UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Electrical conductivity of potassium iodide between 200 C and room temperature Prasad, Mahendra 1968

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1969_A6_7 P73.pdf [ 2.41MB ]
Metadata
JSON: 831-1.0059992.json
JSON-LD: 831-1.0059992-ld.json
RDF/XML (Pretty): 831-1.0059992-rdf.xml
RDF/JSON: 831-1.0059992-rdf.json
Turtle: 831-1.0059992-turtle.txt
N-Triples: 831-1.0059992-rdf-ntriples.txt
Original Record: 831-1.0059992-source.json
Full Text
831-1.0059992-fulltext.txt
Citation
831-1.0059992.ris

Full Text

ELECTRICAL CONDUCTIVITY OF POTASSIUM  IODIDE BETWEEN 200°C AND ROOM TEMPERATURE  by  MAHENDRA PRASAD M.Sc,  Ranchi U n i v e r s i t y ,  Ranchi,  (INDIA) 1964.  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE  i n the Department of Chemistry  We accept t h i s t h e s i s as conforming  t o the  required standard  THE  UNIVERSITY OF BRITISH COLUMBIA  December, 1968  In  presenting  an  advanced  the I  Library  further  for  this degree shall  agree  scholarly  by  his  of  this  written  thesis  in partial  fulfilment  of  at  University  of  Columbia,  the  make  that  it free1y  permission  purposes  may  representatives. thes.is  for  be It  financial  avai1ab le for  by  the  is understood gain  Department Columbia  for  extensive  granted  permission.  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8 , Canada  British  shall  Head  be  requirements  reference copying  that  not  the  of  and  of my  I agree  for that  Study.  this  thesis  Department  copying  or  allowed  without  or  publication my  ABSTRACT  The  electrical  c o n d u c t i v i t y o f pure KI and C d I ~ d o p e d KI 2  has been s t u d i e d i n the temperature range 200 t o 23°C. A and B ( c o r r e s p o n d i n g t o d i f f e r e n t are i d e n t i f i e d .  Two r e g i o n s  a c t i v a t i o n energy o f c o n d u c t i v i t y )  The r e g i o n A can be g i v e n a c o n v e n t i o n a l  interpreta-  t i o n i n terms o f m i g r a t i o n o f c a t i o n v a c a n c i e s i n the b u l k , c o n c e n t r a t i o n b e i n g determined  by i m p u r i t i e s .  migration o f c a t i o n vacancies)  amounts t o 0.96 ± 0.02 eV.  U (the energy f o r  a c t i v a t i o n e n e r g i e s h i g h e r than t h i s value are accounted t i o n and p r e c i p i t a t i o n e f f e c t s . w i t h i m p u r i t i e s (0.48 eV. f o r C d C d l ^ ) o b t a i n e d here  their  Observed f o r by a s s o c i a -  A s s o c i a t i o n energy o f c a t i o n v a c a n c i e s + 2  ) and heat  of solution  (0.25 eV. f o r  a r e comparable w i t h known v a l u e s f o r o t h e r  alkali  halides. Region B found  i n t h i s work r e p r e s e n t s unusual  and has n o t p r e v i o u s l y been observed  behaviour  i n any a l k a l i h a l i d e s .  The  a c t i v a t i o n energy o f c o n d u c t i v i t y i s c o n s i d e r a b l y l e s s than the energy needed f o r the m i g r a t i o n o f c a t i o n v a c a n c i e s  i n the b u l k .  t i o n energy E_ ( f o r r e g i o n B) i s about 0.57 eV. i n a s i n g l e  The a c t i v a crystal  D  and 0.38 eV. i n a pure KI p e l l e t .  Such low a c t i v a t i o n e n e r g i e s  be g i v e n a s i m i l a r i n t e r p r e t a t i o n as f o r region A. that the c a t i o n vacancies such  as d i s l o c a t i o n s  cannot  I t i s suggested  are i n regions o f unusually high m o b i l i t y  and g r a i n b o u n d a r i e s .  T h i s e f f e c t may  arise  p a r t l y from a lower a c t i v a t i o n energy f o r motion o f v a c a n c i e s i n these r e g i o n s and p a r t l y from a vacancy c o n c e n t r a t i o n i n these r e g i o n s which i n c r e a s e s w i t h d e c r e a s i n g temperature,  under the c o n t r o l o f "space-  charge"  effects.  The v a l u e 0.57 eV. appears t o r e f e r t o i s o l a t e d  d i s l o c a t i o n s or low angle b o u n d a r i e s ,  w h i l e the v a l u e o f 0.38 eV.  r e f e r s t o l a r g e angle i n t e r c r y s t a l l i n e boundaries A s t r o n g p i e c e o f evidence  i n a pellet.  f o r t h i s s u g g e s t i o n comes from  the c o n d u c t i v i t y runs on s i n g l e c r y s t a l s .  In an u n t r e a t e d  single  c r y s t a l , j u s t as i n pure p e l l e t s , two r e g i o n s A and B a r e i d e n t i f i e d but r e g i o n B d i s a p p e a r s  i n c r y s t a l s annealed  i n a mechanically strained c r y s t a l . almost  u n d i s t u r b e d i n each case.  o v e r n i g h t and reappears  Moreover, r e g i o n A remains  T h i s means t h a t t h e c o n d u c t i o n  p r o c e s s i n r e g i o n B i s governed by d i s l o c a t i o n s and g r a i n boundaries whereas r e g i o n A i s governed by motion o f c a t i o n v a c a n c i e s i n the bulk.  iv  TABLE OF  CONTENTS Page  T i t l e Page Abstract  ii  T a b l e o f Contents  iv  List  vi  of  Figures  viii  L i s t o f Tables  ix  Ackn owledgements  INTRODUCTION Review o f work on Ionic point  alkali  1  halides  1  defect  Theories of c o n d u c t i v i t y i n region  II  5  (a) Smekal Crack Concept  5  (b) Frozen E q u i l i b r i u m  6  Concept  7  (c) Impurity E f f e c t Concept Association  and p r e c i p i t a t i o n e f f e c t s  P r e v i o u s work on  11 15  KI  17  Object o f p r e s e n t work  EXPERIMENTAL 18  Apparatus Conductivity  18  Cell  Circuit  20  E l e c t r i c Furnace  22  Preparation  22  Analysis  of p e l l e t s  o f the p e l l e t  t o check the  i m p u r i t y content  23  E x p e r i m e n t a l procedure  24  Polarization effects  26  Blank  26  run  V  Page RESULTS  30  DISCUSSION Region  A  (a) A b s o l u t e v a l u e o f a  41 and i m p u r i t y content  (b) E ^ f o r pure samples and U (c) E ^ f o r impure samples;  Region  B  association  41 42  and p r e c i p i t a t i o n  42  44  APPENDIX Tables 1 - 9 BIBLIOGRAPHY  50-55 56  vi  LIST OF  FIGURES  Page  F i g u r e 1.  T y p i c a l Arrhenius p l o t  of conductivity  F i g u r e 2.  Ionic point defects  F i g u r e 3.  P l o t of c o n d u c t i v i t y versus impurity content  2 4 10  1-  (Wagner § Hantlemann J F i g u r e 4.  P l o t o f c o n d u c t i v i t y v e r s u s i m p u r i t y content •8 ( E t z e l and Maurer )  F i g u r e 5.  lfj  ' '  Typical conductivity plot  f o r lower temperatures  12  9 (NaCl, Dreyfus and Nowick •)"' F i g u r e 6.  Baijal's  F i g u r e 7.  Conductivity c e l l  F i g u r e 8.  Circuit  21  F i g u r e 9.  Polarization effect i n ionic crystal  27  Figure  10.  Conductivity plot  f o r b l a n k run  29  Figure  11.  Conductivity plot  f o r pure KI p e l l e t  32  Figure  12.  C o n d u c t i v i t y p l o t f o r doped KI (0.05  conductivity plot  mole% C d l  and  f o r KI  guard  r i n g arrangements  16 19  33  )  F i g u r e 13.  C o n d u c t i v i t y p l o t f o r doped KI (0.10 mole% Cdl ) 2  34  F i g u r e 14.  C o n d u c t i v i t y p l o t f o r doped KI  35  (0.25  mole% Cdl )  F i g u r e 15.  Summary o f c o n d u c t i v i t y p l o t s  36  Figure  P l o t o f c o n d u c t i v i t y v e r s u s i m p u r i t y content  37  16.  ( t h i s work)  /  F i g u r e 17.  Conductivity plot  of single  crystal  of single  crystal  of single  crystal  (untreated) Figure  18.  Conductivity plot (heated  Figure  19.  overnight)  Conductivity plot (strained)  viii  LIST OF TABLES Page Table  1.  Energy o f A s s o c i a t i o n  f o r divalent impurity i o n  14  and c a t i o n vacancy Table  2.  Analysis  Table  3.  Summary o f e x p e r i m e n t a l  Table  4.  Comparison w i t h p r e v i o u s r e s u l t s  o f i m p u r i t y content  24  results  31 31  APPENDIX Table  1.  Electrical  conductivity  T a b l e 2.  Electrical  c o n d u c t i v i t y o f doped KI p e l l e t  o f KI p e l l e t  (23°C - 203°C)  50 50  (0.05 mole% C d l ) (23°C - 215°C) Table  3.  E l e c t r i c a l conductivity  o f doped KI p e l l e t  51  (0.1 mole% C d l ) (23°C - 212°C) Table  4.  Electrical  c o n d u c t i v i t y o f doped KI p e l l e t  51  (0.25 mole% C d l ) (23°C - 200°C) Table  5.  E l e c t r i c a l c o n d u c t i v i t y o f u n t r e a t e d KI s i n g l e c r y s t a l 52 (23°C - 200°C)  Table  6.  Table  7.  Table  8.  Table  9.  Electrical  crystal  conductivity  o f annealed o v e r n i g h t KI s i n g l e t 52  (23°C - 205°C)  Electrical  c o n d u c t i v i t y o f s t r a i n e d KI s i n g l e c r y s t a l 53  (23°C - 201°C) S p e c i f i c a t i o n from F i s h e r S c i e n t i f i c Company o f KI used 54 i n t h i s work. S p e c i f i c a t i o n from M a l l i n c k r o d t i n B a i j a l ' s work  Chemical Works o f KI used 55  ACKNOWLEDGEMENTS  I wish t o express my s i n c e r e g r a t i t u d e Professor the work.  L.G. H a r r i s o n  f o r h i s guidance and s u p e r v i s i o n  Thanks a r e a l s o due t o P r o f e s s o r  Departmental  and thanks t o throughout  C.A. McDowell f o r  facilities.  I am a l s o g r a t e f u l t o Mr. A.K. Rantamaa, who made t h e c o n d u c t i v i t y measurement apparatus.  I N T R O D U C T I O N  Review o f work on a l k a l i The  electrical  halides c o n d u c t i v i t y o f a l k a l i h a l i d e s has been  1-3 4 studied  '  mainly i n the region  from m e l t i n g  300°C and u s u a l l y shows two r e g i o n s  point  down t o about  o f d i f f e r e n t a c t i v a t i o n energy.  A t y p i c a l Arrhenius p l o t o f c o n d u c t i v i t y , i n d i c a t i n g d i f f e r e n t slopes corresponding t o d i f f e r e n t regions,  i s shown i n F i g u r e  i s u s u a l l y c a l l e d the i n t r i n s i c region. is reproducible  ( 1 ) . Region I  The c o n d u c t i v i t y i n t h i s range  from sample t o sample and does not depend on t h e p r e v i o u s  thermal h i s t o r y .  On the o t h e r hand, i n t h e low temperature  region,  u s u a l l y r e f e r r e d t o as Region I I , the b e h a v i o u r i s d i f f e r e n t . i v i t y i n this region  Conduct-  i s not t h e same from sample t o sample and p u r i t y and  thermal h i s t o r y o f the sample p l a y  an important r o l e .  V a r i o u s explana-  t i o n s have been g i v e n by d i f f e r e n t workers i n o r d e r t o account f o r t h i s anomalous b e h a v i o u r . Ionic Point  Defects  The  ionic conductivity of a l k a l i halides  presence o f i o n i c p o i n t the  electrical  d e f e c t s may be 1)  defects,  conductivity  i s due m a i n l y t o the  i n p a r t i c u l a r cation vacancies.  For  o f i o n i c c r y s t a l s , three kinds o f l a t t i c e  distinguished.  Atoms o r i o n s  o f t h e c r y s t a l s may be d i s p l a c e d  l a t t i c e s i t e s t o the i n t e r s t i c e s .  from normal  They are then known as  interstitials. 2)  L a t t i c e s i t e s may be unoccupied;  these s i t e s  are c a l l e d  vacancies. 3)  L a t t i c e p o s i t i o n s may be o c c u p i e d by i m p u r i t y atoms o r i o n s .  or misplaced  2  Fig.  (1)  T y p i c a l Arrhenius p l o t of  conductivity  O .  ~300°C 10 /T 3  C°K)  3  The i s e d with  formation  reference  o f the f i r s t  two types o f d e f e c t may be v i s u a l -  to the i d e a l c r y s t a l .  A c a t i o n o r an anion may be  d i s p l a c e d from i t s normal l a t t i c e s i t e t o an i n t e r s t i t i a l The  position.  r e s u l t i n g d e f e c t i s known as a F r e n k e l d e f e c t and c o n s i s t s o f an  i n t e r s t i t i a l i o n together  with  a c a t i o n o r anion vacancy.  d e f e c t i s common i n s i l v e r h a l i d e s and i s shown i n F i g u r e thermodynamic c o n s i d e r a t i o n s , the c o n c e n t r a t i o n crystal  This sort o f (2.a).  o f the defects i n a  c o n t a i n i n g o n l y F r e n k e l d e f e c t s i s g i v e n by the e q u a t i o n  n.  = (NN.)^  exp(-W./2kT)  2  where n. i s t h e c o n c e n t r a t i o n l  From  (1)  (1)  o f i o n s i n i n t e r s t i t i a l p o s i t i o n s at r  e q u i l i b r i u m , N i s the t o t a l number o f l a t t i c e s i t e s and ftL i s t h e t o t a l number o f p o s s i b l e i n t e r s t i t i a l form a F r e n k e l  i s t h e energy r e q u i r e d t o  defect.  Schottky and  sites.  d e f e c t s a r e formed when, i n an i d e a l  cations  anions a r e removed from t h e i r normal l a t t i c e s i t e s t o e x t e r n a l o r  internal surfaces lattice,  Figure  o f the c r y s t a l w i t h  (2.b).  t h e r e s u l t o f expansion o f the  In order t o m a i n t a i n  the e l e c t r i c a l  o f the c r y s t a l as a whole, c a t i o n and anion v a c a n c i e s number i n a pure c r y s t a l . the d e f e c t  concentrations  n n_ +  and  crystal,  =  N  2  = n  +  = N  must be equal i n  In any c r y s t a l c o n t a i n i n g Schottky a r e r e l a t e d by the e q u a t i o n  exp(-W/H?)  i n a pure c r y s t a l c o n t a i n i n g Schottky  n_  neutrality  exp(-W/2kT)  defects,  (2)  (2)  defects  only  (3)  4 Fig.  2  Ionic point  Fig. Frenkel +  -  +  -  +  -  +  +  +  +  -  -  +  defects  (2.a) Defects  +  -  +  -  +  +  -  +  -  -  +  -  +  +  -  +  -  +  -  +  -  +  -  +  Fig.  (2.b)  Formation o f a S c h o t t k y  +  +  -  -  +  -  +  -  +  +  -  +  -  +  -  +  -  +  -  +  -  +  -  +  -  +  -  +  -  +  -  +  -  +  -  +  -  +  -  +  -  +  -  +  -  +  -  +  -  +  + +  +  +  +  -  -  +  +  -  I  i  I  +  -  ++  -  +  -  +  i  i  -  -  +  -  +  +  -  +  +  -  +  -  +  -  -  +  -  +  +  +  -  +  -  +  -  +  +  +  -  +  -  +  -  +  -  +  -  +  -  +  + _>  +  +  + -  .  -  +  Divalent impurity -  +  -  Fig.  +  pair  +  (2.c) in a 1 : 1 crystal  5  where n  +  and n  respectively.  a r e the c o n c e n t r a t i o n s  W i s the energy r e q u i r e d t o form a S c h o t t k y  Vacancies  or i n t e r s t i t i a l s  i n c o r p o r a t i o n o f another type impurities.  o f c a t i o n and anion  vacancies pair.  can a l s o be produced b y t h e  o f i m p e r f e c t i o n , such as chemical  F o r i n s t a n c e , the s u b s t i t u t i o n o f a d i v a l e n t c a t i o n f o r  a monovalent one i n t r o d u c e s In o r d e r t o p r e s e r v e  an e x t r a p o s i t i v e charge i n the c r y s t a l .  the e l e c t r i c a l  whole, e i t h e r an e x t r a n e g a t i v e  n e u t r a l i t y o f the c r y s t a l as a  i o n should be i n c o r p o r a t e d  inter-  s t i t i a l l y o r a p o s i t i v e i o n vacancy must be formed a t a l a t t i c e Figure  (2.c).  Since the l a t t e r process  r e q u i r e s l e s s energy, a c a t i o n  vacancy i s formed by each d i v a l e n t i m p u r i t y In a l k a l i h a l i d e s the S c h o t t k y  ion.  d e f e c t s predominate and i n t h i s  account, a l l d i s c u s s i o n s are made w i t h r e f e r e n c e t o these Theories  site,  defects.  o f C o n d u c t i v i t y i n Region I I On  the basis o f l a t t i c e  ance o f d i f f e r e n t  r e g i o n s i n c o n d u c t i v i t y p l o t o f a l k a l i h a l i d e s has  been e x p l a i n e d by s e v e r a l authors (a)  d e f e c t s mentioned above, the appear-  2 .  Smekal Crack Concept  : The f i r s t  s u g g e s t i o n was made by  3  Smekal , who suggested t h a t , i n the c o n d u c t i o n  process  f o r the i m p u r i t y  r e g i o n , t h e low a c t i v a t i o n energy and low p r e - e x p o n e n t i a l  factor result  from d i f f u s i o n o f a s m a l l number o f i o n s through g r a i n b o u n d a r i e s and cracks known as "Smekal C r a c k s " . t o have d i f f e r e n t c o n c e n t r a t i o n s  D i f f e r e n t c r y s t a l s would be expected o f cracks  c o n d u c t i v i t y would be s t r u c t u r e s e n s i t i v e .  and consequently the I t seems l i k e l y t h a t the  a c t i v a t i o n energy f o r d i f f u s i o n v i a cracks w i l l be c o n s i d e r a b l y t h a n t h a t through the l a t t i c e  v i a vacancies  less  or i n t e r s t i t i a l p o s i t i o n s ,  6  and t h a t t h i s type o f movement would be f a v o u r e d at low (b)  Frozen E q u i l i b r i u m Concept  temperature.  : Another s u g g e s t i o n based  on 4  the concept o f f r o z e n e q u i l i b r i u m at lower temperature was  made by J o s t .  A c c o r d i n g t o t h i s s u g g e s t i o n , i n Region I , t h e r e i s an e q u i l i b r i u m between the d e f e c t c o n c e n t r a t i o n s and a s m a l l change i n temperature i s f o l l o w e d by a r a p i d adjustment  o f the c a t i o n d e f e c t c o n c e n t r a t i o n t o a new  brium v a l u e a c c o r d i n g t o the e q u a t i o n ( 3 ) .  At lower temperature,  equiliunder  these c o n d i t i o n s a r e g i o n o f low a c t i v a t i o n energy o f c o n d u c t i v i t y i s e x p e c t e d , because  the e q u i l i b r i u m d i s t r i b u t i o n o f the d e f e c t s p r e d i c t e d  by t h i s e q u a t i o n cannot be a c h i e v e d w i t h i n a p p r o p r i a t e time, and changes i n temperature have no e f f e c t  on the d e f e c t c o n c e n t r a t i o n .  In t h i s  s i t u a t i o n the v a r i a t i o n o f c o n d u c t i v i t y w i t h temperature would be t o the e f f e c t  due  o f temperature on the m o b i l i t y o f the d e f e c t s at c o n s t a n t  concentration of defects.  Thus at h i g h e r temperature, the  conductivity  a i s g i v e n by the g e n e r a l e q u a t i o n ( 4 ) a = n ey = (4 n e +  +  2  A r /kT) 2  exp(-U/kT)  -(4)  where r = d i s t a n c e between n e i g h b o u r i n g c a t i o n and a n i o n e = electronic  charge  A = frequency f a c t o r r e p r e s e n t i n g the e n t r o p y e f f e c t o f changes in  lattice vibrations arising  from the f o r m a t i o n o f v a c a n c i e s  u = m o b i l i t y of vacancies and U r e p r e s e n t s a c t i v a t i o n energy f o r the motion o f the c a t i o n  vacancy.  The n u m e r i c a l f a c t o r 4 appears i n the e x p r e s s i o n by c o n s i d e r a t i o n o f the jumps o f a vacancy t o any o f i t s 12 n e a r e s t neighbours i n the f e e c a t i o n sub  lattice . 5  7  In  the i n t r i n s i c  c o n s i s t s o f two terms, a Schottky p a i r c a t i o n vacancy  (W/2);  range the e f f e c t i v e a c t i v a t i o n energy-  ( i ) h a l f t h e energy needed  f o r the f o r m a t i o n o f  ( i i ) the energy r e q u i r e d f o r the m i g r a t i o n o f  (U). Hence t h e above g e n e r a l e q u a t i o n can a l s o be  w r i t t e n as f o l l o w s .  a = a  In  Q  exp  -(U+W/2)/kT  (5)  t h i s e q u a t i o n 0 " i s e q u i v a l e n t t o the p r e - e x p o n e n t i a l term i n q  equation  (4) and r e p r e s e n t s the e x t r a p o l a t e d v a l u e o f a at T =.-<*>;.  S i m i l a r l y a t lower temperature  and  where T  q  a i s g i v e n by e q u a t i o n s (6) & ( 7 ) .  o  = O  exp (-W/2kT )  a  = a ' exp (-U/kT)  exp (-U/kT)  (6) (7)  i s the e f f e c t i v e temperature a t which the d e f e c t  becomes f r o z e n .  equilibrium  T h i s means t h a t b o t h t h e a c t i v a t i o n energy and p r e -  e x p o n e n t i a l term w i l l be lower i n t h e lower temperature range, which  i  4 i s experimentally supported .  T  q  and h e n c e w i l l Accordingly a  vary according to  the  thermal h i s t o r y o f the sample.  for  a c r y s t a l which has been quenched r a p i d l y from h i g h temperature  1  w i l l be g r e a t e r  than f o r one which has been c o o l e d s l o w l y through the range where "freezing"  started. (c)  I m p u r i t y E f f e c t Concept  : A t h i r d suggestion  f o r the  e x i s t e n c e o f the low temperature r e g i o n i s made on t h e b a s i s o f t h e impurity effect  concept, the i m p u r i t y u s u a l l y b e i n g o f a l i o v a l e n t n a t u r e .  The term a l i o v a l e n t means t h a t the v a l e n c y o f a c a t i o n o r an a n i o n  8  impurity i s d i f f e r e n t  from t h a t o f an i o n i n the pure h o s t  crystal.  T h i s s u g g e s t i o n i s based on the f a c t t h a t the s u b s t i t u t i o n o f a d i v a l e n t c a t i o n f o r a monovalent  one, i n t r o d u c e s one c a t i o n vacancy,  i n o r d e r t o m a i n t a i n the e l e c t r i c a l n e u t r a l i t y o f the c r y s t a l as a whole.  Such  c a t i o n v a c a n c i e s w i l l be p r e s e n t at a l l temperatures i n  the same c o n c e n t r a t i o n  ( p r o v i d e d t h a t the i m p u r i t y remains i n s o l i d  s o l u t i o n ) and c o n s e q u e n t l y t h e i r e f f e c t  on c o n d u c t i v i t y w i l l be much  more apparent a t lower temperature, because  at lower temperature the  c o n c e n t r a t i o n o f t h e r m a l l y produced v a c a n c i e s i s lower than t h a t already present.  Now i f the number o f d i v a l e n t c a t i o n  impurities  i s n^ p e r cm , t h i s number o f v a c a n c i e s w i l l be p r e s e n t i n a d d i t i o n 3  t o the v a c a n c i e s produced t h e r m a l l y , and the c o n d u c t i v i t y w i l l be enhanced. The  c o n c e n t r a t i o n o f c a t i o n v a c a n c i e s may be c a l c u l a t e d i n  the doped sample as f o l l o w s .  In an impure  crystal  as w e l l as i n a  pure c r y s t a l , the d e f e c t c o n c e n t r a t i o n s must obey e q u a t i o n (2) b u t i n a doped sample,  n  +  = n_ + n^  S u b s t i t u t i n g the v a l u e o f n n  (n  +  - n ) = N  (8)  i n e q u a t i o n ( 2 ) , i t can be w r i t t e n as, 2  exp(-w/kT) = C  (9)  - C = 0  or  n  iij  ± (n  2  +  4  C)  2 (i)  At h i g h temperature, C » n  , then n  = C = N exp.(-W/2kT) . . 2  (10) and t h i s  corresponds t o Region I .  9  (ii)  At low temperature, r i j > > C , t h e r e f o r e , n  +  =  .. (11)  and t h i s  corresponds t o Region I I .  Most e x p e r i m e n t a l s t u d i e s  i n the l a s t twenty y e a r s have  i n d i c a t e d t h a t , a t l e a s t f o r the c a t i o n s , the i m p u r i t y predominant  i n Region I I .  (Anion d i f f u s i o n , which a l s o shows  Regions I § I I , seems t o be more c o m p l i c a t e d ) . effect  o f added d i v a l e n t i m p u r i t y  to 8000 ppm.)  effect i s  Sr  + 2  ions  For example, the  ( i n the range o f 1000 ppm.  on the e l e c t r i c a l c o n d u c t i v i t y o f KC1 i n t h e temperature  range o f 600-725°C has been s t u d i e d by Wagner and Hantelmann . p l o t o f c o n d u c t i v i t y versus impurity  content at 600°C i s f a i r l y  The linear;  g  see F i g u r e Cd  ( 3 ) . L a t e r E t z e l and Maurer  a l s o s t u d i e d the e f f e c t o f  i o n ( i n the range 10 ppm. t o 688 ppm.)  + 2  ivity  on the e l e c t r i c a l  o f NaCl i n the temperature range 403 t o 256°C.  shown t h a t the graph o f c o n d u c t i v i t y v e r s u s i m p u r i t y deviate for  f a r from l i n e a r i t y  ( F i g u r e ,4 ) •  conduct-  They a l s o have c o n t e n t does not  The d e v i a t i o n may be accounted  by a s s o c i a t i o n and p r e c i p i t a t i o n e f f e c t s which are d i s c u s s e d  next s e c t i o n .  i n the  Fig.  3  P l o t o f c o n d u c t i v i t y versus i m p u r i t y (Wagner  7  § Hantlemann )  Mole r a t i o x 10  s  (Cd ) + 2  content  11  Association  and P r e c i p i t a t i o n E f f e c t s 9  R e c e n t l y , low temperature measurements on sodium have been extended down t o and beyond of other regions established  (5).  t i o n and p r e c i p i t a t i o n e f f e c t s as (i) impurity  room temperature and the  of higher a c t i v a t i o n energies,  as shown i n F i g u r e  The f i r s t  chloride existence  I I I and IV, has been  These are accounted f o r by  associa-  follows.  i s the tendency o f o p p o s i t e l y  charged d i v a l e n t  i o n (which has an e f f e c t i v e s i n g l e p o s i t i v e charge) and the  c a t i o n vacancy  (which has an e f f e c t i v e n e g a t i v e charge) t o a s s o c i a t e  form a n e u t r a l  complex.  (ii)  The second i s the p r e c i p i t a t i o n o f d i v a l e n t i m p u r i t y  at temperatures where t h e i r c o n c e n t r a t i o n bility  to  ion  i n s o l u t i o n exceeds the s o l u -  limit. By the a p p l i c a t i o n o f S t a t i s t i c a l Mechanics  (or even by a  s i m p l e Mass A c t i o n treatment as i n d i c a t e d below) the e f f e c t o f a s s o c i a t i o n r e a c t i o n on c o n d u c t i v i t y i s e a s i l y c a l c u l a t e d f o r the d i l u t e s o l u t i o n . The e f f e c t i v e energy f o r the Region I I I i s found t o be the sum o f U and E /2, where E i s the energy needed f o r the a s s o c i a t i o n r e a c t i o n . Let a a A be the i m p u r i t y  vacancy complex such  A  ^  I  +  where I i s the d i v a l e n t i m p u r i t y vacancy. given  By the Law  "  that,  +  "  i o n and j  o f Mass A c t i o n ,  (12)  1  +  j represents  the  cation  the e q u i l i b r i u m c o n s t a n t K , i s  by (jij  n /n ) +  A  =  K = K  q  exp  (-iykT)  (13)  10 /T 3  13  where  ' i s the  concentration  concentration  o f d i s s o c i a t e d complex and  of undissociated  complex.  n^ i s  the  T h i s e q u i l i b r i u m i s analogous t o  t h a t f o r d i s s o c i a t i o n of a weak e l e c t r o l y t e i n aqueous s o l u t i o n s . the if  case o f a low the  degree o f d i s s o c i a t i o n , n^ ~ n^  temperature i s low  enough f o r the  For  (total impurities)  and  assumption t o be made t h a t  " i n t r i n s i c " v a c a n c i e s can, be neglected,, then  n-j.' ='n ,  therefore,  n  K  +  and  impurities  ities,  exp  J * 3  (-E  2  = ^  K  q  exp(-E /kT)  (14)  a  /2kT)  (15)  a c t i v a t i o n energy f o r c o n d u c t i v i t y becomes (U + E / 2 ) .  so t h a t the the  = (nj  +  n  i n s o l u t i o n are i n e q u i l i b r i u m w i t h p r e c i p i t a t e d impur-  then n^. i s governed by  f u r t h e r a d d i t i o n o f AH On  the b a s i s  a s o l u b i l i t y e q u i l i b r i u m which makes a  o f s o l u t i o n t o the  a c t i v a t i o n energy.  o f a s i m p l e model o f e l e c t r o s t a t i c a t t r a c t i o n  between a p o s i t i v e and n e g a t i v e charge i n a continuum h a v i n g the d i e l e c t r i c constant  E  a  o f the  ~  e /r.,e.  Detailed  from one  crystal, E  &  i s g i v e n by  neighbour d i s t a n c e .  a l k a l i h a l i d e t o another, and  eV.  are g i v e n below i n t a b l e  for C d 1.  static (16)  (16)  2 +  i n NaCl.  This quantity  varies  i s r o u g h l y 0.6  eV.  arrangement o f neighbours  complex g e n e r a l l y g i v e somewhat s m a l l e r  Gammel^ o b t a i n e d 0.44  equation  o  c a l c u l a t i o n s t a k i n g i n t o account the  around the  the  2  where r i s the second n e a r e s t very l i t t l e  If  values.  Reitz  and  Some e x p e r i m e n t a l v a l u e s  14  TABLE 1 Energy o f A s s o c i a t i o n f o r d i v a l e n t i m p u r i t y  Impurity  Host c r y s t a l  +  Cd  NaCl  i o n and c a t i o n vacancy.  Ea(eV.)  0.35  Reference  E t z e l and Maurer  8  Lidiard^ Mg +  Mn Cd  NaCl  0.54  Dreyfus and Nowick  NaCl  0.52  Dreyfus and Nowick  1  NaCl  +  The l a s t  0.42  Dreyfus and Nowick  t h r e e v a l u e s are c a l c u l a t e d from the d i f f e r e n c e o f  a c t i v a t i o n e n e r g i e s i n Region I I and I I I .  Dreyfus and Nowick c o r r e l a t e d  the Region IV w i t h the o c c u r r e n c e o f p r e c i p i t a t i o n and on t h a t they c o n c l u d e d t h a t Region I I I r e s u l t s from a s s o c i a t i o n .  basis  A l s o , the  f a c t t h a t no h y s t e r i s i s o c c u r s i n Region I I I , suggests t h a t p r o b a b l y p r e c i p i t a t i o n i s not i n v o l v e d i n t h i s  region.  However, f o r r e g i o n s o f types I I I and IV, i t i s not y e t c l e a r l y e s t a b l i s h e d which one shows the a s s o c i a t i o n e f f e c t o n l y and which shows a l s o the p r e c i p i t a t i o n e f f e c t .  15  P r e v i o u s Work on Potassium I o d i d e : From work on e l e c t r i c a l c o n d u c t i v i t y o f KI (see a l s o 3 i n the D i s c u s s i o n  table  Section) L e h f e l d t ^ reported that i n the i n t r i n s i c  range, the a c t i v a t i o n energy o f c o n d u c t i v i t y i s 0.82 eV. r e s u l t o f autodiffusion studies  12  From the  o f v a c a n c i e s i n the i n t r i n s i c  range,  13 the  a c t i v a t i o n energy i s 0.67 eV.  E c k l i n et a l .  s t u d i e d the  e l e c t r i c a l c o n d u c t i v i t y o f pure and doped KI (dopants used were and C a  + 2  Sr  ) as a f u n c t i o n o f temperature from 560°C down t o 20°C.  observed f o u r domains i n t h e c o n d u c t i v i t y p l o t .  + 2  They  Domains I and I I  c o r r e s p o n d t o i n t r i n s i c and e x t r i n s i c Regions I and I I , and they have g i v e n t h e c o n v e n t i o n a l arguments f o r t h e i r e x i s t e n c e .  Domain I I I was  dominated by a s s o c i a t i o n b u t the t r a n s i t i o n from I I t o I I I i s at an u n u s u a l l y h i g h temperature  (about 300°C).  They r e p o r t e d the a c t i v a t i o n  energy o f motion o f c a t i o n vacancy as U equal t o 1.21 ± 0.05 eV. e r r a t i c Domain IV was dominated by s u r f a c e effects.  D u r i n g comprehensive  o f KI s i n g l e c r y s t a l and p e l l e t  e f f e c t s and p o l a r i z a t i o n  s t u d i e s o f the e l e c t r i c a l 14  o f ammonium s a l t s , H a r r i n g t o n and S t a v e l e y  The  conductivity  measured the c o n d u c t i v i t y  as a f u n c t i o n o f temperature.  They  found t h e a c t i v a t i o n energy o f c o n d u c t i v i t y i n temperature range 123188°C  f o r a s i n g l e c r y s t a l t o be about 1.30 eV and t h a t f o r a p e l l e t  0.86 eV. i n t h e temperature range 38°C - 138°C. Baijal"^ i n this of e l e c t r i c a l  laboratory  found t h a t the a c t i v a t i o n energy  c o n d u c t i v i t y i n the range 330-90°C  Lehfeldt's value.  was i n agreement w i t h  B a i j a l a l s o observed t h a t t h e r e i s a. regi6n«(Fig.  6) o f  e x c e p t i o n a l l y low a c t i v a t i o n energy from 90°C down t o room temperature. During h i s i n v e s t i g a t i o n o f o x i d a t i o n o f KI by h a l o g e n gases, he n o t i c e d  16  17  t h a t the i n i t i a l  r e s i s t a n c e o f KI p l a y s an important r o l e and t h i s  l e d him t o study the e l e c t r i c a l  c o n d u c t i v i t y a t low temperature.  His  apparatus, however, was n o t d e s i g n e d w i t h such h i g h impedance measurements i n mind, and t h e r e was some doubt as t o whether the e f f e c t was a s p u r i o u s one a r i s i n g from t h e r a t h e r v a r i a b l e r e s i s t a n c e o f the apparatus. w i t h apparatus  leakage  The work t h e r e f o r e needed t o be r e p e a t e d  r e d e s i g n e d f o r t h i s h i g h impedance r e g i o n .  The O b j e c t o f t h e Present Work The  o b j e c t o f t h e p r e s e n t work was t o study the b e h a v i o u r o f  e l e c t r i c a l c o n d u c t i v i t y o f pure and impure potassium used was C d l ) from 200°C down t o room temperature, 2  iodide  (dopant  particularly i n  o r d e r t o determine  whether t h e r e e x i s t s a r e g i o n o f u n u s u a l l y low  a c t i v a t i o n energy,  as p r e v i o u s l y r e p o r t e d by B a i j a l .  E X P E R I M E N T A L  18  Apparatus The A. Rantamaa.  apparatus was  d e s i g n e d a y e a r b e f o r e use  i n t h i s work by  I t consists of a conductivity c e l l , electrometer,  h i g h impedance c i r c u i t  and  a n o n - i n d u c t i v e l y wound e l e c t r i c  (see F i g . 7), a l l o f which were housed i n a grounded copper Conductivity The  simple  furnace case.  Cell conductivity c e l l  (see F i g . 7) c o n s i s t s o f two  P and Q, b o t h o f which are made o f p l a t i n u m  i n the  electrodes  form o f d i s c s .  The  e l e c t r o d e P i s f i x e d i n a c i r c u l a r c a v i t y at the bottom o f a t e f l o n cylinder  (S).  e l e c t r o d e P,  A Pt/Rh(10%) w i r e T i s a t t a c h e d thus forming the hot  t o the  other end  j u n c t i o n o f a thermocouple.  c i r c u l a r guard r i n g G around P i s a l s o p r o v i d e d  so t h a t the  of A  conductivity  can be measured w i t h  e i t h e r the bottom e l e c t r o d e or the guard r i n g  both i n c i r c u i t ,  e i t h e r p a r t may  and  the  or  be grounded when not i n c i r c u i t .  T h i s makes i t p o s s i b l e t o measure s e p a r a t e l y any  c o n t r i b u t i o n from  surface conductivity. The  w i r e s connecting  P, T, G and Q pass along the s i d e o f a  t e f l o n c y l i n d e r and have been wrapped i n t e f l o n f o i l .  At the top o f the  t e f l o n c y l i n d e r , a m e t a l l i c hook i s p r o v i d e d by means o f which weight o f the c y l i n d e r t o g e t h e r supported during cone (B-45). the  The  with  the e l e c t r o d e s  the  and sample i s  assembly on a h o r i z o n t a l g l a s s rod, f i x e d i n a g l a s s electrodes  c y l i n d e r (which c o n t a i n s  are h e l d to the sample by the weight a metal weight o f about 250  t h e r e i s a good c o n t a c t between e l e c t r o d e s  and sample.  gm)  and  Near the  of thus top  o f the g l a s s cone, t h e r e i s an opening through which the c e l l i s connected t o the vacuum system f o r e v a c u a t i o n  or i n t r o d u c t i o n o f  any  19  Fig.  7  Conductivity c e l l and guard r i n g  20  gas when needed.  The  four wires  namely P, T, G and Q pass through  t e f l o n i n s e r t s i n the g l a s s cone and dekhotinski  cement.  i t p o s s i b l e t o use  The the  use  are vacuum-sealed w i t h  o f t e f l o n and  apparatus f o r h i g h impedance measurements.  For o p e r a t i o n the c e l l was  placed i n a large c y l i n d r i c a l  bottomed g l a s s v e s s e l , which c o n t a i n e d  The  c o n d u c t i v i t y c e l l was  K e i t h l e y decade shunt h a v i n g a potential difference E o f a dry c e l l erence was  across  The  connected i n s e r i e s w i t h 3  to 1 Q  12  a  ohms, and  a p p l i e d by means  Almost a l l t h i s p o t e n t i a l d i f f small p o t e n t i a l difference E  2  measured w i t h a K e i t h l e y model 200B b a t t e r y (dcvtvm) h a v i n g  r e s i d u a l c u r r e n t at i n p u t 5 x 10 f u l l scale deflection.  1!  an i n p u t r e s i s t a n c e o f 10 ' ohms, 1If  * amperes and ranges down t o 8 mv.  S i n c e the e l e c t r o m e t e r was  impedance c i r c u i t r y every  care was  the whole c i r c u i t by housing The  flat  l o a d o f the c y l i n d e r .  o f about 22-1/2 v o l t s was  the sample.  electrometer  grounded.  the  r e s i s t a n c e s from 10  as shown i n F i g . ( 8 ) .  a c r o s s the shunt was operated  1  flat  a few p i e c e s o f u n i f o r m  t e f l o n i n the bottom i n o r d e r t o support Circuit:-  d e k h o t i n s k i cement makes  used i n h i g h  taken t o s h i e l d i n p u t leads  i n a b i g copper case which was  and  already  h i g h impedance p a r t o f the c i r c u i t , which must be  i s o l a t e d p a r t i c u l a r l y c a r e f u l l y from ground, i s the p a r t between letters  (PTABCDFE) i n the F i g . ( 8 ) .  a l s o grounded. front  The  operator  o f the machine i s  For t h a t purpose a long p i e c e o f copper i s p l a c e d i n  o f the apparatus,  which has  to be  touched w h i l e  operating  the  machine. The  v o l t a g e El  was  checked at i n t e r v a l s , o f about 4 hours,  on  21  Fig. 8 Circuit  10 Kohms  7  E  A ^ v W v V t B  Keithley Shunt 10  3  - 10 ohms 12  Electrometer Potentio meter  High impedance p a r t o f c i r c u i t K e i t h l e y from F t o e l e c t r o m e t e r  i s PTABCDFE and c o n n e c t i o n s tube.  i n s i d e the  22  e i t h e r by u s i n g an e x t e r n a l meter o r by t u r n i n g the s w i t c h t o s h o r t p o s i t i o n and u s i n g a shunt  r e s i s t a n c e o f 10 "* ohms.  measured on 20 v o l t s c a l e i s doubled  The v o l t a g e  t o f i n d out the a c t u a l  E.M.F. E j o f the b a t t e r y . During  the measurement o f conductance, the thermocouple  leads were d i s c o n n e c t e d case  a t the p l u g s i n t h e w a l l o f the copper  (CD, F i g . 8 ) , t o a v o i d the leakage  t o ground which  e f f e c t i v e l y s h o r t - c i r c u i t s the K e i t h l e y shunt  otherwise  and l e a d s t o s p u r i o u s  low v a l u e s f o r E . 2 Electric  Furnace  :-  An e l e c t r i c  furnace i n o r d e r t o heat  was d e s i g n e d w i t h a m e t a l l i c h o l l o w  the c e l l  c y l i n d e r which c o n t a i n e d an  asbestos p i p e i n which the c e l l was p l a c e d .  The winding  o f the  furnace was n o n - i n d u c t i v e i n order t o a v o i d the i n d u c t i v e e f f e c t arising  from A.C. c u r r e n t s , the furnace b e i n g the o n l y A.C. d e v i c e  i n s i d e the copper case e n c l o s i n g the whole apparatus.  In between  o u t e r and i n n e r w a l l s o f the p i p e and c y l i n d e r r e s p e c t i v e l y , g l a s s wool was f i l l e d  for insulation.  The furnace was u s u a l l y heated by 15-16  v o l t s f o r about 3-4 hours f o r thermal e q u i l i b r i u m . Preparation of p e l l e t s Two kinds  o f p e l l e t s were  1)  Pure KI  2)  C d l - doped KI  (a)  prepared.  P e l l e t s o f pure KI: A.R. grade ( F i s h e r Sc. Co.) KI was  d r i e d at 120°C f o r about 2-3 days and then powdered w i t h mortar and pestle.  T h i s powder was d r i e d o v e r n i g h t and p r e s s e d i n t o p e l l e t s o f  23  1.32 cm i n diameter and about  1.3 - 3.0 mm i n t h i c k n e s s u s i n g h y d r a u l i c  p r e s s u r e o f 7000 l b s . p e r p e l l e t , about 8-10 minutes. minutes.  The l o a d was a l l o w e d t o remain f o r about 2-3  The p e l l e t s were s t o r e d i n a d e s i c c a t o r b e f o r e and a f t e r u s e . (b)  Doped K I :  In t h i s case C d l  d i f f e r e n t compositions were used. Cdl  a f t e r e v a c u a t i n g t h e apparatus f o r  2  was used as dopant  and t h r e e  The c a l c u l a t e d amount o f KI and  f o r d i f f e r e n t compositions were weighed i n the p r e v i o u s l y weighed  2  p l a t i n u m c r u c i b l e and the weighed m a t e r i a l was f u s e d on the bunsen flame. The melt was made homogeneous by s h a k i n g the c r u c i b l e c a u t i o u s l y . o r d e r t o a v o i d a brown c o l o r a t i o n o b t a i n e d i n the f i r s t blown i n t o the melt through a f i n e j e t w h i l e c o o l i n g .  t r i a l , a i r was The s o l i d  o b t a i n e d was powdered and d r i e d f o r 2-3 days at 120°C.  In  thus  Then the p e l l e t s  were p r e s s e d e x a c t l y i n the same way as f o r pure K I . In making the p e l l e t s no q u a n t i t a t i v e procedure was used t o check whether o r n o t the s i z e o f g r a i n s was always the same, b u t t h e same g r i n d i n g procedure was f o l l o w e d i n every case.  Theemicrosopic  o b s e r v a t i o n o f t h e s i z e o f g r a i n s i n d i c a t e d t h a t the g r a i n s were i n the  range 8u - 14u.  A n a l y s i s o f the p e l l e t s t o check the i m p u r i t y content The doped samples  were a n a l y s e d by a c o l o r i m e t r i c method"*"^ i n  o r d e r t o check the i m p u r i t y c o n t e n t b e f o r e and a f t e r the c o n d u c t i v i t y runs.  The e x p e r i m e n t a l procedure was as f o l l o w s .  25 ml, c o n t a i n i n g solution. was  added.  KI was f i r s t  The sample  solution,  t r e a t e d w i t h 5 ml o f 20% Na-K t a r t r a t e  To the r e s u l t i n g s o l u t i o n an equal volume o f 10% NaOH s o l u t i o n The m i x t u r e was e x t r a c t e d w i t h 5% d i t h i z o n e s o l u t i o n i n  24  carbon t e t r a c h l o r i d e  (Sp.grade.)  p o r t i o n became c o l o u r l e s s .  i n a s e p a r a t i n g f u n n e l , u n t i l the l a s t  The e x t r a c t was c o l l e c t e d i n a b l a c k e n e d  v o l u m e t r i c f l a s k , i n o r d e r t o a v o i d any photochemical d e c o m p o s i t i o n o f Cd-dithizonate.  T h i s e x t r a c t was washed w i t h d i s t i l l e d water  w i t h carbon t e t r a c h l o r i d e  and then  and c o l l e c t e d i n another 25 ml v o l u m e t r i c  f l a s k , and the volume was made up t o the mark by adding carbon tetrachloride.  The t r a n s m i t t a n c y was measured at 520 mu w i t h a Cary 14  Spectrophotometer  (which was c a l i b r a t e d w i t h a known amount o f C d l  made up i n s o l u t i o n ) and by comparing impurity  contents were determined.  2  w i t h the c a l i b r a t i o n curve, the  The r e s u l t s  are g i v e n i n t a b l e 2.  TABLE 2 A n a l y s i s o f Impurity Content Impurity Added (mole%)  (Cd  Impurity p r e s e n t  ) (mole%)  Before C o n d u c t i v i t y Run  A f t e r Conduct. Run  0.050  0.0498  0.0499  0.100  0.102  0.103  0.250  0.249  0.248  E x p e r i m e n t a l Procedure t h i s work.  :-  D.C. e l e c t r i c a l  c o n d u c t i v i t y was measured i n  The sample was i n t r o d u c e d i n t o the c o n d u c t i v i t y c e l l  c e l l was evacuated f o r about 20-25 h o u r s , t i l l sample a t room temperature was c o n s t a n t . heated t i l l  a c o n s t a n t temperature  and the  the r e s i s t a n c e o f the  The c o n d u c t i v i t y c e l l was then  o f about 200°C was r e c o r d e d by  25  keeping the c o l d j u n c t i o n at 0°C ( i c e - w a t e r ) . E  x  2  voltage  was measured each day b e f o r e measuring c o n d u c t i v i t y and was  checked at i n t e r v a l s E  The a p p l i e d  o f about 4 h o u r s .  The p o t e n t i a l  difference  a c r o s s the shunt was measured by K e i t h l e y e l e c t r o m e t e r  (see F i g .  t a k i n g an i n t e r v a l o f 15 seconds between s u c c e s s i v e r e a d i n g s . p o l a r i t y was then r e v e r s e d , t h e f i r s t  The  r e a d i n g taken immediately, and  a s i m i l a r s e r i e s o f measurements was made.  The mean v a l u e b e f o r e and  a f t e r r e v e r s i n g the p o l a r i t y was taken as E^.  The conductance o f the  sample was then c a l c u l a t e d as f o l l o w s .  a  =  E  2  I -ohm"  (17)  1  E -E 1  2  where a i s the conductance i n .ohmv  1  marked on the shunt i n amperes resistance).  and I i s the c u r r e n t  range  ( i . e . the r e c i p r o c a l o f t h e shunt  The s p e c i f i c c o n d u c t i v i t y was c a l c u l a t e d by the  following equation.  asp = where %  (A/s)  ohm  cm"  -1  i s t h e t h i c k n e s s o f the sample  (18)  1  and s i s the a r e a o f the  sample. In t h e s e measurements, two types o f c o o l i n g procedures were f o l l o w e d , r a p i d c o o l i n g and slow  cooling.  In r a p i d c o o l i n g the f u r n a c e was s w i t c h e d o f f and the measurements were made t a k i n g an i n t e r v a l  o f about 30-35 minutes  (the temperature range b e i n g ~ 200-100°C)  and about an hour  below  100°C.  8),  interval  In slow c o o l i n g the f u r n a c e s e t t i n g was a d j u s t e d t o  g i v e some c o n s t a n t temperature and r e a d i n g s were taken a f t e r brium was reached at t h a t temperature  (about one h o u r ) .  equili-  The two  26  procedures appear t o g i v e g e n e r a l l y s i m i l a r r e s u l t s . o f the experiments, r a p i d  cooling  In the m a j o r i t y  was used, and i t i s n o t known  whether slower procedures would show any d i f f e r e n t e f f e c t s  i n the  i n s t a n c e s i n which  slow p r e c i p i t a t i o n may occur, (e.g. 0.05 mole%  Cdl  i n which s u p e r s a t u r a t i o n occurs when the r a p i d  doped sample,  2  procedure i s used;  see d i s c u s s i o n  Polarization  :-  that  I t has been observed by s e v e r a l  a f t e r the a p p l i c a t i o n  polarized, the  Effect  o f an e l e c t r i c f i e l d ,  see F i g . ( 9 . a ) .  polarization  section).  Qualitatively  decreases w i t h i n c r e a s i n g  workers*'  an i o n i c c r y s t a l gets  i t i s a l s o observed temperature.  The  o f the sample decreases w i t h time a f t e r t h e a p p l i c a t i o n f i e l d u n t i l the sample i s f u l l y p o l a r i z e d . E.M.F. w i t h time i s shown d i a g r a m a t i c a l l y  The v a r i a t i o n  o f apparent  i n F i g . (9.b). effects  the p o l a r i z a t i o n may be r e p r e s e n t e d by an E.M.F. i n s i d e  which  i s n o t immediately changed at t h e i n s t a n t  E.M.F., s o t h a t applied  the p o l a r i z a t i o n  E.M.F. i n s t e a d  of reversing  E.M.F. i s momentarily  assumes  the c r y s t a l , the applied  added t o t h e  o f opposing i t .  Thus i n o r d e r t o f i n d the c o n d u c t i v i t y the mean o f the l a s t  conductivity  o f the e l e c t r i c  The procedure adopted t o e l i m i n a t e p o l a r i z a t i o n that  that  and f i r s t  o f an u n p o l a r i z e d  sample,  r e a d i n g (before and a f t e r r e v e r s i n g the  p o l a r i t y ) was taken i n t h i s work. Blank Run :-  U s i n g a p i e c e o f t e f l o n o f about p e l l e t s i z e , b l a n k  runs were made from time t o time  ( o f about f o u r months i n t e r v a l ) i n  order t o check the i n t e r n a l r e s i s t a n c e run  i s shown i n F i g .  (10).  o f the apparatus.  An i l l u s t r a t i v e  27 Fig. 9 Polarization  effect in ionic crystal  Fig.  (9.a)  S i t u a t i o n at A  S i t u a t i o n at B.  P o l a r i z a t i o n decreases f i e l d s i n s i d e p e l l e t , decreases apparent conductance.  Fig.  P o l a r i z a t i o n increases f i e l d , i n c r e a s e s apparent conductance,  (9.b)  A  Time  (Min.)  28  The b l a n k r e s i s t a n c e was a t room temperature  at l e a s t  10  times h i g h e r than the h i g h e s t r e s i s t a n c e measured f o r a p e l l e t or a c r y s t a l , and at a l l h i g h e r temperatures t h e r a t i o was much l a r g e r . Thus t h e l i m i t t o which the measurements c o u l d be made w i t h apparatus i s about room  temperature.  this  10  Fig. Conductivity plot with results  f o r b l a n k run compared f o r pure KI p e l l e t  G  G  0 0  o I—I  <H <D +->  G  0  G  —r oo l  -  i  i  i—I  I  , ds . (1 o)  0 i  o  Soq  to  R E S U L T S  30  Two are observed below, one  distinct  r e g i o n s A and B o f d i f f e r e n t  i n each type o f pure and doped KI,  o f these r e g i o n s does not  correspond  activation  ( s i n c e , as d i s c u s s e d to any r e g i o n p r e v i o u s l y  known i n an a l k a l i h a l i d e , the numerals, I , I I , I I I and i n d i s c u s s i n g them).  f o r v a r i o u s treatments The  IV are  avoided  T y p i c a l graphs f o r each type o f sample s t u d i e d  are shown i n F i g u r e ( 6 ) ^  (17-19).  energies  Graphs showing the changes i n b e h a v i o u r  o f a s i n g l e c r y s t a l are a l s o shown i n F i g u r e s  r e s u l t s are summarised i n t a b l e 3.  The  a b s o l u t e value  of  s p e c i f i c c o n d u c t i v i t y at 300°C from d i f f e r e n t i n v e s t i g a t i o n s i s t a b u l a t e d i n t a b l e 4. The  values of o  sp  i n r e g i o n A may  i n g e n e r a l be g i v e n  limits  o f e r r o r ± 10%, but doped samples were v e r y s e n s i t i v e t o the h i s t o r y the p e l l e t ,  and sometimes show e r r a t i c v a r i a t i o n s w e l l o u t s i d e t h i s  range.  sample c o n t a i n i n g 0.05  The  shift in a a  sp  at 476°K  i n c r e a s e s by  c o n t a i n i n g 0.10 The  pellets,  runs two  on two  showed a c o n s i d e r a b l e  a f a c t o r o f 6 on temperature c y c l i n g . mole% and  0.25  mole% C d l  eV.  The  of  Other samples  d i d not show t h i s  2  value  behaviour.  i s g e n e r a l l y r e l i a b l e t o ± 0.02  eV.  Eg gave r a t h e r more s c a t t e r e d v a l u e s f o r pure  f o r which l i m i t s o f ± 0.06 The  2  (203°C) on temperature c y c l i n g .  a c t i v a t i o n energy  and Eg t o ± 0.03  mole% C d l  of  tabulated results  s h o u l d be  are mostly  assigned.  averages o f t h r e e or f o u r  o r t h r e e d i f f e r e n t p e l l e t s ; f o r the s i n g l e c r y s t a l , i n  r u n s , the f i r s t  c r y s t a l showed a s m a l l change i n r e g i o n A on  n i g h t h e a t i n g , w h i l e the second showed v i r t u a l l y no For the p e l l e t s , the r e g i o n B c o n t i n u e d A r r h e n i u s p l o t down t o room temperature, conductivity levelled  o f f at about 60°C.  over-  change.  l i n e a r on  the  but f o r s i n g l e c r y s t a l s  the  T a b l e 3 g i v e s b o t h the a c t u a l  31  c o n d u c t i v i t y a t room temperature and the e x t r a p o l a t e d v a l u e from the r e g i o n B p l o t between 60°C and 23°C, the l a t t e r b e i n g needed f o r comparison w i t h the r e s u l t s on p e l l e t s . TABLE 3 KI  476°K(107T=2.1)  sample  10 a 10  (ohm cm~ ) 1  sp  296°K(107T=3.37) 1  10.1a lh  _  (ohm an ) 1  >Tr  sp  A c t i v a t i o n Energy  E. (eV.) E„ (eV.)  1  v  _  A  1  B  Measured E x t r a p o l a t e d Pure c r y s t a l , untreated  1.2  3.0  0.54  0.96  0.57  Pure c r y s t a l , annealed  1.8  1.9  0.038  0.96  0.89  Pure c r y s t a l , strained  0.66  1.5  0.43  0.87  0.60  Pure p e l l e t  5.80  1.2  1.14  0.38  Doped p e l l e t , 0.05 mole% C d l  140  3.0  1.20  0.48  Doped p e l l e t , 0.10 mole% C d l  330  2.9  1.33  0.66  Doped p e l l e t , 0.25 mole% C d l  380  0.5  1.45  0.75  TABLE 4 Comparison w i t h p r e v i o u s r e s u l t s KI  sample  Reference  Temperature range °C  a  (ohm cm ) 1  at Single  crystal  1  E  A  (eV.)  300°C  Lehfeldt  (250 - 378)  1.00 x 1 0 "  8  0.82  Baijal  ( 92 - 330)  3.18 x 1 0 ~  7  0.817  Single c r y s t a l  P r e s e n t work  ( 97 - 203)  5.91 x 10"  Pressed p e l l e t  P r e s e n t work  ( 97 - 203)  4.91 x 1 0 "  Pressed  pellet  9  8  0.96 1.14  32  Fig. 11 Conductivity plot  -4  - i  -12  J  2.0  f o r pure KI  2.5  pellet  3.0  10 /T(° K) 3  3.5  3.0 10 /T(°K) 3  3.5  34  Fig.  13  Conductivity plot  f o r doped KI  CO.10 mole% C d l J  -4  -12  -  i  J  2.0  2.5  3.0  10 /TC°K) 3  3.5  35  10 /T (°K) 3  36  10 /T(°K) 3  37  Fig.  16  P l o t of c o n d u c t i v i t y versus impurity ( t h i s work)  content  38  Fig. Conductivity plot  17 of single  crystal  (untreated) -4 _  -6  -12  2.0  3.0  2.5  10 /T(°K) 3  3.5  39  Fig.  18  Conductivity plot crystal (heated  of single  overnight)  -6  -8 Region A  O -J  -10  Region B  -12  J  2.0  3.0  10 /T(°K) 3  3.5  40 Fig. Conductivity plot  19 of single  (strained)  -4 ,  crystal  D I S C U S S I O N  41  As mentioned e a r l i e r , the c o n d u c t i v i t y p l o t o f KI i n the range 200°C t o 23°C d i v i d e s i t s e l f i n t o two d i s t i n c t r e g i o n s A and B. R e s u l t s i n r e g i o n A can be g i v e n a c o n v e n t i o n a l i n t e r p r e t a t i o n i n terms of conduction  c o n t r o l l e d by c a t i o n v a c a n c i e s whose c o n c e n t r a t i o n i s  governed by a l i o v a l e n t i m p u r i t i e s t o g e t h e r w i t h a s s o c i a t i o n and precipitation  effects.  Region A (a)  Absolute  values o f a  and i m p u r i t y content:  The a b s o l u t e  v a l u e o f c o n d u c t i v i t y at 300°C i s compared w i t h p r e v i o u s l y o b t a i n e d and i s g i v e n i n t a b l e 4. is  1 x 10 ohm cm 8  x  1  .  L e h f e l d t ' s * value of a  B a i j a l obtained f o r a  v a l u e than L e h f e l d t by a f a c t o r o f 30.  of single  values  crystal  f o r a pure p e l l e t  a greater  In t h i s work the v a l u e o f a sp  at 300°C was c a l c u l a t e d from e x t r a p o l a t e d l i n e i n b o t h samples c r y s t a l and pure p e l l e t ) .  (single  The v a l u e f o r a s i n g l e c r y s t a l i s l e s s by a  f a c t o r o f 6.5 than L e h f e l d t ' s v a l u e , and the v a l u e f o r a pure p e l l e t i s l e s s by a f a c t o r o f 6 than B a i j a l ' s v a l u e .  The d i s c r e p a n c i e s may be  a t t r i b u t e d t o the p u r i t y o f t h e specimen, s i n c e the r e g i o n under i n v e s t i g a t i o n i s the i m p u r i t y r e g i o n , s i m i l a r t o the w e l l - i n v e s t i g a t e d i m p u r i t y r e g i o n o f sodium c h l o r i d e .  The s p e c i f i e d i m p u r i t y l i m i t s  o f my sample  along w i t h B a i j a l ' s i s g i v e n i n the appendix ( t a b l e s 8 and 9) r e s p e c t i v e l y , but the p u r i t y o f L e h f e l d t ' s sample i s n o t known. The v a l u e s o f a  at 203°C i n d i f f e r e n t samples (see t a b l e 3)  o f pure and doped K I , suggests  s a t u r a t i o n a t about 0.1 mole%  (1000 ppm.).  I t i s a l s o seen from the graph o f c o n d u c t i v i t y versus i m p u r i t y  content  (see F i g u r e 16), t h a t the c o n d u c t i v i t y i s l i n e a r up t o 0.1 mole% Cd From the values o f a  .  a t 203°C o f doped and undoped samples, i t appears  42  that impurity  c o n t e n t s i n pure p e l l e t  and s i n g l e c r y s t a l are about  18 ppm. and 4 ppm. r e s p e c t i v e l y .  Comparison o f t h e former f i g u r e  w i t h s p e c i f i c a t i o n o f AR m a t e r i a l  i n d i c a t e s t h a t the e x p e r i m e n t a l  v a l u e i s about f i v e times l e s s than maximum i m p u r i t y the  limits  from  s p e c i f i c a t i o n (about 100 ppm.). (b)  f o r pure samples and U : The a c t i v a t i o n energy o f  c o n d u c t i v i t y E ^ i n r e g i o n A was c a l c u l a t e d from the s l o p e s ponding graphs and the v a l u e s have been t a b u l a t e d  i n t a b l e 4.  case o f a s i n g l e c r y s t a l E ^ i s about 0.96 eV. and t h a t pellet  1.14 eV. w i t h i n the l i m i t s  greater given  than L e h f e l d t  o f corresI n the  o f a pure  o f 0.02 eV., e i t h e r v a l u e b e i n g  and B a i j a l ' s r e s u l t s .  The a c t i v a t i o n e n e r g i e s  i n t a b l e 4 have been c a l c u l a t e d from the s l o p e  o f log(a  T) versus sp  T . l  The same method o f c a l c u l a t i o n r a i s e s the L e h f e l d t  v a l u e s by about 0.04 eV. the  E ^ i n the case o f s i n g l e c r y s t a l i s p r o b a b l y  energy needed f o r the motion o f c a t i o n vacancy  impurity  and B a i j a l ' s  ( U ) , s i n c e the  content i n t h i s case i s p r o b a b l y low enough f o r a s s o c i a t i o n and  p r e c i p i t a t i o n e f f e c t s t o be n e g l i g i b l e . (c)  The  E f o r impure samples ; A,  a s s o c i a t i o n and p r e c i p i t a t i o n :  e f f e c t o f a s s o c i a t i o n energy and heat o f p r e c i p i t a t i o n are p r o b a b l y  responsible table 3).  f o r t h e h i g h e r a c t i v a t i o n energy i n these samples (see The E  values f o r pure p e l l e t  and 0.05 mole% C d  + 2  doped  p e l l e t p r o b a b l y show t h e e f f e c t o f a s s o c i a t i o n uncomplicated by p r e c i p i t a t i o n and hence g i v e the mean a s s o c i a t i o n energy f o r i m p u r i t i e s i n AR m a t e r i a l  as 2(1.14 - 0.96) equal t o 0.36 eV. and the v a l u e f o r C d  i n 0.05 mole% sample as 2(1.20 - 0.96) equal t o 0.48 eV. comparable w i t h r e p o r t e d  These a r e  values o f a s s o c i a t i o n energies i n a l k a l i  as quoted i n the i n t r o d u c t i o n t o t h i s t h e s i s .  + 2  halides  43  At h i g h e r i m p u r i t y c o n t e n t , t h e r e i s evidence ation  for precipit-  effects. Thus F i g u r e  (15) shows t h a t the l i n e  f o r the 0.25 mole%  sample a c t u a l l y c r o s s e s t h a t f o r the 0.05 mole% sample as T T h i s suggests  decreases.  t h a t the 0.05 mole% s o l u t i o n i s s a t u r a t e d at the c r o s s i n g -  p o i n t a t 140°C and t h a t the s l o p e o f the 0.25% l i n e c o n t a i n s the f u l l e f f e c t o f the heat  of solution.  We can t h e r e f o r e c a l c u l a t e AH soln  from the d i f f e r e n c e between t h i s s l o p e and t h a t o f t h e 0.05 mole% sample which shows the f u l l  a s s o c i a t i o n e f f e c t without  precipitation.  AH  + Ea/2 + U) - (Ea/2 + U)  (19)  = (AH  s o l n  s Q l n  = 1.45 - 1.20 = 0.25 eV.  The 0.05 mole% sample i s e v i d e n t l y s u p e r s a t u r a t e d below 140°C, which probably  e x p l a i n s why r e s u l t s a t t h i s i m p u r i t y content were r a t h e r  more e r r a t i c than most other r e s u l t s , as mentioned i n the r e s u l t s section. AH  . may be e s t i m a t e d soln  (a)  1  i n two o t h e r ways from t h e r e s u l t s :J  I f the c r o s s i n g - p o i n t o f the 0.25 mole% l i n e  and the  0.1 mole% l i n e i s taken t o g i v e the temperature at which the s o l u b i l i t y is  0.1 mole%, we have :188°C, s o l u b i l i t y = 0.1 mole% 140°C, s o l u b i l i t y =0.05 mole%  A p p l i c a t i o n o f the Van't H o f f e q u a t i o n t o these r e s u l t s g i v e s A H 0.24 eV.  s o  j  n  =  44  (b) on s o l u t i o n  I f i t i s assumed t h a t t h e r e i s v e r y l i t t l e  (except f o r c o n f i g u r a t i o n a l entropy)  solubility = e "  whence AH Region  . = 0.27 soln  A H  soln  / k T  = 5 x 10'"  entropy  then  at 140°C,  eV.  B: The  e x i s t e n c e o f r e g i o n B found i n t h i s work r e p r e s e n t s unusual  b e h a v i o u r and has not p r e v i o u s l y been observed i n any a l k a l i There i s a sharp d e c r e a s e i n a c t i v a t i o n energy The  charge  halides.  from r e g i o n A t o r e g i o n B.  a c t i v a t i o n energy i n r e g i o n B i s c o n s i d e r a b l y l e s s than the  energy  needed f o r the motion o f c a t i o n v a c a n c i e s i n the b u l k , which f o r KI i s between 0.86  and 0.96  eV.  as d i s c u s s e d above.  Now  i n any  range, below the i m p u r i t y r e g i o n , the a c t i v a t i o n energy  temperature  of conductivity  i s expected t o be g r e a t e r than t h i s v a l u e , s i n c e the a c t i v a t i o n below t h i s temperature  range  i s composed o f two  terms, one  energy  a s s o c i a t e d w i t h the m o b i l i t y o f c a t i o n v a c a n c i e s and another arising  energy  energy  from the a s s o c i a t i o n o f v a c a n c i e s w i t h i m p u r i t i e s o r from the  heat o f s o l u t i o n o f i m p u r i t i e s . n e g a t i v e , but i s u s u a l l y p o s i t i v e  j  c  o  u  ld  o f course p o s s i b l y be  and has been f a i r l y  as p o s i t i v e i n the p r e s e n t case from the r e s u l t s  clearly  established  f o r region A).  Dreyfus  9 and Nowick  have observed h i g h a c t i v a t i o n energy  as expected f o r the  c o n d u c t i v i t y below the i m p u r i t y r e g i o n f o r NaCl doped w i t h C d C l , 2  see F i g u r e (5) and have i n t e r p r e t e d t h e i r r e s u l t s n i c e l y i n terms o f multivalent  c a t i o n i m p u r i t y i n the system.  Results obtained i n t h i s  work are not s i m i l a r t o Dreyfus and Nowick's r e s u l t s f o r NaCl and  are  not amenable t o c o n v e n t i o n a l i n t e r p r e t a t i o n i n terms o f c a t i o n v a c a n c i e s in  the b u l k .  45  The  c o n s i d e r a b l y lower a c t i v a t i o n energy observed here may  be i n t e r p r e t e d i n terms o f v a c a n c i e s m o b i l i t y , such  i n a region o f unusually high  as d i s l o c a t i o n s and g r a i n b o u n d a r i e s .  a r i s e p a r t l y from a lower  The e f f e c t may  a c t i v a t i o n energy f o r motion o f v a c a n c i e s  i n these r e g i o n s and p a r t l y from a vacancy c o n c e n t r a t i o n i n these r e g i o n s which i n c r e a s e s w i t h d e c r e a s i n g Let  temperature.  the c o n c e n t r a t i o n o f c a t i o n and anion v a c a n c i e s i n the  c o r e o f t h e d i s l o c a t i o n or g r a i n boundary be j  and j  respectively.  These c o n c e n t r a t i o n s are governed by ah e q u i l i b r i u m s i m i l a r t o t h a t for bulk defects,  j  +  j _ =  A exp-(W* + W~)/kT  =  (20).  A exp (-Wj/kT)  (21)  where Wj i s p r o b a b l y very much l e s s than t h e v a l u e W f o r b u l k d e f e c t s . T h i s e q u i l i b r i u m i s r e l a t e d t o the b u l k e q u i l i b r i u m by the "space18 charge"  e f f e c t s d i s c u s s e d by Lehovec  i n r e l a t i o n t o s u r f a c e s and l a t e r  19 by  L i d i a r d et a l  f o r d i s l o c a t i o n s which, l i k e s u r f a c e s , a c t as sources  and s i n k s o f v a c a n c i e s . The ing  o r i g i n o f space-charge may be v i s u a l i s e d from the f o l l o w -  consideration.  C o n s i d e r an i d e a l c r y s t a l without  any l a t t i c e d e f e c t .  Now i f t h e energy o f f o r m a t i o n o f a c a t i o n vacancy i s l e s s than the energy o f f o r m a t i o n o f an anion vacancy, i n i t i a l l y more c a t i o n v a c a n c i e s w i l l be formed and m i g r a t e will  leave a p o s i t i v e  i n t o the i n t e r i o r than anion v a c a n c i e s .  charge at the s u r f a c e o f the c r y s t a l .  space-charge d i s c o u r a g e s  This  The r e s u l t i n g  the e m i s s i o n o f f u r t h e r c a t i o n v a c a n c i e s and  46  encourages t h e e m i s s i o n o f anion v a c a n c i e s .  Assuming the b u l k o f the  c r y s t a l t o be e l e c t r i c a l l y n e u t r a l the p o s i t i v e charge q on the s u r f a c e i s b a l a n c e d by an equal and o p p o s i t e n e g a t i v e charge c l o u d p e n e t r a t i n g some d i s t a n c e i n t o the c r y s t a l . Now and  j_- j  +  = q  (22)  combining t h i s w i t h e q u a t i o n (21) j  whence If  q  2  j  (4  +  J ) =  +  +  = h  »  (q  2  A expf-Wj/kT)  + 4A  exp -Wj/kT)* - q 5  4 A exp(-Wj/kT), t h i s reduces t o  j  = A exp(-Wj/kT,)/q  +  From Lehovec's  account, 2  (24)  one can w r i t e q as  q = (2 e e k T Z e ) exp [ ( V / 2 ) %  o  where  (23)  -(W/4)]/kT  (25)  i s the p o t e n t i a l d i f f e r e n c e between b u l k and s u r f a c e produced  by the space-charge e f f e c t  C  and i s g i v e n by  = (W - WJ/2  (26)  where Z i s the number o f molecules f o r m a t i o n o f anion v a c a n c i e s  p e r u n i t v o l , W_  and e o  i s the energy o f  i s the d i e l e c t r i c c o n s t a n t : '  e i s the  permittivity of material. Thus j  +  = A (2 e e . k T Z e o  =  (constant)  2  ) ^ exp [ (W/4) - (VJ/2)-Wj ] /kT  exp (Ej/kT)  S i n c e f o r a l k a l i h a l i d e s W/4  (27)  (28) ~ 0.5 eV. and V" i s l i k e l y t o be n e g a t i v e  47  (energy o f f o r m a t i o n o f anion vacancy g r e a t e r and  s i n c e Wj may  be  than t h a t o f c a t i o n v a c a n c y ) ,  q u i t e s m a l l , i t i s r e a s o n a b l e t o expect Ej t o  p o s i t i v e , and hence t o make a n e g a t i v e c o n t r i b u t i o n to the  be  activation  energy o f c o n d u c t i o n . These e f f e c t s become c o m p l i c a t e d i n doped samples because these structures  ( g r a i n b o u n d a r i e s and  d i s l o c a t i o n s ) i n t e r a c t with  impurities.  19 At h i g h  temperature t h e r e  i s Very l i t t l e  a l i o v a l e n t c a t i o n i c i m p u r i t i e s may d i s l o c a t i o n and  effect  b o u n d a r i e s p r o b a b l y s e r v e a l s o as p l a c e s  the  divalent impurity  r a i s e s the  at low  conductivity blocking the  of unusually (table 3).  conductivity  from 3.0 i n 0.25  x 10~  1If  ohm" ™" 1  mole% sample The  0.25  h i g h m o b i l i t y , but  f o r 0.05  (see t a b l e  v a l u e o f 0.57  2 +  .  on grain  the  (3)]  s i g n o f the  The  since charge  concentration  heavy doping reduces  l a t t e r e f f e c t probably represents  mole% C d 1  and  [see t a b l e  c a t i o n vacancy  o f d i f f u s i o n paths w i t h p r e c i p i t a t e s .  sample c o n t a i n i n g  temperature  charge  Dislocations  temperature r e v e r s e s  The  low  at which p r e c i p i t a t e s aggregate.  on the g r a i n b o u n d a r i e s l e a d i n g t o a h i g h i n the r e g i o n  at  cause the s i g n o f the  g r a i n boundaries to reverse.  Doping at f i r s t  , but  This  the  the  i s c l e a r l y noted i n  conductivity  mole% sample t o 0.5  at 296°K changes x 10~  lk  ohm" ™" 1  1  3).  eV.  (see t a b l e 3)  f o r the r e g i o n  B activation  energy i n s i n g l e c r y s t a l s , p r o b a b l y r e f e r s t o motion o f v a c a n c i e s i n i s o l a t e d d i s l o c a t i o n s and f o r a pure p e l l e t  low  angle b o u n d a r i e s , w h i l e the v a l u e o f 0.38  corresponds to motion i n l a r g e angle b o u n d a r i e s .  I f i t i s assumed the the 10  j  i s independent o f temperature, so  e x p e r i m e n t a l a c t i v a t i o n energy i s a m o b i l i t y term, and  1 3  place  sec"  1  i n equation  o f n ) the  eV.  (4)  (j  concentration  +  =  (4 j  e r 2  +  2 Q  A/kT)  that  taking A ~  exp(-U/kT) (with  j  o f charge c a r r i e r s i n a pure p e l l e t i s  +  in  48  about 6.5 x 1 0  1 0  p e r cm  3  which leads f o r a g r a i n s i z e o f lOu t o a  d e f e c t c o n c e n t r a t i o n o f about 1 0  7  d e f e c t s p e r cm  2  o f g r a i n boundary.  In a s i n g l e c r y s t a l the charge c a r r i e r s ' c o n c e n t r a t i o n i s s i m i l a r l y c a l c u l a t e d as about 9 x 1 0 c m 16  c r y s t a l i s o f course  3  .  The d i s l o c a t i o n d e n s i t y i n the  very u n c e r t a i n .  I f the c r y s t a l i s assumed t o  have i s o l a t e d d i s l o c a t i o n s at about one p e r square m i c r o n , then the concentrations  o f jogs i n the d i s l o c a t i o n s becomes more than one p e r  o  A-% on t h i s b a s i s ; b u t i f the c r y s t a l i s broken up i n t o mosaic b l o c k s o f about l u s i z e , then jogs are about 60 A apart i n the low angle boundaries. the  This i s s t i l l  assumption r e g a r d i n g  t h a t the v a l u e  a h i g h v a l u e , and p r o b a b l y  i n d i c a t e s that  the a c t i v a t i o n energy i s i n c o r r e c t , and  o f 0.57 eV. c o n t a i n s  an energy e f f e c t i n the c o n c e n t r a -  tion j . + A s t r o n g p i e c e o f evidence of d i s l o c a t i o n i s obtained  from the c o n d u c t i v i t y runs on s i n g l e c r y s t a l s .  As f o r pure and doped KI p e l l e t s , single  t h a t r e g i o n B i n v o l v e s an e f f e c t  r e g i o n A and B are i d e n t i f i e d i n  c r y s t a l s , but r e g i o n B e s s e n t i a l l y d i s a p p e a r s  heating  and i s r e p l a c e d by an e x t e n s i o n  erature  (see F i g . 1 8 ) ;  o f r e g i o n A down t o room temp-  but r e g i o n B reappears on s t r a i n i n g the c r y s t a l .  In a d d i t i o n t o t h i s important  e f f e c t o f s t r a i n i n g i n r e g i o n B, i t i s  n o t e d t h a t s t r a i n had a very s m a l l e f f e c t table 3).  These e x p e r i m e n t a l 1)  identical.  on o v e r n i g h t  observations  The mechanisms f o r c o n d u c t i o n  on r e g i o n A (see F i g . 19 and suggest t h a t i n r e g i o n A and B a r e n o t  C o n d u c t i o n i s n o t governed p r i m a r i l y by d i s l o c a t i o n and  g r a i n b o u n d a r i e s i n r e g i o n A.  49  2)  Overnight  h e a t i n g reduces the c o n c e n t r a t i o n o f d i s l o c a t i o n  so t h a t the a c t i v a t i o n energy becomes t h a t f o r b u l k motion o f v a c a n c i e s . 3) m i g r a t i o n path  S t r a i n i n g i n t r o d u c e s d i s l o c a t i o n s and thus r e s t o r e s the o f low  a c t i v a t i o n energy.  A P P E N D I X  50  TABLE 1 E l e c t r i c a l C o n d u c t i v i t y o f KI P e l l e t  (23°C - 203°C)  t°c  T°K,  10 /T°K  203  476  2.10  7.53  185  458  2.18  7.07  154  427  2.34  9".90  136  409  2.44  9". 35  111  384  2.60  10.35  101  374  2.67  10.10  84  357  2.80  lT.63  74  347  2.88  11.45 .  56  329  3.04  fl.12  23  296  3.37  12.50  3  Log (ggpT)  TABLE 2 Electrical  C o n d u c t i v i t y o f KI Doped P e l l e t  (0.05 mole% C d l ) ( 2 3 ° - 215°  10 /T°K  2  t°c  T°K  215  488  2.05  5". 287  187  460  2.17  6.487  162  435  2.30  7.461  140  413  2.42  "8.827  115  388  2.58  "8.099  97  370  2.70  9". 136  75  348  2.87  10.363  60  333  3.00  11.980 .  40  313  3.20  11.599  23  296  3.37  11.000..  3  Log(a  sp  T)  51  TABLE 3 Electrical  C o n d u c t i v i t y o f KI -Doped P e l l e t  (0.1 mole% C d l ) (23° - 212°C)  t°c  T°K  10 /T°K-  212  485  2.06  5.550  186  459  2.18  6. 752  168  441  2.27  6.058  145  418  2.39  7.166  113  380  2.59  9". 921  82  355  2.82  10". 084  65  338  2.95  10.194  52  325  3.07  il.845  23  296  3.37  12.920  3  Log  (o^pT)  TABLE 4 E l e c t r i c a l Conductivity  o f KI Doped P e l l e t  (0.25 mole% C d i p ( 2 3 ° - 200°C)  t"c  ;T°K'  > /T°K  200  473  2.11  "5.150  185  458  2.18  "6.729  166  439  2.28  7.818  150  423  2.36  7.166  129  402  2.49  "8.315  108  381  2.62  9.425  91  364  2.75  f0.662  74  347  2.88  TO.076  3  Log •  (a. ' sp  Continued  52  Table 4  (continued)  65  338  2.96  11.784  50  323  3.10  11.183  23  296  3.37  12.600  TABLE 5 E l e c t r i c a l C o n d u c t i v i t y o f K I S i n g l e C r y s t a l (Untreated)(23° - 200°C) t°c  T°JC  10 /T°K  200  473  2.11  "8.720  186  459  2.18  "8.436  162  435  2.30  9.664  144  417  2.40  9.243  127  400  2.50  10.804  111  384  .2.60  10.413  95  368  2.72  10.104  76  349  2.80  fl.639  65  335  2.98  11.253  38  311  3.21  11.100  23  296  3.37 .  12.950  3  ;  Log  (q^T)  TABLE 6 Electrical  C o n d u c t i v i t y o f Annealed (Overnight) K I S i n g l e C r y s t a l (23° - 205°C)  t°c  T°K  10 /T°K:  205  478  2.09  "8.500  191  464  2.16  "8.749  175  448  2.23  "8.308  151  424  2.36  9".572  3  Log  (q  g p  T)  Continued  Table 6  (continued)  137  410  2.44  "9.176  125  398  2.51  10.843  116  389  2.57  10.572  109  382  2.62  10.405  98  371  2.69  10.072  .86  359  2.79  11.631  60  333  3.00  12.798  45  318  3.14  12.550  23  296  3.37  12.770  TABLE 7 E l e c t r i c a l Conductivity  o f S t r a i n e d KI S i n g l e C r y s t a l  t°c  T°K-  10 /T°X'  201  474  2.11  "8.431  172  445  2.24  9". 775  152  425  2.35  9". 305  138  411  2.43  9.067  124  397  2.52  10.680  107  380  2.63  10.330  94  367  2.72  11.989  80  353  2.83  11.698  61  334  2.99  11.169  45  318  3.14  F2.918  23  296  3.37  12.619  3  Log ( q ^  1  54  TABLE 8 S p e c i f i c a t i o n from F i s h e r S c i e n t i f i c Company o f KI used i n t h i s work C e r t i f i e d A.C.S. Potassium I o d i d e C r y s t a l  Appearance  and odor  Transparent,  colorless  c r y s t a l , odorless Insoluble matter  0.001%  Sulphate  0.0008%  (SO^)  Loss on d r y i n g at 150°C  0.04%  pH o f a 5% s o l u t i o n at 25°C  6.70  C h l o r i d e and bromide  0.005%  Iodate  (as CI)  (10 )  0.0003%  N i t r o g e n compounds Phosphate  (as N)  0.0005%  (PO^)  0.000%  Barium (Ba)  0.000%  C a l c i u m magnesium and R 0 2  Heavy metals  (as Pb)  3  precipitate  0.000% 0.0000%  I r o n (Fe)  0.0002%  Sodium (Na)  0.0013%  55  TABLE 9 from M a l l i n c k r o d t Chemical Works o f KI used i n B a i j a l ' s work  Specification  Potassium I o d i d e A r (ACS) C r y s t a l s  Appearance  Transparent,  and odor  crystal,  odorless  Insoluble matter  0.005% max.  S u l p h a t e • (SO )  0.005% max.  Loss on D r y i n g  0.20%  pH o f a 5% s o l u t i o n  (25?C)  C h l o r i d e and bromide  as (CI)  Iodate ( I 0 )  max.  6.0 - 9.2 0.10  max.  To pass t e s t  3  colorless  (limit  0.0003%) N i t r o g e n compounds Phosphate  (as N)  (PO^)  0.001% max. 0.001% max.  Barium (Ba)  0.002% max.  C a l c i u m magnesium and R203 p r e c i p i t a t e  0.005% max.  Heavy metals  0.005% max.  (as Pb)  I r o n (Fe)  0.0003% max.  Sodium (Na)  0.005% max.  S i e v e t e s t #20 U.S. s t a n d a r d  25% max. through  about  56  BIBLIOGRAPHY  1.  W. L e h f e l d t , Z., P h y s i k , 85, 717, 1933.  2.  F.S. Stone, "Chemistry Butterworth's  o f the S o l i d S t a t e " , (ed. W.E. G a r r e r ,  S c i . Pubs.,  1955) Chapt. 2.  3.  Smekal, Z., E l e c t r o c h e m ,  4.  W. J o s t , D i f f u s i o n , Academic P r e s s , New York, 1952, Chapt. 4.  5.  L.G. H a r r i s o n , "Theory o f S o l i d Phase K i n e t i c s " , i n "Comprehensive Chemical  Kinetics"  34, 726, 1928.  (ed. C.H. Bamford  § C.F.H. T i p p e r , E l s e v i e r ,  i n course o f p u b l i c a t i o n ) V o l . 2, Chapt. 5. 6.  ' E. Koch and C. Wagner, Z. P h y s i k . Chem., B38 (1937) 295.  7.  C. Wagner and P. Hantlemann, J . Chem. Phys., 1_8, 72, 1952.  8.  H.W.  Etzel  9.  R.W.  Dreyfus  10.  J.R. R e i t z and J . L . Gammel, J . Chem. Phys., 19_, 894, 1951.  11.  A.B. L i d i a r d , Phys. Rev., 94, 29, 1954.  12.  J . F . Laurent and J . Benard, J . Phys. Chem. S o l i d s , _3» > 1957;  and R.J. Maurer, J . Chem. Phys., 18, 1003, 1950. and A.S. Nowick,  Phys. Rev., 126, 1367, 1962.  7  7_, 218, 1958. 13.  D. E c k l i n , C. N a d l e r e t J . R o s s e l , H e l v . Phys. A c t a , 37, 692, 1964.  14.  T.M. H a r r i n g t o n and L.A.K. S t a v e l e y , J . Phys. Chem. S o l i d s , 25_, 921, 1964.  15.  M.D. B a i j a l , Ph.D. T h e s i s , 1964.  16.  E. S a n d e l l , " C o l o r i m e t r i c D e t e r m i n a t i o n o f T r a c e s o f M e t a l s " , I n t e r s c i e n c e Pub., 1944, p . 172.  17.  C.E. Skov and E.A. P e a r i s t e i n , Phys. Rev. 137, 1483, 1965.  K. Lehovec, J . Chem. Phys., 21_, 1123, 1953. J.D. E s h e l b y , C.W.A. Newey, P.C. P r a t t and A.B. L i d i a r d , P h i l . Mag., 3, 75, 1958.  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0059992/manifest

Comment

Related Items