o f t h e p a i r o f p l a t e s i n t h e c e n t r e a r e approximately p a r a l l e l to the plane of p o l i s h .  32 i r r e g u l a r boundaries and  n e e d l e - l i k e protuberances seemingly  isomorphous w i t h the widmanstatten needles An  increased  transformation  cadmium c o n c e n t r a t i o n  temperatures i n c r e a s e d  f o r formation of p l a t e s and  needles.  temperatures a l s o decreased the observed t h a t the s i z e and quenching was 1-2  and  Lower  and  time  transformation  average p l a t e s i z e .  It  appearance of p l a t e s formed  s i m i l a r t o p l a t e s formed i s o t h e r m a l l y ( F i g . 7).  assumed t h a t the p l a t e s formed d u r i n g  nucleate  lower  the i n c u b a t i o n  seconds at temperature of 280-320°C  i t was  ( F i g . 6).  was during  after Thus,  quenching  grow at or above temperatures e q u i v a l e n t  to  those employed f o r i s o t h e r m a l p r e c i p i t a t i o n . The i n the  3'  observed c h a r a c t e r i s t i c s of the p r e c i p i t a t e s  phase of Ag-Cd a l l o y s are very s i m i l a r t o  the  c h a r a c t e r i s t i c s of the analogous p r e c i p i t a t e s i n Cu-Zn alloys  (31-36).  The  phenomenological s i m i l a r i t y between  these systems, which a l s o have p a r a l l e l chemical and p r o p e r t i e s , w i l l be made use The p l a t e s was during any  incubation  of i n f u r t h e r  discussion.  time f o r n u c l e a t i o n o f b a i n i t e  d i f f e r e n t i n d i f f e r e n t matrix grains.  the e a r l y annealing  times, one  g r a i n was  Often, f r e e of  v i s i b l e p r e c i p i t a t e s , while a neighboring grain  s e v e r a l hundred b a i n i t e chevrons. p l a t e s and  physical  The  had  average s i z e of  the number of b a i n i t e h a b i t plane v a r i a n t s  changed from one  the also  g r a i n t o another g r a i n . In most g r a i n s ,  the p l a t e s grew on s e v e r a l v a r i a n t s , r e s u l t i n g i n chevrons  33  /  i-—200 um—H  FIGURE 7  B a i n i t e p l a t e s i n Ag-45 a t . p e t Cd a l l o y formed a f t e r approximately 2 s a t 2 80°C.  j—100 um—i  FIGURE 8 The v a r i a t i o n o f b a i n i t e p l a t e morphology i n d i f f e r e n t - m a t r i x  grains.  35  o r i e n t e d i n many d i f f e r e n t d i r e c t i o n s . grains, chevrons tended to belong i l l u s t r a t e d i n F i g . 8.  However, i n some  to the same v a r i a n t s , as  T h i s suggests t h a t the  formation  o f b a i n i t e depends on the o r i e n t a t i o n of the matrix g r a i n , most probably  due  to the e f f e c t of d i f f e r e n t quenching  stresses i n different grains. important 3.3.  Thus, s t r e s s may  have an  i n f l u e n c e on the n u c l e a t i o n o f b a i n i t e .  X-Ray S t r u c t u r e A n a l y s i s Debye-Scherrer p a t t e r n s were obtained  from the  Ag-45 a t . pet Cd a l l o y at d i f f e r e n t stages o f  transformation.  The  s e t of  p a t t e r n s contained two  s e t s of l i n e s ; one  r e l a t i v e l y sharp and i n t e n s e  but s p o t t y l i n e s  corresponding  to the bcc s t r u c t u r e of the c o a r s e - g r a i n e d matrix  and  a set  of much weaker, d i f f u s e l i n e s from the p r e c i p i t a t e . The p r e c i p i t a t e l i n e s appeared at 20 v a l u e s corresponding fee s t r u c t u r e .  major  to an  However, some a d d i t i o n a l , extremely weak l i n e s ,  f o r which the 28 values c o u l d not be a c c u r a t e l y determined, were observed.  No  s u p e r l a t t i c e l i n e s due  to o r d e r i n g c o u l d  be observed s i n c e the atomic s c a t t e r i n g f a c t o r s f o r Ag Cd are n e a r l y e q u a l .  The v a l u e s o f the l a t t i c e parameters  c a l c u l a t e d from the p a t t e r n s of the matrix t a t e are given i n Table I . analyzed  and  and  the  The m i c r o s t r u c t u r e s of  precipithe  specimens are shown i n F i g s .9-11. I t was  d i f f i c u l t to o b t a i n w e l l d e f i n e d p r e c i p i t a t e  36  TABLE I L a t t i c e Parameters o f the bcc M a t r i x , a , and the fee P r e c i p i t a t e , a f , i n the Ag-45 a t . p e t Cd A l l o y A f t e r A n n e a l i n g a t 160, 200 and 240°C.+ b  Treatment  0  a , A b  3.324  Quenched Annealing  f  -  time at 160°C, s  12,600  3.325  4.178  25,600  3.326  4.177  57,600  3.329  4.175  529  3.324  4.186  900  3.326  4.180  2,116  3.327  4.177  25  3.324  4.185  64  3.326  4.183  144  3.326  4.180  Annealing  Annealing  +  a , A  time at 200°C, s  time a t 240°C, s  Each f i g u r e i s a mean o f 2-4 measurements. The e r r o r f o r a i s approximately ±0.001 A, f o r a approximately ±0.002 A. b  f  37  FIGURE 9 A n n e a l i n g temperature 160°C; a n n e a l i n g time 12,600 s (a), 25,600 s ( b ) , and 57,600 s (c) .  38  FIGURE 10 A n n e a l i n g temperature 200°C; a n n e a l i n g time 529 s ( a ) , 900 s (b), and 2,116 s ( c ) .  39  FIGURE  11  A n n e a l i n g temperature 240°C; a n n e a l i n g time 25 s ( a ) , 64 s (b), and 144 s ( c ) .  40  l i n e s a t h i g h 2© angles f o r the specimens annealed s h o r t p e r i o d s o f time.  T h i s was  due  volume f r a c t i o n o f the p r e c i p i t a t e  f o r very  i n p a r t t o the s m a l l which tended t o  decrease  the l i n e i n t e n s i t y w i t h r e s p e c t t o the background i n t e n s i t y , but a l s o due t o the s m a l l s i z e of the p r e c i p i t a t e s  which  caused broadening  the  of the l i n e s .  For these reasons,  measurement e r r o r of the 26 v a l u e s f o r i n i t i a l growth was  precipitate  q u i t e l a r g e , making i t i m p o s s i b l e t o i n v e s t i g a t e  any t e t r a g o n a l d i s t o r t i o n of the f a c e - c e n t r e d u n i t The  cell.  l a t t i c e parameter v a l u e s l i s t e d i n Table I  show t h a t the d e n s i t y of the bcc parent and the fee product —7 was  almost  identical  (for a = b  l a t t i c e d e n s i t y i s 5.446 x 10  3.324 x 10  19  mm,  3  the bcc  atoms/mm ; f o r a =4.186 x 10 19  mm,  the fee l a t t i c e d e n s i t y i s 5.453 x 10  —7  f  ?  atoms/mm ),meaning J  t h a t the volume change d u r i n g the t r a n s f o r m a t i o n was  negligible.  The v a r i a t i o n of the l a t t i c e parameters w i t h a n n e a l i n g tempe r a t u r e and time was p i t a t e and enrichment  c o n s i s t e n t w i t h d e p l e t i o n of the p r e c i of the m a t r i x i n cadmium.  When the  p r e c i p i t a t e i n i t i a l l y develops w i t h a composition c l o s e t o t h a t of the m a t r i x , i t w i l l be r i c h i n cadmium (see Table VII and the metastable  phase diagram i n Appendix E ) .  If  composition o f the p r e c i p i t a t e as i t grows changes towards the lower, i . e . , e q u i l i b r i u m cadmium content, then the of  loss  the l a r g e r cadmium atoms should be r e f l e c t e d i n a decrease  i n the l a t t i c e parameter of the p r e c i p i t a t e and a corresponding  41 i n c r e a s e i n the l a t t i c e parameter o f the m a t r i x . was  a l s o more pronounced at lower a n n e a l i n g  The  change  temperatures,  which i s c o n s i s t e n t w i t h the shape o f the metastable phase diagram.  However, the e r r o r o f measurement was  relatively  l a r g e , o f the same order o f magnitude as the l a t t i c e parameter changes.  T h i s prevented q u a n t i t a t i v e i n t e r p r e t a t i o n o f the  data. 3.4.  Surface R e l i e f The b a i n i t e p l a t e s formed a s i m p l e - t i l t type o f  s u r f a c e r e l i e f , which i s t y p i c a l o f an i n v a r i a n t plane strain  ( F i g . 12).  In most cases, the t i l t  by some accomodation was  s t r a i n i n the m a t r i x .  was  accompanied  The t i l t  angle 0  c a l c u l a t e d from the f o l l o w i n g e x p r e s s i o n : fx tane = 2TF -  where f i s the f r i n g e displacement a c r o s s the t r a c e measured in  the d i r e c t i o n normal t o the f r i n g e s i n the m a t r i x ,  X(=0.54ym) i s the wavelength  o f the t h a l l i u m - v a p o r l i g h t ,  T i s the width o f the p l a t e t r a c e measured on the scanning e l e c t r o n micrograph, matrix.  and F i s the f r i n g e d i s t a n c e i n the  The maximum observed t i l t  Cd a l l o y was  12+1°.  angle i n the Ag-45 a t . p e t  Accuracy o f the measurement was  limited  by the s m a l l s i z e o f the p l a t e s . The s u r f a c e r e l i e f c r e a t e d by the  widmanstatten  needles growing p a r a l l e l t o the specimen s u r f a c e was  42  HlO/tmn  FIGURE 12 I n t e r f e r e n c e micrographs o f the s u r f a c e r e l i e f caused by formation o f b a i n i t e p l a t e s .  HO/xmH  FIGURE 13 I n t e r f e r e n c e micrographs o f s u r f a c e r e l i e f caused by formation of widmanstatten n e e d l e s .  44 different.  I t was  symmetrical  about the c e n t r e of the  needle, forming the so c a l l e d t e n t - t y p e r e l i e f 3.5.  ( F i g . 13).  B a i n i t e Habit Plane Measurements B a i n i t e p l a t e h a b i t planes were measured i n e i g h t  matrix g r a i n s w i t h i n f o u r d i f f e r e n t specimens, at  240°C.  a l l annealed  A l l of the measured h a b i t plane p o l e s are p l o t t e d  i n Fig.14 but r o t a t e d t o the u n i t t r i a n g l e [ 0 0 1 ] - [ O i l ] - [ 1 1 1 ] of  the m a t r i x .  In s e v e r a l cases i t was  p o s s i b l e to  determine  the h a b i t plane p o l e s of both p l a t e s i n a chevron. In such cases, one of the p o l e s was  r o t a t e d t o the standard u n i t  t r i a n g l e , and the o t h e r was  plotted in i t s original  r e l a t i v e t o the The  position  first.  l a r g e s c a t t e r of r e s u l t s i n Fig.14 may  to wrong matching  of t r a c e s on two s u r f a c e s .  approximately 3.5°  be  due  However, two  t h i r d s of the p o l e s l i e w i t h i n the marked c i r c l e  of  radius.  The p l a t e s forming p a i r s are o r i e n t e d i n such a  way  as t o have t h e i r p o l e s symmetric t o each o t h e r with r e s p e c t to the n e a r e s t [011]^ p o l e of the m a t r i x . 3.6.  T r a n s m i s s i o n E l e c t r o n Microscopy R e s u l t s T r a n s m i s s i o n e l e c t r o n microscopy was  used to study  the morphology and s t r u c t u r e of the b a i n i t i c  precipitates,  t h e i r o r i e n t a t i o n r e l a t i o n s h i p w i t h the matrix and  b  the  45  22o  o  FIGURE 14 P o r t i o n of the standard [001]^ s t e r e o g r a p h i c p r o j e c t i o n of the matrix showing the measured h a b i t plane p o l e s of b a i n i t e p l a t e s formed d u r i n g a n n e a l i n g a t 240°C. The c i r c l e below the [ 0 1 1 ] p o l e (radius approximately 3.5) encompasses two t h i r d s o f a l l measurements. The c i r c l e above the [011]^ p o l e has the same s i z e and i s c e n t e r e d i n the c r y s t a l l o g r a p h i c a l l y e q u i v a l e n t p o s i t i o n w i t h r e s p e c t t o the [ 0 1 1 ] p o l e . The poles marked w i t h numbers belong t o i n d i v i d u a l p l a t e s j o i n e d i n p a i r s , e.g., 31 and 31a. The open t r i a n g l e r e p r e s e n t s the t h e o r e t i c a l h a b i t plane p o l e [0.180747; 0.667566; 0.722279] (see S e c t i o n 3.7). b  b  b  46 changes t h a t o c c u r r e d d u r i n g a prolonged 3.6.1.  i s o t h e r m a l anneal.  Morphology and S t r u c t u r e o f B a i n i t e F r e s h l y formed b a i n i t e p l a t e s were l o n g and narrow,  had p a r a l l e l s i d e s and a very f i n e t i p . micrograph  Fig.15a shows a  o f a b a i n i t e p l a t e i n a Ag-45 a t . p e t Cd a l l o y  a f t e r 15,900 s a t 160°C.  A micrograph  o f a p l a t e i n the  same specimen b u t a t a h i g h e r m a g n i f i c a t i o n i s shown i n Fig.15b.  The p l a t e s c o n t a i n a h i g h d e n s i t y o f s t r i a t i o n s .  A range o f s t r i a t i o n d e n s i t i e s were v i s i b l e i n a l l p l a t e s except those annealed  f o r long p e r i o d s o f time.  Fig.15c  shows t h a t the s t r i a t i o n s are i n f a c t two-dimensional f a u l t s l y i n g w i t h i n the p l a t e s . p a r a l l e l t o the { l l l }  f  These  faults  planar  were always  planes o f the p l a t e s .  A s e l e c t e d area d i f f r a c t i o n p a t t e r n from a b a i n i t e p l a t e a f t e r 15,900 s r e p r e s e n t i n g a {110} l a t t i c e plane i s shown i n F i g . 1 6 .  reciprocal  f  The s t r u c t u r e i s r e c o g n i z e d  as the 3R s t r u c t u r e , a s t a c k i n g modulation  o f the f e e  s t r u c t u r e , which i s d e r i v e d from the f e e l a t t i c e by i n t r o ducing a s t a c k i n g f a u l t a t each t h i r d c l o s e  packed l a y e r .  (A d e t a i l e d s t r u c t u r e a n a l y s i s i s g i v e n i n Appendix A.) The {110}f r e c i p r o c a l l a t t i c e plane o f the 3R s t r u c t u r e i s c h a r a c t e r i z e d by s p l i t t i n g o f the o r i g i n a l f e e spots i n t o a s e r i e s o f three spots each i n one o f the ( i l l ) f d i r e c t i o n s . In each s e r i e s , the spots are arranged weak-medium.  i n the order s t r o n g -  The s p l i t t i n g should not occur i n the  (c)  FIGURE 15 B a i n i t e p l a t e s i n a Ag-45 a t . p e t Cd a l l o y a f t e r 15,900 s a t 160°C (a,b) and 36s a t 240°C (dark f i e l d ) (c) .  FIGURE 16 Selected are d i f f r a c t i o n pattern of a b a i n i t e p l a t e a f t e r 15,900 s a t 160°C. The s t r u c t u r e i s 3R.  49  r e c i p r o c a l l a t t i c e l i n e s of the z e r o t h k i n d .  The  fact that  i n F i g . 16 the e x t r a spots do appear along the l i n e  through  the o r i g i n , as w e l l as along the l i n e s which are t h i r d the o r i g i n  from  (both k i n d s o f l i n e s are o f the z e r o t h kind)  can  be r e a d i l y t r a c e d t o double d i f f r a c t i o n - predominantly  the  double  d i f f r a c t i o n from the s t r o n g 3R r e f l e c t i o n s , f o r example  r e f l e c t i o n 114.  T h i s was  confirmed by the disappearance  the e x t r a spots when the specimen was ( l l l ) f d i r e c t i o n of The  r o t a t e d around the  splitting.  s p l i t spots i n Fig.16 are accompanied by s t r e a k s  i n the d i r e c t i o n o f s p l i t t i n g . the random s t a c k i n g f a u l t s apparent  of  The  s t r e a k s are caused  by  i n the 3R l a t t i c e , which are  as the s t r i a t i o n s shown i n F i g . 1 5 . Prolonged  a n n e a l i n g of b a i n i t e p l a t e s causes them  to t h i c k e n and to change t h e i r s t r u c t u r e .  F i g s . 17a,  b  show micrographs of t y p i c a l b a i n i t e p l a t e s a f t e r s u c c e s s i v e l y l o n g e r p e r i o d s of time a t 160°C.  I t can be seen t h a t the  d e n s i t y o f s t r i a t i o n s decreases with i n c r e a s i n g time, i n d i c a t i n g t h a t the random s t a c k i n g f a u l t s are a n n e a l i n g out.  In F i g s . 18a, b, s e l e c t e d area d i f f r a c t i o n p a t t e r n s  are shown which correspond  to the above micrographs.  The  most s i g n i f i c a n t e f f e c t of i n c r e a s i n g time i s the appearance o f d i f f u s e fee spots o f i n c r e a s i n g i n t e n s i t y and Simultaneously,  sharpness.  the 3R s t r u c t u r e spots are becoming weaker  and more d i f f u s e .  The  change can b e s t be seen i n F i g . 1 9 , i n  FIGURE 17 B a i n i t e i n a Ag-45 a t . p e t Cd a l l o y a f t e r 19,800 s (b) and 25,600 s (b) a t 1 6 0 ° C .  FIGURE 17 - continued  52  (a)  FIGURE 18 S e l e c t e d area d i f f r a c t i o n p a t t e r n s o f b a i n i t e i n a Ag-45 a t . p e t Cd a l l o y a f t e r 19,800 s (a) and 25,600 s (b) a t 160°C. Note the appearance o f fee spots and dissappearance o f 3R s p o t s .  53  (b)  FIGURE 18 - continued  FIGURE 19 Changes i n the d i f f r a c t i o n p a t t e r n s due t o the to fee s t r u c t u r e t r a n s f o r m a t i o n .  3R  which are reproduced only s i n g l e m a g n i f i e d rows o f s p o t s . The  change i n the appearance o f the 3R spots  i s accompanied  by t h e i r displacement from the o r i g i n a l e q u i d i s t a n t p o s i t i o n s . The  strong-weak d i s t a n c e remains approximately the same, w h i l e  the medium-strong becomes l a r g e r and the weak-medium A f t e r a s u f f i c i e n t l y long annealing  shorter.  time, whole  p l a t e s o r l a r g e areas w i t h i n p l a t e s become f r e e o f the stacking f a u l t s .  The micrograph i n F i g . 20a shows a p l a t e  w i t h only a few s t a c k i n g , f a u l t s , e a s i l y r e c o g n i z a b l e their characteristic extinction fringes. the same f i e l d  by  Fig.20b shows  a few moments l a t e r , a f t e r one o f the  s t a c k i n g f a u l t s has disappeared l e a v i n g o n l y what appears t o be a d i s l o c a t i o n r e s o l v e d i n t o two p a r t i a l s .  A number  of these r e s o l v e d : d i s l o c a t i o n s are v i s i b l e i n the lower p a r t o f the micrograph i n F i g . 21. F i g . 22 shows a p l a t e completely f r e e o f l a r g e s t a c k i n g f a u l t s .  Dislocation  d e b r i s l e f t by the s t a c k i n g f a u l t s can be observed. T h i s behaviour can be e x p l a i n e d to fee structure transformation  i n terms o f a 3 R  which occurs by a random  disappearance o f the r e g u l a r l y d i s t r i b u t e d s t a c k i n g The  faults.  3 R s t r u c t u r e w i t h some random s t a c k i n g f a u l t s i s  c h a r a c t e r i z e d by s t r o n g , split  spots  sharp and r e g u l a r l y d i s t r i b u t e d  accompanied by s t r e a k s .  The random disappearance  of the r e g u l a r l y d i s t r i b u t e d s t a c k i n g f a u l t s d i s o r d e r , causing  the 3 R spots  introduces  t o become d i f f u s e and d i s p l a c e d  56  FIGURE 20 Micrographs o f a b a i n i t e p l a t e a f t e r 900 s a t 240°C. Note t h a t the s t a c k i n g f a u l t i n the upper r i g h t h a n d corner i n (a) disappeared i n (b) l e a v i n g a d i s l o c a t i o n r e s o l v e d i n t o two p a r t i a l s (A).  FIGURE 21 Micrograph of a b a i n i t e  plate  a f t e r 900 s a t 240°C.  FIGURE 22 Micrograph of a b a i n i t e p l a t e a f t e r 900  s a t 240°C  59  from t h e i r p o s i t i o n s . i s introduced  Simultaneously, fee s t a c k i n g  l o c a l l y , but due  s t a c k i n g f a u l t s , fee spots  order  t o the l a r g e number of random  are a l s o broadened. With a  decrease i n the number of 3R s t a c k i n g f a u l t s , the become weaker, more d i f f u s e and more d i s p l a c e d .  spots  Simul-  taneously,  the fee spots become s t r o n g e r  eventually  the s t r u c t u r e becomes fee with random s t a c k i n g  faults. and  An  a d d i t i o n a l f a c t o r causing  fee spots  and  3R  sharper, u n t i l  broadening o f the  i s the extremely s m a l l t h i c k n e s s  bands of these two  Stacking  of the d i s c r e t e  s t r u c t u r e s which e x i s t d u r i n g the  s i t i o n a l p e r i o d o f the s t r u c t u r e  3R  tran-  transformation.  f a u l t s probably disappear by  generating  a p a r t i a l d i s l o c a t i o n on the i n t e r f a c e between the m a t r i x and  the b a i n i t e p l a t e . T h i s i s supported by the  observation  t h a t the s t a c k i n g f a u l t s always s t a r t d i s a p p e a r i n g the p l a t e - m a t r i x : i n t e r f a c e  (Figs. 2 0 a , b).  d i s l o c a t i o n then sweeps across f a u l t , canceling i t .  The  the plane of the  from  partial stacking  I f the p a r t i a l d i s l o c a t i o n i s prevented  from t r a v e l l i n g to the other  i n t e r f a c e by meeting another  p a r t i a l d i s l o c a t i o n coming from the opposite  direction, a  p a i r of p a r t i a l d i s l o c a t i o n s remains i n the p l a t e , t h e i r s e p a r a t i o n d i s t a n c e r e f l e c t i n g the s t a c k i n g f a u l t energy of the a l l o y and magnitude o f the l o c a l l a t t i c e s t r e s s . I t was was  observed t h a t the t h i c k e n i n g of b a i n i t e p l a t e s  i n f l u e n c e d by the random s t a c k i n g f a u l t s w i t h i n the p l a t e s .  FIGURE 23 Micrographs of b a i n i t e p l a t e s a f t e r 900 s a t 240°C. The p o r t i o n s with zero s t a c k i n g f a u l t d e n s i t y t h i c k e n e d f a s t e r than the r e s t of the p l a t e s .  61 F i g s . 23 a, b show micrographs o f p l a t e s a f t e r 900 240°C.  The  plates  contain  portions  w i t h zero  s at  stacking  f a u l t d e n s i t y which have t h i c k e n e d f a s t e r . T h e p r e c i p i t a t e m a t r i x i n t e r f a c e has  bulged out between the p o r t i o n s  that  were seemingly slowed down by the remaining s t a c k i n g I t appears t h a t the disappearance of s t a c k i n g the nature of the  i n t e r f a c e i n such a way  faults.  f a u l t s changed  to allow i t to  migrate more e a s i l y . 3.6.2.  Orientation The  and  Relationship  o r i e n t a t i o n r e l a t i o n s h i p between the  the m a t r i x was  determined from the  (lll)  composite e l e c t r o n d i f f r a c t i o n p a t t e r n s , shown i n F i g . 24. the  The  one  -  b  bainite (OlD^  of which i s  r e s u l t s , expressed as angles between  four d i f f e r e n t s e t s of d i r e c t i o n s i n the m a t r i x and  the b a i n i t e l a t t i c e cubic notation),  (the b a i n i t e l a t t i c e was  are g i v e n i n Table I I .  are presented s c h e m a t i c a l l y relationship established Bain o r i e n t a t i o n The  i n F i g . 25.  i s within  in  indexed i n  the  The  same r e s u l t s  The  orientation  several  degrees of  the  relationship.  mutual o r i e n t a t i o n of p l a t e s  joined  in a pair  arid t h e i r o r i e n t a t i o n r e l a t i o n s h i p w i t h the m a t r i x were determined u s i n g the  same technique.  In F i g s . 26a,  shown d i f f r a c t i o n p a t t e r n s which were taken from the of the b a i n i t e chevron shown i n F i g . 26c.  The  b  are branches  branches  FIGURE  24  S e l e c t e d area d i f f r a c t i o n p a t t e r n composed of ( l l l ) b and ( O l l ) f r e c i p r o c a l l a t t i c e p l a n e s .  TABLE I I Experimental O r i e n t a t i o n R e l a t i o n s h i p Between t h e g» Parent Phase and the B a i n i t e *  Angle between p o l e s , degrees  D i r e c t i o n in the L a t t i c e of Parent  [Ul]  b  [oii] U12]  +  b  b  D i f f r a c t i o n P a t t e r n Number  Bainite ,  [011]  f  [100]  f  [lll] [011]  +  f  +  10  ±0  1  2  3  4  5  6  7  8  0.9  0.9  0.8  0.6  0.6  1.0  0.3  0.7  0.6  0.5  0.7±0.2  0.9  1.6  1.2  1.3  1.1  0.7  0.6  1.1±0.4  4.3  4.7  4.5  4.8  4.6  3.8  4.1  4.3±0.4  1.3  1.3  1.6  0.9  0.9  1.0  0.9  1.1±0.3  f  Mean v a l u e  .3.9 —  3.8  4.0  9  A l l measurements were performed on e l e c t r o n d i f f r a c t i o n p a t t e r n s composed o f [ l l l ] and [ 0 l l ] zones. The angle between the zone axes was determined by the method developed by Ryder and P i t s c h (41,42).  b  f  ++ The p o l e o f the s t a c k i n g f a u l t plane  (Tl LO  64  FIGURE 25 Schematic s t e r e o g r a p h i c p r o j e c t i o n diagram o f the o r i e n t a t i o n r e l a t i o n s h i p between the B parent and bainite. The b a i n i t e l a t t i c e i s indexed i n c u b i c n o t a t i o n ; although the [111]^ and [011]f p o l e s are here shown t o c o i n c i d e , they are a c t u a l l y approximately 1  0.7° appart.  65  The composite m a t r i x - b a i n i t e d i f f r a c t i o n p a t t e r n s (a,b) obtained from the branches o f the chevron shown i n ( c ) .  66  FIGURE 27 O r i e n t a t i o n r e l a t i o n s h i p between the two b a i n i t e p l a t e s (I and II) and the m a t r i x . The normal t o the p r o j e c t i o n i s p a r a l l e l t o the o p t i c a l a x i s i n F i g . 26. Poles marked p , and P-^ are the t h e o r e t i c a l h a b i t plane p o l e s o f the p l a t e s I and I I . T h e i r i n d i c e s are p x - [ - 0 . 6 6 7 5 6 6 ; -0.180774; 0.722279] and p - _ H = [0.722279; -0.180747; -0.667566] . 1  11  1  b  b  67 were o r i e n t e d i n such a way 51.5°  t h a t a r o t a t i o n of approximately  about the o p t i c a l a x i s , f o l l o w e d by a r o t a t i o n o f  approximately 180°  about the  [111]^ d i r e c t i o n , the d i r e c t i o n  along which the s t r e a k i n g o c c u r r e d , d i f f r a c t i o n patterns, shown s c h e m a t i c a l l y 3.7.  brought the  a and b, i n t o c o i n c i d e n c e .  in Fig.  s e c t i o n s , i t was  b a i n i t e i n i t s e a r l y stages of formation r e g u l a r p l a t e - l i k e morphology.  The  inhomogeneity, s t a c k i n g f a u l t s , was i t was  formation type.  This i s  27.  A p p l i c a t i o n of the Phenomenological Theory t o the Formation o f B a i n i t e In the previous  and  two  Martensite  shown t h a t  displayed a highly  presence o f an i n t e r n a l e s t a b l i s h e d i n the  found t h a t the s u r f a c e r e l i e f caused by of the p l a t e s was  I t was  the  of an i n v a r i a n t plane  plates  the strain  a l s o shown t h a t the o r i e n t a t i o n r e l a t i o n s h i p  between the m a t r i x and correspondence.  the b a i n i t e was  c l o s e t o the  These c h a r a c t e r i s t i c s , u s u a l l y  Bain  associated  w i t h a m a r t e n s i t i c product, n a t u r a l l y l e d to the a p p l i c a t i o n of the phenomenological theory the formation  of martensite  of the b a i n i t e p l a t e s i n the bcc  of the Ag-Cd a l l o y .  The  martensite  theory  observations.  p r i n c i p l e s o f the a n a l y t i c a l treatment o f phenomenology, as a p p l i e d t o the p r e s e n t  are given i n Appendix B.  The  Bain  to  B' matrix  r e s u l t s p r e d i c t e d by the  were compared with the experimental The  formation  lattice  the  system,  correspondence  >  68 was  assumed, as shown i n F i g . B-1.  The l a t t i c e parameters  of the parent and the product a t the t r a n s f o r m a t i o n temperature  (160-240°C) were assumed t o be those v a l u e s measured  at room temperature at 20Q°C f o r 529  i n the Ag-45 a t . p e t Cd a l l o y  s (Table I ) .  The e f f e c t o f  on the l a t t i c e parameter v a l u e s was  annealed  temperature  n e g l e c t e d s i n c e the data  on the thermal expansion o f the ordered 8  1  phase were not  a v a i l a b l e . A p o s s i b l e t e t r a g o n a l d i s t o r t i o n of the product, r e s u l t i n g from the o r d e r i n g (CuAu I type) i n h e r i t e d from parent, was  a l s o n e g l e c t e d , s i n c e i t was  d i f f r a c t i o n patterns.  I t was  ( l l l ) f shear plane was  of s t a c k i n g f a u l t s on {111} [112]  f  was  (112)  f  d i r e c t i o n s i n the  f  (111)  [ll2] . f  Two  planes.  The  shear  (111)  f  direction  plane which does not  obtained. and the  violate strain,  crystallographically distinct variants  of the i n v a r i a n t l i n e - i n v a r i a n t plane normal  1  choice  c o n s i s t e n t w i t h the o b s e r v a t i o n  s o l u t i o n s of the i n v a r i a n t l i n e  S, corresponding t o two  (x , n )  The  shear  chosen because t h i s i s the o n l y one of the t h r e e  the atomic o r d e r .  were  i n the  f u r t h e r assumed t h a t the  system o p e r a t i n g i n the product was of the  not observed  the  combinations,  The two v a r i a n t s are r e f e r r e d t o as the (x-j_, n ) 2  variants.  The r e s u l t s f o r both  v a r i a n t s d e r i v e d from the theory are g i v e n i n Table I I I . The a p p l i c a t i o n of the i n v a r i a n t l i n e s t r a i n  matrix  (bSb) on the l a t t i c e of the parent r e s u l t s i n the o r i e n t a t i o n r e l a t i o n s h i p g i v e n i n Table IV.  The mean v a l u e s of the  69 TABLE I I I S t r a i n s and H a b i t Planes P r e d i c t e d by the M a r t e n s i t i c Theory Assuming the B a i n L a t t i c e Correspondence w i t h L a t t i c e Parameters a = 3.324 A and a = 4.186 & and the shear system (111) [ 1 1 2 ] . b  f  Variant  f  Habit Plane Pole, p  Invariant Line S t r a i n Matrix, (bSb)  ±  l' l>  0.884593 0.099149 •0.024814  -0.091389 0.064720 0.864098 -0.270022 0.194768 1.228335  •0.667566 •0.722279 0.180747  (X!,n )  0.884593 0.024814 •0.099149  -0.012685 0.143425 0.883812 -0.149754 0.108019 1.242139  0.667566 0.180747 •0.722279  Variant  Direction of the Shape Deformation,  ( x  n  2  Magnitude o f the Shape Deformation, m.  Magnitude o f the L a t t i c e Invariant Shear, m 2  Angle o f the Lattice Invariant Shear, <x 2  (x^n^  0.748615 -0.643169 0.160966  0.230924  0.428838  24.20  (x ,n )  -0.748615 -0.160966 -0.643169  0.230924  0.237831  13.56'  1  2  v  70  TABLE IV T h e o r e t i c a l and Experimental O r i e n t a t i o n R e l a t i o n s h i p Between the Parent and Product L a t t i c e s  Angle Between P o l e s , Degrees  D i r e c t i o n i n the Lattice of  Theoretical Parent  Bainite  [Hl]  b  [011]  [iio]  b  [100]  [011]  b  [112].  Experimental  Variant (x ,n ) Variant 1  1  (x ,n ) 1  2  0.78  0.78  0.7±0.2  9.51  1.25  1.1±0.4  [HI]/  4.30  4.30  4.3±0.4  [011],  9.54  1.05  1.1±0.3  f  f  + Pole of the plane of l a t t i c e i n v a r i a n t  shear.  71 experimental o r i e n t a t i o n r e l a t i o n s h i p from Table I I are a l s o i n c l u d e d i n Table IV f o r  comparison.  R o t a t i o n of the h a b i t plane p o l e s of the two  variants  to the standard u n i t s t e r e o g r a p h i c t r i a n g l e r e s u l t s i n the pole with i n d i c e s is  [0.180747; 0.667566; 0.722279] , which b  2.25° from the p o l e  [ 1 4 4 ] , as shown i n F i g . 14. b  I t can  be seen t h a t the t h e o r e t i c a l h a b i t plane p o l e i s a p p r o x i mately  1° from the c e n t r e of the c i r c l e encompassing  t h i r d s of the experimental h a b i t  two  plane measurements.  The angle between the h a b i t plane normal and  the  d i r e c t i o n of the shape deformation f o r both v a r i a n t s i s c l o s e t o 90° variant  (90.35° f o r v a r i a n t  (x-p n ) 2  (x  1 #  and 93.69° f o r  ), which means t h a t the maximum t i l t  angle  should occur when the h a b i t plane i s approximately p e r p e n d i c u l a r t o the s u r f a c e o f the specimen.  For the  theoretical  magnitude of the shape deformation m-^ = 0.230924, the maximum tilt  angle i s 13.3°. T h i s value agrees w e l l with the maximum  measured value of 12°, c o n s i d e r i n g the l a r g e e r r o r of the • measurement. The two v a r i a n t s p r e d i c t an i d e n t i c a l magnitude f o r the shape deformation.  However, the magnitude of the  i n v a r i a n t shear f o r v a r i a n t  (x-^, n ) 2  i s approximately  lattice a  f a c t o r of two s m a l l e r than the magnitude f o r the v a r i a n t (x^,  n ^ ) , i n d i c a t i n g t h a t the t r a n s f o r m a t i o n i s more l i k e l y  72  to  occur by the mechanism a s s o c i a t e d w i t h the  variant.  (x^,  n) 2  The magnitude of the l a t t i c e i n v a r i a n t shear f o r  the v a r i a n t  (x^, n )  corresponds t o a shear angle of  2  13.56°,  which i s very c l o s e t o the shear angle o f 13.26° r e s u l t i n g from the c r e a t i o n o f an i d e n t i c a l s t a c k i n g f a u l t on third  (lll)  plane, as i s p r e s e n t i n the 3R  f  each  structure.  The e x p e r i m e n t a l l y determined mutual o r i e n t a t i o n of chevron p a i r s If  ( F i g s . 26, 27) was  each o f the two p l a t e s i s a s s i g n e d a t h e o r e t i c a l h a b i t  plane of the v a r i a n t of  d e s c r i b e d i n S e c t i o n 3.6.2.  (x^, n ) , as shown i n F i g . 27, the p o l e s 2  t h e i r h a b i t planes are symmetrical w i t h r e s p e c t t o the  nearest pole.  (110)^ p o l e o f the m a t r i x , i n t h i s case the The  analysis  same r e s u l t was  ( S e c t i o n 3.5.).  theoretical  habit  [101]^  o b t a i n e d by the two-surface  trace  I t can be shown t h a t when the  planes are a s s i g n e d t o two p l a t e s having  the d e s c r i b e d o r i e n t a t i o n r e l a t i o n s h i p , the angle between the t r a c e s of the p l a t e s in  ( i . e . , the branches  of the chevron)  the f o i l has t o be 165.5° p r o v i d i n g t h a t the specimen i s  o r i e n t e d so t h a t the d i r e c t i o n s  [Oil]  1 f  ,[Oil]  1 1 f  are approximately p a r a l l e l to the o p t i c a l a x i s .  and  [lll]  b  This i s i n  e x c e l l e n t agreement w i t h the measured angle of 164° between the branches shows t h a t  o f the chevron c o n t a i n e d i n F i g . 2 6 c .  This  the t h e o r e t i c a l h a b i t plane i s not o n l y  c r y s t a l l o g r a p h i c a l l y s i m i l a r t o the experimental h a b i t plane, but i d e n t i c a l t o i t ,  i . e . , the h a b i t plane i s p r e d i c t e d  73 uniquely. A comparison of the t h e o r e t i c a l and  experimental  o r i e n t a t i o n r e l a t i o n s h i p s , T a b l e IV, shows t h a t  the  t h e o r e t i c a l o r i e n t a t i o n r e l a t i o n s h i p of the v a r i a n t i s very c l o s e t o the experimental one, the two being l e s s than 3.8.  n^)  (x^,  the d i f f e r e n c e s  between  0.5°.  Comparison w i t h the M a r t e n s i t i c Products Observed i n Ag-Cd, Ag-Zn and Cu-Zn A l l o y s The c r y s t a l l o g r a p h i c  c h a r a c t e r i s t i c s of b a i n i t e i n  the Ag-Cd a l l o y are s i m i l a r t o the c r y s t a l l o g r a p h i c t e r i s t i c s of m a r t e n s i t i c  charac-  products i n Ag-Cd, Ag-Zn and Cu-Zn  alloys. Krishnan  (28) r e p o r t e d a good agreement between the  experimental and t h e o r e t i c a l r e s u l t s f o r the m a r t e n s i t e w i t h the 2H s t r u c t u r e alloy.  Ayers  found i n the Ag-45 a t . p e t Cd  (27) found even b e t t e r  p l a t e s of the i s o t h e r m a l twinned  thermal  agreement f o r the  fee m a r t e n s i t e formed a t  280°C i n the Ag-37.8 a t . pet Zn a l l o y ; the experimental  habit  plane p o l e s were c l u s t e r e d  plane  around the t h e o r e t i c a l h a b i t  p o l e s and the d i f f e r e n c e between the experimental and o r i e n t a t i o n r e l a t i o n s h i p was  l e s s than 0.5°.  Wayman (24, 36) a l s o o b t a i n e d e x c e l l e n t  Cornells  theoretical and  agreement between  the experimental and t h e o r e t i c a l v a l u e s f o r both the m a r t e n s i t e and b a i n i t e i n Cu-Zu a l l o y s .  They found t h a t the  characteris-  t i c s of m a r t e n s i t e and b a i n i t e i n t h i s a l l o y were i d e n t i c a l ,  74 except t h a t the b a i n i t e p l a t e s had much s m a l l e r  a 3R s t r u c t u r e and were  than the m a r t e n s i t e p l a t e s which had  a twinned  fee structure " w i t h a s l i g h t orthorhombic d i s t o r t i o n . -1  + Such d i f f e r e n c e s r e s u l t from the d i f f e r e n t modes o f the l a t t i c e i n v a r i a n t shear and do not n e c e s s a r i l y i n f l u e n c e the macroscopic c h a r a c t e r i s t i c s of the transformation.  In a l l c a s e s , the t h e o r e t i c a l p r e d i c t i o n s were based on the assumption of a B a i n correspondence and l a t t i c e i n v a r i a n t shear.  The  {111}(112^  experimental h a b i t plane  were c l u s t e r e d c l o s e t o the l i n e connecting the [1443^ p o l e s , The  poles  [133]^  and  s i m i l a r to t h a t o b t a i n e d i n the p r e s e n t r e s u l t s .  l a t t i c e o r i e n t a t i o n r e l a t i o n s h i p was  essentially identical  to t h a t found f o r b a i n i t e i n the Ag-Cd a l l o y . The  Ag-Cd data  a l s o agreed w e l l with the o r i e n t a t i o n r e l a t i o n s h i p o b t a i n e d f o r the i s o t h e r m a l being l e s s than  m a r t e n s i t e i n the Ag^-Zn a l l o y , the  difference  0.5°.  In l i g h t of the e x c e l l e n t agreement between the observed c r y s t a l l o g r a p h y a l l o y and and  of b a i n i t e i n the Ag-45 a t . pet  the r e s u l t s p r e d i c t e d by the m a r t e n s i t i c  considering  theory  the s i m i l a r i t y w i t h the c r y s t a l l o g r a p h i e s of  b a i n i t e and m a r t e n s i t e formed from the  g  1  phase o f Cu-Zn  type a l l o y s , i t can be concluded t h a t the n u c l e a t i o n e a r l y growth o f b a i n i t e occurs by a t h e r m a l l y martensitic  Cd  process.  and  activated  75 3.9  O r i g i n and  S t a b i l i t y of the  In a systematic  3R S t r u c t u r e  a n a l y s i s of e q u i l i b r i u m  i n Au-Mn a l l o y s w i t h 20-28 a t . pet Mn to AugMn) , Sato e-t al.  (44,  45)  of B a i n i t e structures  (the composition near  e s t a b l i s h e d the e x i s t e n c e  of  close-packed s t r u c t u r e s having a long p e r i o d s t a c k i n g  fault  modulation  sensi-  i n which the type of modulation was  t i v e to composition. The thought to be due  quite  s t a b i l i t y o f these s t r u c t u r e s  to the lowering o f the energy o f  was  the  conducting e l e c t r o n s by the c r e a t i o n o f the B i r i l l o u i n zone boundaries at the Fermi s u r f a c e . due  The  to the i n t r o d u c t i o n of s t a c k i n g  n e g l i g i b l e , s i n c e the s t a c k i n g energy boundaries accross atoms does not  opposing energy term  f a u l t s was  assumed to  f a u l t boundaries are  low  which the number o f nearest  S i m i l a r s t r u c t u r e s were found i n o t h e r noble  alloys  (46)  i n c l u d i n g some m a r t e n s i t e s found i n the  b a i n i t e i n Cu-Zn (36).  atom r a t i o i n the of the  and  Cu-Zn (24) ,  In a l l cases the  3 phase i s c l o s e t o 1.5.  electron-toThe  fee s t r u c t u r e i n these a l l o y s occurred  fee s t r u c t u r e i s not the  and  i n m a r t e n s i t e s o f nonferrous  3-phase a l l o y s of Au-Cd (46), Ag-Cd (28) and  neighbor  change.  t r a n s i t i o n metal a l l o y s and  3-phase.  a martensitic  modulation  because  the  s t a b l e i n the composition range of  I t should be p o i n t e d transformation  out t h a t i n the case of  the p o s s i b l e r e s u l t i n g  s t r u c t u r e s are l i m i t e d by the s t a r t i n g s t r u c t u r e s .  be  In  the  76 present work i t has been shown t h a t the observed  3R  s t r u c t u r e i s compatible w i t h a 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 . The o r d e r o f appearance o f modulated s t r u c t u r e s i n 8 phase a l l o y s w i t h i n c r e a s i n g e l e c t r o n - t o - a t o m r a t i o i s always 3R t o 2H approximately  (24, 28, 46), w i t h the 3R appearing a t  45 a t . pet of the d i v a l e n t component.  An important q u e s t i o n i s whether the b a i n i t e i n the Ag-Cd a l l o y can i n i t i a l l y  form w i t h the e q u i l i b r i u m  composition of the fee a phase s t a b l e a t t h a t a n n e a l i n g temperature.  An assumption  t h a t the composition of the  b a i n i t e a d j u s t s t o i t s e q u i l i b r i u m value by long range d i f f u s i o n d u r i n g the i n i t i a l  stages o f the t r a n s f o r m a t i o n  would not e x p l a i n the 3R modulation observed  3R modulation  i n the s t r u c t u r e .  The  c o u l d occur e i t h e r as a d i r e c t  r e s u l t of a 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 , or as a way  of  s t a b i l i z i n g a c l o s e packed s t r u c t u r e having a h i g h e r e l e c t r o n to-atom r a t i o than allowed by e q u i l i b r i u m . the  f o l l o w i n g c o n c l u s i o n i s reached.  In e i t h e r  case,  The b a i n i t e  forms  w i t h a composition e i t h e r i d e n t i c a l or very c l o s e t o the composition of the p a r e n t . In  the view o f the dependence on composition of the  s t a c k i n g modulation  of the fee s t r u c t u r e , i t should be  expected t h a t the s t a c k i n g f a u l t energy increasing electron-to-atom r a t i o .  decreases  with  Indeed, Howie and  Swann (41) found t h a t the s t a c k i n g f a u l t e n e r g i e s of  copper  77 and s i l v e r c o n t i n u a l l y decreased w i t h i n c r e a s i n g amounts of added aluminum or z i n c , r e a c h i n g a value l e s s than  one  t e n t h of t h e i r v a l u e s f o r pure copper and s i l v e r a t the e l e c t r o n - t o - a t o m r a t i o of approximately 1.35  (17.5 a t . p e t  A l o r 35 a t . p e t Zn). Howie and Swann a l s o e s t a b l i s h e d the s t a c k i n g f a u l t energy  that  i n Ni-Co a l l o y s v a r i e d w i t h an  i n c r e a s i n g amount o f c o b a l t i n a s i m i l a r f a s h i o n , e x t r a p o l a t i n g t o zero a t approximately 75 wt. pet Co, which i s the composition where the fee t o hep t r a n s i t i o n o c c u r r e d . I f the s t a c k i n g f a u l t energy changes with i n a s i m i l a r manner throughout Ag-Cd system,  composition  the a-phase r e g i o n i n the  the b a i n i t e p l a t e s w i t h t h e i r h i g h d e n s i t y  of s t a c k i n g f a u l t s w i l l tend t o form w i t h a composition which has a lower s t a c k i n g f a u l t energy,  i . e . , a higher  concen-  t r a t i o n o f cadmium, than the e q u i l i b r i u m a phase. T h i s has a l r e a d y been deduced from the s t r u c t u r e a n a l y s i s . Only  the  prolonged a n n e a l i n g allows the r e a l i z a t i o n o f the lower e q u i l i b r i u m a phase composition by l o n g range d i f f u s i o n . i n t u r n , i n c r e a s e s the energy o f the s t a c k i n g f a u l t s t h e i r disappearance  This,  and  f u r t h e r reduces the energy o f the  To summarize, i t appears  energy  system.  t h a t the l o n g p e r i o d s t a c k i n g  f a u l t modulation of the fee s t r u c t u r e i s an important  energy  f a c t o r i n s t a b i l i z i n g the b a i n i t e i n Ag-45 a t . pet Cd  alloy.  However, t h i s s t a b i l i z a t i o n e f f e c t i s necessary and only i n the i n i t i a l stages of b a i n i t e f o r m a t i o n .  possible  The  78 prolonged  annealing a t e l e v a t e d temperatures  allows  p a r t i t i o n i n g o f s i l v e r and cadmium between the b a i n i t e and the matrix,  thereby  r a t i o o f the b a i n i t e  d e c r e a s i n g the e l e c t r o n - t o - a t o m  and d e s t a b i l i z i n g the 3R s t r u c t u r e  with i t s i n t r i n s i c h i g h d e n s i t y o f s t a c k i n g f a u l t s . T h i s simultaneously  s t a b i l i z e s the f e e s t r u c t u r e , which has the  lowest p o s s i b l e volume f r e e energy a t t h a t temperature. 3.10  Growth K i n e t i c s Growth k i n e t i c s measurements were made on the  Ag-45 a t . p e t Cd a l l o y .  T h i s a l l o y was c o n s i d e r e d t o be  the most s u i t a b l e as t h e 3  1  phase c o u l d be completely  r e t a i n e d on quenching and p r e c i p i t a t i o n a t low temperatures produced the d e s i r e d p r e c i p i t a t e morphology. B a i n i t e p l a t e s and widmanstatten needles e x h i b i t e d d i f f e r e n t modes o f n u c l e a t i o n and growth.  The p l a t e s  n u c l e a t e d , grew r a p i d l y t o a g i v e n l e n g t h and maintained l e n g t h f o r extended t r a n s f o r m a t i o n times, although continued t o t h i c k e n .  that  they  The t e r m i n a t i o n o f the r a p i d  lengthening o f the f i r s t i s o l a t e d p l a t e s i n most cases appeared not t o be due t o impingement w i t h other Some o b s e r v a t i o n s  precipitates.  i n d i c a t e d t h a t p l a t e s continued t o lengthen  very s l o w l y a f t e r the t e r m i n a t i o n o f the r a p i d l e n g t h e n i n g . However, the a d d i t i o n a l l e n g t h d e v i a t e d from the o r i g i n a l p l a t e d i r e c t i o n o r branched o f f i n t o two new p l a t e s o r needles. At l a t e r t r n a s f o r m a t i o n times, a f t e r p l a t e s had ceased t o  79 lengthen, new p l a t e s continued t o n u c l e a t e same f a s h i o n .  and grow i n the  This behavior i s i l l u s t r a t e d  by the s e r i e s o f  micrographs shown i n F i g s . 28 and 29. In c o n t r a s t  t o the p l a t e s ,  the widmanstatten needles c o n t i n u e d t o both lengthen and thicken  f o r extended growth times u n t i l the impingement w i t h  other p r e c i p i t a t e s . The  growth k i n e t i c s o f i s o l a t e d p l a t e s were  measured a t 160, 200 and 240°C. Lengthening o f the p l a t e s o was so r a p i d a t 200 and 240 C t h a t i t was not p o s s i b l e t o measure the i n i t i a l annealing  method.  lengthening  using  the i n t e r r u p t e d  However, the lengthening  r a t e was measured  at 160°C; a s e r i e s o f micrographs i l l u s t r a t i n g  the  lengthening  of a p a i r o f p l a t e s i s shown i n F i g . 30. Thickening be  o f the p l a t e s was much  s u c c e s s f u l l y monitored u s i n g  procedure a t a l l three  thickened 3.10.1  the i n t e r r u p t e d  temperatures.  Fig.31 i l l u s t r a t e t h i c k e n i n g  slower and c o u l d annealing  Micrographs shown i n  o f a b a i n i t e p l a t e ; the p l a t e  on both s i d e s .  A n a l y s i s o f B a i n i t e Thickening A p l o t o f the h a l f - w i d t h  as a f u n c t i o n o f the annealing shown i n F i g . 32.  Data  o f the p l a t e t r a c e , X,  time f o r a t y p i c a l p l a t e i s  The curve has a p a r a b o l i c  suggesting t h a t b a i n i t e t h i c k e n i n g equation f o r d i f f u s i o n c o n t r o l l e d  shape,  obeys the p a r a b o l i c thickening.  rate  80  3 0 ^.m  FIGURE 28 O p t i c a l micrographs o f l i g h t l y etched s u r f a c e o f a Ag-45 a t . pet Cd specimen annealed a t 200°C. (a) A f t e r 625 s: A number o f chevron shaped b a i n i t e t r a c e s appeared with an o c c a s i o n a l widmanstatten needle (A). (b) A f t e r 900s: B a i n i t e t r a c e s present i n (a) have e i t h e r maintained t h e i r o r i g i n a l l e n g t h or have lengthened s l i g h t l y , but a l l have i n c r e a s e d t h e i r t h i c k n e s s . The t i p s o f some o f the p l a t e s a p p a r e n t l y a c t e d as n u c l e a t i o n s i t e s f o r widmanstatten needles (B). Widmanstatten needles continued to l e n g t h e n . A number o f new b a i n i t e t r a c e s appeared (C). (c) A f t e r 1,225 s: The same behaviour i s continued; o l d b a i n i t e t r a c e s t h i c k e n and new ones keep appearing, while widmanstatten needles which have not impinged upon o t h e r p r e c i p i t a t e s continue t o l e n g t h e n .  81  FIGURE 29 Scanning e l e c t r o n micrographs o f the unetched s u r f a c e o f a Ag-45 a t . p e t Cd specimen annealed a t 240°C. (a) A f t e r 16 s: A b a i n i t e chevron appeared, (b) A f t e r 36 s: The lower arm of the chevron from (a) d i d not lengthen although i t t h i c k e n e d a p p r e c i a b l y , w h i l e t r a c e s o f new p l a t e s appeared from the l e f t , the lower one s t o p p i n g b e f o r e impinging upon the o r i g i n a l p l a t e , (c) A f t e r 49 s: T h i c k e n i n g continued without l e n g t h e n i n g .  82  9,025 sec  11,025 sec  15,625 sec  24,025 sec  FIGURE 30 Scanning e l e c t r o n micrographs o f a p a i r o f b a i n i t e p l a t e s i n a Ag-45 a t . p e t Cd a l l o y s h o w i n g t h e i r e a r l y g r o w t h a t 160°C. B o t h l e n g t h e n i n g and t h i c k e n i n g a r e v i s i b l e .  FIGURE 31 Scanning e l e c t r o n m i c r o g r a p h s showing t h i c k e n i n g o f t h e t r a c e o f a b a i n i t e p l a t e a t 240°C i n a Ag-45 a t . p e t Cd a l l o y  84  0  2000  4000  6000  8000  ANNEALING  TIME,  S  FIGURE 32  Thickening k i n e t i c s of a b a i n i t e p l a t e a t 200°C i n a Ag-45 a t . p e t Cd a l l o y  trace  10000  85  FIGURE The  X  2  t  a  p l o t f o r the  33  bainite plate  trace  from  Fig.32.  8  The  p a r a b o l i c r a t e equation  can be w r i t t e n i n the  + An o u t l i n e of the theory of volume d i f f u s i o n c o n t r o l l e d p r e c i p i t a t e growth i s given i n Appendix C. f o l l o w i n g form: X = L[D  (t  t_ = — L  . D  - x)] ,  t  h  a  a  >  (1)  T  or  where t  2  x  +  2  T  ,  (la)  i s the t o t a l annealing  a  time and  time f o r n u c l e a t i o n o f the p l a t e .  Eq.  T i s the  incubation  (la) shows t h a t t_ i s ci  l i n e a r l y dependent on X . 2 2  p l a t e t r a c e s , X , was  Square of the h a l f - w i d t h of  p l o t t e d as a f u n c t i o n o f the  the  annealing  time, t , as shown i n F i g . 33 f o r the p l a t e from F i g .  32.  L i n e a r r e l a t i o n s h i p s were obtained  slopes  a  d(X )/dt 2  a  The  are l i s t e d i n Table V.  The deviated  i n a l l cases.  X  2  vs.  t  p l o t s obtained  a f t e r long growth times  from a s t r a i g h t l i n e behaviour.  the d e v i a t i o n o c c u r r e d  I t was  assumed t h a t  when the d i f f u s i o n f i e l d o f the  t a t e overlapped w i t h the d i f f u s i o n f i e l d s of  precip  neighboring  precipitates. The width of the p l a t e t r a c e s and  therefore  the  measured growth r a t e s o b v i o u s l y have to depend on the angle a between the p l a t e s and  the specimen s u r f a c e .  made to determine t h a t angle.  The  An  attempt  was  p l a t e s gorwn at 240°C  ( l i s t e d i n Table V) were chosen because of t h e i r  relatively  87 TABLE V 2 2 B a i n i t e P l a t e T h i c k e n i n g Slope d(X ) / d t i n n r / s f o r Traces o f B a i n i t e P l a t e s Grown i n a Ag-45 a t . pet Cd A l l o y a t 160, 200 and 240°C a  Plate  240°C  200°C  160°C [d(X )/dt ]x 2  a  10  1 8  [d(X )/dt ]x 10 2  a  1 6  [d(X )/dt ]x 2  a  No. 1  2.71  5.43  1.82  2  2.41  2.37  2.04  3  1.72  5.43  1.88  4  1.92  17.31  2.23  5  1.13  6  2.38  2.34  1.73  7  2.01  3.10  4.74  8  1.24  2.82  4.00  9  1.95  2.22  1.84  10  1.31  2.34  3.56  11  1.15  3.20  3.29  12  1.17  3.28  2.31  13  2.31  5.20  5.00  14  2.41  2.46  +  15  + Minimum observed growth r a t e  2.02  2.10  +  2.75 +  88  large s i z e .  I n i t i a l l y , i t was  assumed t h a t the growth r a t e  i s equal f o r a l l p l a t e s growing without i n t e r f e r e n c e w i t h neighboring  p r e c i p i t a t e s , so t h a t a l l the p l a t e s grow to  same t h i c k n e s s  T  at time t a f t e r n u c l e a t i o n .  for d i f f e r e n t plates  the  Then the  v a r i a t i o n o f the measured t r a c e t h i c k n e s s , 2X^, be assumed to be o n l y due  the  a t time t  can  to the v a r i a t i o n o f the angle a  (Fig.34).  I t was  a l s o assumed t h a t  the  p l a t e with the slowest measured growth r a t e , or p l a t e No.6 Table V,  in  i s normal to the s u r f a c e , i . e . , t h a t the angle a f o r  t h i s p l a t e i s 90°.  Using these assumptions, i t i s p o s s i b l e  to c a l c u l a t e the angle a f o r a l l p l a t e s u s i n g the  following  relation:  t  T s i n  a  calc " —  w i t h the parameter T p l a t e No.6,  2X  t  ( 2 )  equal t o the measured t r a c e width of  f o r which s i n a = 1.  trace thickness, a  '  In F i g . 35, the measured  a t t=49 s i s p l o t t e d as a f u n c t i o n of  calc* In F i g . 35 the same measured t r a c e width was  as a f u n c t i o n o f  a e X  p/  the angle determined  by the method d e s c r i b e d  i n S e c t i o n 2.8.  The  plotted  experimentally experimental  curve shows t h a t the v a r i a t i o n of the t r a c e width i s predominantly due  to the v a r i a t i o n i n « p / e X  although  there  i s a s u b s t a n t i a l s c a t t e r of the data, e s p e c i a l l y f o r angles  89  FIGURE 34  Schematic r e p r e s e n t a t i o n o f the dependence o f the p l a t e t r a c e width, 2X , on the angle between the p l a t e and the specimen s u r f a c e , q, and on the p l a t e t h i c k n e s s , T ( s i n a = T ./2X .) . t  t  +  +  90  FIGURE 35 Thickness of p l a t e t r a c e s a t a g i v e n growth time p l o t t e d as a f u n c t i o n o f the angle between the p l a t e and the specimen s u r f a c e , a. © - A n g l e a c a l c u l a t e d assuming t h a t the growth r a t e was the same f o r a l l p l a t e s and t h a t p l a t e No.6 was p e r p e n d i c u l a r t o the s u r f a c e o f the specimen. • — Angle a measured by s e r i a l d i s s o l u t i o n . The number r e f e r t o the 240°C b a i n i t e p l a t e s i n Table V.  *  l e s s than 70  .  There i s no reason to b e l i e v e t h a t the  width depends on a the Eq.(2).  Therefore,  F i g . 35 i s e x p l a i n e d a p. e X  100  i n any  exp  other way  than as p r e d i c t e d  the discrepancy  o f the two  by a l a r g e systematic  The  curves i n  a e X  p,  approaching  sources o f the e r r o r  probably the technique f o r measuring the t h i c k n e s s e l e c t r o l y t i c a l l y removed specimen l a y e r s and  by  e r r o r i n measuring  This e r r o r increases with i n c r e a s i n g  pet f o r the t h i c k e s t t r a c e s .  trace  of  (see S e c t i o n  are  the 2.8)  the p r e f e r e n t i a l e l e c t r o l y t i c a t t a c k o f the m a t r i x i n the  v i c i n i t y of the p l a t e s .  These may  a l s o cause the  scatter  of the data around the experimental curve, although  the  s c a t t e r might to a c e r t a i n degree r e f l e c t a t r u e v a r i a t i o n of the p l a t e t h i c k n e s s . was  In the l i g h t o f the above d i s c u s s i o n i t 2  concluded t h a t the observed s c a t t e r i n the d(X  values  i n Table V f o r a l l three temperatures was  n a n t l y due  )/dt  a  predomi-  to the v a r i a t i o n of the angle between the  i n d i v i d u a l p l a t e s and  the specimen s u r f a c e .  A l s o , i t was  assumed t h a t those p l a t e s e x h i b i t i n g a minimum growth r a t e (marked i n Table V) were p e r p e n d i c u l a r specimen and  to the s u r f a c e of  t h e r e f o r e e x h i b i t e d the t r u e t h i c k e n i n g  D i f f e r e n t i a t i n g Eq. following expression 1  was  d(x2) d t  a  (la) and  s o l v i n g f o r D,  the  rate. the  obtained: (3)  92  The e f f e c t i v e d i f f u s i v i t i e s f o r the t h i c k e n i n g o f p l a t e s at 160,  200 and 240°C were c a l c u l a t e d u s i n g Eq.  the minimum v a l u e s o f d(X )/dt  from Table V.  (3) and The  results  a are g i v e n i n Table V I . Eq.  The v a l u e s of L, c a l c u l a t e d u s i n g  (C-2), and the v a l u e s of o t h e r p h y s c i a l parameters used  i n the c a l c u l a t i o n are summarized i n Table V I I . The  a c t i v a t i o n energy  and the frequency  factor for  d i f f u s i o n were found from the A r r h e n i u s p l o t shown i n Fig.36.  The c a l c u l a t e d v a l u e f o r the a c t i v a t i o n  energy,  E =1.89 x 10^ J/mole, agreed v e r y w e l l w i t h the estimated A  value o f 1.658  x 10  J/mole (see Appendix D). The 4  v a l u e f o r the frequency f a c t o r D  Q  = 3.74  x 10  calculated  2 m /s  was  s e v e r a l o r d e r s of magnitude h i g h e r than the expected One  value.  p o s s i b l e reason f o r t h i s c o u l d be the l a r g e e r r o r  i n t r o d u c e d due t o the s m a l l temperature which the A r r h e n i u s p l o t was  drawn.  range,  80°C, over  A rough estimate of  t h i s e r r o r can be c a r r i e d out assuming t h a t the e r r o r made 2  by choosing the minimum measured v a l u e s of d(X ) / d t  a  as  r e p r e s e n t a t i v e of the t r u e growth r a t e s a t the g i v e n temperatures  i s not l a r g e r than the s c a t t e r of the data i n  Table V. Thus, standard d e v i a t i o n about the mean value o f the data i n Table V was  used t o c a l c u l a t e the e r r o r bars  i n F i g . 36.  Drawing a l i n e w i t h minimum s l o p e through the 5 2 e r r o r b a r s , E = 1.61 x 10 J/mole and D = 31 m /s were A  Q  o b t a i n e d ; f o r a l i n e w i t h maximum s l o p e , E =2.09 x 10 A  J/mole  93  TABLE VI Calculated Effective D i f f u s i v i t i e s and Estimated D i f f u s i v i t i e s  2  C a l c u l a t e d E f f e c t i v e D i f f u s i v i t y , m /sec Temperature ' Estimated o Bainite Bainite Widmanstatten Diffusivity T h i c k e n i n g Lengthening Lengthening m /sec 2  160  6.1 x 1 0 "  1 9  1.1 x 1 0 "  200  5.0 x I O "  1 7  -  240  2.1 x 1 0 "  1 5  -  1 6  -  2 x 10"  1 9  -  1 x 10"  1 7  3 x 10~  1 6  1.9 x 1 0 "  1 5  94  TABLE V I I P h y s i c a l Parameters  Used i n the C a l c u l a t i o n s  Parameter  Value  Obtained From  Temperature,  L c,at.pet  Cd  c , a t . p e t Cd Q  ft  200  240  1.36  2.01  2.84  42.5  43.6  44.2  49.5  49.4  49.3  V . m /mole  1.12 x 10"5  a  0.5 J/m  3  e  c d  gi  °C  160  0.643  Q  2  0.759  0.843  -  1.13 x 1 0 ~  (=o /gi a  13 ( = e g i Z n  i  f o r Cu-Zn)  f o r Cu-Zn)  Eq. (C-2) M e t a s t a b l e Ag-Cd phase diagram (Fig.E-l,App.E)  QQ=(c„-c )/(c -c ) 0  5  Ref. (88)  Ref. (71) Ref. (71)  op  0  95  TEMPERATURE, °C 240 200  14  160  -15 h  -16 h 0J  o  -17 K  -18 h  -19  1-9  20  21  1/T,  2-2  l/°Kxl0  2-3  3  FIGURE 36 Log D  e f f  V-6 .1/T f o r a Ag-45 a t . p e t Cd a l l o y .  2  96  and D =7.6 x 10 Q  of  D  Q  m /s.  C l e a r l y , the c a l c u l a t e d v a l u e  i s very s e n s i t i v e t o s m a l l changes i n s l o p e o f t h e  Arrhenius p l o t . The e f f e c t i v e d i f f u s i v i t i e s  o b t a i n e d from the  b a i n i t e t h i c k e n i n g k i n e t i c s c o u l d n o t be compared w i t h independently measured d i f f u s i v i t i e s  i n the Ag-Cd B  1  phase.  Such i n f o r m a t i o n was n o t a v a i l a b l e i n the l i t e r a t u r e . Experimental measurement o f d i f f u s i v i t y  i n the metastable  ordered B ' phase e x i s t i n g o n l y i n a narrow composition r e g i o n o f the phase diagram  temperature-  i s very  difficult.  However, the s i m i l a r i t y between the Ag-Cd and the Cu-Zn systems and the e x t e n s i v e d i f f u s i o n data a v a i l a b l e f o r both the a and B phases o f the Cu-Zn system of  the Ag-Cd system  and f o r t h e a phase  allowed an estimate o f the d i f f u s i v i t i e s  i n the B'Ag-Cd t o be made (see Appendix D). The r e s u l t s are shown i n Table V I . diffusivities  I t i s e v i d e n t t h a t the c a l c u l a t e d  f o r t h i c k e n i n g o f b a i n i t e p l a t e s agree  the estimated d i f f u s i v i t i e s  effective with  f o r thickening of b a i n i t e  p l a t e s w i t h i n one o r d e r o f magnitude.  T h i s agreement i s  s a t i s f a c t o r y c o n s i d e r i n g the u n c e r t a i n t y o f the e x a c t p o s i t i o n of  the a / ( a + B ' )  and the ( a + B ' J / B  Ag-Cd b i n a r y phase diagram  3.10.2  1  phase boundaries  a t low temperatures  A n a l y s i s o f B a i n i t e Lengthening  i n the  (see Appendix E ) .  Data  C o n s i d e r the t i p o f a b a i n i t e p l a t e  (Fig.37a) which  T  (to-T)  TIME, t  FIGURE 37 Schematic diagram o f a p a i r o f b a i n i t e p l a t e s which n u c l e a t e d i n the i n t e r i o r o f the specimen a t p o i n t N, emerged on the s u r f a c e o f o b s e r v a t i o n at p o i n t E and formed the t r a c e ABC a t time t ( a ) , and l e n g t h e n i n g k i n e t i c s o f the t r a c e EC(b).  98  nucleated  i n the i n t e r i o r o f the specimen and which  continued  t o grow a t a s t e a d y - s t a t e r a t e v.  it  A t time t  f  forms a s e m i - c i r c u l a r p l a t e o f r a d i u s r ( t ) = v ( t - T ) ,  where T i s the i n c u b a t i o n time.  The l e n g t h o f the t r a c e  o f the p l a t e on the s u r f a c e o f o b s e r v a t i o n measured from the p o i n t o f emergency t o the t i p i s then given by t h e following  equation:  l(t)  where t  =  v[(t -  T )  -  2  (t  Q  -  T) ] , 2  H  t  *  t  Q  (4)  f  i s the time when the p l a t e f i r s t emerges on the  surface of observation. of a hyperbola,  Equation  (4) d e s c r i b e s a p a r t  as shown i n F i g . 37b. When t  when the p l a t e i s n u c l e a t e d on the o b s e r v a t i o n the hyperbola  Q  = T, i.e., surface,  becomes the s t r a i g h t l i n e I = v ( t - x ) .  D i f f e r e n t i a t i n g Eq. (4) with r e s p e c t t o t and rearranging  gives [(t - t ) - ( t 2  D  v = v (t) obs where  v o b s  (t)  x) ] 2  h  (5) t — x  = (d£/dt) _ , t  t  t h e observed growth r a t e o f  the t r a c e a t time t . When t = x, v = v . , as expected. o ob s The  l e n g t h o f the t r a c e s o f b a i n i t e p l a t e s grown  at 160°C was p l o t t e d as a f u n c t i o n o f t h e annealing  time,  as shown i n F i g . 38 f o r three t y p i c a l p l a t e s c o v e r i n g the range o f observed lengthening  rates.  The curves  conformed  99  Lengthening k i n e t i c s at 160°C of b a i n i t e p l a t e i n a Ag-45 at.pet Cd a l l o y .  traces  100  to the h y p e r b o l i c  shape, although at longer  a n e g a t i v e d e v i a t i o n was  observed.  I t was  growth times thought t h a t  r e f l e c t e d the g r a d u a l decrease i n growth r a t e w i t h the t i p of the p l a t e e n t e r i n g other p r e c i p i t a t e s . r a t e , v,  associated  the d i f f u s i o n f i e l d s  In o r d e r to e s t a b l i s h the  from an observed growth r a t e , v  to know the  incubation  time, x, and  t h i s was  i t was  the h y p e r b o l i c The to be  Q  r e l a t i o n s h i p a t longer  surface.  I t was  nucleated  axis  (200  on the  seconds) was  I t was plate  time, x = 200  ones  close  plate  ( p l a t e 1 i n Fig.38)  I t s i n t e r c e p t with the  f u r t h e r assumed t h a t the  s.  first  a l l nucleated  then equal to the  ( p l a t e 3 i n Fig.38) had  from  times.  t h e r e f o r e assumed t h a t the  surface.  by  However,  f a c t t h a t the measured p l a t e s were the  e x h i b i t i n g the minimum growth r a t e had  found  curves i n Fig.38 d e v i a t e d  observed i n d i c a t e d t h a t they had  to the  necessary  the emergence time, t .  the asymptote of i t s h y p e r b o l a .  d i f f i c u l t because the  of  t r u e growth  In p r i n c i p l e , T f o r a p a r t i c u l a r p l a t e c o u l d be constructing  this  incubation  time  time,  x.  f a s t e s t growing  also nucleated  at the same  Extrapolating t h i s l i n e to I  = 0 gave -9  t ~7.500 s. o  m/s.  From the  same l i n e , v  Q  b  s  (10,000 s) = 1.2  x  10  S u b s t i t u t i n g these v a l u e s i n t o Eq.(4) y i e l d e d  v = 6.76  x 10~^°  m/s.  calculating diffusivity Table V I I I .  The  parameter v a l u e s necessary f o r  from the growth r a t e are l i s t e d i n  These were o b t a i n e d  i n the  f o l l o w i n g way.  The  101  TABLE V I I I Values o f the Parameters f o r C a l c u l a t i o n o f D Lengthening K i n e t i c s o f B a i n i t e P l a t e s  e f f  from the  a t 160°C and o f  Widmanstatten Needles a t 240°C i n the Ag-45 A t . Pet Cd A l l o y  C r i t i c a l Plate T i p Radius, m  Dimensionless Growth Rate  Plate T i p Radius, m  Bainite Plate Lengthening at 160°C  P =9.50 x 10~  9  p=0.276  p=8.83 x 10  Widmanstatten Needle Lengthen i n g a t 240°C  p'=2.33 x 1 0 "  8  p=2.480  p=6.87 x 10  c  _ 0  8  R  102  c r i t i c a l plate t i p radius p  = 9.50 x 10 *" m was o b t a i n e d c u s i n g the m o d i f i e d Gibbs-Thornson Equation (Eq. (C-6)) w i t h the data from Table V I I .  The d i m e n s i o n l e s s growth r a t e —8  p=0.276 and p l a t e t i p r a d i u s p=8.83 x 10  m,  both c o r r e s -  ponding to the maximum growth r a t e f o r the g i v e n  dimensionless  s u p e r s a t u r a t i o n fi =0.643 f o r the Ag-45 a t . pet Cd a l l o y a t Q  160°C, were o b t a i n e d from Eq.  (C-3) by T r i v e d i ' s method  d e s c r i b e d i n Appendix C. Knowing v, p and p, the  effective  d i f f u s i v i t y f o r l e n g t h e n i n g o f b a i n i t e p l a t e s a t 160°C  was  then c a l c u l a t e d from the e x p r e s s i o n D=vp/2p; a value o f D  e f  f = 1.1  x 10*"-^ m /s 2  H i l l e r t Equation was  was  obtained.  The m o d i f i e d  Zener-  (Eq. (C-5)) y i e l d e d the same v a l u e .  This  more than two o r d e r s of magnitude l a r g e r than the  effective  d i f f u s i v i t y o b t a i n e d from the 160°C b a i n i t e t h i c k e n i n g k i n e t i c s . T h i s means t h a t the b a i n i t e l e n g t h e n i n g r a t e two  was  o r d e r s of magnitude l a r g e r than t h a t allowed by a volume  d i f f u s i o n c o n t r o l l e d growth p r o c e s s . 3.10.3. A n a l y s i s of Widmanstatten Lengthening The  Data  l e n g t h e n i n g . r a t e o f widmanstatten needles  on and along the specimen s u r f a c e was  growing  measured a t 240°C.  A s e r i e s o f micrographs i l l u s t r a t i n g the growth i s shown i n Fig.  39a.  The p l o t of the needle  l e n g t h as a f u n c t i o n of  the growth time i s shown i n Fig.39b A l i n e a r r e l a t i o n s h i p was slowest observed of  obtained.  f o r three t y p i c a l The  f a s t e s t and  growth r a t e s were approximately  needles. the  factor  t h r e e d i f f e r e n t , the average growth r a t e b e i n g equal t o  FIGURE 39 Scanning e l e c t r o n micrographs showing the growth o f a widmanstatten needle (a) and l e n g t h e n i n g k i n e t i c s of widmanstatten needles (b) i n a Ag-45 a t . p e t Cd a l l o y a t 240°C.  104  FIGURE 39 - continued  105 v=1.38 x 1 0 ~  7  m/s. _Q  The  c r i t i c a l needle t i p r a d i u s , p '=2.33 x 10 c  m,  was c a l c u l a t e d u s i n g the m o d i f i e d Gibbs-Thomson Equation (Eq.  (C-6a)) w i t h the data from Table V I I .  parameter v a l u e s are l i s t e d i n Table V I I I .  The c a l c u l a t e d The dimensionless _g  growth r a t e p=2.48 and needle t i p r a d i u s p=6.87 x 10  m  f o r the d i m e n s i o n l e s s s u p e r s a t u r a t i o n nQ=0.84.3 f o r the Ag-45 at.  p e t Cd a l l o y a t 240°C were o b t a i n e d by the method  d e s c r i b e d i n Appendix C.  The e f f e c t i v e d i f f u s i v i t y f o r  l e n g t h e n i n g o f widmanstatten needles was then  calculated  u s i n g the average measured needle l e n g t h e n i n g r a t e and the c a l c u l a t e d v a l u e s f o r p and p. The o b t a i n e d value o f —15 D f f = 1.9 x 10 e  2  m/s  effective diffusivity  agreed very w e l l w i t h the v a l u e o f the  o f 2.1 x 10~ m /s o b t a i n e d from the 5  2  240°C b a i n i t e t h i c k e n i n g k i n e t i c s (Table V I ) . 3.10.4 D i s c u s s i o n o f the Growth K i n e t i c s R e s u l t s The i n t e r p r e t a t i o n o f the t h i c k e n i n g k i n e t i c s f o r b a i n i t e p l a t e s a t 160, 200 and 240° C i s s t r a i g h t f o r w a r d when i t i s assumed t h a t the estimated v a l u e s f o r d i f f u s i v i t i e s are c o r r e c t w i t h i n one order o f magnitude; t h i s i s supported by the comparable value f o r the d i f f u s i v i t y o b t a i n e d by measurements o f the l e n g t h e n i n g k i n e t i c s o f the widmanstatten needle a t 240°C.  The r e s u l t s o f the  t h i c k e n i n g k i n e t i c s are then i n good agreement with the  106 Zener-Frank model of volume d i f f u s i o n c o n t r o l l e d of  a precipitate plate.  T h i s means t h a t the  between the matrix and the broad  growth  interface  s i d e s of the b a i n i t e  p l a t e s i s d i s o r d e r e d and advances u n i f o r m l y over i t s e n t i r e area.  T h i s c o n c l u s i o n does not agree w i t h the s t u d i e s  which found t h a t t h i c k e n i n g o f p r e c i p i t a t e p l a t e s o c c u r r e d by a ledge growth mechanism (48, 49), i n agreement w i t h Aaronson's g e n e r a l theory of p r e c i p i t a t e morphology The  i n t e r p r e t a t i o n of the l e n g t h e n i n g  (50,  51).  kinetics  measurements of b a i n i t e p l a t e s d u r i n g t h e i r e a r l y stage of growth a t 160°C r e q u i r e s a r e a p p r a i s a l i n l i g h t o f the estimated v a l u e s f o r the d i f f u s i v i t i e s estimated d i f f u s i v i t i e s diffusivity  (Table V I ) . I f the  are c o r r e c t , the l a r g e r than  expected  o b t a i n e d from the l e n g t h e n i n g k i n e t i c s shows  t h a t the l e n g t h e n i n g i s a c c e l e r a t e d beyond the r a t e p e r m i t t e d by volume d i f f u s i o n .  S i m i l a r o b s e r v a t i o n s have been r e p o r t e d  f o r b a i n i t e p l a t e s i n Cu-Zn a l l o y s t h a t the p l a t e s lengthened  (31, 52).  Repas (52)  found  a t r a t e s up to two o r d e r s o f  magnitude h i g h e r than t h a t p r e d i c t e d by the  Zener-Hillert  volume d i f f u s i o n model. Hornbogen and Warlimont s i m i l a r l e n g t h e n i n g r a t e s and  (31)  found t h a t l e n g t h e n i n g  very soon, while t h i c k e n i n g continued f o r an extended  observed ceased time.  (Both s t u d i e s were performed by measuring the s i z e of the l a r g e s t p l a t e i n the f i e l d of o b s e r v a t i o n as a f u n c t i o n o f the specimen a n n e a l i n g time.)  I t should be  emphasized,  though, t h a t i t i s d i f f i c u l t to a s c e r t a i n the  significance  107  of these o b s e r v a t i o n s s i n c e i t i s not c l e a r whether they r e f e r r e d t o the same, e a r l y stage of growth d u r i n g which the p r e s e n t o b s e r v a t i o n s on Ag-Cd a l l o y s were made. Onthe other hand, i f i t i s allowed t h a t the a c t u a l d i f f u s i v i t i e s are approximately h i g h e r than was  two o r d e r s o f magnitude  estimated, the measured b a i n i t e  lengthening  r a t e would agree w i t h t h a t of a volume d i f f u s i o n growth p r o c e s s .  controlled  This p o s s i b i l i t y i s less l i k e l y since i t  r e q u i r e s anomalously h i g h d i f f u s i v i t e s .  Nevertheless, i t i s  a t t r a c t i v e because i t then allows the p o s s i b i l i t y t h a t the broad  faces of the p l a t e s are p a r t i a l l y coherent  and  growing  at a slower r a t e , c o n t r o l l e d by the l a t e r a l movement of i n c o h e r e n t ledges, i n agreement w i t h Aaronson's theory of p r e c i p i t a t e morphology. However, the p r e s e n t measurements have c l e a r l y shown t h a t the t h i c k e n i n g k i n e t i c s i s p a r a b o l i c , which i s c h a r a c t e r i s t i c of a p l a n a r d i s o r d e r e d i n t e r f a c e . The k i n e t i c s of t h i c k e n i n g r e s u l t i n g from the movement of r e g u l a r l y d i s t r i b u t e d ledges w i l l be the same as the k i n e t i c s of i n d i v i d u a l l e d g e s , which i s l i n e a r f o r w i d e l y ledges having i s o l a t e d d i f f u s i o n f i e l d s  spaced  (53).At the o t h e r  extreme, i f the ledges were c l o s e r to each o t h e r , c a u s i n g t h e i r d i f f u s i o n f i e l d s to o v e r l a p , t h e i r k i n e t i c s would d e v i a t e from l i n e a r towards the p a r a b o l i c d i f f u s i o n r a t e of a competely d i s o r d e r e d i n t e r f a c e . on v a r i o u s systems qualitatively.  T h i c k e n i n g measurements  (48, 49, 54) have confirmed  this conclusion  U l t i m a t e l y , i f t h i c k e n i n g by ledges o c c u r r e d  at a v o l u m e - d i f f u s i o n c o n t r o l l e d r a t e , the d i s t a n c e between  108  the ledges would have to be  zero and  the i n t e r f a c e would  become i n d i s t i n g u i s h a b l e from a completely  disordered  interface. Thus, on balance, i t i s more l i k e l y t h a t the b a i n i t e p l a t e s lengthened at a r a t e f a s t e r than p e r m i t t e d volume d i f f u s i o n c o n t r o l l e d model. conclusion derived  by  the  T h i s r e i n f o r c e s the  from the c r y s t a l l o g r a p h i c s t u d i e s  that  the n u c l e a t i o n and e a r l y growth o f b a i n i t e p l a t e s occurs by a m a r t e n s i t i c p r o c e s s .  L a t e r t h i c k e n i n g then occurs  by a d i f f u s i o n c o n t r o l l e d growth 3.10.5 General The  process.  Discussion  choice of the b a i n i t e growth mechanism may  on competitive  growth k i n e t i c s .  depend  The m a r t e n s i t i c process i s  able t o lower the f r e e energy of the system by  producing  a q u a n t i t y of b a i n i t e f a s t e r than i s p o s s i b l e by a d i f f u s i o n a l mechanism. the t h e r m a l l y by  The  n u c l e a t i o n and  growth of b a i n i t e by  a c t i v a t e d m a r t e n s i t i c process may  be a s s i s t e d  the r e s i d u a l s t r e s s e s i n the quenched 8' phase. As  these  s t r e s s e s are accommodated by a m a r t e n s i t i c growth process  and  adverse s t r e s s e s accumulate, the m a r t e n s i t i c growth ceases. In the meantime the p a r t i t i o n i n g o f s i l v e r and long range d i f f u s i o n becomes s i g n i f i c a n t .  cadmium through  The r e s u l t i n g  composition changes a f f e c t the s t r u c t u r e of the b a i n i t e by a n n i h i l a t i n g the s t a c k i n g f a u l t s , t r a n s f o r m i n g  i t into  109  equilibrium  a phase.  Thus, the l a t t e r stage  of growth  i s c o n t r o l l e d by long range d i f f u s i o n g i v i n g the growth r a t e .  parabolic  4. (1)  CONCLUSIONS  There are many s i m i l a r i t i e s i n the morphology, s t r u c t u r e and growth o f p r e c i p i t a t e s formed a t low temperatures i n the g' phase o f Cu-Zn and Ag-Cd alloys.  (2)  The b a i n i t i c t r a n s f o r m a t i o n i n 44-46 a t . p e t Cd g' Ag-Cd a l l o y s can be suppressed by r a p i d quenching. When formed d u r i n g quenching, the b a i n i t e n u c l e a t e s and grows b e f o r e o r d u r i n g the c o m p e t i t i v e t r a n s f o r m a t i o n t o the massive a phase.  (3)  P l a t e - l i k e b a i n i t i c p r e c i p i t a t e s form i s o t h e r m a l l y i n 44-46 a t . p e t Cd a l l o y s i n the temperature 160-320°C.  A t h i g h e r temperatures the p l a t e s form  c o m p e t i t i v e l y w i t h the n e e d l e - l i k e precipitate.  range  widmanstatten  A t lower temperatures the p l a t e s are  the o n l y i n t e r g r a n u l a r t r a n s f o r m a t i o n product. Some g r a i n boundary (4)  s i d e needles a r e always p r e s e n t .  The 3R s t r u c t u r e o f the f r e s h l y formed b a i n i t e p l a t e s , t h e i r s u r f a c e r e l i e f , h a b i t plane and o r i e n t a t i o n r e l a t i o n s h i p w i t h the m a t r i x were c o n s i s t e n t w i t h the phenomenological theory o f m a r t e n s i t e f o r m a t i o n .  (5)  Prolonged a n n e a l i n g o f the b a i n i t e p l a t e s a t t h e i r temperature o f f o r m a t i o n causes t h e i r s t r u c t u r e t o change t o f e e .  110  Ill (6)  The  i n i t i a l lengthening  appears to be  o f the b a i n i t e p l a t e s  f a s t e r than p e r m i t t e d by a volume  d i f f u s i o n c o n t r o l l e d process. (7)  Volume d i f f u s i o n probably c o n t r o l s the t h i c k e n i n g the b a i n i t e p l a t e s d u r i n g  (8)  Needle-like  the l a t e r growth  of  stages.  widmanstatten p r e c i p i t a t e s lengthen at  a r a t e c o n t r o l l e d by volume d i f f u s i o n . (9)  The  morphology, s t r u c t u r e and  of the  other c h a r a c t e r i s t i c s  f r e s h l y formed b a i n i t e p l a t e s are  with t h e i r f o r m a t i o n by a t h e r m a l l y martensitic  process.  consistent  activated  SUGGESTIONS FOR FUTURE WORK A deeper i n s i g h t i n t o the processes o f b a i n i t e formation i n the Ag-45 a t . p e t Cd a l l o y would be achieved by and  i n v e s t i g a t i n g the e f f e c t s o f s t r e s s on the n u c l e a t i o n growth o f b a i n i t e p l a t e s .  i f used w i t h the p r e d i c t i o n s could help explain and  The r e s u l t s o f such a study, o f the m a r t e n s i t i c  the mechanism o f n u c l e a t i o n  theory, of plates  determine the f a c t o r s r e s t r i c t i n g t h e i r l e n g t h e n i n g  to the i n i t i a l  stage o f growth.  Another important o b j e c t matrix i n t e r f a c e .  o f study i s the b a i n i t e -  The i n f o r m a t i o n about the degree o f the  coherency o f the i n t e r f a c e and i t s m o b i l i t y , about the e f f e c t o f the 3R t o f e e s t r u c t u r e would c o n t r i b u t e  as w e l l as transformation  towards the understanding o f the mechanism  of the b a i n i t e growth i n the v a r i o u s stages o f i t s formation.  112  APPENDIX A Structure The  e f f e c t of a high d e n s i t y o f s t a c k i n g f a u l t s i n  the fee l a t t i c e was Hirsh  (56)  Analysis  and  s t u d i e d by Paterson  Sato et al.  k i n e m a t i c a l theory  (44,45,57).  (55), Whelan By using  and  the  of X-ray d i f f r a c t i o n , Paterson showed  t h a t a h i g h d e n s i t y of random s t a c k i n g f a u l t s d i s t o r t e d the fee r e c i p r o c a l l a t t i c e , w h i l e by u s i n g the dynamical df e l e c t r o n d i f f r a c t i o n , Whelan and  theory  H i r s c h found t h a t  the  d i s t o r t i o n o f the l a t t i c e was  accompanied by s t r e a k i n g  along  the  to the s t a c k i n g f a u l t s .  Sato  (ill)£ a x i s p e r p e n d i c u l a r  et al'  s t u d i e d the modulation of the  fee s t r u c t u r e due  r e g u l a r d i s t r i b u t i o n o f s t a c k i n g f a u l t s u s i n g the theory  of e l e c t r o n d i f f r a c t i o n .  kinematical  They found t h a t the  p r o c a l l a t t i c e of the modulated s t r u c t u r e was  to a  reci-  characterized  by s p l i t t i n g of c e r t a i n fee r e c i p r o c a l l a t t i c e p o i n t s i n the (ill)  direction.  They a l s o analyzed  the e f f e c t of random  s t a c k i n g f a u l t s on the r e c i p r o c a l l a t t i c e of the modulated s t r u c t u r e s and  found t h a t they c o u l d cause broadening  displacement of the s p l i t  and  spots.  A c l o s e packed s t r u c t u r e i s s p e c i f i e d by a  stacking  order of the c l o s e packed hexagonal l a y e r s which occupy of the three p o s s i b l e p o s i t i o n s , A,B of the plane o f l a y e r s  and C, i n the p r o j e c t i o n  ( F i g . A - l ) . I t can be  113  one  assumed t h a t  114  FIGURE A-1 S t a c k i n g sequence o f c l o s e packed [ l l l ] f l a y e r s i n the f e e lattice. Atoms A are i n the p l a n e o f the drawing; the l a y e r beneath has atoms i n C p o s i t i o n s , the l a y e r above i n B positions. The shear v e c t o r s R o f a s t a c k i n g f a u l t are i n d i c a t e d i n the diagram.  115 the fundamental c l o s e packed s t r u c t u r e i s the fee s t r u c t u r e w i t h the simple s t a c k i n g o r d e r ABCABCABC, as shown i n F i g . A - 1 . Shearing a B l a y e r r e l a t i v e t o the A l a y e r by any of the v e c t o r s R, e.g., ABCA/CABC  [112]^, w i l l change the p a t t e r n t o  i n t r o d u c i n g a s t a c k i n g f a u l t i n the middle  the sequence. to  R-^ =  The phase change f o r a r e f l e c t i o n  the r e c i p r o c a l l a t t i c e v e c t o r g =  of  corresponding  (hk£) produced  by  the  shear R^ i s  $ = 2 TT g. R Since h,k,£  x  = i  (-h-k+2£) .  are e i t h e r a l l odd or a l l even, $ w i l l assume the  following values: F o r h+k+£ = 3N, for  $ =  0,  h+k+l = 3N±1,$= ± 2TT/3,  where N i s any i n t e g e r , choosing the p r i n c i p a l v a l u e s of $ l y i n g between - I T and  T T . T h e r e f o r e , o n l y those  reflections  f o r which h+k+£ i s equal t o 3N w i l l be u n a f f e c t e d by s t a c k i n g f a u l t s ; those f o r which h+k+-£ i s e q u a l t o ($=2TT/3) and 3N-1  the 3N+1  (0=-2TT/3) w i l l be a f f e c t e d i n a way  on the d i s t r i b u t i o n of the s t a c k i n g f a u l t s , as w i l l d e s c r i b e d s h o r t l y . However, the a f f e c t e d r e f l e c t i o n s remain p o s i t i o n e d along the ( i l l )  f  depending  be will  d i r e c t i o n perpendicular  to  the s t a c k i n g f a u l t p l a n e , and consequently  of  the modulated r e c i p r o c a l l a t t i c e  a l l features  can be v i s u a l i z e d i n one  116  h +k+l  3N  - i — 333  242  151  0  27T  3N-I  ' 3  222  131  27T  3N + I  3  II 3N 000  I II  III 27T  3N-I  020  I I  •  REGULAR  FCC  REFLECTIONS  x  TWINNED  FCC  REFLECTIONS  3  FIGURE A-2 (101)f r e c i p r o c a l l a t t i c e plane w i t h twinned l a t t i c e s p o t s . The plane c o n s i s t s o f rows o f r e f l e c t i o n s w i t h s u c c e s s i v e phase s h i f t s 0, 2TT/3 and -2ir/3, every t h i r d l a y e r having the same phase s h i f t . S t a c k i n g f a u l t s on (111)f plane cause broadening and displacement o r s p l i t t i n g o f spots with $=±2T\/3 i n the d i r e c t i o n p a r a l l e l t o [ l l l ] f .  117 of the  {110}^ r e c i p r o c a l l a t t i c e planes which c o n t a i n s  <111>£ d i r e c t i o n of s t a c k i n g , f o r example, the i n F i g . A-2. [lll]  f  The  plane  r e c i p r o c a l l a t t i c e l i n e s p a r a l l e l to  d i r e c t i o n i n F i g . A-2  k i n d s , the z e r o t h , f i r s t and phase changes due  (110)^  the  the  can be c l a s s i f i e d i n t o three second k i n d , f o r which the  t o a s t a c k i n g f a u l t are 0, -2TT/3 and 27r/3  respectively.  A.l.  D i s t o r t i o n o f the FCC R e c i p r o c a l L a t t i c e due to a High D e n s i t y o f Random S t a c k i n g F a u l t s (55,56) A high d e n s i t y of randomly d i s t r i b u t e d s t a c k i n g  f a u l t s causes broadening o f the r e f l e c t i o n s and placement.  The  e f f e c t s occur p a r a l l e l to the  their  (111)  dis-  f  d i r e c t i o n , with the r e f l e c t i o n s being d i s p l a c e d towards the nearest of the  twin s p o t s .  In the e l e c t r o n d i f f r a c t i o n  ( l l O ) ^ -zone, s t r e a k s are observed running  r e c i p r o c a l l a t t i c e l i n e s of the f i r s t and due  t o the m u l t i p l e d i f f r a c t i o n they may  has  along  the  second k i n d , although be a l s o observed  along the r e c i p r o c a l l a t t i c e l i n e s of the zeroth Paterson  patterns  kind.  e s t a b l i s h e d the f o l l o w i n g r e l a t i o n s h i p  between the amount o f displacement of the a f f e c t e d r e f l e c t i o n s and h  3  the d e n s i t y o f s t a c k i n g  = 3N - I  + | a r c tan  where h^ i s the c o - o r d i n a t e  [/T  faults: (l-2a)],  (A-1)  of a r e f l e c t i o n measured i n the  118 d i r e c t i o n o f displacement  (for undisplaced  r e f l e c t i o n s hg  i s equal t o h+k+Z = 3N±1; f o r d i s p l a c e d r e f l e c t i o n s t o 3N±1 plus the f r a c t i o n o f the d i s t a n c e t o the twin spot, which i s equal t o l / 3 d ^ ^ ^ ) .  N i s any i n t e g e r , a i s the p r o b a b i l i t y  of a f a u l t o c c u r r i n g a t any l a y e r and the s i g n  (+)corres-  ponds t o the phase change s i g n $ = ±2TT/3 r e s p e c t i v e l y . Inspecting  Eq.(A-l) i t i s seen t h a t the r e f l e c t i o n s which  f o r a = 0 a r e a t hg, = 3N±1 become d i s p l a c e d towards the nearest  twin spots  f o r a>0.  r e f l e c t i o n s occur a t values  F o r a = 0.5, the peaks o f the o f hg = 3N-(3/2), where,  according  to Paterson, the i n t e g r a l breadth o f r e f l e c t i o n s has i t s l a r g e s t value.  As a becomes s m a l l e r o r l a r g e r than 0.5,  the r e f l e c t i o n s g r a d u a l l y decrease i n breadth and approach the sharp r e f l e c t i o n s c h a r a c t e r i s t i c o f the p e r f e c t c r y s t a l : or i t s twinned c o u t e r p a r t A.2.  respectively.  Long P e r i o d S t a c k i n g Order Modulation o f the FCC L a t t i c e (44,45,57) I f i t i s assumed t h a t the fundamental c l o s e packed  s t r u c t u r e i s t h e f e e s t r u c t u r e w i t h the simple s t a c k i n g ABCABCABC, a l l c l o s e packed s t r u c t u r e s can be d e r i v e d i t by i n s e r t i n g s t a c k i n g f a u l t s i n an a p p r o p r i a t e the s t a c k i n g f a u l t s are i n t r o d u c e d r e s u l t i n g s t a c k i n g order  way.  order  from When  a t every t h i r d l a y e r , the  i s ABC/BCA/CAB  and the p e r i o d which  b r i n g s a c l o s e packed l a y e r A o f the modulated l a t t i c e i n t o coincidence 9.  w i t h a c l o s e packed l a y e r A o f the f e e l a t t i c e i s  T h i s modulation o f the f e e s t r u c t u r e i s s p e c i f i e d by the  119  symbol 3 R . divided  The number 3 s i g n i f i e s t h a t the p e r i o d i s  i n t o s e r i e s o f t h r e e l a y e r s each, w i t h s e r i e s  to each o t h e r by a u n i t s t a c k i n g the  shift,  (1/6)a[112]£,  related and  l e t t e r R s i g n i f i e s t h a t the modulation has a rhombohedral  symmetry. Modulation o f the f e e s t r u c t u r e  i s characterized  by a s p l i t t i n g o f ,the o r i g i n a l r e c i p r o c a l l a t t i c e  points  l y i n g i n the f i r s t and second k i n d o f l i n e s i n t o s e r i e s o f spots.  The number o f the s p l i t spots i n the s e r i e s i s  equal t o the number o f l a y e r s i n the fundamental s e r i e s o f modulation.  T h e r e f o r e , as shown i n F i g . A - 3 , the number  of s p l i t spots i n a 3 R l a t t i c e i s t h r e e .  The rhombohedral  symmetry i s manifested i n the manner o f s p l i t t i n g ;  i . e . , the  s p l i t spots are s h i f t e d by 1 / 3 o f the u n i t o f s p l i t t i n g (or  1/9  o f the  I/C^-Q)  away from the p o s i t i o n s  o f the f e e  spots, the spots i n the adjacent l a y e r s being s h i f t e d i n the o p p o s i t e d i r e c t i o n s .  The r e s u l t i s t h a t the spots e x i s t  at p o s i t i o n s which are a m u l t i p l e  of l / ^ d - ^ ^ .  r e c i p r o c a l l a t t i c e l i n e s o f the zeroth spots appear a t each u n i t d i s t a n c e , i n t e r l a y e r spacing The  In the  kind, d i f f r a c t i o n  which i s the r e c i p r o c a l  (1/d^-^) .  modulated s t r u c t u r e  can be b e s t d e s c r i b e d i n  terms o f an orthorhombic u n i t c e l l w i t h the c l o s e packed (lll)  f  plane as i t s b a s a l plane  of modulation, [ l l l ] , f  as i t s o  (Fig. A-4), 3  axis.  and the d i r e c t i o n  The s t r u c t u r e  factor  120  I orth  6  3  020, 18  "  0  •I  Pri-  112  II  114  27T 3  117  orth o  ll I  111  - ® -  H§H-  009  000  009  020 11  0  172  O  FCC  REFLECTIONS  •  3R  REFLECTIONS  8  27T 3  FIGURE A-3 I n t e n s i t y d i s t r i b u t i o n i n the 3R r e c i p r o c a l l a t t i c e plane (110) i n the orthorhombic n o t a t i o n or (101)£ i n the c u b i c n o t a t i o n . o  121  R  -9  ©  oAg  Eid, L  • Cd  (a)  A  Ag  O  B  C •  A  Cd  (c)  FIGURE A-4 (a) The l a t t i c e correspondence between the fee (CuAu I-type) and orthorhombic l a t t i c e , (b) The u n i t c e l l o f the b a s a l plane of the orthorhombic l a t t i c e . The orthorhombic c o o r d i n a t e s of atoms i n the plane a r e : Ag - 0, 0; Cd - h,h(c) The d i s t r i b u t i o n of atoms i n the b a s a l plane i n the A, B and C layers. The orthorhombic c o o r d i n a t e s o f the Ag atoms i n the l a y e r s a r e ; A - 0, 0, 0; B - 0, 1/3, 1/9; C - 0, 2/3; 2/9.  122 f o r the orthorhombic l a t t i c e can be w r i t t e n  as the product  of t h r e e terms: F = where (A-2)  F1  The F  A  product F^.F^ i s u s u a l l y d e s i g n a t e d as F^. i s the s t r u c t u r e  t h a t the s t a c k i n g period the by  The f a c t o r  f a c t o r f o r the b a s a l p l a n e . F-^ i n d i c a t e s  o r d e r i n each s e r i e s o f the u n i t  i n the Or> d i r e c t i o n i s ABC, and F  s e r i e s o f the u n i t c e l l p e r i o d a unit stacking  shift.  d i s t r i b u t i o n , neglecting specimen t h i c k n e s s ,  cell  indicates  that  are r e l a t e d t o each o t h e r  The c a l c u l a t e d r e l a t i v e i n t e n s i t y the modulation o f i n t e n s i t y by the  f o r the Ag-Cd a l l o y o f the s t o i c h i o m e t r i c  composition i s g i v e n i n Table A - I . The i n t e n s i t y d i s t r i b u t i o n i n the orthorhombic r e c i p r o c a l l a t t i c e plane i s equivalent  t o the c u b i c  i s shown s c h e m a t i c a l l y  (110)  o  r e c i p r o c a l l a t t i c e plane  i n F i g . A-3.  (which (101) ) f  123 TABLE  A-1  C a l c u l a t e d R e l a t i v e I n t e n s i t i e s , |F| , f o r the 3R Modulation o f the CuAu I-Type S t r u c t u r e Based on Equations (A-3) and (A-4) f o r k = 0, 1, -1.  Reciprocal L a t t i c e P o i n t i n the Orthorhombic Coordinates 110 111 112 113 114 115 116 117 118 119 001 002 003 004 005 006 007 008 009 110 111 112 113 114 115 116 117 118 119  Reciprocal L a t t i c e P o i n t i n the Cubic Coordinates  020  III  111  Relative Intensity, |F| 2  0 0 905 0 0 6217 0 0 1217 0 0 0 0 0 0 0 0 0 10034 0 2178 0 0 6631 0 0 598 0 0  124 Sato zt at.  found t h a t a random d i s t r i b u t i o n  s t a c k i n g f a u l t s i n the and  s t r u c t u r e can  displacement of c e r t a i n  analysis and  3R  on As  the  analyzed the reciprocal  i t was  l a t t i c e of the  their intensity  as weak (W),  and  reflections The  the  r e g u l a r 3R  the  the broadening and a = 0 state  be  ties.  The  The  specified  arrangement o r d e r S-W-M.  specified  as  having  Since  the  structure,  specified  as having a = 1.  displacement of the direction  Thus,  reflections  of the  of  The S-W  least diffuse,  and  d i s t a n c e i s about one i s l o n g e r and  W-M  the  reflect-  their relative  intensi-  t h a t a l l are  d i s t a n c e s between the  d i s t a n c e , w h i l e M-S  IR),  ;  nearest  r e s u l t i s t h a t W r e f l e c t i o n s become most  streaks.  or  taken i n t o account i s t h a t  1 s t a t e , weighted by  S reflections  e q u a l ; the  be  reflections  be  ( s i m i l a r to fee  to be  occurs i n the  ions of the a=  by  can  (S).  s t r u c t u r e can  other d i s t i n c t state  Whelan  structure.  three  p a t t e r n i s i n the  R symmetry  of a twin, which can  and  strong  fee  s t a c k i n g f a u l t d e n s i t y parameter a = 0.  s t r u c t u r e has the  i n the  Their  e f f e c t of random s t a c k i n g  shown above, t h e r e are  medium (M)  as w e l l .  t h a t o f Paterson and  i n a u n i t d i s t a n c e , and  of the  cause broadening  reflections  followed e s s e n t i a l l y  H i r s c h , who  faults  3R  of  spots are  t h i r d of the i s shorter.  diffuse  accompanied no  longer  unit  APPENDIX  B  A n a l y t i c a l Treatment o f M a r t e n s i t i c Transformations The phenomenological  theory of m a r t e n s i t e  formation  allows p r e d i c t i o n o f the h a b i t p l a n e , d i r e c t i o n and magnitude of  shape deformation, magnitude  of l a t t i c e i n v a r i a n t  and o r i e n t a t i o n r e l a t i o n s h i p between the parent and  shear  product  f o r an assumed l a t t i c e correspondence  between the parent  and  product and known l a t t i c e parameters,  as w e l l as a known o r  assumed shear system i n the product. The m a t r i x a n a l y s i s of the bcc  (CsCl) to fee (CuAu I)  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 , as a p p l i e d t o the t r a n s f o r m a t i o n of  g'-AgCd t o a-AgCd i s o u t l i n e d here. The theory f o l l o w s  e s s e n t i a l l y the f o r m u l a t i o n o f Bowles and Mackenzie w i t h the d e t a i l s o f the mathematical  (2-4,58)  development and n o t a t i o n  borrowed from Wayman (5). The  l a t t i c e correspondence  correspondence [x]  f  =  where [ x ] ^ and  matrix,  i s d e f i n e d by  the  (fCb), so t h a t  (fCb)[x] , b  [x]  b  symbolize  a column m a t r i x x  r e l a t i v e to the f and b bases r e s p e c t i v e l y .  (vector x)  The b b a s i s  d e f i n e s the i n i t i a l bcc u n i t c e l l w i t h l a t t i c e parameter a , w h i l e the b a s i s f d e f i n e s the f a c e c e n t r e d u n i t b  w i t h l a t t i c e parameters /2" a , b  125  /2 a  b  and a  b  cell  ( F i g . B-1).  o Ag • Cd  FIGURE B-1 Schematic r e p r e s e n t a t i o n o f the correspondence between the parent C s C l - t y p e l a t t i c e (b b a s i s ) and the product CuAu I-type l a t t i c e (f b a s i s ) .  127  Alternatively, (n) where  (n) f  f  = (n)  b  (bCf) ,  and (n)]-, symbolize a row m a t r i x n (plane normal n)  r e l a t i v e t o the bases f and b r e s p e c t i v e l y . The n o t a t i o n o f the correspondence  m a t r i x (fCb)  symbolizes the t r a n s f o r m a t i o n o f c o o r d i n a t e s from the b t o f basis.  Naturally (bCf) =  (fCb)" . 1  In the p r e s e n t case, the f o l l o w i n g correspondence was  (Fig.B-1)  assumed: h h 0 (fCb) = -h h 0 0 0 1  which i s a v a r i a n t of the Bain correspondence. the shear system  Therefore,  ( 1 1 1 ) [ 1 1 2 ] , which was assumed t o operate f  i n the product, corresponds t o the shear system  (Oil)[011]^  i n the parent. The p r i n c i p a l axes o f s t r a i n a s s o c i a t e d with correspondence  can be taken as p a r a l l e l t o the v e c t o r s  d e f i n i n g the b a s i s b. d i a g o n a l matrix (or extends)  this  R e f e r r e d t o these p r i n c i p a l axes, the  (bBb) r e p r e s e n t i n g the s t r a i n which compresses  the base v e c t o r s b t o t h e i r f i n a l l e n g t h s  without r o t a t i o n i s the f o l l o w i n g : (bBb) = d i a g ( n ^ r ^ r " ^ ) r  128  where the p r i n c i p a l d i s t o r t i o n s are as f o l l o w s :  n  n3  = 0.890478  2  1  af  1.259326.  A c c o r d i n g t o the theory, the t o t a l s t r a i n due t o the transformation ( i . e  the shape d e f o r m a t i o n ) , P 1' i s  composed of a simple shear a l a t t i c e deformation  (the l a t t i c e i n v a r i a n t shear),P,  (the Bain s t r a i n ) , B, and a r i g i d body  r o t a t i o n , R, i . e . , P_ = RBP, L  or P P 1  -1  = RB.  Since both P^ and P are i n v a r i a n t plane s t r a i n s , RB must be an i n v a r i a n t l i n e s t r a i n , S, the i n v a r i a n t l i n e o f which must l i e i n the shear p l a n e .  However, s i n c e the i n v a r i a n t  line  of S becomes Bx^ a f t e r the s t r a i n B, the r o t a t i o n R must be such t h a t i t r e s t o r e s Bx^ t o x^.  A l s o , R must s i m u l -  taneously r e s t o r e n|B t o n | (see Footnote ) , where n | i s the 4-  +  The prime, as i n n!, symbolizes the t r a n s p o s i t i o n o p e r a t i o n .  129  i n v a r i a n t plane normal o f S. determined.  The f i r s t  T h i s r o t a t i o n w i l l now  step i s t o i d e n t i f y  be  which w i l l  be r e p r e s e n t e d as u n i t v e c t o r s . The cone x'  which s a t i s f i e s the equation  (bBb)" x = x'x  g i v e s the i n i t i a l p o s i t i o n of a l l l i n e s t h a t are not changed i n l e n g t h by the s t r a i n S. i s c i r c u l a r with  [°01]  b  as i t s a x i s and the semiapex angle  1 - n  $ = a r c tan  2  In the p r e s e n t case, the cone  2s  = 59.27'  i  The i n t e r s e c t i o n o f the cone  w i t h the u n i t sphere i s  shown i n Fig.B-2. S i m i l a r l y , the c i r c u l a r cone C • 2  also  shown i n F i g . B-2, which s a t i s f i e s the equation -2 x'  (bBb)  x = x'x  g i v e s the f i n a l p o s i t i o n s a f t e r the s t r a i n B of a l l l i n e s t h a t are not changed i n l e n g t h by the s t r a i n S. I t s semiapex angle i s <  1 -n$' = a r c t a n  2 "1  49.95°.  The same cone, C , g i v e s the i n i t i a l p o s i t i o n of plane normals 9  130  FIGURE  B-2  S t e r e o g r a p h i c p r o j e c t i o n showing some of the o p e r a t i o n s i n d e t e r m i n a t i o n of i n v a r i a n t l i n e s t r a i n s compatible w i t h the shear system ( O i l ) [ O i l ] , .  131  t h a t are not changed i n l e n g t h by s t r a i n S, i . e . ,  n'  -2 (bBb) n = n'n.  Now, s i n c e the i n v a r i a n t l i n e x. o f the s t r a i n S x  must l i e i n the shear plane w i t h normal P ', the f o l l o w i n g 2  relationship P and  2  holds:  ' *  ±  = 0,  the two p o s s i b l e v a l u e s o f x.,x, and x~, are the l 1 2'  i n t e r s e c t i o n s of The  w i t h the great  circle  (011)^  a l g e b r a i c s o l u t i o n s f o r x^ are as f o l l o w s  (Fig.B-2).  (the u n i t  v e c t o r s with p o s i t i v e b^ components were chosen): x  = [0.691214;  1  -0.510991;  x„ = [-0.691214; -0.510991;  0.510991]  b  0.510991]  . b  A l s o , s i n c e the plane w i t h an i n v a r i a n t normal must the shear d i r e c t i o n d , the f o l l o w i n g 2  V and  d  2  contain  holds:  = 0,  the two p o s s i b l e v a l u e s o f n . , n ' and n„', are the 1  intersections of C  2  w i t h the great c i r c l e  (011)j-,.  The  a l g e b r a i c s o l u t i o n s f o r n-^' are the f o l l o w i n g row v e c t o r s : n  1  n« 2  = ( 0.414493; = (-0.414493;  0.643504; 0.643504;  0.643504), 0.643504) . b  To  f a c i l i t a t e the d e t e r m i n a t i o n of the  c a r r i e s Bx.  i n t o x. , the i  1  rotation R i s resolved  r o t a t i o n which makes the and  a generalized  i s defined  by  shear plane p  r o t a t i o n about x^.  orthonormal bases are the  r o t a t i o n which  p  an u n r o t a t e d plane  F i r s t , two  i n t r o d u c e d . The  u n i t v e c t o r s x^,  1 2  into a  2  subsidiary  f i r s t basis, basis i , (where p ' 2  is  i n i t i a l p o s i t i o n of the normal to the plane of the i n v a r i a n t shear) and (bR i) =  The  i 7  r o t a t i o n of the b a s i s  and  2  p o s i t i o n of the and  p '  of the normal p latter  basis, basis  v = x^  x p  2  , where x^ =  i n v a r i a n t l i n e due  due  1 2  i s g i v e n by  p '  p 2  _  the  '  t o the  [ p ' (bBb) 2  strain S  The  (fS f) = R O  Q  —  is  the  deformation position The  relation:  '  PV 2  so  that  (bBb)  i n v a r i a n t l i n e x^  with normal p_*  i  2  defined  R ' 1 2  final  x  unit  - 1  =F 2  to the  lattice  b.  by the  (bBb)  l a t t i c e deformation.  following  (bBb)  ~  =  2  leaves the  t o the  i i n t o the b a s i s  j , i s defined  i s the u n i t v e c t o r p a r a l l e l  2  matrix  2  second s u b s i d i a r y  v e c t o r s x.^ , p  Thus, the  2  lattice  (x p ,u)  1  r e p r e s e n t s the  u = x^*p .  the  i n v a r i a n t and  the  u n r o t a t e d . Since the d e s i r e d  shear plane  invariant  line  133  strain  ( f S f ) does i n f a c t r o t a t e the p l a n e P  1 2  /  a n c  *  n e c e s s a r i l y o n l y about the i n v a r i a n t l i n e i t s e l f , t h e generalized the  r o t a t i o n about x^ has t o be i n t r o d u c e d .  s t r a i n (fS f ) i s r e f e r r e d t o the b a s i s o  When  i , i t follows  that (iS i ) = R ' (bBb)'R , O 2 1 and the d e s i r e d  invariant:  1 0 0  (iSi) =  l i n e s t r a i n becomes  0  0 cos 6 sin 0  -sinB COSB  R  (bBb) R,  0  The r o t a t i o n angle B i s determined u s i n g  the f o l l o w i n g  relationship: n '  (iSi) = n '  i  i  F i n a l l y , the i n v a r i a n t l i n e s t r a i n can be r e f e r r e d t o the original b basis, i . e . , (bSb) =  R  (iSi)  R-_'  .  As mentioned e a r l i e r , the s t r a i n S l e a v e s a l i n e x^ and a normal n / . s t r a i n B l e a v e s two l i n e s (n^' and n possible  1 2  ) unchanged  rotations R  nations of ^ » i " x  4.  n  invariant  S i n c e i n the p r e s e n t case the  (x and x_) and two normals 1 ->  i n length,  there are four  c o r r e s p o n d i n g t o four p o s s i b l e  (i.e.,  1. x^,n^'; 2. x , n ' ; 2  2  3. x^,n ';  x , n . ' ) , which w i l l make these l i n e s and normals 0  combi2  invariant  134  as w e l l .  T h i s leads t o f o u r s o l u t i o n s f o r S.  p o s i t i o n s o f x_^ and n^  are symmetrical t o the p o s i t i o n s of  1  and n ' w i t h r e s p e c t t o the plane 2  t h a t the combinations  However, the  1  and 3  e q u i v a l e n t t o the combinations number o f r o t a t i o n s t o two,  ( 1 0 0 ) , which means b  are e r y s t a l l o g r a p h i c a l l y 2  and 4.  T h i s reduces  the  and consequently leads t o o n l y  two e r y s t a l l o g r a p h i c a l l y d i s t i n c t s o l u t i o n s f o r S. only the s o l u t i o n s corresponding t o combinations  Thus,  1 and 3  need be c o n s i d e r e d , and they w i l l be r e f e r r e d t o as v a r i a n t s ( x , n ) and 1  1  (x-^n ).  The i n v a r i a n t l i n e s t r a i n S i s now  resolved into i t s  two component s t r a i n s : the i n v a r i a n t plane s t r a i n on the h a b i t plane  (the shape deformation)  (the l a t t i c e i n v a r i a n t s h e a r ) . t a t i o n t h i s has the f o l l o w i n g (bSb) =  and the simple  In the m a t r i x r e p r e s e n form:  (I + d p » ) ( l + d p ' ) , 1  1  shear  2  (B-1)  2  where d^ i s the d i r e c t i o n of the shape deformation, p-^" i s the h a b i t plane normal,  and d  2  and p  1 2  , as s p e c i f i e d  • e a r l i e r , are the d i r e c t i o n and the normal t o the plane of the l a t t i c e i n v a r i a n t shear r e s p e c t i v e l y .  The h a b i t plane,  shape deformation and magnitude o f the simple shear can be determined from Eq.  from the f o l l o w i n g e x p r e s s i o n s t h a t are d e r i v e d  (B-1):  135  P l  « || p ' ( b S b ) " (bSb)  d  -P  1  2  - A  2  =  d  Pl  d  2  The n o r m a l i z a t i o n f a c t o r mi  of the v e c t o r d  1  magnitude of the shape deformation. f a c t o r m_  of the shear v e c t o r d  determines the 1 A l s o , the n o r m a l i z a t i o n  given by the f o l l o w i n g 2  Z  expression:  , .  -  y  2  ( b S b )  P' 2  "  l y  !  (bSb) y _1  determines the magnitude of the simple i n Eq.  (B-2)  shear.  The v e c t o r y  i s any u n i t v e c t o r d i s t i n c t from x^ and  lying  i n the plane P j ' • The o r i e n t a t i o n r e l a t i o n s h i p r e s u l t s from the a p p l i c a t i o n of the i n v a r i a n t l i n e s t r a i n s  (bSb)  to v e c t o r s and normals of the parent l a t t i c e The  and  (bSb)"'  respectively.  data used i n the a p p l i c a t i o n of the Bowles-  Mackenzie m a r t e n s i t e  theory t o the p r e s e n t case of the  B' to a t r a n s f o r m a t i o n i n the Ag-45 a t . pet Cd a l l o y the r e s u l t s of the theory are summarized i n Table  and  B-I.  TABLE B-I A p p l i c a t i o n o f the Bowles-Mackenzie M a r t e n s i t e Theory t o The g' to a T r a n s f o r m a t i o n i n the Ag-45 A t . Pet Cd A l l o y Summary of the Used Data and R e s u l t s  S t r u c t u r e and L a t t i c e Parameters: Parent - Ordered bcc  (CsCl); a  b  = 3.324 A  Product - Ordered fee (CuAl I ) ; a  f  = 4.186  A  Parent - Product L a t t i c e Correspondence: h (fCb)  = _0  h  0  h  0  0  l  Shear System: Parent - ( O i l ) [ 0 1 1 ] ; b  Homogeneous S t r a i n  Product - (111) [112]  (Bain S t r a i n ) :  (bBb)=diag(0.890478;  0.890478; 1.259326)  Semiapex Angle o f the I n i t i a l Cone o f Unextended  Lines:  $ = 59.27° Semiapex Angle of the F i n a l Cone o f Unextended  Lines:  $' = 49.95° Invariant x  1  x  2  =  Lines: [0.691214;  -0.510991;  0.510991]  b  = [-0.691214; -0.510991;  0.150991]  b  -Continued-  137 TABLE B-I - Cont. I n v a r i a n t Plane Normals: n  ' = ( 0.414493;  0.643504; 0.643504)  b  n ' = (-0.414493;  0.643504; 0.643504)  b  2  Invariant Line Variant  Variant  Strain:  (x^n^ —  (x^,n ) — 2  (bSb) =  0.884593 0.099149 •0.024814  •0.091389 0.864098 0.194768  0.064720 •0.270022 1.228335_  (bSb) =  0.884593 0.024814 -0.099149  •0.012685 0.883812 0.108019  0.143425" •0.14.9754 1.242139  Habit Plane P o l e : Variant  (x^,n^)  Variant  (X^n^ —  •0.667566 •0.722279 0.180747  —  Pi  =  0.667566 0.180747 -0.722279  D i r e c t i o n and Magnitude o f the Shape Deformation: Variant  (x^,n^) —  d-^ -  0.748615 -0.643169 0.160966  ; m  = 0.230924  Variant  (x-^,n ) —  d^  -0.748615 -0.160966 -0.643169  ; m  = 0.230924  2  1  Magnitude and Angle o f the L a t t i c e I n v a r i a n t Shear: Variant  (x^n ) —  m  Variant  (x n ) —  ™  l f  2  2  2  =0.428838;  a  2  = 24.20°  = .0.237831;  a  2  = 13.56  -Continued-  138  TABLE B-I - Cont.  O r i e n t a t i o n R e l a t i o n s h i p between the Parent and Product Direction  i n the L a t t i c e o f  Angle between P o l e s , degrees  Parent  Product  V a r i a n t (x jn-^  [lll]  [Oil]  0.78  0.78  1  V a r i a n t (x^ ,n^)  b  [oii]  b  [112]  b  Lattices  [100]  f  9.51  1.25  [lll]  f  4.30  4.30  [011]  f  9.54  1.05  APPENDIX  C  Theory of the Volume D i f f u s i o n P r e c i p i t a t e Growth  Cl.  T h i c k e n i n g of Zener (59)  t h i c k n e s s , X,  Plates  and  of the  Frank  (6) showed t h a t the  i n the  diffusivity,  following  half-  p r e c i p i t a t e p l a t e Whose growth i s  c o n t r o l l e d by d i f f u s i o n of s o l u t e r e l a t e d to the  Controlled  D,  and  through the m a t r i x i s the growth time, t ,  way:  X = L(Dt) ,  (C-l)  Js  where L i s a dimensionless growth c o e f f i c i e n t t h a t only on  the dimensionless s u p e r s a t u r a t i o n , fi  Q  '(c„:-c„) op o .  c  m  i s the  respectively  the  the m a t r i x at the  diffusivity  p r e c i p i t a t e - matrix  are  does not  the  = 0  :  in  and  the C  are  q  depend on  the  2 £ L Lexp (—) e r f c h. . 2 4 2 139  in  interface.  i s o l a t e d d u r i n g growth, and concentration, Q  n  o p  Q  i n t e r f a c e remains p l a n a r ,  r e l a t i o n e x i s t s between Sl  following  c  - c )/  c o n c e n t r a t i o n s i n the p r e c i p i t a t e and  Assuming t h a t the p r e c i p i t a t e s  =(0^  concentration of solute  matrix f a r away from the p r e c i p i t a t e , and  depends  and  that  that the  L:  (C-2)  the  140 C.2.  Lengthening o f P l a t e s and The most advanced  Needles  treatment of the volume d i f f u s i o n  c o n t r o l l e d l e n g t h e n i n g o f p r e c i p i t a t e p l a t e s and needles was  p r e s e n t e d by T r i v e d i  (61,62) .  H i s s o l u t i o n s , based  on the o r i g i n a l Ivantsov treatment o f the problem  (63,64),  i n c l u d e d the e f f e c t o f the n o n - i s o c o n c e n t r a t e nature o f the i n t e r f a c e a t the p r e c i p i t a t e t i p . The c o n c e n t r a t i o n at the t i p can vary due t o the c a p i l l a r i t y interface kinetics effect.  e f f e c t and due t o the  Other authors who  previously  s t u d i e d the problem e i t h e r d i s r e g a r d e d t h i s e f f e c t , or gave o n l y an approximate mathematical treatment  (65-69).  The p r i n c i p a l approximations used by T r i v e d i were: (1) the steady s t a t e shape o f the i n t e r f a c e near the growing t i p i s a p a r a b o l i c c y l i n d e r f o r the case o f a p l a t e - l i k e precipitate,  (2) the e l a s t i c s t r a i n energy and a n i s o t r o p y  of  s u r f a c e p r o p e r t i e s can be n e g l e c t e d , (3) the c o n c e n t r a t i o n  of  s o l u t e i n the m a t r i x i s such t h a t the theory o f c a p i l l a r i t y  a p p l i c a b l e t o d i l u t e s o l u t i o n s can be used, and diffusivity  (4) the  i s independent o f c o n c e n t r a t i o n .  T r i v e d i ' s r e s u l t s , r e l a t i n g the d i m e n s i o n l e s s s u p e r s a t u r a t i o n , -fl ,-to the d i m e n s i o n l e s s growth r a t e , p a vp/2D, of the t i p o f the p r e c i p i t a t e , when the interface k i n e t i c s e f f e c t i s neglected, are:  o  = ( i f p ^ e P e r f c t p ) [1+ —  S (p) ]  35  O  D  0  —'  (C-3)  141 f o r p l a t e s , and P'  1  fi = pePEi(p)[±+-± fi R  (p)]  Q  °  (C-4)  P  f o r needles, where v i s the growth r a t e o f the t i p o f the p r e c i p i t a t e , p i s the r a d i u s o f c u r v a t u r e a t the advancing tip,  p  and p ' are the c r i t i c a l r a d i i f o r growth (the  C  •  c  r a d i i a t which the c o n c e n t r a t i o n g r a d i e n t i n the matrix v a n i s h e s ) , E i i s the e x p o n e n t i a l i n t e g r a l f u n c t i o n , and S  2  and R  2  are c o m p l i c a t e d , f u n c t i o n s  papers by T r i v e d i . The  d e f i n e d i n the o r i g i n a l  >  f i r s t term on the r i g h t h a n d s i d e o f each  equation i s the r e s u l t o b t a i n e d by Ivantsov the i s o c o n c e n t r a t e i n t e r f a c e .  f o r the case o f  The second term i s a  c o r r e c t i o n due to. the c a p i l l a r i t y  effect.  The value o f fi can.be obtained from the phase Q  diagram knowing the average composition t r a n s f o r m a t i o n temperature. of  o f the a l l o y and the  However, many exact s o l u t i o n s  Eqns. (C-3) and (C-4) are p o s s i b l e f o r a g i v e n value o f  fi , depending upon the value o f the r a d i u s o f c u r v a t u r e . In accord with the experimental  observations,  Trivedi  assumed t h a t only one o f these s o l u t i o n s i s s t a b l e with respect to a small perturbation i n the radius of curvature of  the t i p o f the p l a t e .  In agreement with Zener (68),  T r i v e d i s t a t e d t h a t t h i s corresponds  t o the r a d i u s o f  * * c u r v a t u r e , p , which g i v e s the maximum growth r a t e , v . The  142  maximum g r o w t h Eq.  r a t e c a n be o b t a i n e d by  ( 0 3 ) o r (C-4) w i t h  giving  another  simultaneous (C-4) for  then  differentiating  r e s p e c t t o p, and s e t t i n g  r e l a t i o n s h i p b e t w e e n fi , p and p .  solution  of this  equation with  g i v e s unique values  a given value  of  fi . +  Q  Finally,  The  E q . (C-3) o r  (=p*) and p  forp  9v/8p=0,  the expected  ( = p*) maximum  + An e q u i v a l e n t , g r a p h i c a l p r o c e d u r e c a n be a p p l i e d u s i n g T r i v e d i ' s (62) d i a g r a m s f o r t h e v a r i a t i o n o f P * / P and p* w i t h fi . c  Q  growth r a t e , p  c  v*, i s c a l c u l a t e d  ( = v*p*/2D)  from p*  and D a r e known.  Recently,  Hillert  (70) r e p o r t e d t h e f o l l o w i n g new  m o d i f i c a t i o n o f t h e w e l l known Z e n e r - H i l l e r t the  growth o f p r e c i p i t a t e  v  * c p  D It  when  1 o = i _ _ _ 4(i-jj )  plates:  a  exp[-5.756  f o r medium and h i g h v a l u e s  The calculated form t h i s  (1-fi ) ] .  (C-5)  0  o  was r e p o r t e d t h a t i t a g r e e s  used  Equation f o r  critical  with  Trivedi's  o f fi . Q  r a d i u s f o r n u c l e a t i o n , p , c a n be c  from t h e Gibbs-Thompson E q u a t i o n ; equation  a n a l y s i s when  i n i t s original  i s applicable only to ideal  or dilute  143  solutions.  In the case o f a p r e c i p i t a t e growing i n a r i c h  n o n i d e a l s o l u t i o n , the f o l l o w i n g m o d i f i e d form o f the GibbsThomson E q u a t i o n has t o be used (71):  p  -  C  °  (  1  -  C  ° '  V  «  (C  -6)  or p' = 2p , c c where a  (C-6a)  . , i s the i n t e r f a c i a l f r e e energy, V a/0  a  volume o f the a phase, and the thermodynamic S  18'  =  1  +  9 1 n Y  18'  / 3 1 n X  l8- '  i s the molar factor  APPENDIX  D  An Estimate o f the Chemical D i f f u s i v i t y i n the 0' Phase of Ag-Cd A l l o y s on the B a s i s o f a Comparison Between the Cu-Zn and Ag-Cd Systems  D i f f u s i o n data f o r the ordered 0 a l l o y s are not a v a i l a b l e  1  phase o f Ag-Cd  i n the l i t e r a t u r e .  T h e r e f o r e , the  s i m i l a r i t y between the Ag-Cd system and the Cu-Zn system was used t o examine the d i f f u s i v i t y data o b t a i n e d from the growth k i n e t i c s . A comparison of Home and Mehl's data  (72) f o r  chemical d i f f u s i v i t i e s i n the a phase o f a Cu-25 a t . p e t Zn a l l o y i n the i n t e r v a l 724-915°C  (Fig.D-1) and a s e t o f  analogous data f o r the a phase o f Ag-Cd a l l o y s i n the temperature i n t e r v a l 600-780°C  (73-75) showed t h a t the  d i f f u s i v i t i e s i n the a phase o f Ag-Cd a l l o y s were approximately three times l a r g e r and t h a t the a c t i v a t i o n energy was 10 pet larger. The e a r l y work o f Petrenko and R u b i n s t e i n  (76)  p r o v i d e s the only a v a i l a b l e d i f f u s i o n data f o r the 0 phase of a Ag-Cd a l l o y . 3.767 x 1 0  4  They r e p o r t e d an a c t i v a t i o n energy o f  J/mole, which was s i g n i f i c a n t l y l e s s than the  analogous a c t i v a t i o n e n e r g i e s f o r z i n c i n the 0 phase o f Cu-Zn a l l o y s r e p o r t e d by Kuper tt and  Camagni  (78) (9.22 x 1 0  4  al,  J/mole).  144  (77) (7.86 x 1 0  4  J/mole)  However, the data  TEMPERATURE, 1000  7  8  °C  800  700  9  10  ^  i  1/T,  600  i  IO"  4  i  II  l/°K  FIGURE D - l  Comparison o f the d i f f u s i v i t y a-Cu-Zn and a-Ag-Cd phase.  data f o r  146 of Petrenko and R u b i n s t e i n are o f dubious q u a l i t y ; they 4 a l s o r e p o r t e d and a c t i v a t i o n energy o f 1.109  x 10  J/mole  f o r the d i f f u s i v i t y  o f z i n c i n the B phase o f a Cu-Zn  alloy  T h i s i s almost an o r d e r o f magnitude  (500-800°C).  l e s s than the more r e l i a b l e r e s u l t s o f Kuper and Camagni. Thus the only b a s i s f o r comparison i s the p r e v i o u s l y d e s c r i b e d r e l a t i o n s h i p between the d i f f u s i v i t i e s  i n the  a phases o f the Cu-Zn and the Ag-Cd a l l o y s . Ugaste and Pimenov (79) r e p o r t e d an a c t i v a t i o n energy o f 1.507  x 10  J/mole and a frequency f a c t o r 0.144  f o r the chemical d i f f u s i v i t y pet  (Fig.D-2).  I n c r e a s i n g the a c t i v a t i o n energy by 10 p e t . t o 1.658  resulting diffusivities  z  i n the B ' phase o f a Cu-48 a t .  Zn a l l o y i n the temperature i n t e r v a l 318-447°C  J/mole, and d i f f u s i v i t i e s  m /s  x 10^  approximately t h r e e times, the  (Table VI) are w i t h i n one o r d e r  of magnitude agreement w i t h the d i f f u s i v i t i e s o b t a i n e d from the  bainite thickening k i n e t i c s .  s t r e s s e d t h a t the d i f f u s i v i t y  However, i t should be  v a l u e s o b t a i n e d from the b a i n i t e  t h i c k e n i n g k i n e t i c s a l s o depend on the u n c e r t a i n p o s i t i o n of  the metastable a / ( a + B ' )  and  (a  +  B')/B'  phase b o u n d a r i e s .  147  TEMPERATURE, °C 240 200  19  20  22  23  Comparison o f the d i f f u s i v i t y B'-Cu-Zn and B'-Ag-Cd phase.  data f o r  1/T,  21  160  IO'  4  l/°K  FIGURE D-2  24  APPENDIX  The E q u i l i b r i u m  and t h e M e t a s t a b l e Ag-Cd Phase  The g e n e r a l l y solubility  E  accepted  (80) e x t e n t o f cadmium  i n t h e a p h a s e o f t h e Ag-Cd s y s t e m i s b a s e d on  the  m e t a l l o g r a p h i c work o f Hume-Rothery at al.  the  l a t t i c e p a r a m e t e r work o f Owen  v a l u e s , which agree only plotted  ttal.  t h e same f i g u r e  the upper l i m i t s  by A y e r s  (29).  (82,83). T h e i r are  are a l s o p l o t t e d  the p o i n t s  which  f o r the formation o f massive a  T h e s e p o i n t s match  g' phase, as  measured  the curve obtained  by  e x t r a p o l a t i o n o f the high-temperature p o r t i o n o f the  solubility  limit.  The p o i n t s  c o n t a i n i n g up t o 1.6 of  and  a t t e m p e r a t u r e s n e a r 700°C,  d u r i n g p u l s e h e a t i n g o f the quenched  the  (81)  in Fig. E - l .  In define  Diagram  t h e a-phase  show t h a t  a  formed i n a l l o y s  m  a t . p e t Cd i n e x c e s s o f t h e u p p e r  field.  The  limit  e x t e n s i o n o f the formation o f a m  into  the e q u i l i b r i u m  systems s i m i l a r Cu-Zn  (29,34)  found t h a t  two-phase  and 1.2  than the s o l u b i l i t y  the  a t . pet i n Cu-Al  i n t h e Ag-Zn s y s t e m a  field  was  less  i n other  t o t h e Ag-Cd s y s t e m : 0.3-0.45 a t . p e t i n .  c o n t a i n i n g up t o 39.1  a-phase  field  m  (34).  formed o n l y  a t . p e t Zn, i . e . , 1.1  limit.  These r e s u l t s  Ayers i n the  two-phase  field  148  1-1.5  alloys  a t . pet less  indicated  i n t h e m e t a s t a b l e Ag-Cd d i a g r a m may  equilibrium  also  that  extend  a t . p e t beyond  the  . the into  149  SILVER,  CADMIUM,  AT. P C T  AT. P C T  FIGURE E - l The r e l e v a n t p o r t i o n o f the Ag-Cd e q u i l i b r i u m phase diagram ( t h i n l i n e s ) and the Ag-Cd metastable phase diagram ( t h i c k lines). In the metastable phase diagram,the formation o f the c phase i s suppressed by r a p i d quenching from t h e B p h a s e to the 6 phase. 1  150 p r e v i o u s l y assumed  limits.  A sharp change i n the d i r e c t i o n o f the  solubility  l i n e a t 440°C i n the e q u i l i b r i u m Ag-Cd diagram the appearance  o f the e u t e c t o i d hep  ? phase.  i s due t o  I f the  formation o f the r, phase i s suppressed by quenching,  the  s o l i d s o l u b i l i t y o f cadmium i n s i l v e r should be l a r g e r than the e q u i l i b r i u m s o l u b i l i t y ,  s i n c e i t was  observed t h a t i n  a system o f t h i s k i n d the:primary s o l u t i o n can reach h i g h e r c o n c e n t r a t i o n s when i t i s f o l l o w e d by c u b i c 3 phase, than by hep  5 phase  (84).  The s o l u b i l i t y  rather  l i n e should  t h e r e f o r e extend u n i f o r m l y t o the 3 phase o r d e r i n g temperature (240°C), as i n d i c a t e d i n F i g . E - l , and then bend towards the s i l v e r s i d e , s i m i l a r t o the s o l u b i l i t y diagram.  l i n e i n the Cu-Zn  In F i g . E - l , the p o r t i o n o f the a - s o l u b i l i t y  below 240°C was  line  c o n s t r u c t e d u s i n g data o b t a i n e d from the  shape and s l o p e o f the e q u i v a l e n t p o r t i o n of the l i n e i n the Cu-Zn diagram  solubility  (85,86).  The e x i s t e n c e o f the ordered bcc 8'-phase f i e l d i n the Ag-Cd phase diagram was  proven by Durrant  (87), but i t s  boundaries, based on the s t r u c t u r e o f one a l l o y a t one temperature, were not p r e c i s e l y e s t a b l i s h e d . the boundaries were s h i f t e d s l i g h t l y  In  Fig.E-l,  from the p o s i t i o n g i v e n  by Hansen t o b e t t e r match the e x t r a p o l a t e d high-temperature 8-field  boundaries and s t i l l be c o n s i s t e n t with the thermal  and m i c r o g r a p h i c r e s u l t s o f Durrant.  REFERENCES 1.  M.S.  Wechsler, D.S.  Lieberman, T.A.  AIME, 1953, v o l . 197, p.  Read: Trans.  1503.  2.  J.S. Bowles, J.K. Mackenzie: A c t a Met.,  3.  J.K. Mackenzie,  4.  J.S. Bowles, J.K. Mackenzie:  5.  CM.  6.  J.S. Bowles: i b i d . ,  1954, v o l . 2 , p . l 2 9 .  p.138.  i b i d . , p.224.  Wayman: I n t r o d u c t i o n to the C r y s t a l l o g r a p h y o f 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 , Macmillan, New York,1964. J.W. C r i s t i a n : The Theory o f Transformations i n Metals and A l l o y s , p.824, Pergamon P r e s s , Oxford, 1965.  7.  T. Ko, S.A. C o t t r e l l : J . Iron S t e e l I n s t . , 1952, p. 307.  8.  G.R.  9.  S.J. Matas, R.F. p. 179.  vol.172,  S p e i c h : The Decomposition o f A u s t e n i t e by D i f f u s i o n a l P r o c e s s e s , p. 353, I n t e r s c i e n c e P u b l i s h e r s , New York, 1962. Hehemann: Trans. AIME, 1961,  vol.221,  10. F.E. Werner, B.L. Averbach, M. Cohen: i b i d . , 1956, v o l . 206, p.1484. 11. G.R.  Speich, M.Cohen: i b i d . ,  1960,  v o l . 218, p.150.  12. L. Kaufman, S.V. R a d c l i f f e , M. Cohen: The Decomposition of A u s t e n i t e by D i f f u s i o n a l P r o c e s s e s , p. 313, I n t e r s c i e n c e P u b l i s h e r s , New York, 1962. 13. R.F.  Hehemann: Phase T r a n s f o r m a t i o n s , p.397, ASM, Park, Ohio, 1970.  14. R.F. Hehemann, K.R. Kinsman, H.I. Aaronson: Trans., 1972, v o l ; 3, p. 1077. 15. A.L. T i t c h e n e r , M.B. p. 303.  17. H. Warlimont:  Met.  Bever: Trans. AIME, 1954,  16. H. Pops, T.B. M a s s a l s k i : i b i d . ,  1964,  v o l . 200  v o l . 230, p.1662.  I.S.I. S p e c i a l Report 93, 1965,  p.58.  18. Z. Nishiyama, S. K a j i w a r a : Jap. J . A p p l . Phys., v o l . 2, p.478. 151  Metals  1963,  152  19. H. Sato, R.S. Toth, G. Honjo: A c t a Met., 1967, v o l . 1 5 , p.1381. 20. J . B r e t t s c h n e i d e r , H. Warlimont: Z.Metallkunde, 1968, v o l . 59, p.740. 21. H.Warlimont, D. H a r t e r : Proceedings o f t h e 6th I n t e r n a t i o n a l Conference on E l e c t r o n Microscopy, p.453, Maruzen, 1966. 22. S. Sato, K. Takezawa: Trans. Jap. I n s t . Metals,1968, v o l . 9, p.925. 23. L. Delaey,  I . i C o r n e l i s : A c t a Met., 1970, v o l . 18,  p. 1061. 24. I . C o r n e l i s , C M . Wayman: i b i d . ,  1974, v o l . 22, p.291.  25. D.B. Masson: Trans. AIME, 1960, vol.218, p.94. 26. H.C Tong, C M . Wayman: S c r i p t a Met., 1973, v o l . 7 , p.215. 27. J.D. Ayers: A c t a Met., 1974, vol.22, p.611. 28. R.V. Krishnan: Ph.D. T h e s i s , U n i v e r s i t y o f B r i t i s h Columbia, 1971. 29. J.D. Ayers, T.B. M a s s a l s k i : Met. Trans., 1972, v o l . 3 p.261. 30. R.D. Garwood, D. H u l l : A c t a . Met.,  1958, v o l . 6 , p.98.  31. E. Hornbogen and H. Warlimont: A c t a Met., 1967, v o l . 1 5 , p.943. 32. P.E.J. F l e w i t t and J.M. Towner: J . I n s t . Metals, 1967, v o l . 9 5 , p.273. 33. G.R. Srinavasan and M.T. p.1121.  Hepworth: A c t a Met., 1971, v o l . 1 9 ,  34. T.B. M a s s a l s k i , A . J . P e r k i n s and J . J a k l o v s k y : Met. Trans., 1972, v o l . 3, p.687. 35. R.D. Garwood: J . I n s t . M e t a l s , 1954-55, v o l . 8 3 , p.64. 36. I. C o r n e l i s and C M . Wayman: A c t a Met., 1974, vol.22 p. 301.  153  37.  I . C o r n e l l s and C M . v o l . 7, p.579.  Wayman: S c r i p t a Met., 1973,  38. C.W.  Lorimer, G. C l i f f , H.I. Aaronson and K.R. Kinsman: S c r i p t a Met., 1975, v o l . 9, p.271.  39. M.M.  K o s t i c , E.B. Hawbolt: S c r i p t a Met.: 1975, v o l . 9, p.1173.  40. W. K o s t e r : Z. Metallkunde, 1940, v o l . 32, p.151; ibid., 41.  p.145.  P.L. Ryder, W. P i t s c h : P h i l . Mag.,  42. P.L. Ryder, W. P i t s c h : i b i d . , 43.  1967, v o l . 15, p.437.  1968, v o l . 18, p.807.  1969 Book o f ASTM Standards, P a r t 32, p. 404, ASTM, 1969.  44. H. Sato, R.S. Toth, G. S h i r a n e , P.E. Cox: J . Phys. Chem. S o l i d s , 1966, v o l . 27, p.413. 45. H. Sato, R.S. Toth, G. Honjo: i b i d . , 1967, v o l . 2 8 , p. 137. •• 46. R.S. Toth, H. Sato: A c t a Met., 1968, v o l . 16, p.413. 47.  A. Howie, P.R.  Swann: P h i l . Mag.,  1961, v o l . 6,p.1215.  48. R. Sankaran, C. L a i r d : A c t a Met. 1974, v o l . 22, p.957. 49.  K. R. Kinsman, E. E i c h e n , H.I. Aaronson: Met. Trans.A, 1975, vol.6A, p.303. 50. H.I. Aaronson: "Decomposition o f A u s t e n i t e by D i f f u s i o n a l P r o c e s s e s " , p.387, I n t e r s c i e n c e P u b l i s h e r s , New York, 1962. 51.  H.I. Aaronson, C. L a i r d , K.R. Kinsman: "Phase Transformations", p.313 ASM, Metals Park, Ohio, 1970.  52. P.E. Repas: Ph.D. T h e s i s , Case I n s t i t u t e , C l e v e l a n d , 1965 53.  G.J. Jones, R.K. T r i v e d i : J . A p p l . Phys., 1971, v o l . , 42, p.4299.  54. H.I. Aaronson, C. L a i r d : Trans. AIME, 1968, v o l . 242, p.1437. 55.  M.S.  P a t e r s o n : J . A p p l . Phys., 1952, v o l . 23, p.805.  154  56. M.J. Whelan, P.B. H i r s c h : P h i l . Mag., 1957, v o l . p.1121; i b i d . , p.1303. 57.  2,  H. Sato, R.S. Toth, G. Honjo: A c t a Met., 1967, v o l . 15, p.1381.  58. J.S. Bowles, J.K. Mackenzie: i b i d . ,  1962, vol.10  p.625. 59.  C. Zener: J . A p p l . Phys., 1949, v o l .  20, p.950.  60. F.C. Frank: P r o c . Roy. S o c , 1950, v o l . 61.  A 201, p.586.  R. T r i v e d i : A c t a Met., 1970, v o l . 18, p.287.  62. R. T r i v e d i : Met. Trans., 1970, v o l . 1, p.921. 63.  G.P. Ivantsov: Dokl. Akad. Nauk SSSR, 1947, vol.58, p.567.  64. G.P. Ivantsov: Growth o f C r y s t a l s , v o l . 3, p.53, C o n s u l t a n t s Bureau, New York, 1962. 65. D.E. Temkin: Dokl. Akad. Nauk SSSR, 1960, vol.132, p.1307. 66. G.E. B o i l i n g and W.A. v o l . 32, p.2587. 67.  T i l l e r : J . A p p l . Phys., 1961,  G.R. K o t l e r and L.A. T a r s h i s : J . C r y s t a l Growth, 1969, vol.  5, p.90.  68. C. Zener: Trans. AIME, 1946, v o l . 167, p.550. 69.  M . H i l l e r t : Jernkont. Ann., 1957, v o l .  70. M. H i l l e r t : Met. Trnas. A, 1975, v o l . 71.  G.R. Purdy: Metals S c i .  141, p.757. 6A, p.5.  J . , 1971, v o l . 5 , p.81.  72. G.T. Home and R.F. Mehl: Trans. AIME, 1955, vol.203, p.88. 73. N.R. I o r i o , M.A. Dayananda and R.E. Grace: Met. Trans., 1973, v o l . 4, p.1339. 74. J.R. Manning: Phys. Rev., 1959, vol.116, p.69. 75.  Yu. E. Ugaste, V.N. Pimenov and V.S. Khlomov: F i z . Met. i M e t a l l o v e d . , 1973, v o l . 36, p.211. 76. B.G. Petrenko and B.E. R u b i n s t e i n : Zhur. F i z . Chem. (USSR), 1939, v o l . 13, p.508.  155  77. A.B. Kuper, D. Lazarus, J.R. Manning and C.T. Tomazuka: Phys. Rev., 1956, v o l . 104, p.1536. 78. P. Camagni: Proc. 2nd Geneva Conf. Atomic Energy, v o l . 20, p.1365, Geneva, 1958. 79. Yu.Ugaste and V.N. Pimenov: F i z . M e t . i v o l . 31, p.363.  M e t a l l o v e d , 1968,  80. M. Hansen: C o n s t i t u t i o n o f B i n a r y A l l o y s , second e d i t i o n , p.13, McGraw-Hill Book Co., New York, 1958. 81. W. Hume-Rothery, G.W. Mabbot and K.M. Channel-Evans: P h i l . Trans. Roy. S o c , 1934, v o l . A. 233, p . l . 82. E.A. Owen, J . Rogers and J.C. G u t h r i e : J . I n s t . M e t a l s , 1939, v o l . 65, p.457. 83. E.A. Owen and E.W. Roberts: P h i l . Mag., 1939, v o l . 27, p.294. 84. C.S. B a r r e t t , T.B. M a s s a l s k i : S t r u c t u r e o f M e t a l s , e d i t i o n , p.345, McGraw-Hill, New York, 1966.  third  85. S.T. Konobeevsky and V. Tarasova: Phys. Zhur. Sowjetunion, 1936, v o l . 10, p.427. 86. F. L i h l :  Z. M e t a l l k d e . , 1955, v o l . 46, p.434.  87. P.J. Durrant: J . I n s t . M e t a l s , 1935, v o l . 56, p.155. 88. W.B. Pearson: Handbook o f L a t t i c e Spacings and S t r u c t u r e s o f Metals and A l l o y s , f i r s t e d i t i o n , v o l . 2, p.510 Pergamoh Press, Oxford, 1967.  

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