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Quenched in defects in silver and silver alloys Ssu, Yun I 1960

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QUENCHED I N D E F E C T S AND S I L V E R  IN  SILVER  ALLOYS  by  TUN I .  A THESIS  SUBMITTED  SSU  I N P A R T I A L F U L F I L M E N T OF  T H E R E Q U I R E M E N T S F O R T H E D E G R E E OF DOCTOR O F P H I L O S O P H Y •  in  the  Department of  M I N I N G AND M E T A L L U R G Y  We a c c e p t standard degree  of  this  thesis  required  as  from  conforming  candidates  to  for  the the  DOCTOR OF P H I L O S O P H Y .  Members Mining  of and  the  Department  Metallurgy.  T H E U N I V E R S I T Y OF B R I T I S H C O L U M B I A October,  I960  of  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  the r e q u i r e m e n t s f o r an advanced degree a t the  University  o f B r i t i s h C o l u m b i a , I agree t h a t the L i b r a r y s h a l l make it  freely  a v a i l a b l e f o r .reference and  agree t h a t p e r m i s s i o n f o r e x t e n s i v e f o r s c h o l a r l y purposes may  study.  I further  c o p y i n g of t h i s  be g r a n t e d by the Head o f  Department o r by h i s r e p r e s e n t a t i v e s .  Department o f  be a l l o w e d w i t h o u t my w r i t t e n  •  The U n i v e r s i t y of B r i t i s h Vancouver 8, Canada. Date  Columbia,  my  I t i s understood  that copying or p u b l i c a t i o n of t h i s t h e s i s f o r g a i n s h a l l not  thesis  financial  permission.  FACULTY OF GRADUATE STUDIES  PROGRAMME OF THE FINAL O R A L E X A M I N A T I O N FOR T H E DEGREE OF  D O C T O R OF  PHILOSOPHY of  Y. I. SSU B . A . , National Tsing Hua University, M . S c , University of British Columbia,  "THURSDAY, OCTOBER 6, 1960, IN ROOM M . 201,  P.M.  MINING BUILDING  COMMITTEE Chairman: C . A . F. A . F O R W A R D W. M . A R M S T R O N G E. T E G H T S O O N I A N J. A . L U N D A. M. A R M S T R O N G  AT 4:00  1938 1955  IN  CHARGE  McDOWELL J. B. B R O W N R. E. B U R G E S S G. M . GRIFFITHS M . P. B E D D O E S P. H O  External Examiner: G . R. P I E R C Y Atomic Energy of Canada Limited, Chalk River, Ontario  G R A D U A T E STUDIES QUENCHED IN DEFECTS IN SILVER A N D SILVER ALLOYS  Field of Study: Physical Metallurgy  ABSTRACT An investigation has been made of the formation energy, and its alloys with Cu, Au and Pd. In pure silver the quenched in In the alloys,  however, the quenched in resistivity decreases at first, passes through The decrease in the quenched iii resistivity in these alloys  may be attributed to the destruction of short range order existing in the well annealed specimens.  Phase Transformations  W. M. Armstrong  Plastic Deformation  V. Griffiths  Nuclear Metallurgy  D. R. Wiles  Solid State Physics  R. E. Burgess  Nuclear Engineering  S. D. Cavers  This mechanism is similar to that  PUBLICATIONS  invoked by both Damask and Korevaar in similar experiments. The annealing characteristics of these quenched specimens also confirm this view. A method, other than that used by Korevaar, for evalu-  1.  t  of 0.8 ev and E  m  Phys., 37, 858,  ranging from. 70  ev to 1.02 ev. These results seem reasonable, although it is felt they  G. M. Griffiths, P. P. Singh, Y. I. Ssu, and J. B. Warren, "A simple gamma-ray insensitive fast neutron counter", Can. J.  ating the formation energy, of a vacancy was used. The results so obtained yield values for E  H . P. Myers  Related Fields:  a minimum and only begins to rise at fairly high quench temperatures.  W. M . Armstrong  Theory of Alloys  the activation energy of migration of vacancies in pure silver and resistivity rises with increasing quench temperature.  Diffusion in Metals  2.  1959.  P. P. Singh, G. M. Griffiths, Y. I. Ssu, and J. B. Warren, "The  are insufficiently accurate and extensive to warrant detailed con-  neutron yield from heavy ice targets bombarded with protons  clusions concerning the effects of specific alloying elements.  below the D(p,n) 2p threshold", Can. J. Phys., 37, 866,  1959.  ABSTRACT  An i n v e s t i g a t i o n has been made o f t h e f o r m a t i o n energy, and t h e a c t i v a t i o n energy o f m i g r a t i o n o f v a c a n c i e s i n pure s i l v e r and i t s a l l o y s w i t h Cu, Au and Pd. increasing  I n pure s i l v e r t h e quenched i n r e s i s t i v i t y r i s e s w i t h  quench t e m p e r a t u r e .  I n t h e a l l o y s , however, t h e quenched i n  r e s i s t i v i t y d e c r e a s e s a t f i r s t , passes t h r o u g h a minimum and o n l y b e g i n s t o r i s e a t f a i r l y h i g h quench t e m p e r a t u r e s .  The d e c r e a s e i n the quenched  i n r e s i s t i v i t y i n t h e s e a l l o y s may be a t t r i b u t e d t o t h e d e s t r u c t i o n o f s h o r t range o r d e r e x i s t i n g i n t h e w e l l a n n e a l e d specimens.  T h i s mechanism i s  s i m i l a r t o t h a t i n v o k e d by b o t h Damask and K o r e v a a r i n s i m i l a r e x p e r i m e n t s . The a n n e a l i n g c h a r a c t e r i s t i c s o f t h e s e quenched specimens view.  also confirm t h i s  A method, o t h e r t h a n t h a t u s e d by K o r e v a a r , f o r e v a l u a t i n g t h e form-  a t i o n energy, o f a vacancy was u s e d . f o r E|> o f 0.8  The r e s u l t s so o b t a i n e d y i e l d v a l u e s  ev and Em r a n g i n g from .70  ev t o 1.02  ev.  These r e s u l t s  seem r e a s o n a b l e , a l t h o u g h i t i s f e l t t h e y a r e i n s u f f i c i e n t l y a c c u r a t e and e x t e n s i v e t o w a r r a n t d e t a i l e d c o n c l u s i o n s c o n c e r n i n g the e f f e c t s o f s p e c i f i c a l l o y i n g element s.  ACKNOWLEDGEMENT  The a u t h o r the  work c a r r i e d  thereafter. for He  their also  wishes  their  thesis. the  He i s  t i l l '  1959  grateful  to thank  assistance,  to  M r . R. also  Department  of  wishes  to  was  s  Grant  Number 7 5 1 0 - 3 3 ,  Dr. E.  on  by the  and b y the  Burgess  on v a r i o u s  and Mr. R,  and u n t i r i n g the  his  Teghtsoonian  R.E.  comments  Butters  obtained  i;  V. Griffiths for  Professor  Technical  Thei w 6 r k - w a s f i n a n c e d under  and t o  acknowledge  Mines and  potentiometer  Dr.  M r . W. I r v i n e ,  c r i t i c a l discussions He a l s o  vernier  indebted to  p r e l i m i n a r y reading and  advice and for  out  is  parts  Richter  i n the  cooperation  Surveys  for  his  supervision  of  for  the  manuscript.  their  technical  and M r . S .  preparation of  the  t h r o u g h whose  Mines  courtesy  Saimoto of  the  Branch the  loan.  Defence  of  and Mrs. A . M . Armstrong  Mr. K . G . Davis help  supervision  Research  N a t i o n a l Research  Board of Council.  Canada  of  T A B L E OF  CONTENTS Page  INTRODUCTION PART  I  0  «  a  o  *• P U R E S I L V E R  o  o  «  ©  o  o  «  o  »  »  III.  o  «  1.  Formation of  2.  Evidences for  3.  Relative  o  o  o  o  «  o  a  o  «  of  .  c  >  o  o  «  .  .  .  .  o  o  »  o  .  «  »  o  .  «  .  «  a  .  #  .  4  »  l  |  «  o  o  o  o  I  o  o  2  o  .  2 3  and o t h e r  quenched  i n  on e l e c t r i c a l r e s i s t i v i t y  .  1.  Preparation of  2.  Quench experiments  3  Procedures  b.  Results  Annealing  .  .  .  o  o  o  .  .  .  .  .  .  .  .  .  o  .  . .  .  . .  . .  . .  . .  Annealing  .  .  .  .  .  9  .  .  .  .  .  9  .  Ik 19  of  annealing curves  behaviour of  spe cimens  temperatures  behaviour of  580°C  o  •  quenched  .  19  specimens  quenched  t  o  o  Cu i n Ag specimens  .  Preparation of  2.  Quench experiments  .  3.  Negative quenched i n - r e s i s t i v i t y  •  0  0  Au i n Ag  1.  Preparation of  2.  Negative quenched  3.  Damask?s  0  o  specimens  .  0  .  .  o  . .  and e x p l a n a t i o n  0  . O  O  0  •  o  2U 28  o  O  O  O  O  0  O  O  28  o  •  ©  o  o  o  28  .  . •  O  0  . 9  O  0  0  e  o  . .  o  o  •  0  o  o  i n resistivity  experiments  19  «  0 0 0 0 0 0 0 0 0 0  Percent  . .  1.  Atomic  8  .  Annealing  Percent  .  and accuracy  b.  .  .  8  .  General feature  .  .  .  a.  SILVER ALLOYS  2  .  experiments  from  2 Atomic  .  7  specimens  a.  c.  II,  o  o  vacancies  from high  I.  o  o  v a c a n c i e s . ,«  Measurements'- and R e s u l t s  -  o  P r e v i o u s - W o r k on Quench Experiments  3.  PART 2  o  vacancies  effect  defects II,,  o  O  O  0  0  . O  0  . "O  0  28 •  O  ...  0  0  .  0  0  0  30 3^  30 31 31  Table  of  III.  IV.  Contents  25  25  (cont'd.)  ,4.  Korevaar's  5.  X-ray evidence  6.  A a r t s and J a r v i s '  II.  and  short  explanation  range  order  0  0  0  i n Au-Ag  0  0  33  0  alloys  .  E  8.  Annealing  experiments  Atomic  Percent  4  .  Au i n Ag  .  .  33  34  experiments  of  •  0  e  0  0  0  34  .  o  e  .  0  0  36  . . . .  39  .  .  39  1.  Preparation of  2.  Quench experiments  . . . .  40  3.  Annealing  . . . .  40  Atomic  Percent  . . . .  44  specimens  .  .  44  ,  47  experiments Pd i n Ag  1.  Preparation of  2.  Quench experiments  .  .  .  3.  Annealing  ,  .  &  specimens  experiments  o .  BIBLIOGRAPHY  I.  of  Evaluation  SUMMARY'  APPENDIX  experiments  o  o  «  .  50 53  .  56  . . . .  .  ,  d  Measurements Possible tion.  of  Quench  Sources  0 0 » •  « 0  of O  59 o  e  s  Rates  * .  e 0  o 0  4  59  0  E r r o r and P r o v i s i o n s Taken f o r *  0 ^ 0  *  0  0  0  0  0  0  0  0  0  their 0  0  0  0  Elimina0  0  61  LIST  OF F I G U R E S  No. 1.  (a)  Balanced  2.  R e s i s t i v i t y versus  Temperature;  3.  Quench Experiments  of  4.  l n A P v e r s u s -i-s P u r e '  Circuit  (b)  Pure  Series  Circuit  (c)  Pure S i l v e r  Silver  .  .  .  .  .  . .  . .  .  .  Layout  .  of  .  12  .  15  Silver  16  T  5.  I n i t i a l Rate  of  A n n e a l i n g ; Pure  Silver  6.  I n i t i a l Rate  of  Annealing; Pure  Silver  7.  Annealing Experiments  of  Pure  Silver  2&  8.  Annealing Experiments  of  Pure  Silver  27  9.  R e s i s t i v i t y versus  10.  Quench Experiments;  11.  ln(T -£££- ) versus 2  dT  Temperature; 2 — ;  At. 2  Percent  of  2  13.  Quench Experiments  of  25  At.  14.  ln(T -£££-) dT  ~ ; T  15.  Annealing Experiments  versus  25  of  Quenched f r o m two e  Annealing Experiments;  17.  R e s i s t i v i t y versus  18.  Quench  19.  ln(T  2  Experiments P  dA  ) versus  dT  25  At.  .  .  .  .  .  .  .  .  .  .  .  .  19 21  Percent  Au i n  Au i n Ag A l l o y  .  .  .  29  Ag A l l o y  32  Au i n Ag A l l o y  37  Percent  At.  25  Percent  of  Au i n Ag A l l o y  A t . Percent At.  .  . .  Au i n Ag A l l o y  Temperatures  25  .  .  .  .  .  38 41  Au i n Ag A l l o y  A t , Percent  High  .  Au i n Ag A l l o y  Percent  Temperature;  .  .  .  .  .  Au i n Ag A l l o y Percent  .  0  0  A t . Percent  Pd i n Au A l l o y  - i - ; 25  A t . Percent  Pd i n Ag A l l o y  A t . Percent  Pd i n Ag A l l o y  42  0  Specimens  .  . .  43 .  .  .  .  Au i n Ag A l l o y  25  .  .  .  .  .  .  45  . . . .  .  46  .  48 51  -l  20.  Annealing Experiments;  21.  R e s i s t i v i t y versus  22.  .  T-  Annealing Experiments  16  At.  A t . Percent  12.  2  2  .  25  Temperature;  25 ,•  (a.)  Measurement  of  Quench R a t e ,  (b)  Measurement  of  Quench Rate  At.  Percent ......  .  Pd i n Ag A l l o y  52 . . .  54 «>  59 60  QUENCHED  I N DEFECTS  AND S I L V E R  I N SILVER  ALLOYS  INTRODUCTION  In  the  past  ten  years  there  on quenching and annealing techniques diffusion  i n metals.  tion  often  were  agree  with  quench  used  those  m e t a l whose  properties  affect  as  the  on a l l o y s  of  annealing techniques. is  that  on  to  investigate  formation  a 7 atomic the  is  migration of  also  further on the view  of  is  diffusion  the  resistant  of  of  known,  a  rate  Cu i n  the  activation energy  markedly,  considerations  (less  with  an  Au a l l o y .  the  i f  A few than  oxida-  f o r these  metals  Silver is  a  as  aware,  we  are  noble no  foreign  experiments  If?)  There  has  have  by quenching  exceptionally high been  element  formation energy can be  these  experiments element  migration of that  obtained  s i m i l a r methods  alloying of  of  been  and  alloying  no  content  attempt  as  energy  of  on the  yet  vacancy.  i n silver  of  far  energy  towards  obtained  s m a l l a d d i t i o n s of  a particular alloying  ascertain  results  so  based  reported.  One e x p e r i m e n t percent  experiments  activation  Results  studied, yet  low concentration  a vacancy  effect  these  been  deemed u s e f u l i f  From the the  evaluate  investigations.  generally  effect  interesting to  alloys.  a number of  platinum being highly  been w e l l  have  and m i g r a t i o n of  It of  have  on i t  Moreover,  performed  i n these  to  been  obtained by s e l f - d i f f u s i o n experiments.  experiments  substances  Gold and  has  the  on the  a vacancy  present  by these  can  it  and the  be  might  activation methods.  applied to be  possible  formation energy i n these  alloys.  i n v e s t i g a t i o n was  energy  ' It  is  silver to as  <probe. well  It  is  undertaken.  as i n  PART 1 - PURE SILVER I.  T h e o r e t i c a l Review 1.  Formation of vacancies. V a c a n c i e s a r e formed a t e l e v a t e d t e m p e r a t u r e s by t h e r m a l e x c i t a t i o n  and r e a c h e d an e q u i l i b r i u m c o n c e n t r a t i o n g i v e n by an e q u a t i o n o f t h e form c = A exp^- | ~ J where Ef i s t h e f o r m a t i o n energy o f a v a c a n c y , i . e . ,  the  energy r e q u i r e d t o e x t r a c t an atom f r o m t h e i n t e r i o r o f t h e m e t a l and p l a c e i t on t h e s u r f a c e o f t h a t m e t a l , and A is t h e f r e q u e n c y f a c t o r .  The t h e o r e -  t i c a l c a l c u l a t i o n o f t h i s energy f o r copper has been c a r r i e d out by H u n t i n g t o n and S e i t z  1  2 3 and by H u n t i n g t o n . ' H u n t i n g t o n a r r i v e d a t a v a l u e f o r t h e f o r m a t i o n  e n e r g y o f a v a c a n c y i n copper o f 1.5  t o 1,8  ev.^  Once a v a c a n c y i s formed i t  may move t h r o u g h t h e l a t t i c e by a p r o c e s s o f p o s i t i o n exchange w i t h n e a r e s t n e i g h b o u r atoms.  B e f o r e and . a f t e r t h e exchange t h e atom i s i n a s t a b l e  p o s i t i o n where t h e p o t e n t i a l energy i s a minimum.  I t requires a certain  amount o f energy t o surmount t h e p o t e n t i a l b a r r i e r between t h e s e e q u i l i b r i u m p o s i t i o n s and t h i s e n e r g y , E migration.  m J  I s r e f e r r e d t o as t h e a c t i v a t i o n energy  of  H u n t i n g t o n a l s o gave t h e a c t i v a t i o n e n e r g y o f m i g r a t i o n as 0.9  ev.  The sum o f t h e s e two e n e r g i e s i s i n r e a s o n a b l e agreement w i t h t h e e x p e r i m e n t a l l y measured  a c t i v a t i o n energy o f s e l f d i f f u s i o n i n copper, namely 1.92  by Kuper e t a l . ' '  measured  The f r e q u e n c y w i t h w h i c h s u c h exchanges o c c u r can be e x p r e s s e d /  by an e x p o n e n t i a l f u n c t i o n  B exp^-  upon t h i s f r e q u e n c y i s o b v i o u s .  E \ m  The p r o f o u n d e f f e c t o f t h e t e m p e r a t u r e  T a k i n g 5 ^ - 0 . 5 ev, t h e r a t i o o f t h e r a t e a t  600°K t o t h a t a t 300°K i s about 4?5x10^, i . e . , per  ev,  I f t h e jumping f r e q u e n c y i s one  second a t 600°K i t w i l l be one i n 4.5x10^ seconds, i . e . ,  t w e l v e hours a t 300°K.  about one i n  2,  Evidences Visual  obtained hardly  since  be  diffusion  with  its  vacancies  evidence  they  are  disputed.  self  density  for  i n  for  the  voids  of  Vacancies  metals  and,  existence atomic  are  no v i s i b l e  a quenched holes  are  metal  more  is  sine.  Their  It  is  also  account  of  Tiny voids which  a  readilycan,  the  however,  magnitude  Kirkendall observed  slowly  are  not  for  the  generally  that  is  existence  convincingly, for  lower than  present.  vacancies  considered to  accompanying porosities.. of  of  clusters  of  effect  that  cooled  of.  the  metal  although  vacancies  have  6 '7 actually  been  observed  However, general  made  physical  3.  not  using  small angle  quantitative  by any of  property  such  as  Relative  effect  measurements  these  means,  hardness  of  X-ray  or  but  scattering  concerning vacancies rather  electrical  vacancies  techniques,  and other  by t h e i r  *'  are  effect  i n  on  some  resistivity,  defects  on  electrical  resistivityo The perfect  p e r i o d i c i t y of  component defects  of  the  more  vacancies effective  boundaries  bution  resistance  or  exert than  surfaces. to  important  and makes  quench  Thus,  instance,  to and  temperature  freeze-in inner  the  parts  to  0°C  the  large  line  electrical  or  metal  and  wire,  arises  influence  and a r e  defects  point  of  view of  as  point  orders  of  dislocations,  measuring the  difference  is  contri-  very  useful.  when a w i r e  of  finite  immediately plunged  and nay  several  such  the  thermo-vibrational  r e s i d u a l component,  resistivity this  thermal  f r o m d i s t o r t i o n of  Disregarding the  planar  experiments  vacancies, of  a  From the  vacancies  high  a  c o n s i d e r i n g o n l y the  of  for  of  ideal lattice.  r e s i s t i v i t y and  such as  magnitude grain  electrical  stresses generate  into  may be  size  is  quenched  from  liquid  nitrogen  i n  order  the  outer  created  dislocations  between and  stacking  a  faults.  - 4-  The  imperfections  of these  effect  on e l e c t r i c a l r e s i s t i v i t y i s u s u a l l y r e l a t i v e l y  s m a l l i n comparison w i t h t h a t due t o f r o z e n - i n v a c a n c i e s . Another  complication a r i s e s from the formation of divacancies  v a c a n c y c l u s t e r s i n c l o s e packed m e t a l s . B a r t l e t t and Dienes  9  I n f e r r e d from Bauerle  and by K i e r s t a d t ,  and  T h i s p r o c e s s has been I n v e s t i g a t e d b y  10  Some e v i d e n c e s o f such phenomena i s  and K o e h l e r ' s ^ " work on t h e a n n e a l i n g o f quenched pure  gold wire. Theoretical c a l c u l a t i o n s of the e l e c t r i c a l r e s i s t i v i t y  associated  12 13 w i t h v a c a n c i e s have been made b y v a r i o u s authors? Dexter, Jongenburger, 14 15 16 Abeles, B l a t t , ' and b y S t e h l e and Seeger„ Various expressions f o r the potential fields  a r i s i n g from vacancies  b u t t h e p r e d i c t e d e f f e c t s on e l e c t r i c a l ment.  have been assumed by t h e s e  authors,  r e s i s t i v i t y are g e n e r a l l y i n agree-  D e x t e r * s v a l u e o f t h e r e s i s t i v i t y increment p e r a t o m i c p e r c e n t  of  v a c a n c i e s was l o w e r (04/fr.fl--cm„) t h a n t h o s e f o r t h e o t h e r i n v e s t i g a t o r s w h i c h o  ranged f r o m 1.25 t o 1.67/ttQ.-cm  0  The e l e c t r i c a l r e s i s t i v i t y r e s u l t i n g f r o m s c a t t e r i n g due t o d i v a c a n c i e s 17 i n monovalent m e t a l  has  been c a l c u l a t e d b y Bross and Seeger.  Provided  t h e r e i s no p r e f e r r e d o r i e n t a t i o n . o f t h e d i v a c a n c i e s t h e r e s i d u a l r e s i s t i v i t y d e c r e a s e s b y 1 0 % upon t h e a s s o c i a t i o n o f s i n g l e v a c a n c i e s  t o form d i v a c a n c i e s .  I t i s a l s o i n t e r e s t i n g t o note t h a t i n t h e i r i n v e s t i g a t i o n , d e v i a t i o n s f r o m Matthiessen's  l a w were n e g l i g i b l e .  The e l e c t r i c a l  s c a t t e r i n g o f e l e c t r o n s a t a c l u s t e r o f vacancies  r e s i s t i v i t y r e s u l t i n g from has been c a l c u l a t e d  by  18 Dexter,  H i s r e s u l t s , because s p h e r i c a l c a v i t i e s were assumed, were more  a p p l i c a b l e t o l a r g e r c l u s t e r s . He f o u n d t h a t as t h e c l u s t e r s I n c r e a s e the  in  size  s t o r e d energy a s s o c i a t e d w i t h t h e c l u s t e r d e c r e a s e s w h i l e t h e r a t i o o f  r e s i s t i v i t y / s t o r e d e n e r g y o f t h e d e f e c t s increases,, Some o f h i s r e s u l t s a r e c i t e d  - 5 below: TABLE  Vacancy  cluster  formed  Resistivity  M^--cm  Resistivity  p e runit  by n vacancies  1  n  p e rA t . percent stored  effect  10  100  1000  10000  2.22  1.35  0.686  0.343  0.168  17.4  18.8  19.8  energy  density^L-cm/ev/cc.  The  1  12.2  o f t h e presence  o f edge  16.0  dislocations  on electrical  ng vity and  h a s been Dexter  22  dislocation calculated other  investigated and t h a t  was  hand,  tion  considered  Koehler  there  8  from screw listed  displacements  potential  Seeger  associated "with  and Stehle  dislocations  2*3  with  line.  scattering A l l authors  screw  dislocations  their  smaller.  the scattering  the electrical  On t h e potentials  varies  t o be even  may b e  line.  dislocations  g i v e n f o r copper  that  An edge  edge  .had c a l c u l a t e d  The r e s u l t s  a n d i t may b e n o t e d  obtained  8  strength  the dislocation  thedislocation  r e s i s t i v i t y i s thought  dislocations.  below;  about  nr\ 91 Landauer"  Nabarro.  d i p o l e whose  and Sondheimer  about  and Sondheimer,  b y H u n t e r and  as a line  i s no d i l a t a t i o n a s s o c i a t e d  and  Mackenzie  dislocations  and Mackenzie  to t h e electrical  Nabarro  7  b y Landauer  displacements  the scattering  Since  o f screw  from t h e elastic  from t h e ionic that  by Kohler,  agreed slowly. contribu-  Hunter  of  by various  resisti-  and  electrons  authors a r e  resistivities  due t o  are anisotropic, TABLE 2  Type Edge  of dislocation dislocation  Direction of Current J_ slip in in  Screw  dislocation  plane  s l i p plane dislocation s l i p plane  gsfJt-cmyl0 1.37  _L (1  »  0  -L-  slip  plane  0.26'  in  slip  plane  in  slip  plane  dislocation  0.6  0.44  dislocation • - L  dislocation  /L-cm.xl0 f o r random o r i e n t a t i o n  0.26 ll 0  0.17  - 6 Blatt, of  stacking  copper  Ham a n d K o e h l e r  faults  24  on e l e c t r i c a l  and s i l v e r t o  be s m a l l .  have  investigated  theoretically  r e s i s t i v i t y and have They  gave  found the  the following  Metal  the  effect  effect  i n  values:  Copper  Silver  Gold  0.021  0.056  1.55  20 ^Pn-cmxlO These the  results  change  of  higher than  (unit  density  are not undisputed. electrical  the values  of S.F.)  Most  experimental  r e s i s t i v i t y associated  derived from theoretical  with  results  dealing  plastic  deformation  calculations.  There  with are  have 18  been has tion  two suggestions suggested  that  to  explain this  vacancies  c o u l d be r e s p o n s i b l e  discrepancy.  or vacancy  for a  large  clusters  part  of the  On t h e one h a n d , generated  Dexter  by p l a s t i c  resistivity  deforma-  increase  26  25 associated suggested  with that  discrepancy.  plastic the  There  deformation;  stacking is  faults  experimental  on the other  themselves evidence  hand,  Broom  and Koehler  c o u l d be r e s p o n s i b l e to  support  the  latter  f o r the view.  27 Christian contribute  and Spreadborough  found i n t h e i r  significantly to the  eletrical  experiments  r e s i s t i v i t y of  that  stacking  a deformed  faults  metal.  II.  P r e v i o u s Work on Quench  One o f They  found the  the  quench  energy  of  Experiments  experiments  was  f o r m a t i o n E-f o f  reported  a vacancy  by  in  Bauerle  gold to  and  be  Koehler.  0,98  1 1  ev.  2ft This  value  cooled  is  possess  the  l i t t l e  h e l i u m gas  from various to  a  as  smaller  the  quenching  temperatures  activation  quenching  than  and  agent  annealed  energies  temperature,  Kauffman's  of  being  migration  Quench temperature Activation  The  explanation  whose that  Em i s the  the  higher  150  hours,  decayed  in  were  the  a more  It  annealed  quenched-in  complicated  room temperature  ment  the  recent  Similar  for  was  higher  pre*  Specimens of  40°C were  which  m  quenched  temperatures,  1000°C  0.82  0.66  0.63  0.60  was  during the  temperature  was  practically  out  completely  about The  10  the  greater  annealing  exponential at  higher  of  divacancies, treatment  the  kinetics  and the  quench  +  is  Okkerse,  p l a t i n u m have  of  for  quenchedin  about  temperatures  persisted  E-f  and  number  room temperature  percent  s e l f - d i f f u s i o n measurements  some  annealing  the  measured  concerning  that  on  e.g.,  900°C  effect  found  depended  800°C  resistivity for  investigations  E  ev w i t h  700°C  this  annealing.  1,28  water.  vacancies  found that  way and  of  is  neighbourhood  of  for  very early  f r o m 700°C  prolonged with  adcoiint  formed.  c o u l d be  while  to  o r i g i n a l quenching  quenched  resistivity  migration ev.  were.formed  the  that  specimen  of  offered  smaller  divacancies  in  energy  instead  i n the  smaller  which  even  after  i n good  agree-  carried  out  29 7  been  by  30 several workers. a  vacancy  Bradshaw  and  i n p l a t i n u m and i t s  Pearson  determined  corresponding  the  formation  activation  energy  of  obtained  slightly  energy  of  migration  to  31 be  1.4  values;  and  1.1  the  quenching  respectively.  formation  and  1,23  energy  Ascoli of  ev w i t h w a t e r  a  et  al^  vacancy was quenching.  found to Their  be  1 19 0  annealing  different ev w i t h  experiments  air were  = 8 ~  carried the be  o u ta t seven temperatures  r a n g i n g f r o m 453°C t o 5 7 8 ° C ,  a c t i v a t i o n energy o f migration from t h e half 1,42 e v  0  The measured  + EJJJ a g r e e d w i t h  time  2,6  calculated  o f r e s i s t i v i t y decay t o  the results  performed b y Lazarev and Ovcharenko,-^ namely,  They  ev  s  of similar  andwith  experimennts  activation  energy  33 for  self  diffusion  o f Kidson  and Ross  Similar  experiments  have  who o b t a i n e d a v a l u e o f 2,9 e v .  also  been  performed o n aluminum,  e. g.  34 Bradshaw and Peaison  E ^ = 0,76 e v  E  E  M  = 0.44 e v  35 Panseri  et a l ^  E  f  = 0„74 e v  DeSorbo  andTurnbull^  E  f  = 0,79 e v  For t h e last  example,  .  m  = 0 25 e v O  EL^ «= 0,52 e v  t h e measured E ^ + E  m  (1,31 e v ) c o r r o b o r a t e s  that  37 (1.4 e v ) o b t a i n e d b y S p o k a s  u s i n g nuclear magnetic  resonance  measurements,  38 and a l s o  agrees The  indicates III,  with  thetheoretical  good agreement  that  current  Measurements  suction  interpretations  which were slowly  Thei n g o t s  subsequently  i nthefurnace.  were  employed i n t h e experiments. i n diameter,  o f about  experiments  are essentially  silver  i n open a i rand cast cold  (Johnson  correct,  given a further  h e l d a t 60°C„  diameter  were  spot  also  welded onto  7 t o 8 cms f r o m t h e e n d s .  annealing  20 c m s l e n g t h s  Potential leads  This  wires,  and cooled treatment  o f w i r e were c u t  made o f p u r e  each  left  and Mattey)  i n a quartz tube b y  d r a w n t o 0,0143 i n c h  The w i r e s were  and  positions  numerous  g r a i n - s t a b i l i z e d a t 900°C f o r f o u r h o u r s  one week i n a w a t e r bath  0,002 i n c h  o f t h e process  o f 99.9995 p u r i t y  for  wire,  o f these  and Results  i n a n alundum c r u c i b l e  action.  (l„43 e v ) o f Norwick,  between t h e r e s u l t s  A twenty-gram sample was m e l t e d  estimate  silver  o f t h e specimen a t  a length of the useful  middle  section  mounted  of  Quench  a.  1,  deflection  method of  measuring quenched  The  assembly  A standard  resistor  resistance  the  is  following  d  r  these  u n i t s were  that  r  i n r e s i s t i v i t y was  c o n s i s t e d " of dimensions.  Rj_ w a s  so  +  s  =  s  d  I  x  Od-L  follows  Two o f  now  specimen  The  inserted  adjusted  a  to  that  and  devised  is  the  by  a dummy w i r e  arrangement measure  the  that  shown  current.  galvanometer  shows  of  i n When  no  condition applies;  I  i t  cms„  experiments,  Bauerle,  variable  5  frame.  same m a t e r i a l a n d g e o m e t r i c a l  Figure the  and  silver  about  Procedures  hThe  the  specimen of  on a rectangular  2.  Koehler  the  I  =  r  -  »  d  r  d  ) l  d  r  d  =  s i  I  s  (r  ~  v  I  1/2 =  v  12  +  e i  r  s  ) l  =  12 ~ 3/j v  -  s  ^  V34  r  I«3  Matthiessen's one  due t o  and the arm  rule  Impurities  other  due t o  cancelled  that  r  where  the  s  "  r  d  that  resistances  (in the thermal  i n the  subscripts  The vessel,  states  r  s  scattering  other  ( s i  =  +  present  r  sT)  arm.  "  and d denote  are case,  rrp.  with  a  vacancies  The  latter  two a d d i t i v e  and  parts,  dislocations)  contribution i n  one  Thus:  (*di  +  r  dT)  specimen  heating and quenching processes  partially f i l l e d  composed o f  saturated  =  r  s i  "  r  d i  =  ^  r  i  a n d dummy r e s p e c t i v e l y .  were  brine  carried  out  s o l u t i o n whose  in a  lucite  temperature  - 10 -  Figure  1(c).  Layout  of  Apparatus  -  was  maintained  horizontally Selected  about  current  for  least  from a  ten  cm t o  lead  storage  During  specimen  current  and the  the  curve  dropping the  immediately then  pure  after which  Subsequent  the of  ice the  due t o water,  current  the  the  this  the  of  large  of  water  definite  and f a i r l y r e p r o d u c i b l e  applied  at  temperature  with  The  s i m p l y assumed  was m a i n l y due t o  the  conduction of  was  pass  through the  specimen  presumably less  p o t e n t i a l drop across with  a  shut  a  liquid  the  hot  was t h e n  was  temperature quenched  the  The  air  tank  The  calculated  then  off.  clamp,  assembly made  not  of  was styro-  ±10°C  specimen  For  o  a  temperature given  its  indicated a  and  heating  separation  reasonably  resistivity.  along but  u n i f o r m i t y of the  the  this  specimen was  check  heating  at  could not the  n o n - u n i f o r m i t y of  through the  hot  c r i t i c a l l y on  results  since  the  troublesome,  r e a l i z e d and the  about  in  specimen was  between  temperature  for  the  potentiometer.  specimen  depended  the  heat  arm  e q u i l i b r i u m vacancy  was  an o p t i c a l pyrometer  was  loss  of  increase  range  conduction  of  therein.  limits of  heating  lower temperatures.  amount  gradient  Nevertheless  uniformity of  high temperatures  made  specimen  from the  at  surface.  into  c o n d i t i o n s were  the  appropriate  s o l u t i o n by r e l e a s i n g  temperature  fluctuated within  an  The  current  mounted clamp.  temperature  2).  was  spring  of  by  known r e s i s t i v i t y v e r s u s  possible were  surface  measured  heating  temperature  state  temperature  The  were  brine  heating  the  to  assembly  -  a  period the  (Fig.  the  measurements  steady  specimen  into  q u i c k l y as  Measurement because,  it  silver  water  establishment  i n f e r r e d from the  of  as  at  the  specimen  by a l l o w i n g  heating  through  The  battery  ensure  this  assembly  transferred  foam.  to  specimen  temperature  calibration by  of  cm a b o v e  achieved  concentrations.  resistivity  1  -8°C„  to  were  minutes  and the  »4°C  range  0.5  temperatures  direct at  i n the  11  leads  smaller  to  the  be  lower temperature  frame  temperature  checked  and  gradient.  - 13 The speed with which the specimen was transferred into the l i q u i d a i r a f t e r quenching was important, e s p e c i a l l y f o r pure s i l v e r specimens. I f , by some accident, t h i s process had been delayed, subsequent measurements showed smaller quenched-in r e s i s t i v i t y .  The necessity f o r the second rapid  quench can be understood with reference t o the annealing experiments  conducted  38 by Cooper et a l defects„  i n connection with e f f e c t s on r e s i s t i v i t y of I r r a d i a t i o n  According to t h e i r f i n d i n g s , the vacancies i n i r r a d i a t e d s i l v e r  begin to anneal out at about 200°K whereas the corresponding temperature f o r pure gold i s about 2Z4.0°K,  Hence, f o r s i l v e r a fast quench rate and r a p i d  transfer i s e s s e n t i a l . I n i t i a l l y , a Leeds and Northrup K-2 potentiometer, which was capable of detecting d i r e c t l y 0.5 Aiv was used.  Later, a Vernier potentiometer manu-  factured by Cambridge Instrument Co. and accurate to 0.1 ,-uv was obtained.  The  measuring current was n e c e s s a r i l y limited to 50 ma or l e s s , since otherwise, a steady current could not be maintained.  This s i t u a t i o n was improved but  not eliminated completely by continuously charging the battery with another battery.  The cause of the changing current seemed due not only to the  changing e.m.f, of the battery, but also to thermal e.m.f. along the c i r c u i t , or other factors.  At these necessarily small currents the balanced  circuit  method of Koehler, because the voltages Yj2 and V ^ were small, d i d not permit an accuracy of measurement i n excess of three or four f i g u r e s , and the l a s t figure was, i n general, not d e f i n i t e .  Furthermore, i t was found that the  balance condition s h i f t e d s l i g h t l y during the course of measurements. Therefore, the balanced c i r c u i t method was abandoned and some points of the quench curve were obtained by using a current of less than 0.05 amp through a series arrangement consisting of the specimen, the dummy and the standard resistance, and measuring i n d i v i d u a l l y the p o t e n t i a l drops across them. A l l  -  these  measurements  meter  leads  quenched with  were  were a l s o  c a r r i e d out  occasionally reversed  i n resistivities  those  twice with  measured w i t h  measured w i t h a  series  to  the  circuit  reversed check  parasitic  balanced  as  is  e.m.f.'s.  14  The  galvano-  e.m.f.'s.  circuit  were  shown on the  same  -  The  consistent plot  (Figure  3).  b.  Results  The  formation energy,  Ef,  from the  of  the  A /  oo  statistically assuming the  where n  is  was  is the  out was as  ,02  Ef  ev.  too  Also the  the  so  that  of  (as  of  1/T  s i l v e r was  curve  evaluated  (Figure  4),  by  were  the 0,82  The  number o f  ev.  The  the  from the  at  which the  standard  deflection  defect  large.  An accurate believed to  of  three  to  occurred during the unknown.-  of  be  less  than  e r r o r was  0.1  or  of  is  and  of  such  current,  did  not  fluctuating measured  measurements.  these  0,2  factors  error  ev  carried  the  These were  Since  no  not  i n t e r v a l between  the  specimen  galvanometer).  effect  five  relatively uncertain.  o v e r a l l estimate  the  A l l these  resistivity greatly,  the  resistance,  the  vacancies,  q u e n c h i n g was  specimen  simultaneously.  q u e n c h was  from which  statistical  measured  c o o l i n g which  i n  i n quench temperature  instant  result  quenched  temperature  not  e n t r y was t h e  actual  the  )  accurately  been  is  exp (~|^  n  estimate  quench temperature  i t  v  to  the  make b u t  n oo  uncertainty  observed  effects  to  versus  drop across  temperature f a i r l y  i n pure  p o t e n t i a l drop across  potential  V and I  and each  amount  the  difficult  specimen and the  knowledge  ln^^s  and T i s  given above.  rapidly  since  sites  However, the  nevertheless  alternately  a vacancy  so d e t e r m i n e d was  error  selected  voltages  of  i n r e s i s t i v i t y , nv i s  measured f r o m the  is  slope  atomic  The  i n the  fluctuate It  quenched  quenched.  included  accuracy;  relationships  number o f  more t h a n  and  the  made  the  quench  in E  errors  releasing  f  is  may  have  difficult  corresponding to  an  - 15 -  46r  Quench  Figure  3.  Temperature  Quench Experiments  of  °K  Pure  Silver.  -  uncertainty error  is  quench temperature  estimated  ^ -  A  i n the  J£  i n the  following  of  about  10°C  at  1000°K.  This  17  -  approximate  ways  «P(-|§-)  A  = In A P.- lnAfi  "TT ~ "Ti  from the at  T  -  quench  800°K  experiments =  AT  10°C  it  and  is  found  that  AJ> = 3 2 0 X 1 0 "  dU^= 40x10" while  at  T -  1000°K  - io°C  AT  and  In likely  that  the the  light actual  equilibrium value decreased  the  » 0.2  at  vacancy high  of  the  ohm-cm.,  10  ohm-cm.  1 0  ev.  quench  quenched  the  ohm-cm.  10  600xl0"  'A  AE  ohm-cm.,  2600xl0~  A£= d^P«  By s u b s t i t u t i o n ,  1 0  quench  from  quenches  from lower temperatures  measurements  i n vacancy  temperatures  to  a  The  a  was  i n i t i a l  lower value.  involved the and thus  ( Appendix 1  concentration  temperature.  concentration  quenches  rate  loss  smaller  It of  air is  more  )  smaller  it  appears  than  the  cooling  could  probable  that  vacancies  have  than  f o r m a t i o n e n e r g y was  found.  - 38 ~ 3o  Annealing Experiments It was f i r s t thought possible to determine the formation energy of a  vacancy from the i n i t i a l annealing rates of specimens quenched from two high temperatures but annealed at the same temperature, and the activation energy of migration from the half-time of the annealing curves or from the annealing rates obtained at two successive annealing temperatures f o r specimen quenched from the same high temperature.  However the methods involving i n i t i a l rates  were unsuccessful.  a„  General features of annealing curves;  After the quenched i n r e s i s t i v i t y measurements had been made, some quenched specimens were annealed i n a constant temperature water bath at selected temperatures between 20°C and 50°C accurately controlled t o 0 l°C. o  The r e s i s t i v i t y dropped very r a p i d l y during the f i r s t half minute and subsequently the rate decreased. Figure 5.  Some of these annealing curves are shown i n  Although the numerical values of the annealing rate depended on  quench temperature as w e l l as on annealing temperature, the general shapes of these curves are c h a r a c t e r i s t i c a l l y a l i k e . The t e c h n i c a l . d i f f i c u l t i e s encountered i n evaluating the i n i t i a l rate of annealing were mainly due to the fact that the defects annealed very f a s t even at room temperature,.  I t was so fast that no curve composed of  c l o s e l y linked points could be obtained and therefore the precise slope of the curve was d i f f i c u l t to e s t a b l i s h .  This d i f f i c u l t y arose from several factors.  F i r s t of a l l , both the specimen assembly and the annealing medium have f i n i t e heat capacities.  When the assembly was brought into the annealing v e s s e l  the  temperature of the l a t t e r , as indicated on a thermometer located close to  the  specimen, showed a d r a s t i c decrease and recovered i t s i n i t i a l value only  a f t e r a few minutes.  Therefore the a c t u a l temperature f o r short time  (a)  quenched  from  691°C,  annealed  at  18 9°C  (b)  quenched  from  693°0,  annealed  at  29o2°C  0  (c) q u e n c h e d f r o m 6/42°C, a n n e a l e d a t 29<.2°C (a)  10  \  3 hours  _Li  I  5o  annealing  annealing  I  Annealing  Figure  hours  » Time  I n i t i a l Rate  pf  I Mins  B  Annealing!  Pure  Silver  20  -  annealing was  not p r e c i s e l y known.  Secondly, the specimen assembly had to be  transferred from the l i q u i d a i r tank to the annealing vessel f o r annealing then brought back to the l i q u i d a i r tank f o r measurement. took a "second or two  -  and  Each transference  and inasmuch as the specimens were at temperatures above  200 K during these i n t e r v a l s i t i s possible that the defects annealed. C  Thirdly,  the quench temperature and a l s o the corresponding quenched i n r e s i s t i v i t y were not exactly reproducible f o r each p a r t i c u l a r point (although i t i s quite reproducible for the entire curve) since the quenching conditions could not be accurately controlled.  There were also d i f f i c u l t i e s associated with the complex nature of the quenched i n defects themselves.  The fact that the annealing curves f o r  high temperature quenches were not exponential, (e.g. Figure 6) migh+ i n d i e that the defects were not single vacancies alone but rather a combination of single vacancies, divacancies, vacancy-clusters and/or d i s l o c a t i o n s . b„  Annealing behaviour of the specimens quenched from high temperature;  According t o Bauerle and Koehler's r e s u l t s concerning the annealing behaviour of gold wires quenched from 800°C and 900°C, the decay of the defect r e s i s t i v i t y was slow at f i r s t , then increased continuously (for 900°C quench) or broke suddenly to a much f a s t e r rate (for 800°C quench) and then decreased  slowly again to some asymptotic  quench temperatures.  The i n i t i a l annealing rate was  observed f o r quenches "from 700°G. from 700°C was  value which was  larger f o r higher  consistent with the rate  The decay curve of the specimen quenched  exponential and the measured a c t i v a t i o n energy of migration  (0.82 ev) was a t t r i b u t e d to single vacancies.  The a c t i v a t i o n energy of  migration of the defects,at the l a t t e r part of the annealing curve f o r specimens quenched from 800°C and above was  smaller (0.65 ev) and  was  ~21  quenched  from  691°C,  annealed  at  18.9°C  14  (b)) q u e n c h e d  from  693°C,  annealed  at  29o2°C  13  (c))  from  642°C,  annealed  at  29<,2°C  15  (a)  ©  quenched  -  12 11 10  8  4 -  0  10  Figure  ,  6„  1  20  30  Annealing  Time  I n i t i a l late  of  40 Secs  50  0  A n n e a l i n g ! Pure  Silver  60  attributed  to  a  combination  prolonged  annealing,  depending  on the  for  specimens  the  (1),  less  than  stage  (3),  upwards of  Stage corresponded pure the  gold.  begins pure is  the  involved.  It  move  gold.  placed  a  the  i n the  i n i t i a l  vacancies is  resistivity  be  mentioned activation  been  before  does  electrons  is  energy  not  of  of  of  the  is  very  curves  respect  minute to  curve  this  for  remained helpful pure  to  time;  one  hour,  might  the  less  move  after  to  and or  been  made.  may n o t  have  been  vacancy-clusters  effectively  since than  the  rates  which as  in  only  to  i n the  physical  i n pure  silver  corresponding point  have  moreover,  silver  related  a vacancy  vacancy-clusters  curve  is  a difference  second  very well  or  and  a  pur.e  annealing  difference  a b o u t 40 °C b e l o w t h e of  for  i n i t i a l  indicate  i n a fraction  bath,  the  combine  with  might  disappear  Thus,  changes Once  defects  divacancies  single  specimen  detected.  the  for  the  concentra-  and  vacancies  in  vacancy-  the  quenched  sharply.  annealing  i n view of the  f r o m one  shown p r e v i o u s l y t h a t  divacancies  the  analysis  stages w i t h  After  resistivity  annealing  slower  any measurements  rate  into  change  before,  with  form divacancies  decreases  impractical  portion  examination  d r a s t i c a l l y and,  scatter  To to  has  annealing  reduced  clusters in  sink  no  graph and  vacancies,  to  combine  was  associated  annealing  vacancies  (2),  defect  This  The  three  stage  200°K, w h i c h  Single  suitable  tion  at  into  the  used.  experiments.  on c l o s e r  of  to  nearby at  However,  appearance  process  part  of  and d i v a c a n c i e s „  hour.  There  the  specimen  divided  one  vacancies  percent  10  a minute,  (l)s  to  the  present  may be  stage  single  much as  p u r i t y of  understanding  silver  as  of  precise  the  temperature rapidly  shape  migration of  of  the  at  changing  the  this  slopes  c u r v e was  defects  at  early  this  not  s t a g e was  involved,  and  established.  stage  could  found as No  be  calculated,  (  Stage calchlated be  the  from the data  activation  single  vacancies  i t s  remaining  during  should  make  migration and,  complex  Often,  value.  If  necessary  differences  i t  possible  In  This  the  have  is  as  considered  a combination  be  specimen even  might  from a quench  as  to  of  t h e quenched  indicate  that that  specimen  1000°K  impurities.  energy  of  the  as  for  c o u l d be r e p r o d u c e d at  o x i d a t i o n was n o t a s e r i o u s  was about  Oxygen  expected  heated  quenched  300x10  ^  i n  the  impurities  as w e l l  to  had been  i n v e s t i g a t i o n the measured from  adopted,  a  the  value,  i n r e s i s t i v i t y obtained  low temperature  after  at  percent  30  is  The p r e s e n c e  E f was c l o s e  rates  measured  h i g h as  due t o  formation  uncorrected  be  interpretation  considered  for the  from a  annealing  too small to  p e r i o d was c o n s i d e r e d .  was found t h a t  present  were  the  i n r e s i s t i v i t y was as  to  corrections  scattering  temperature.  This  defects,  between  Kauffman and Koehler's  However, the  a> v i r g i n  resulting  the  room tempe-rature  the heating  energy.  ev.  0.67  defects  divacancies.  (3)?  furthermore,  quenching the  of migration of  r e s i s t i v i t y would  pick-up  of migration f o r the  7 is  The r e m a i n i n g quenched  i n i t i a l  energy  shown i n F i g u r e  temperatures.near  accurately. of  energy and  Stage various  The a c t i v a t i o n  (2):  by  within high  factor.  resistivity  ohm-cm.  A  severely  12 c o l d worked specimen may have locations unit  2 p e r cm .  density of  a dislocation density of the  and, according to  Hunter and Nabarro's  edge d i s l o c a t i o n w o u l d  give  rise  to  order  of  calculation,  an e l e c t r i c a l  d i s -  10 8  a  resistivity  -20 of  1.37x10  slip for  plane a  ohm-cm and  severely  0.44x10  for a  current  running i n a d i r e c t i o n normal to  ohm-cm i f  i t  c o l d worked specimen the -  is  parallel to  due t o  dislocations  137/300 = 46% o f not  expected  to  the  anneal  is  i n i t i a l  about  1.37x10  quenched  r e a d i l y at  the  contribution to  -20 t i v i t y  the  =20 slip  the  12 xlO  eletrical  Thus resis-  -10 =137x10  i n resistivity.  room temperatures  plane.  this  Since  ohm-cm, t h a t dislocations  amount  of the  is are  e l e t r i -  0  2  4  6  8  10  12  1 4 1 6  l i  A n n e a l i n g Time  Figure: 7c  20  22  24  Mins.  Annealing Experiments  of  Pure  Silver,  26  28  30  -25 cal of  r e s i s t i v i t y would the  tion  annealing  of  the  c u r v e may a l s o  would  vacancies  approximately clusters  remained  vacancy-clusters  Dissociation single  have  be  formed at  increased  constant  the  concentration  change  have  a  the  A l t e r n a t i v e l y , stage  s m a l l and the  beginning of  number o f  of  defects.  of  the  annealing centers  sinks  process  but  0  the  leading to  an  the  number  of  the  net  effect  on the  a n n e a l i n g would have  (3)  dissocia-  Since  processes,  rate  involving  scattering  a n n i h i l a t i o n at  r a p i d l y i n these  been  long time.  explained by a process  formed would undergo  d i d not  t i v i t y would  have  for  vacancy  been  resis=  very  slow,  c„  Annealing behaviour  Occasionally would  give  could  be  the  due t o  point  with the  evaluated d In A P — dl  decay  deviates  the  formation of  , A exp(=  m  1  than that  obtained with  the tion  sum o f i n  activation the  silver  the  was  value  in-this  specimens energy  of  The  ease  which is  vation  energy  of  vation  energy  for  self  ev,  8  580°C.  and  in  is  quenched  resistivity  an example;  This  deviation  of  migration  SJOAP so  by successive ev.  This  was  that  anneals  value  attributed  and I t s  again  by various  was  r  is  a  at  in fair  K> l i s t  of  energy  agreement the  investigators  self is  with  s  vacancy of  s  migra=  the  diffusion given  larger  Therefore  to -single  activation  two  l i t t l e  from high temperatures.  a vacancy  only  i n resistivity  energy  and  kT  diffusion i n silver.  silver reported  600°G  rapid decrease  —5S_)'  0.79  from  quenched  Figure  m i g r a t i o n may be  is  1.61  the  activation  quenched  of  than  expression.  obtained  formation-energy thus  of  i n i t i a l  quenched  less  annealing.  exp(-  dt  The  up to  exponential  -5°—  Em •, " ) J kl  temperatures  higher  from the  -  J  specimens  and most  divacancies.  by assuming  the  heated  curves  assumption that  different  this  specimens  removed by room temperature  first  accords  exponential  of  a c t i acti-  below,,  ~  Activation  Energ  y  of  Self  ASuthors  i n  2,00 and  Slifkin,  Turnbull  Lazarus,  Johnson, Slifkin,  Lazarus  Naehtrieb,  Petit  2.00  Tomizuka  Hoffman and  and  Turnbull  Tomizuka  and Wehrenberg  1„98 1.90 1.90  Johnson  and  Martin  1.77  Krueger  and  Hersher  1.95  Kryukov  and  Zhukovitski  2.06  Finkelstein  and  Yamashchikova  1.96  Zhukovitski  and  Geodakyan  1.96  Kucsynski Tomizuka  1.83 and  Sonder  -  Ag  Activation  Johnson Hoffman  Diffusion  26  1.92  Energy  ev  c  -  0  10  20  30  A n n e a l i n g Tim®Figure  8  0  40  60  50  Sees,,  Annealing Experiments  of  Pure  Silver  27  «*  - 28 PART  I,  2 Atomic  Percent  0.2400 percent gas  at  purity  some  time  less  subject  gas it  worked  of  of  high  purity  melted  i n the  i n a  tube.  over  the  was  of  and f u r n a c e  frame  with  Quench  2.  As  cooled.  0.002  inch  Specimen  inch  at  764°C  a n d dummy l e n g t h s  six  potential  were  nitrogen  became  were  wire and  for  relatively with  melt  for  nitrogen  stirred  crucible  ingots  99.9995 with  being  When t h e  diameter  as  filled  alloy,  The  of  clear  slightly days.  cold-  These  subsequently cut  and  mounted  leads.  experiments  general  h o r i z o n t a l l y mounted specimen,  the  pre-cooled brine  following  /  tube  open  melt.  grams  constantly  the  i n an  action.  silver wire  f o r .pure s i l v e r t h e  The  was  atmosphere  0.0145  The  quenched.  the  by suction  d r a w n down t o  quartz  melt  remelted  and homogenized i n a n i t r o g e n  annealed  sealed The  19.7616  and  Subsequently  surface  i n a quartz tube  were then  copper  atmosphere.  1/3  oxygen a t t a c k ,  gently  cast  samples  on the  to  S I L V E R ALLOYS  specimens.  s i l v e r were  and c o o l e d  blowing was  grams  a pressure  -  Cu i n A g .  Preparation of  1,  II  solution  resistivities  results  were  were  b e i n g p o s i t i o n e d about  (about were  experiments  -5°C),  measured  was in  a  made one  i n open cm o r  air.  less  heated  electrically  liquid  nitrogen tank,  above  and and  the  obtaineds  TABLE 4 Heating  current  amp.  0  8.47  9.75  10.45  10.72  11.60  • • 9 Quenohed i n resistivity^.x:10~ For these calibration  curve  of  results, the  ohm-cm. • approximate  2 A t . percent  0, -22.42 ^27.74 *37.51 <*47.72 -53.71 temperatures  Au i n Ag a l l o y  were  estimated  (Figure  9)  and  from were  the  Figo9 R e s i s t i v i t y versus 2 A t . Fercent  Temperature.  A u in A g A l l o y  believed  to  be  i n the  range  400°C t o  800°C  i n ascending  order with  the  30  -  heating  currents,,  Negative quenched  3.  as  due  were in  to  The  observed  the  result  oxidized  decreased  resistivity  negative  of  thereby  in  quenched  diffusion  reducing the  resistivity.  In  alloys  quench  and t r a n s f e r  the  faster  than  pure  design  a method whereby the  a l l  made w i t h o u t b r i n g i n g t h e  it  be  would  inch At,  have  leads  2  2  taining grams  of  A t . percent high  purity  melted together genized ,013  the  samples hours  at  actual  750°C  and f i n a l l y  surface  copper  content  of  the  matrix  of  more  to  the  the  it  rapid  air  and of  they  resulting  vacancies  desirable  in  to  for  measurements  However, i t  was  difficult  into  provide for  been  where  vessel  quenching,  envelope.  diffusion  would have  liquid  specimen  even  to  and t r a n s f e r r i n g processes contact  with  air-tight  Therefore,  the  sealing  the  a i r . of  Moreover,  0,002  the  experiments  could  with  2  abandoned,  specimens.  avoid the  adverse  effects  A u i n A g were" made t o gold  and  air.  19,2767 The  experiments one  grams  ingots at  The p o s s i b i l i t y o f  for  the  interpreted  Au i n Ag,  i n open  wire.  to  experiments.  i n a n i t r o g e n atmosphere  inch  during  to  first  atoms  heating,  a l l o y s were  Percent  order  silver  copper  silver,  specimen  protective  Preparation of In  pure  impossible to  the  copper  Atomic  1„  the  been  with  percent  II,  compared w i t h  view  silver  for  of  i n r e s i s t i v i t y was  were  o x i d a t i o n , specimens  replace of  were  784°C f o r  the  Cu-Ag  99,9995  percent  silver  were  s l i g h t l y cold-worked and.homonine  days.  eliminated by f i r s t  i n the  con-  0,7233  alloy,  They were  drawn  r e c r y s t a l l i z a t i o n and g r a i n g r o w t h  hour and subsequently  cooling slowly  of  at  furnace.  annealing the  900°C The  for  more  crystals  into  effects  wire  than,two  c o u l d be  seen  - 31 with  t h e unaided e y e , andwere,  grain  structure  remained stable  Negative quenched  2,  The q u e n c h been  been was  annealed,  ampere one  amperes was  were heat  repeated treatment  every  five  i t was shut  established  hour  experiments.  on three  specimens,  described  above.  of a negative curve  again  twoof which had  i t with  specimen  a twelve  reducing the heating  When t h e c u r r e n t  c o n c l u s i v e l y b u t t h e quench  were  The t h i r d  ordered by heating  The e x i s t e n c e  method t h a t h a d  i n resistivities  andsubsequently  t o t e n minutes.  o f f .  of the  This  ,  quenched  grain s t a b i l i z e d andthen f o r one h a l f  0.1 mm d i a m e t e r .  c o n d u c t e d b y t h e same  andnegative  t o t h e same  current  ampere  were  about  t h e course  i n resistivity  Thesevexperiments  subjected  during  experiments  used f o r pure s i l v e r  observed.  o n the average,  was reduced t o  quenched  seemed  current three  i n resistivity  t o depend  i n some w a y  i on t h e p r e v i o u s heat specimens  i s given i n Figure As  was is  treatment  a result  alloy  hadbeen  at fault  shown u p i n t h e pure negligible  3.  with  range with  experiment^  in  and  component  effect  Gold  i nthe have  had been  explanation was sought.  above  r e s i s t i v i t y o f CU3AU  t h e c r i t i c a l temperature  t h e r e s i s t i v i t y measured  quench temperature  i n resistivity.  explanation.  the electrical  He d e t e r m i n e d t h a t  increasing  However, as t h i s  an alternative  from various temperatures  order.  quenched  of the alloy  o f oxidation of s i l v e r would also  experiment.  Damask h a dmeasured quenches  of t h e negative  the effect  silver  f o r t h e f i r s t two  o x i d a t i o n o f a component  than s i l v e r andi f t h e s i l v e r  pure s i l v e r ,  Damask's  experiment  cause  oxidation-resistant  The r e s u l t  10,  of this  r u l e d o u t as t h e s o l e more  o f t h e specimen.  u p t o 485°C.  a t 77°K  after f o r long decreases  A b o v e 496°C t h e q u e n c h e d  r e s i s t i v i t y increased with t h e quenching temperature.  At liquid  helium  Quench Figure  10.  Temperature  °E  Quench Experiments 5 2 A t .  %. A u i n :  Ag  Alloy  - 33temperatures (4°K) a similar behaviour was observed which d i f f e r e d only.in that the slope of the quench curve at 4°K was about 2 percent steeper than that at l i q u i d a i r temperature. of  I t was accordingly surmised that the e f f e c t  short range ordering on the thermal contribution of r e s i s t i v i t y up to  was small.  77°K  The o r i g i n of the r e s i s t i v i t y decrease was assigned t o the  destruction of short range order i n the a l l o y , 4.  Korevaar's experiment^ and explanation. Similar experiments had also been carried out by Korevaar on a  7 At. percent Cu i n Au a l l o y , quenched from temperatures i n the range 6 0 ° to The quenched i n r e s i s t i v i t y measured at  900 C, C  ing  77°K  rose s l i g h t l y f o r quench-  temperatures from 60°C to 200°C but dropped steeply at approximately 200°C,  The curve l e v e l l e d o f f thereafter and increased gradually from 500°C-upward. The same explanation as that above, i . e . , advanced to explain these r e s u l t s .  based on short range ordering was  From the i n i t i a l rates of ordering during  annealing a f t e r quenching from 900°C and from 450°C, the energy of formation of  a vacancy was estimated t o be 0,93 ev. The activation energy of migration  of a vacancy i n t h i s a l l o y was determined to be 0.60 ev. The sum of these ;  values i s i n reasonable agreement with estimates of the activation energy for  self diffusion. 5.  X-ray evidence of short range order i n g o l d - s i l v e r a l l o y . The l i t e r a t u r e was surveyed for* X-ray evidence of short range order  in gold-silver alloys.  Norman and Warren  using- X-ray techniques had found  considerable short range order at 300°C i n the a l l o y containing 25 At. percent Au. first  The r e s u l t s indicated about 9 . 4 5 s i l v e r atoms were associated with the coordination s h e l l of a gold atom as compared with the random value of 9 .  The c r i t i c a l ordering temperature computed from these results by Cowley's theory i s 160°K which i s so low that long range order could not possibly be  established  at  a  Aarts  6.  reasonable  34  -  rate.  and J a r v i s '  experiments. 43  Aarts specimens an  and J a r v i s  decreased  increase  to the  at  suddenly with  in resistivity  room t e m p e r a t u r e . strain  the  These  better  air  at  when t h e  were  liquid  deformed  of.Au-Ag air  alloy  wire  temperatures  and  alloy  was  annealed  explained by assuming that  increased  However,  using Korevaar's  Evaluation of  Single  resistivity  the  degree  of  order  produced d i s o r d e r i n g which remained  temperature.  interpreted  7.  results  the  stretching  occurred  low temperature  room temperature liquid  found that  it  is  considered  on  at  elastic  and that  heating  cooling again  that  these  to  results  are  explanation,  Ef.  vacancies  might  undergo  any  or  a l l  of  the  following  three  form a divacancy.  The  processes? (1)  (2)  A single  vacancy  rate  of  this  tion  of  single  process  this  A single  vacancy  this  is  would  process  process  decrease  combine  vacancies.  centres,  of  might  also  By reducing the  diffuse to  another  the  to  the  n  where  2  number  and  n  is  the  concentra-  power of  scattering  resistivity.  and be  decrease  proportional to  to  proportional to  decreases  might is  be  with  the  removed  at  resistivity  concentration  of  sinks.  The  and the  rate  single  effect of  vacancies,  i . e . ,  n. (3)  A single  vacancy  ordering, decrease tion  of  effect due t o  the  might of this  single  interact  with  a  gold  which is  to  increase  process  is  proportional to  vacancies  and t h a t  of  the  atom t o  produce  resistivity. the  g o l d atoms  product i n the  short The of  rate  range of  concentra-  alloy.  The resultant effect on r e s i s t i v i t y of t h e s e processes can be expressed by the following equation  ™  » -CT. n  2  . -  C  2  n  + C  3  n  where the C's are constants f o r a p a r t i c u l a r composition.  Thus, unless the  formation of divacancies was n e g l i g i b l e , the i n i t i a l r e s i s t i v i t y change d u r i n g annealing would not be proportional to the concentration of single vacancies. T h i s was found to apply to pure s i l v e r and possibly also to 2 A t . p e r c e n t Au i n Ag a l l o y s .  Hence, Korevaar's method f o r estimating the formation energy o f  a vacancy i n s i l v e r alloys from the i n i t i a l rates of annealing of specimens quenched from two d i f f e r e n t temperatures for t h i s a l l o y . method.  cannot be considered a suitable one  There are also p r a c t i c a l d i f f i c u l t i e s inherent i n Korevaar's  F i r s t , the i n i t i a l annealing rate depends on the quench temperature  used which, however, as.^mentioned before, could not be controlled precisely,, Second, since E^ i s determined  from the annealing rates f o r any two quenches, -  the s t a t i s t i c a l assembly would be small unless a large number of a n n e a l i n g experiments were carried out.  Third, graphical measurement of the slopes  i s . generally inaccurate e s p e c i a l l y f o r the r a p i d l y changing i n i t i a l p a r t of the annealing curve.  If i t I s assumed, f i r s t , that at the temperature corresponding t o the minimum of the quench curve, short range ordering was  small and,, s e c o n d l y ,  that the tendency f o r a decrease i n the e l e c t r i c a l r e s i s t i v i t y due to the destruction of short range order i s compensated f o r by an increased t e n d e n c y for  r e s i s t i v i t y change due to the quenched i n vacancies, then the increase i n  r e s i s t i v i t y i n the l a t t e r part of the quench curve at high temperatures be due s o l e l y to the l a t t e r cause. manipulated  i n the following manners  The o r i g i n a l vacancy equation may -Ef d i f f e r e n t i a t i n g n sx> *L\f ~ A e ™  would be and  - 36 assuming  that  Ef  is  p r a c t i c a l l y cpnstant  interests  ••' •  i n the  temperature  range  of  '  "dT-  KT2"  e  K  T  Ef i . e . ,  where  BT  A and B are  «  2  dT  constants  e  ~ K T  and  can be  found from the  quench  curve  for  dT each 1,  temperature.  Figure  From the  slope  of  a  11,  the  formation energy of  obtained  for  the  secondary plot a vacancy,  Ef,  of  In  T  2  d  versus  dT determined.  is  The  Ef  T thus small jon  to  a 25  be  to  the  present  a f u l l y  ©ccurred likely to due  at  that  quenched to  and the  annealing  A possible  alloy  (2  Ati percent in t h e  the  increase  measured  i n vacancies  the  was  short  present  range  d i l u t e Au-Ag  one  similar to  this  range  than the  true  too  experiments  order  correspond-  beyond 850°K.  the  was  value  later  quench  f r o m 560°K t o  value  For  curve  850°K  i t  attributed  vacancies  annealing experiments  by an  were  them i s  shown i n F i g u r e  12,  of  silver}  of  pure  no  d i s s i m i l a r i t y between  those  e x p l a i n e d by two of  of  those  The  alloy with  low concentration  number o f  minimum o f  eu, a  is  solely amount  order.  several  for  for  At the  less  range  persist  in r e s i s t i v i t y w h i c h  actually  r e s i s t i v i t y was o b s e r v e d .  (1)  found i n  short  found to  temperature  study,  results  curves were  be  was  the  only 0J»7  experiments  typical  might  e x p l a n a t i o n was  Au i n Ag) the  560 " K j t h u s ,  cal  Korevaar  A u in A g a l l o y i s  ordered Ag^Au s t r u c t u r e  Annealing  In  At,; p e r c e n t  Au i n Ag a l l o y f o r which  destruction of  8,  out  reasonable,  A t . percent  ing  2  for  the  rise the  carried The the  annealing  Cu-Au a l l o y studied  electricurves  by  factors:  gold  combined w i t h  involved, each  it  is  other i n t o  possible  that  divacancies  a or  large  Annealing Figur®  12o  Annealing  Time  Experiments;  Hrs  0  2 A t . Percent  An i n Ag  Alloy  - 39 vacancy atoms The  (2)  clusters,  so  that  Au a l l o y . the  alloy  apparent  in  the  i n the  due t o  r e s i s t i v i t y due  12  that  III.  order  to  At.  an  alloys  that  alloys was  at  an  earlier  silver,  it  time.  range • o r d e r i n g , vacancies. were  gold  the  7 At„  Au i n  percent  only  small  pronounced  Cu i n amounts  i n the  Cu-Au  impractical to  At the  later  partly  cancelled  net  rate  times  of  obtained.  change the  the  the  increase  decrease  annealing  estimated  was  from  in  in so Figure  more  thoroughly i t  of-"high gold  atabout  was  decided  to 1  concentration.  Au i n A g .  of  specimens.  N o r m a n a n d •••Warren t h e r e  b y melting  were  are  corresponding  7.5433  grams  of  to  gold  two ordered  states  AuAg and A u A g , 3  i n  the"melt  seven d a y s ; A f t e r  i n c h i n  into  a quartz  i n a h e l i u m atmosphere  homogenization  diameter."  'This w i r e  by  to  heating  a  A  19.9241 g r a m s - o f  slightly--cold-workedand"homogenized in a  '900*0 f o r  drawn downtowire-0.013 order  in  2 A t . percent  contained  was  -The  not  effect  alloys  the-compositions  The-ingots  atmosphere-  i n the  more  alundum c r u c i b l e - i n " open - a i r " a n d " c a s t i n g  before.  and  pure  on Au-Ag  Percent  a l l o y was p r e p a r e d in  of  study- t h i s  According to silver  encountered  alloy.  measurements'  Preparation  1,  than  both  they  observed,  resistivity  ordering effect  removal of  e^erimehts  25  before  ev.  In perform  short  accurate  0.66  was  to  at  sinks  o r d e r i n g was  although  Au-Ag  case  annealing- temperature resistivity,  some  on e l e c t r i c a l  Therefore,  than  to  p r o b a b l y much s m a l l e r  a d d i t i o n , the  As  small  diffused  ordering effect  Ag a l l o y was  of  no  or  one  for  AuAg  of  3  silver tube  as  helium ingot  grain' stabilized  temperature  gold  900°C  and  was  - 40 gradually cooled down at a rate of about 30°C per hour to 700°C and 10°C hour to 200°C and about 5°C per hour to room temperature.  per  The cooling was  arrested and the temperature held overnight at each of 700°C, 300°C, 200°C, 120°C and 50°C, a f t e r which the wire was taken out of the furnace, 2. \_>.-  Quench experiments The quenches were conducted i n the usual manner, i . e . , i n the pre-  cooled brine s o l u t i o n . i n Figure 13.  The results of a set of quench experiments are shown  Different specimens of the same a l l o y gave similar quench  curves; these did not always coincide very w e l l at low quench temperatures but f i t t e d ' q u i t e c l o s e l y at high quench temperatures where the vacancy effect  was  more prominent than the ordering effect. as before, the quantities of T d A f were calculated from the dT quench curve and plotted on a semilogarithmic scale against 1 (Figure 14), a T If  2  s  straight l i n e was obtained.  The slope was comparatively less than that of the  graph of InAp versus i of pure s i l v e r and thus a smaller formation energy of a vacancy, namely, 0..75  ev. resulted.  The method used to derive Ef from the i n i t i a l rates of increasing resistivity  was  not successful.  Reasons given f o r the case of 2 At. percent  Au i n Ag a l l o y can also be applied here.  One example i s shown i n Figure  15.  The Ef obtained t h i s way was smaller than the one given above. 3.  Annealing experiments The specimen was heated up once more to some point above the tempera-  ture at which the quenched i n r e s i s t i v i t y versus quench temperature curve showed a-minimum.  After the quenched i n r e s i s t i v i t y was measured, the specimen  was annealed isothermally at 19«4°C (±0.1°C) for f i v e or ten . seconds several times and the residual quenched i n r e s i s t i v i t i e s at l i q u i d nitrogen temperature  F i g u r e ; 13e  Quench Experiments  of  25  A t . Percent  Au i n Ag  Alloy  42  - 43 -  200  1 6 0  (a)  quenched  from  1208°Kj,  annealed  at  19o4°C  (b)  quenched  from  1 0 3 0  K j  annealed  at  19.4°C  (c)  quenched  f r o m 1010°K,  annealed  at  3 8 . 1 * 0  (d)  quenched  from  annealed  at  3 8 . 1 ° C  9 9 0  3  3  K  P  120  8 0  3 o  40  a  o I  o -p  > •H •P 0) •rl CO  0  PS  - 4 0 -  - 8 0 -  - X  •120  J  i  L 40  8 0  Annealing  Figure  15.  Annealing  1 2 0  Time  Experiments  of  1 6 0  2 0 0  Sec,  25  At.  Specimens, Quenched f r o m two  Percent  High  Au i n Ag  Temperatures  Alloy-  - 44 were  measured  again  at  19.4°C.  o n l y when t h e possible The  each  to  predict  The  this  to  specimen  extra  annealing would This  process  had a t t a i n e d  future  of  course.  vacancy  over  continued  e v e n t u a l l y have  p r e d i c t i o n was  verified  of  at  the  temperature  a  bath  stable  These  form such  results  are  a l l o y was  i n i t i a l  the  residual vacancies.  reduced  but the  it  value  is  experiments  that  about  before  believed  quenched  was  then  changed it  seemed  s h o w n }.n F i g u r e  its  further  i n the  33.6 (± 0.1°C) a n d  repeated  migration in this  contribution  not  was  experiments  resistivity  the  were  curve  its  energy  be  This  During these  annealing  activation  considered  time.  ev.  0.70  quench  16.  was  Measurements that  on  additional  i n r e s i s t i v i t y to  on Pd i n Ag a l l o y s  zero.  described  below. The . r e s i s t i v i t y v e r s u s the  same w a y a s  Figure  17.  IV.  At.  25  1.  Percent  Preparation - The  13.9219 air  for  grams  pure  silver  to  of  at  a l l o y was  made b y m e l t i n g  of99.9995  950°C  percent  for  hours  a n d - f i n a l l y subjected  hours  and s u b s e q u e n t l y  The  six days.  inches- in"diameter.  tubes. f i n a l  curve  grams  is  shown  out . i n  in  ingots  of  specimens  were  ......  rate  were  in  open and  s l i g h t l y c o l d worked  and  wires  stabilized  an o r d e r i n g treatment a  p a l l a d i u m and  remelted  drawninto  were' g r a i n  c o o l i n g s l o w l y at  sponge  i n an alundum c r u c i b l e  These  They were  - These w i r e s to  4.5896  purity silver  i n quartz  0,013  12  calibration  carried  spe c i m e n s .  improve -homogeneity;  homogenized  and the  c a l i b r a t i o n was  Pd i n A g .  and c a s t i n g - t h e - m e l t "  cast  temperature  of  at  ofapproximately  '640° C  by holding at 15°C  per  hour  for  950°C to  12 for  -45 -  240  200  O—^  >  ^  19.4°C  @  160  1  ®  /  120  •rl -P  33.6°C  80  Specimen  quenched  1208°K.  EJJJ =  from  0.70  ev.  /  ra  ©  •H  (0  ©  40 © 19.2°C  0  -40  J  0  L  40  J  L  Annealing  Figure  16.  120  80  Annealing Experiments;  Time  25  160  200  Sees?.  A t . Percent  Au i n Ag  Alloy  520°C.  They were  5°C  hour to  per  2.  room  negative  quenched about  leads  (on  above above  as  temperature  c o u l d be  The  that  could this  Pd-Ag hot  the  whole composition range  to  solutions  the  i n resistivity  0.004"  ^1200°K,  experiment  system  range  order.  With  1350 K.  annealed,-  compositions  state an  30  repeated  potential  quench  to  a l l o y of  is  strongly the of  existence  the  short  But  such as  of  exhibits  a  continuous  superlattice was  no  had been  potential  the  quench  a l l o y of  temperatures increase  percent  of  similar  the  Pd.  this  i n i t i a l  alloy about'  short i n  solution Since  formation of  ideal  some known  When a q u e n c h e d  increase  over  local  r e s i s t i v i t y wan obs-erved The  order  studied  any  18.  the  c o m p o s i t i o n ^ was  below 600°G. i n  of  the  observed.^  led to  same  range  solid  l o n g range- o r d e r ,  c a s e may have  Pd-Cu  extensively of  the  information  contradicted  range  As  silver  the  order of  the  a  shown i n F i g u r e  short  range  none  Pd-Cu  of  was  rise.  u s i n g as  leads,  curve  a l l o y system had been  i n i t i a l  6 to  At  quench"~curve-for this- a l l o y ' a n d ' t h a t  and no  at  was  these The  o  The  began  d i m e n s i o n made f r o m a n  r a r e l y occur and there  an ordered  specimen-was of  The  Au i n Ag a l l o y .  during  from homogeneity i n t h i s  short  exhibit  alloys  to  A  which  broke  So  This  minimum of  became v e r y weak and o f t e n  s i m i l a r a l l o y systems  assumption.^  the  inch  D i r e c t measurements  the  of  of. 1 0 °  0.002  of the  early 1930's.  sort  a rate  described previously.  At.•percent  beyond  specimen.  the  deviation  25  be- f o u n d i n - a v a i l a b l e / l i t e r a t u r e .  order  solid  at  the  Au i n Ag suggested  of  as  again observed,  quenched  increased  x  conducted  the  the  raised to  alloy.  alloy or  range  of  resemblance'  25- A t . p e r c e n t the  was  0.002''  composition  ' '  of  950°K  specimens).  t h i n wire' of  .  that  p o t e n t i a l leads  three  were  i n r e s i s t i v i t y was  100°C  s e r v i n g as  quench  In  experiments  quench temperature  wire  further  temperature.  quench  quench temperature the  overnight and cooled  Quench -experiments. The  located  held there  in  for  a l l  resist!-  - 48 -  Quench Temperature  Figure  18.  Quench Experiments of  25  °K  A t . Percent  Pd  i n Ag  Alloy  - 49 vity  during  phase. are  a n n e a l i n g was  The  authors  proposed  i n i t i a l  smaller  in  conduction  electrons.  scattering  centers  increases, such  the  that  path. the  the  Then  Thus  to  at  annealing  decrease.  linear the  also  order, '  The  8  range  order  linear  dimensions  a. c r i t e r i o n endorsed.  for In  the  to  400  observed  is  in this  region,  used  Damask  increases  bad  range  due  the  that to  only to the  behave  as  additional  is  of  grown t o  above  mean  the  free  is  the  super-  range short  idea that  not  r e s i s t i v i t y of  would  that  path  of  ordering  short  The  free  resistivi-  show  fact  size  that  reasoning in  the  a  mean  lower than  i n view of  assert  decrease  nuclei  cause the  resistivity.  or  found that  the  increase  appropriate  increase  of  w i l l  the  an  nuclei  appropriate  argued  ordered  path  n u c l e i have  material  may be  here  the  number  than the  the  Pd-Gu a l l o y d i d not  It  i n r e s i s t i v i t y were  free  As t h e  domains  450°C.  comparison with  short  the  A t . percent  6.4  resistivity to  fact,  increasing  growth of  mean  the  ordered  Pd-Gu a l l o y  in  until  of  process,  nuclei to  resistivity.  the  quotation  i n the  the  resistivltyfbf  rise  above  expect  the  larger  However, the  the  than  increase  further  process  i n any n u c l e a t i o n  would the  nucleation  are  not, b e i n g  apply i f  "  the  dimensions  temperature  lattice lines  one  and increase  mean  to  dimensions  resistivity w i l l  since  ty  that,  linear  disordered material,  with  attributed  the  serve  as  necessarily a  brass  decreased  order.  47 Recent tiated  the  experiments  result  of  the  conducted  present  by Aarts  investigation.  Pd  i n Ag a l l o y a decrease  i n  resistivity with  an  increase  of  conduction  Brillouin ...However,  i n the  zone i n the  as  number a  result  present  deformation  could not  inclined to  accept  On  close  the  of  plastic  quench have  been  extention  10%  lue  deformation the  appreciable  the  They observed  electrons  experiments  s h o r t .range  examination,  and Houston-Mcmillan  order quench  is  to  i n a 25  was  consequently  At.percent  and suggested  that  d i s t o r t i o n of  responsible  specimen  and  the  substan-  so  for  thin  the  the  ;  the  change.  that  plastic  author  is  explanation. curve  of  the  25  At.  percent  Pd i n Ag  alloy  seems t o  quenched 1100°K  be  to  the  up i t  specimens,  before  the  secondary  The plot  temperature section.  of  formation of  T  2 d  section  -^~  of  is  s t i l l  step  is  considered  resistivity  is"  from the  thmic  is  plot  3.  then  about  in  and  Figure  smaller  higher  20.  The  for  accidental  of  this  0.88  It  due  it  various  maximum, t h e  false  and  a  breakage from the  1.6 for  step  is  observed  ev  for  the  low  i n the  of  curve  potential  slope  of  the  high  a  temperature quench  i n o r e d and the  formation energy  in  of  resistivity versus-^-  curve.  vacancy a  in  vacancy semilogari-  ev.  heated was  up t o  937°C  subsequently  107°C  to  the  (t  1 or  decrease  levelled off  i n r e s i s t i v i t y due t o  to  or  as  ev  s h o u l d be  slower  r  about  0.77  were  the From  p l o t t i n g a quench  such  is  is  vacancy  and quenched  annealed  2°C)  five  by the  electrical  the  higher  at  the  such as  effect  of  times.  the  are  shown  successively concentration.  vacancies which the  range  ordering loss  and surfaces. -  slowly.  in  six  r e s i s t i v i t y rose  i n r e s i s t i v i t y due t o  r e s i s t i v i t y decreased  2°C)  results  with  a maximum a t  grain boundaries  quenched  1 or  vacancy  electrical  short  its  (-  The  but  available  the  and  95°C  m o b i l i t y of  and reached  decrease  sinks,  i n the  raised  a while by virtue of  then  and  for  calculated  19)  reached.  features  r e s i s t i v i t y continuously increased  presumably balanced  this  curve  annealing"temperature-was  temperature;  vacancies  (Figure  cause  is  r e s i s t i v i t y becomes  These  from theminimum, the  continuously at  rate  increase  a vacancy  specimen was  increments  When t h e  energy  quench  of  enough p o i n t s some  1100°K  minimum,  experiments  r e s i s t i v i t y measured. times  again.  by  of  about  increse  known why t h e r e  slope  Annealing The  not  counted  calculated  gave  versus—-  It  the  destroyed  the  After passing the  sharply t i l l  steeply  which  were  sections.  1200°K  increases  two  specimens  etc.  this  three  neighbourhood pf  three  If  of  i n r e s i s t i v i t y increases  and f r o m 1200°K  leads  composed  Further  of  at  at  that  rate  of  was the  Passing annealing  a'  - 52  A n n e a l i n g Time  Figure 20.  Annealing  Experimentsj  Hrs. 25  Au.  Per@@nt  P d i n Ag A l l o y „  - 53at  250°C  its  (±2°C)  i n i t i a l  process Cu-iu that  for  value  several  before  f o l l o w e d even  alloy  in  increase  more  the  and decrease  ev,  open  air  0  The and  the  It  component  of  electrical  energy  of  versus  result, is  resistivity in this  pattern  experiments.  temperature the  closely  the  the  Therefore  silver  The' a c t i v a t i o n 1 02  reduced  quenches.  Korevaar's  oxidation of  hours  seemed  d i d not  migration of  resistivity  shown i n F i g u r e  a  level  of  the  by the  to  annealing percent  the  assumption  significantly to  the  the  specimen.  vacancy  calibration  close'"to  7 At.  justify  contribute  resistivity  a  specimen  developed  also  to  in this was  alloy  carried  is.  out  in  21.  SUMMARY  In  Part  reviewed^and-the  1 the use  i n v e s t i g a t i o n were  of  various  electrical  discussed.  the  experiments  and  results  and  discussed.  The  formation  a vacancy  Part  :  percent  i n pure  in  A g , 25  devoted  At,  percent  q u e n c h i n g ' arid a n n e a l i n g from those tion order  ,  of  also  the  on e l e c t r i c a l  differences--betweenthat of  of  its  a vacancy  present  energy  silver  were  7  was  the  of  ev  (2  pure  A t , percent alloys  described. alloys-was  a p p l i e d and i t  was  and  described  migration  Ag),  very  of  of  short  to  of- p u r e  the  The •  explanarange  explain silver  formation  found that  2-At.  different  suggested  effect  the  were  Cu i n A g ,  considered  evaluate  of  respectively,  were  and his The  means  of  Pd i n  a n d ••annealing' - b e h a v i o u r to  ev  were  experiments,  energy  A t . percent  experiment  method  as-a  silver  and 0.79  silver  problem  quench  activation  0,82  alloys  these  An a l t e r n a t i v e alloys  the  be  Damask's  the-quenching  i n these  work with  A u i n A g a n d 25  r e s i s t i v i t y of  alloys'.  and  found to  experiment  of  work concerning  characteristics  pure m e t a l ,  Korevaar's  the  to  treatments  r e s i s t i v i t y measurements  Previous  of  s i l v e r were  2 was  theoretical  the and  energy  energy  of  --"55 formation  of  a  vacancy  i n pure  silver  alloyso  T h i s was  i n agreement  energy.  From the  s i m i l a r i t y of  25  At.  percent  is  naturally  From an  led  to  assessment  reasonable branched  to  The  found to  activation surmount  plot  curve.  feature. was  Pd i n  assume of the  be  greater  potential  force  here  migration  would  be  Lazarus.^  is  the  of  there energy  the  of  that  barrier  affect"'  a 1  of  of  migration  short  range  alloy  adequate of  Au-Ag  a  the  the  formation  the  Au i n  18)  it  as  a  migrating atoms,  of  the one  this alloy  silver. atom  was  This  to the  energy  This  strain  former.  Pd-Ag  Since  activation energy.  local  double  for  pure  silver  seems  a  i n the  and i n  in  Ag a l l o y ,  i n the  explanation  alloy  nature,  of  results,  vacancy  for  that  behaviour  order  (Figure  by neighbouring  range  than  annealing  experimental  no  than  corresponding  work required  short  greater  contribution  and  the  Pd-Ag  been  exerted  more  the  i n the  from the  of  quenching  of  has  slightly  expected  existence  accuracy  than  arises  the  the  and t h a t  results  activation  repulsive  by  the  However,  energy  the  Ag a l l o y  with  was  of predicted  BIBLIOGRAPHY  1.  Huntington,  B . H . and S e i t z ,  2.  Huntington,  B . H . , Phys.  R e v . , 61,  3.  Huntington,  B . H . ,Phys.  Rev. ^ 1 ,  4.  Brooks,  H . and Mckay,  the 5.  Kuper,  Dexter,  7.  Blin,  8.  Hunter,  9.  Bartlett,  H. Jr.,  R e v . 26,  Phys.  6.  G . ,  American Society  A . , Letaw,  D . L . , Phys.  J . ,  1224  J . H . and Dienes,  10.  Kierstadt,  H . A . ,Phys.  11.  Bauerle,  12.  Dexter,  13.  Jongenburger,  14.  Abeles,  15.  Blatt,  F . J . ,  Phys.  16.  Blatt,  F.J-.,  " S o l i d  17.  Brass,  H . and Seeger,  18.  Dexter,  19.  Koehler,  20i  MacKenzie,  21.  Landauer,  22.  Dexter,  D . L . , Phys.  23.  Seeger,  A . and S t e h l e ,  D . L . , Phys.  4  J.S., R. R<,  . 24.  Blatt,  F.J-.,  25.  Bloom,  T.  :  Phys.  and I m p e r f e c t i o n s " , p.  State  F.R.N.,  S o l i d " ,  G . J . , Phys.  J.S.,  245  and Tomizuka, C . T . ,  A220.  848  Rev. 107,  796  (1953).  1905  (1956).  237  Academic  Chem.  107  Solids,  542  (1953).  (1953).  1493  (1957).  (1953).  Press, 6  f  324  322  4,  (1957).  ,.  (1958),  (1956).  and Spndheimer,  E . H . ,Phys.  Phys.  520 770  (1955)  (1955).  106-(1949).  R e v . 86,  420  (1952).  Physics'*,  82,  p.  Roy. S o c ,  R e v . 25.,  and Barrett,  E.  Rev. 8£,  Phys.  768  237.  Rev. 103.  Ham, F . S .  by  (1955).'  L . , Sender  Proc.  A . J . , Phys.  Rev.  1  published  (1953).  1007  R e v . , 10^,  D . L . , Phys.  (1953)  S c i . R e s e a r c h BJI,  Rend.,  (1942).  (1954).  R e v . 82,  P . , Appl.  Compt.  >  1092  Slifkin,  315  (1942).  f o r Metals,  R e v . , 9j3,  and Koehler,  R e v . £l,  325  i n Crystalline  S.G-. and Nabarro,  F  Phys.  "Impurities  Rev.  "Defects  J.E.  F.  R e v . Jl>  264'(1949).  (1951). (1952).  H . , Z . Physik and Koehler,  146. J.S.,  C . S , , Acta Met. 1,  242 Bull. 305  (1956).. Am, Phys. (1953).  Soc.  1,  114  (1956).  BIBLIOGRAPH  26.  (cont'd.)  Koehler,  J.S.,  "Impurities  American  Society  for  Christian,  28.  Kauffman,  J.W.,  Ph.D.  Kauffman,  J.W.,  and K o e h l e r ,  Seitz,  and K o e h l e r ,  Thesis,  F,  .JJ.,  J,S.,  Phil.  U n i v e r s i t y o f J.S.,  published by  the  162 (1955).  p.  and S p r e a d b o r o u g h ,  149 (1952).  29.  Imperfections"  Metals,  27.  J.W.  and  Phys.  " S o l i d  Mag.  (1955). 555 (1955),  Illinois  Rev.  State  8 , 1, 1069 (1956).  9JL,  Physics",  Ibid.,  88  Press  2,  Academic  379 (1956). 30.  Bradshaw,  31.  Ascoli,  32.  Laaarev,  F.J.  and  Pearson,  A . , Asdente,  M .  S.,  Phil.  Germagnoli,  ?  Mag. E.  1, 812 (1956).  and Manara,  A . , J.  Phys.  Chem.  6, 59 (1958).  Solids  B.G.  and  Ovcharenko,  O.N., Dokl.  Akad.  Nauk U . S . S . R .  100.  875  (1955). 33*  l i d s o n , G . V . and Ross, R . , P r o c . Sci. R e s . P a r i s (1957).  34.  Bradshaw,  35.  Pahseri,  F.J, C ,  and Pearson,  Gatto.  F.  S.,  of  International  Phil.  Mag.  and F e d e r i g h i ,  T.,'  Radio-Isotopes  in  2, 570(1957), Acta Met,  50 (1957).  Ibid,  6, 198, (1958). .36.  D.eSorbo,  37.  Federighi,  38.  Nowick, A . S . ,  39.  Seitz,  W. and  F.  T.,  Turnbull, D., Phil.  J.  Mag.  Appl.  and K o e h l e r ,  4,  Acta. Met.  £,  83 (1959).  502 (1959).  Phys.  22, 1182. (1951).  J.S.,  " S o l i d  Chem.  Solids  State  Physics",  Academic  Press  2, 412 (1956). 40.  Damask,  41.  Kbrevaar,  42.  Norman ,  43.  Aarts,-W.H„  44.  Jaumot,  A . C . , J.  Phys.  B . M . , Acta Met. N ,  F.E.  and Warren, and J a r v i s , Jr.  1, 23 (1956).  6, 572 (1958). B.E.,  J.  Appl.  R.H. Acta'Met.  and Sawatzky  ,  Jaumot,  Jr.,  Phys.  22, 483 (1951).  2, 87 (1954).  A . , Acta Met.  4., 118 (1956),  Ibid,,  127 (1956), Sawatzky,  A , and  F.E.  Phys.  Rev.  9j8, 1555 (1955).  4^  - 58 BIBLIOGRAPHY  45.  Mott,  (cont'd.)  N . F . and J o n e s , Alloys,  46.  Damask,  •47.  Aats  48.  Lazarus,  W.H.  Oxford  A . C . , J.  H . , 1936,  Appl.  "The  Theory  Clarendon  Phys.  £2,  610  of  the.  Sociaty  "Impurities; for  Metals,  of  Metal  and  Press. (1956).  and H o u s t o n - M c M i l l a n A . S . . A c t a Met. D.,  Properties  and  Imperfections"  107  (1955)  £,  525  (1957).  published  by The  American  - 59 APPENDIX  Measurements  of  The 22a  is  a  Quench  quench  Rates,  rate  photograph of  from 400°C  into  was m e a s u r e d w i t h  the  a brine  pattern  obtained  v e r t i c a l scale  length  and t h e  s p e c i m e n was  on t h e  oscilloscope  horizontal scale  kept  in  when a  solution maintained  Figure  The  a Tetronix  to  10  was  at  oscilloscope.  silver  Figure  s p e c i m e n was  a temperature  of  about  quenched -4°C,  22a  adjusted  milliseconds  a horizontal position less  to  50 m i l l i v o l t s  per  than  1  unit cm.  per  length.  above  unit  The  the  quench  solution.  The rate  i n i t i a l  corresponded  solution.  The  The  bottom  line  was  turned  off.  quenched  to  second  portion of the  air  Fig.  from 580°C,  22b other  the is  curve which  quench before  p o r t i o n of  indicates  the  the  zero  curve  the  exhibited  specimen  represents  potential  conditions  the  being the  same.  a  slower  entered  level after  a s i m i l a r photograph f o r  a  true the  silver The  the  cooling quench  water  quench.  heating  current  specimen  vertical  scale  - 60 -  Figure  in the  this  c a s e was  same a s  value  at  decreased  100  Both  millivolts  pictures  light  quenched  the the  of  the  above  i n vacancy  give  unit  the  length  average  supposed quench vacancy  measurements  concentration  temperature.  concentration  quenches  from high temperatures  quenches  from lower temperatures  found.  per  and t i m e  quench  rate  scale  was per  10°C  approximately.  In the actual  at  before.  millisecond  the  set  22b  to  a  was  The  appears  smaller  i n i t i a l  lower value.  involved the and thus  it  a  loss  of  smaller  than  air It  more  quite the  likely  that  equilibrium  cooling could is  probable  vacancies  formation energy  have  that  than was  - .61 II.  Possible  Sources  Reference sources or  of  error  calculate  sented,  is  in  sources and  addition  to  these,  ing  air  not  the  the  been  specimen  considered;  rate  either  the  be  have  i n more  has  them  be  pre-  experimentally  temperature of  in  the  on Pages  quenchquenched  s e n s i t i v i t y were  discussed  detail  possible  used.  complex nature  been  to  eliminate  avoided  quench  the to  14  major 17  below.  also  during  (3)  constancy  of  been  given to  quenching,  liquid  equality  (2)  nitrogen  the  bath  temp-  0  during  the  blast  the  vacancies  true  eliminated by a  thesis  discussion w i l l  potentiometer  quenching  measurements  preceding  with  however,  emf's  of  of  vacancies  quench  quench  have  of  could not  consideration  retention  thermal  of  to  Elimination  e x p e r i m e n t a l methods  which  these  with  a n d dummy l e n g t h s ,  As  could  of  In  (4)  the  made  their  i n the  detailed  experiments,  limitation Some  a more  for  places  were  uncertainty  annealing  basic  Retention  slower  from the  (1)  various  of  error  dealt  (1)  a  of  be  and  at  Here  and w i l l  specimen  erature,  source  uncertainty.  poihtss  P r o v i s i o n s Taken  provisions that  20,  following of  made  elaboration  For  and the  of  Page  an  derives  experiments. defects  been  and  magnitudes.  major  which  Error  and the  along with  that  ing  has  their  The  of  of  have  water  changing liquid  shown  quench.  the  of  technical  calculation  of  Ef,  This  liquid  nitrogen  because  (Appendix I)  into  i n i t i a l  quench a  there air  medium.  this  was  quench Quench-  vacuum v e s s e l  complications  was  not  was pursued  further.  In implicitly escape the  of  the  been  provided.  vacancies  number o f  during  vacancies  so  a  correction  in this  The  o n l y a s s u m p t i o n made  the  quenching  escaped  was  in  regard  connection  and t r a n s f e r r i n g  proportional to  had  the  periods  already  with was  vacancies'  the that present,  62  -  i„e„  A n = n°e  C o n c e n t r a t i o n o f v a c a n c i e s a t t e m p e r a t u r e Ts Vacancies  excaped p e r u n i t volume:  xf"  % n = fn° ~^£ KT e  Vacancy c o n c e n t r a t i o n r e t a i n e d and measured: Thus, i f l n A ^ i s p l o t t e d a g a i n s t  -  ( l - f ) & n - (l-f)n«e  —Ef ^  and t h e s l o p e i s measured, t h e c o n s t a n t  c o e f f i c i e n t (1-f) n •• does n o t appear and hence E f i s n o t a f f e c t e d . (2)  E q u a l i t y o f specimen and dummy l e n g t h s The r  c o n d i t i o n f o r Bauerle a n d Koehler's  balanced  si - di r  +  r  st - s i = r  J± (h" U  whereis  t h e i m p u r i t y r e s i s t i v i t y , J£  h  +  }d\  A )  s  d/  I  s  circuit i s :  1  \ s A  ^ /  "the t h e r m a l r e s i s t i v i t y , 1 i s  the l e n g t h and A i s t h e c r o s s - s e c t i o n a l a r e a o f the specimen. length condition, l  g  - 1^  As  =  0  Thus i f t h e  i s n o t s a t i s f i e d t h e n e r r o r s r e s u l t not o n l y  Ad  f r o m t h e t h e r m a l p a r t o f the r e s i s t i v i t y but a l s o , and more s e r i o u s l y , from the i m p u r i t y p a r t i t s e l f . exactly equal.  P h y s i c a l l y t h e r e i s no way t o make l  F o r any s e t o f e x p e r i m e n t s ,  cut f r o m the same w i r e .  The d i a m e t e r  h a l f centimeter along the l e n g t h .  s  and l  d  .  specimen and dummy w i r e s were  o f the w i r e was measured t w i c e  every  To ensure the u n i f o r m i t y o f h e a t i n g between  t h e p o t e n t i a l l e a d s , 20 cms l e n g t h s were needed b o t h f o r t h e speciment and f o r t h e dummy.  S i l v e r w i r e s o f 0,002 inch i n d i a m e t e r were spot-welded onto each  o f them about 5 cms a p a r t as p o t e n t i a l l e a d s .  These specimens were s t r e t c h e d  on a g l a s s p l a t f o r m of t r a v e l l i n g m i c r o s c o p e and the l e n g t h s between t h e p o t e n t i a l l e a d s were measured.  F i v e figures were t a k e n , t h e l a s t one was  e s t i m a t e d f r o m t h e f r a c t i o n on t h e v e r n i e r scale and was n o t r e a l l y  significant,  The f o u r t h f i g u r e o f t h e l e n g t h o f a specimen, i n g e n e r a l , may d i f f e r w i t h t h a t of the c o r r e s p o n d i n g dummy specimen by a small number; non-matching w i r e s were d i s c a r d e d . was  The two matched wires -ere then mounted on the frame w h i c h  a l s o made o f pure s i l v e r , and t h e assembly was immersed i n a l i q u i d a i r  bath.  - 63 The  same c u r r e n t  and  ment  and r  with  reversed  The If  first the  was  s  were  three  to  some  was a g a i n  leads  The  regarded  values  as  the  g  In  by  any  ^ A  Excluding  the  r  .  time  rate  liquid  / r  d  s  liquid  V  the spot  Lj/1  3  ratio.  often  welding point  that  In  arrange-  repeated  fourth figure  affected.  was  before  case.the  differed.  was  de-  specimen  I  _->  V  s  f-  I  <—•  V  the a  were  The  oxygen i s oxygen  nitrogen  i n '  <-  series  at  -182.9  0.  five  in  the  of  It  specimens  correct  thus  v  of  the  the  of  before  obtained  subsequently  the  resistance  carried  out  a n d the  measurements with  least  quenched  dummy  quenched specimen  resistance.  i n the  following  reversed  current  to  attain  current.  one hour before  i s not k n o w n  'However,  just  condense even  . i f  their  required from three The  actual  of l i q u i d nitrogen i s -195»8  a i r would  minutes,  virgin  V  I  repeated  point  gas  to  temperature  boiling 4  =  was  temperature  I  d  circuit  —!*=—=•  S 0  v/ere  d  balanced  on the  substruction  measurements  contact with a i r f o r  in  the  nitrogen bath  - »  V  & T  used  circuit,  f o r -the  and I  V34,  difference  required for  started.  the  V}2>  s  Measurements  liquid  of  ratio  equilibrium values,  was  what  series  of c o u r s e ,  was,  the  or  varying lengths  series  r u n the  —*  I  minutes.  were  of  one  for  r e a d i n g and  the  I  the  respective  of  was  dummy i n a  the  compared w i t h  but  obliquely  figure  resistance  For  sequence;  that  third  then  identical  attached  and  measurement  ratio was  B  readings  zero  Constancy  nitrogen  specimen  This  always  correction  ^r *s.  of  (3)  ments  the  i n i t i a l  was m u l t i p l i e d  five  T^/T  were v/ere  taking i n i t i a l  heating. was  the  discarded.  Further made b y  The  figures  extent  through  measured.  current.  potential  formed  sent  or  to w h a t  one  liquid measureC  and  extent  dissolve  to  in  were 1 t o \  and the  at  64  -  assume ing  an  to  exaggerated  the  value  50s50 m i x t u r e )  condensation  or  of  a  during  6 degree a  dissolution rate,  12  temperature  increase  hour i n t e r v a l , then  the  temperature  change  (correspond-  assuming a would  constant  be  6 . 12  0.04°  C.  during  in  electrical  is  about  0 . 0 0 6 / u A -cm.  and t h i s  would  limits  During  cut  above  places  close  about the  In  were  bath  Now t h e -100  temperature  resistivity is  about  of  to  0.04°  2.4 x  change  -200°  C.  C„,  the  10~^ohm-cm  potentiometer, which  surface.  circuit,  the  out  Thus  the  i n the  technique  of  air  surface  lead wires  l e n g t h and  is  to  was  kept  the  frame,  soldered onto  and K o e h l e r ' s  i n a  and the  liquid  outside  Bauerle  arranged  geometrically  cancelled  within  balanced  the  about-two which  frame  circuit,  at  the  currents  s y m m e t r i c a l and p a r a l l e l manner  two arms thermal  were  kept  emf's  sample  the  of  the  current  elect-  same d e p t h  developed i n any part  corresponding part  r e v e r s i n g the  at  dummy.  under of  In"the  and the  was  the  series  potentiometer  followed.  Next, experiments.  consider  The  the  problems  adequacy  of  adequacy  involved  figure  8,  (2)  ability  of  isochronal recovery  the  available  apparatus  pertinent  to  a discussion of  It  has  three  in  s i l v e r between  ytiv o n t h e  the  same  specimen  have  pure  measurements.  60  measurements.  of  and  (1)  0.1  measurements  together.  was  electrical  same m a t e r i a l ,  air  for  change  the  rically  battery  a  of  potentials  liquid  for  C.  end j o i n t s  and t h e  the  as  1°  the  X 5 =  X  emf's the  the  from the  required for  for  i n the  register  Thermal  (4)  Thus  change  uncertainy  inches  5 minutes  r e s i s t i v i t y per  corresponding  the  the  -  or  relationship.  and the  been  four  as  the  were:  single  methods  (1)  slope  these  sources  that' the  the  The of of  the  i n the  annealing  of  the  data  method f o r  Em,  (3)  limited  of desir-  s e n s i t i v i t y of  quenched  in defects  the  are  error.  recovery  mariyrpoints to  used  adequacy  change  experiments.  complex nature  suggested  times  of  curve  establish  of  figure  a dependable  8  should  exponential  -  Even  d i s r e g a r d i n g the  described  i n the  of  points  on t h e s e  of  the  were has  a  of  of  leads  of  14.3  was  18  were  an  associated to  20,  This  microvolt would  to  inch  annealing  provide a of  the  greater  limited  as  i n diameter  (the  specimen f o r  an i n c h )  R = JL  about  require  can  short  seen  Thus:  of  attempts  the  be  thousandth of  used.  with  unwarranted because  available.  a measuring current one  Pages  curves  thousanth  diameter  potential  For  thesis  potentiometer  .0127  uncertainty  50  an  ma,  and a  =  to  follows.  5  cms  5 ?  =  i n the  quenched  time number  specimens  figure  length  -  sensitivity  Most  8  between  the  P  6100  develop a p o t e n t i a l  increase  65  difference  in resistivity  of  whence:  difference x  between  to  15  10-10  to  0.33  to  or  four  parts,  of  this  magnitude  present  the  ohm-cm w h i c h  0.5  uv.  If  then  i n terms  this  the  of  difference be  was  i n the  range  of  potential difference  q u a n t i t y was  could not  Other values  table.  mination in  neighbouring points  to  would  be  be  further  only 0.1  measured w i t h  sufficient  x  would  divided to  10  0.16  only  into uv.  accuracy  10""  x u  amount  three A quantity  using  the  apparatus.  (2) in  two  These for  mined  and t h u s  later  stage,  resistivity  values  each  i n i t i a l  the  Em d e t e r m i n e d  were  quench.  stage,  the  of  the  change  The  reason  for  annealing rate i n  reasonable  change  i n slope  determined from separate  slope  annealing rate  within  by  was  time  method was so  quenches;  employing this was  always not  were  too  the  one  technique fast  applicable  sluggish that  intervals  methods  to  be  while  decreases  negligible.  are  listed  deterwas  that  deterin i n  the  - 66 Table  4  Quench Temp.°C. pure  25A % A u i n A g  The  annealing  2At$ A u i n Ag t  use  of  effects  higher  The statistical from the the  not  to  were  (3)  The  the  details  can  be  the  since  calculate  as  recovery  annealings.  isothermal  presented  Some  general  features  temperatures  precluded region  Em v a l u e s  not  be  unique.  were  For  the  deviations  to  be  latter  0.57  0.72  0.54 0.73  40.0  could  of be  the  utilized.  from  (1)  possible  the and  from different  the  (2) quenches  same a n d t h u s  reason  f r o m them  0.75 0.80  ,  measurements  determined  expected  0.70  50.0 40.0 40.0  because  only  the  0.45  25.0  LO.O  originate  of  0.72  30.0  i t  was  and hence  each  thought  no  statistical  thesis. of  isochronal  stages,  merits  fact,  of  isothermal  curves  if  the  could  annealing  some  annealings  In  isothermal thesis  the  values  standard  annealing  i n the  was  C.  30.0  60.0  hour 4 min  20  limited accuracy  could  desirability  of  min 4 min 2 min 10 h o u r  restricted  of  these  i n the  during a-series  curves.  at  to  drawn from i s o c h r o n a l  isothermal  The  variations  regarded  given  a  Annealing Temp."  8  temperatures  Thus  composition  proper  trolled  5.0 15.0 10.0 20.0 20.0 30.2 20.0  due  that,  s h o u l d be  errors  the  large  error  fact  defect  value  19.5  on d i s l o c a t i o n s .  Bath  change  2 min 1 min 4 min  10.0  703 678 670 667 640 710 675 715  of  Temp,  l)  0  718  silver  Time  A n n e a l i n g , ' •> Temp. C)  quench  were  as lov; as  a l l 0-5°  it  C.  the  while  at  provide  few  into  obtained;  i n i t i a l a  be  any  rate  minutes  determine  from  precisely  isochronal  additional always  later  con-  temperatures,  however, t h i s  was  that  inferred  were  various  transformed  d i d not  alike:  also  temperature  annealings  annealing data were because  can  to  Conclusions  discussion.  normally  be  experiments  it  annealing was  not  information. very  fast  became v e r y  even slow.  -  This  was  also  able  for  the  annealings  not  quench  not  temperatures  s t a g e was carried  could not  exactly  ancies,  for  i n i t i a l  were  temperature was  true  be  not  out  vacancy-clusters  at  as  equal  C.  A time  interval  the  later  stage;  intervals.  Also,  since  c o n t r o l l e d , the the  dislocations)  latter  60°  for  and moreover,  and/or  The  high  suitable  accurately  reproduceable  from another.  as  quenched  condition, precludes  have the  -  suit-  therefore the  in  composition of  may a l s o  67  quench  resistivity defects,  (vac-  differed for  use  the  of  the  one  isochronal  method.  Finally, could with and  combine a gold  of  sink  which does  the  that  effect  above  every  10  $  a  or  p o i n t e d out vacancy  the  her3  another  measurements. the  another  factor  many t h e n  been  since  sites  encounter  probability  has  with  atom  significant to  it  while is  the  not  for  of  -  vacancy  gold  easily  step  v/hereas  30  and  combine  with  another  vacancy.  may  assume  jump t h e  gold  direction.  atom must  For  probability  :I  the  gold  is  relative a  will  atom  gold  with  interaction in  on the  steps  40  are  Nov/ f o r  the  atom  to  -S p r o p o r t i o n a l t o  another move  the  of  was  of 2$,  atom b u t with  other  interacting order  for  rather  the  gold  face  vacancy  However, a  the  gold  i n  the  the vacancy resultant  Only  cubic a  gold  it'can  jump o f  i n the  vacancy  then  alloy atom  of on  encounter  gold  atom  However, for' a meaningful moves  0.01$  resistivity  centered  encounter  of  atom  atoms.  register  first  times the  the  probabilities  vabancsy w h i c h  three  cube  was  lequired before the  a  s i n k .before  average,  readily available.  encounter  a  interact  positions  w i l l ,  improbable that  vacancies  shown t h e t ,  third  a vacancy  to  of  encounter  ordered  is  removed at  the  vacancies  composition a vacancy  that  :  to  it  concentration  f ;old  simply  it  number of  c a n be  be  concentration  diffuse'to  It  or  that  i n from the  we second forward  forward direction,  concentration,  i.e.  the / -4\3 ^10 ). -14  Since  the  gold  concentration  is  2 x  10  the  resultant  probability is  2 x  10  *  On t h e  other  hand,  for  However,  once  ments  immediate.  (lQ~f)^  is  which  demonstrate  they  is  a  vacancy  do m e e t , The  they  meet  combine  resultant  considerably  qualitatively  to  another,  than that  that divacancy  must  such  above.  formation  is  m o v e 30  68  -  to  40  times.  on r e s i s t i v i t y  and the effect  p r o b a b i l i t y of  larger  one  -  a  process Thus,  not  is  measure-  therefore  calculations  improbable.  


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