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Electrical properties and defect structure of cuprous chloride Prasad, Mahendra 1973

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ELECTRICAL PROPERTIES AND DEFECT STRUCTURE OF CUPROUS CHLORIDE  by  MAHENDRA PRASAD  M.Sc.  The University of B r i t i s h Columbia, 1969  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of CHEMISTRY  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA February, 1973  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 o f the r e q u i r e m e n t s f o r  an a d v a n c e d d e g r e e at tin'; U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e I f u r t h e r agree t h a t permission f o r s c h o l a r l y p u r p o s e s may by h i s r e p r e s e n t a t i v e s .  for extensive  and  study.  copying of t h i s t h e s i s  be g r a n t e d by the Head o f my Department o r I t i s understood that copying or p u b l i c a t i o n  o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t written  permission.  Department o f  P^rrxUWy  The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, Canada  Date  my  ii  ABSTRACT  Measurements of e l e c t r i c a l conductivity (a), thermoelectric power (6) and transport numbers i n the temperature range 24 - 240°C have been made on CuCl i n the pure state and a f t e r reaction with chlorine to varying extents.  Attempts to measure the H a l l E f f e c t gave negative  r e s u l t s for a l l samples.  Data for pure CuCl confirm e a r l i e r reports that conduction i s e l e c t r o n i c (positive hole) at low temperatures and i o n i c (cation i n t e r s t i t i a l s ) at higher temperatures  (above 160°C, f o r our samples).  For the  low-temperature range, the s i g n i f i c a n c e of various reported apparent a c t i v a t i o n energies of conduction (E ) has been c l a r i f i e d i n the present 0  work i n terms of an acceptor l e v e l at E. = 0.51 eV above the valance band A (cation vacancy as trapping s i t e ) . behaviour, E  = E^.  Less pure samples show "uncompensated" behaviour,  being close to E /2.  ways:  The purest samples show "compensated"  % i o n i c conduction has been estimated i n three  from the conductivity data, from c l a s s i c a l gravimetric transport  number measurements, and from the 6 - T curve (which has not previously been interpreted, although measurements of 0 have been reported by other workers). The behaviour of s l i g h t l y - c h l o r i n a t e d CuCl (which conducts much better than pure CuCl) correlates with current interpretations of the conduction mechanism i n NiO. at a l l temperatures  Conduction i s e l e c t r o n i c ( i . e . not ionic)  (24 - 240°C).  maximum at about 100°C.  The 9 - T curves have a pronounced  They can be explained, and correlated with a  data, only on the basis of two conduction mechanisms i n p a r a l l e l , by holes  iii  i n the valence band and electrons "hopping" at the acceptor l e v e l with an a c t i v a t i o n energy of migration E^^ = 0.36  eV.  electron conduction predominates and E  .  = E a  conduction predominates and CuCl).  yn  At low  temperatures,  Above 100 - 110°C, hole '  = E^ (as for the lower range i n pure  An energy calculated from the r i s i n g portion of the 6 - T curve  correlates well with (E. - E ), as theory predicts i t should. A yn CuCl reacted extensively with chlorine (20 - 65% conversion to CUCI2) shows conduction phenomena believed to be those of the CuCl component of the heterogeneous s o l i d , but with E^ = 0.88 > 50% conversion) and 0.15  eV (low T, > 20% conversion).  eV (high T, Conduction i s  by holes-(contradicting an e a r l i e r suggestion from this laboratory that the higher value was  f o r cation i n t e r s t i t i a l s ) , and the higher value i s  assigned as another acceptor l e v e l , E^ = 0.88 i n t e r s t i t i a l s as hole traps.  eV, probably f o r anion  The lower value has not been f u l l y  explained. The o r i g i n of the two d i f f e r e n t trap depths, E^ = 0.51 0.88  and  eV, i s b r i e f l y considered, and i t i s suggested that the difference  between them, 0.37  eV, may  represent approximately the c r y s t a l f i e l d  s p l i t t i n g of Cu 3d t2 o r b i t a l s from Cu 3d e o r b i t a l s i n the tetrahedral s i t e symmetry of CuCl.  iv  TABLE OF CONTENTS PAGE TITLE PAGE  i  ABSTRACT  i i  TABLE OF CONTENTS  iv  LIST OF TABLES  v i i  LIST OF FIGURES  vlii  ACKNOWLEDGMENTS  x  1. 1.1  INTRODUCTION  1  E l e c t r i c a l Conductivity of Copper Chlorides  1  1.1.1 1.1.2  1  Previous Work i n this Laboratory The Need f o r Further Study of E l e c t r i c a l Conductivity i n C u C l Systems Previous Work on Pure CuCl i n Other Laboratories Scope of the Present Work x  1.1.3 1.1.4 1.2  Other Experiments Giving Information on the Nature of the Charge Carriers  6 8 11  13  Introductory page 1.2.1 1.2.2 1.2.3 1.2.4 1.3  Interpretation of Conductivity and Thermoelectric Data for an Impurity Semiconductor 1.3.1 1.3.2 1.3.3  1.4  The H a l l E f f e c t Direct Determination of Transport Numbers I n j e c t i o n or Suppression of Carriers at a MetalSemiconductor Contact Thermoelectric Power  Fermi Level and Concentration of Holes Simultaneous Conduction by Valence-Band Holes and Electrons at E^ Thermoelectric Power for a Mixed Ionic and Hole Conduction  14 19 21 27 31 31 33 37  Band Structure and Charge Carriers i n Cuprous Halides  39  1.4.1 1.4.2  39 43  Band Structure Charge Carriers  V  2. 2.1  EXPERIMENTAL Sample Preparation 2.1.1 2.1.2 2.1.3  2.2  2.3  2.4  2.5  3. 3.1  46  P u r i f i c a t i o n of CuCl Reaction of Sublimed CuCl with C l Preparation of P e l l e t s  46  2  46 48 51  Conductivity Measurements  53  2.2.1 2.2.2 2.2.3  53 55 60  Conductivity C e l l Electric Circuits Procedure  Transport Number Measurement  61  2.3.1 2.3.2  61 64  Gravimetric Method Wagner's Method  Thermoelectric Power Measurements  65  2.4.1 2.4.2 2.4.3  65 67 69  Thermoelectric Power C e l l Thermoelectric Furnace Procedure  H a l l E f f e c t Apparatus  70  2.5.1 2.5.2 2.5.3 2.5.4 2.5.5  70 72 74 76 76  Sample Holder and Heating Assembly Electrical Circuit Magnet Sample Preparation Procedure  RESULTS  78  E l e c t r i c a l Conductivity 3.1.1 3.1.2 3.1.3  E f f e c t s of Electrode M a t e r i a l , AC versus DC, and Surface Conductivity Pure CuCl Chlorinated CuCl  78 78 80 83  3.2  Thermoelectric Power  3.3  Transport Numbers  103  3.3.1 3.3.2  103 111  3.4  Gravimetric Method, and Data from Conductivity The Wagner Method Suppressing Ionic Conduction  The H a l l E f f e c t  89  121  4. DISCUSSION  123  4.1  General Interpretation of Results  123  4.2  Models of the Acceptors  128  4.3  Positions of the Acceptor Levels  129  4.4  Summary of Proposed Defect Influence on E  Structures, and  a  5.  SUGGESTIONS FOR FURTHER WORK  Their 133  135  5.1  Doping Experiments  135  5.2  Electron Paramagnetic Resonance  136  5.3  The H a l l E f f e c t  136  5.4  Thermoelectric  5.5  Calculations on Acceptor Levels  REFERENCES  Power  137 138 139  vii  LIST OF TABLES  TABLE  1.  PAGE  D.C. Conductivity of Pressed P e l l e t s of P a r t l y Chlorinated C u C l  5  2 c  2.  Comparison of Previous Results on Pure CuCl  3.  A c t i v a t i o n Energies and S p e c i f i c Conductivities  10  of Pure CuCl  82  4.  Conductivity Results of Chlorinated CuCl  84  5.  Transport Number of Pure CuCl (22.5 Volt Applied Voltage) Transport Number of Pure CuCl (0.5 Volt Applied Voltage)  6. 7.  Transport Number (CuCl^ 143^  8.  Conductivity of CuCl, . , „ and CuCl, ,. Estimated 1.0143 1.645  9. 10.  104 107 1  0  9  0  n  c  from Transport Number Data  110  Data f o r Non-ohmic Current Voltage Plot f o r Selected Temp.  112  Ionic Contribution Estimated by Wagner Method  116  vili  LIST OF FIGURES  FIGURE  PAGE  1.  Conductivity Data of Harrison and Ng  3  2.  A c t i v a t i o n Energies of d.c. Conduction i n P a r t l y Chlorinated CuCl (Harrison and Ng)  4  3.  Summary of Previous Conductivity Results  9  4.  Ionic Transport i n CuCl  19  5.  Cu 3d and CI 3p Levels  39  6.  S p l i t t i n g of d-Orbitals i n Tetrahedral F i e l d  39  7.  Atomic O r b i t a l s for Tight-binding Calculation on CuCl  42  8.  Apparatus for CuCl Sublimation  47  9.  Apparatus for Reaction of CuCl with Chlorine  49  10.  Perkin Elmer KBr P e l l e t Making Die  52  11.  Conductivity C e l l  54  12.  Guard Ring  54  13.  C i r c u i t Diagram for Conductivity Measurement  56  14.  C i r c u i t Diagram for Low  58  15.  C i r c u i t Diagram for the 200 CPS O s c i l l a t o r  59  16.  Current Versus Time Plot i n CuCl  62  17.  Thermoelectric C e l l  66  18.  C a l i b r a t i o n Curves for Thermocouples  Sample Resistance  (Thermoelectric C e l l )  68  19.  H a l l Sample Holder  \  71  20. 21.  Hall Effect E l e c t r i c a l Circuit Block Diagram of Magnetic F i e l d C a l i b r a t i o n Apparatus  73 75  ix  22.  Conductivity Plot of Pure CuCl  81  23.  Summary Conductivity Plot of Chlorinated CuCl  84  24.  Log  88  25.  Thermoelectric Power of Pure CuCl  90  26.  Thermoelectric Power Data of Chlorinated CuCl  91  27.  P e l t i e r C o e f f i c i e n t of Pure CuCl  93  28.  (a) (b)  94 95  29.  Percentage of Ionic Conductivity i n Pure CuCl  30.  Comparison of Thermoelectric  1 0  a  Versus C u C l  g p  x  Plot  (1 i x i 1.65)  P e l t i e r C o e f f i c i e n t of Chlorinated CuCl P e l t i e r C o e f f i c i e n t of Chlorinated CuCl  97  Power of CuCl  (1 < x < 1.0675) with NiO  x  99  31.  Plot of Log 8T Versus 1/T  101  32.  Change i n Conductivity with Time at 222°C  106  33. 34.  Logio Applied Voltage Plot Conductivity of Pure CuCl by Wagner Method  113 114  35.  Ohmic Current-Voltage Electrode at 24°C  36.  1Q  1  V  e  r  s  u  s  Plot with Wagner  Current-Voltage Plot of Pure CuCl with Wagner Electrode (high temperature, 236°C)  117 118  X  ACKNOWLEDGEMENT S  I wish to express my sincere thanks to Prof. L.G. Harrison for h i s continuing i n t e r e s t , guidance and i n s p i r a t i o n throughout this work, who not only taught me how to work at the bench but also taught me how to stand on my own.  I am deeply g r a t e f u l to Prof. C.A. McDowell for providing Departmental f a c i l i t i e s . I would l i k e to express my appreciation to Prof. L. Young, Dept. of E l e c t r i c a l Engineering,  U.B.C., for his advice and assistance  i n s e t t i n g up H a l l E f f e c t apparatus.  Thanks are also due to my senior colleagues Dr. Y. Koga and Dr. B. Saunder for many useful discussions from time to time, and to Miss R.M. Chabluk for typing this t h e s i s . F i n a l l y , I would l i k e to extend my thanks to my wife for many assistances, e s p e c i a l l y i n drawing the diagrams.  1.  1.1  INTRODUCTION  ELECTRICAL CONDUCTIVITY OF COPPER CHLORIDES  1.1.1  Previous Work i n This Laboratory The work reported  i n t h i s thesis a r i s e s out of studies of  the r e a c t i v i t y and c a t a l y t i c a c t i v i t y of copper chlorides c a r r i e d out i n t h i s laboratory by C.F. Ng  1 2 a b c ' ' ' ' .  In that work, copper chloride  prepared by reaction of CuCl with chlorine ( o v e r a l l composition repre1 2b sented as CuCl ) was x  found '  to have anomalously high c a t a l y t i c  a c t i v i t y f o r the c h l o r i n a t i o n of propane from x = 1.5  to x =  1.85.  Correlation of these r e s u l t s with k i n e t i c data on the CuCl /CI? reaction x * led to a proposed mechanism for the c a t a l y t i c e f f e c t involving the simultaneous presence of C u and Cu^ i n a CuCl2 l a t t i c e . Studies i n 2 +  support of the k i n e t i c work included x-ray d i f f r a c t i o n and  electrical  2c conductivity CuCl  x  .  The former revealed  that the only l a t t i c e s present i n  were those of CuCl and CuCl2, the CuCl2 l a t t i c e being s l i g h t l y  d i s t o r t e d i n a manner a t t r i b u t a b l e to a small f r a c t i o n of displaced cations. While most of the i n t e r e s t i n the CuCl  system thus centred  on  x the CuCl2 phase, e l e c t r i c a l conductivity r e s u l t s were interpreted as r e l a t i n g p r i n c i p a l l y to the CuCl phase.  The conductivity of CuCl  exceeded that of CuCl2 by a factor > 10 ,  and even up to x = 1.7  3  conductivity of a pressed p e l l e t of C u C l CuCl2«  x  was  at l e a s t 10 times that of  The p o s s i b i l i t y of the defective CuCl2 phase having  high conductivity was  the  unusually  rejected on the grounds that, although a v a r i e t y  2  of a c t i v a t i o n energies for conduction was observed, none of the values correlated with the a c t i v a t i o n energy f o r cation d i f f u s i o n (0.49 eV) found i n studies of the CuCl / C l reaction. x 0  The same d i f f u s i o n data,  converted to i o n i c mobility by use of the Einstein r e l a t i o n s h i p , would account f o r only 0.1 to 10% of the observed conductivity up to x = 1.75. The r e s u l t s of Ng's e l e c t r i c a l conductivity work were as T  0  follows » : -  Three types of behaviour were found (Figs. 1, 2, Table 1)  each associated with a range of composition as follows: Type I, C u C l  (1 < x < 1.4, F i g . 1, Curve A) - In t h i s case  x  plots of log o" p versus 1/T were l i n e a r up to some i l l - d e f i n e d tempera1Q  s  ture above which the slope decreases,and l i n e a r part i s 0.34 eV.  the a c t i v a t i o n energy i n the  S p e c i f i c conductivity up to 20% reacted sample  did not show any appreciable difference from that of CuCl i t s e l f at 130°C, and the p o l a r i s a t i o n up to 30% reacted sample was s i m i l a r to CuCl. Type I I , C u C l  x  (1.4 < x < 1.75, F i g . 1, Curve B) - The conduc-  t i v i t y plot showed two d i s t i n c t regions of d i f f e r e n t slopes, the t r a n s i t i o n being i n the temperature  range of about 120 - 130°C.  energy i n the higher temperature  The a c t i v a t i o n  region was the highest seen i n h i s work  and reached 0.92 eV i n the composition range of about 65 - 75% reacted CuCl.  The value of s p e c i f i c conductivity at 130° showed an increase i n  the composition range of 60% reacted CuCl but the data were rather scattered.  In this composition range the a c t i v a t i o n energy showed an  apparently continuous v a r i a t i o n with composition as shown i n Figure 2.  0.9H  Figure 2 Activation Energies of D.C.  0.8 H  0.7H  0.6 H  Conduction  In Partly Chlorinated CuCl (Harrison and Ng) 9  compositions which gave one activation energy only  A  • higher and lower values for compositions which gave two activation energies M, mechanical mixture  0.5i  0.4  0.3  0.2 1.0  1.1  1.2  1.3  1.4  1.5 x i n CuCl x  1.6  1.7  1.8  1.9  —I 2.0  5  TABLE 1  o D.C.  C o n d u c t i v i t y of Pressed P e l l e t s  log._a x in  CuCl  of P a r t l y - c h l o r i n a t e d  A c t i v a t i o n Energy  (130°C)  '  Polarization  (eV)  (%)*  1.000  -5.34  0.277  160.0  1.048  -5.16  0.368  150.0  1.100  -4.84  0.328  150.5  1.207  -4.71  0.352  150.0  1.325  -5.63  0.306  144.0  1.396  -5.90  0.378  72.0  1.503  -6.82  0.575 and  0.401  38.5  1.573  -6.76  0 . 6 4 0 and  0.348  30.0  1.608  -6.27  0.761 and 0.409  45.5  1.631  -7.12  0 . 7 7 6 and  0.542  10.5  1.677  -7.19  0 . 9 3 5 and  0.628  9.7  1.741  -7.69  0 . 9 1 5 and 0 . 6 1 5  6.0  1.755  -8.18  0.708  4.7  1.757  -8.12  0.703  4.6  1.887  -8.25  0.655  6.0  2.000  -8.60  0.670  3.0  1.741(M)  -7.62  0.602 and  Polarization effect polarity, 80 s .  CuCl  78.0  0.376  c a l c u l a t e d as change i n  conductivity  a s a p e r c e n t a g e o f mean c o n d u c t i v i t y .  on change o f  P o l a r i t y changed every  6 Type I I I , C u C l  x  (1.75 < x < 2.0, F i g 1, Curve C) - In t h i s  range of composition the a plots were straight l i n e s with an a c t i v a t i o n energy of 0.67 eV, s i m i l a r to that of CuCl2«  The numerical values of  a c t i v a t i o n energies, s p e c i f i c conductance and p o l a r i s a t i o n e f f e c t s are given i n Table 1.  In Table 1 and Figure 2, M represents the mechanical  mixture of CuCl and CuCl2« 1.1.2  The Need for Further Study of E l e c t r i c a l Conductivity i n CuCl  x  Systems  Further work on e l e c t r i c a l conductivity was considered to be necessary for the following reasons:(1)  Ng's preliminary survey was r e s t r i c t e d to temperatures below about  160°C.  In consequence, when two regions of d i f f e r i n g a c t i v a t i o n energy  were observed, the higher range was often only just seen and not studied over a wide enough temperature range for the a c t i v a t i o n energy to be accurately established; and where an upper range was not observed, t h i s might mean only that i t started s l i g h t l y above the maximum temperature studied. (2)  The apparently continuous v a r i a t i o n of a c t i v a t i o n energy with  composition i n the composition range from x = 1.4 to x = 1.74  ( F i g . 2)  i s an unusual phenomenon and very d i f f i c u l t to explain mechanistically. In the l i g h t of the remarks under (1) above, r e p e t i t i o n of these determinations over an extended temperature range (3)  i s c l e a r l y desirable.  The CuCl s t a r t i n g material i n Ng's work was reagent grade powder  without further p u r i f i c a t i o n .  At high x, this may not be s i g n i f i c a n t ;  but close to the stoichiometric composition, the conductivity of CuCl i s  7 known to be very s e n s i t i v e to p u r i t y .  I t was,therefore  considered  desirable to repeat the work with s t a r t i n g material more highly p u r i f i e d and w e l l characterized by conductivity so that i t s properties i n this respect could be compared with those of previous reported studies on the conductivity of pure CuCl i n other laboratories (see Section 1.1.3). (4)  Again i n r e l a t i o n to the known s e n s i t i v i t y of stoichiometric CuCl  to impurities, i t should be noted, that Ng d i d not investigate any compos i t i o n s between x = 1 and x = 1.048. have occurred (5)  Many i n t e r e s t i n g changes could  i n the intervening 4.8% composition range.  Harrison and Ng  gave a speculative i n t e r p r e t a t i o n of the a c t i v a -  t i o n energies as follows:-  Assuming that the conductivity below CuCl^ ,_ 7  i s e s s e n t i a l l y that of CuCl component, there are three p o s s i b i l i t i e s f o r charge c a r r i e r s :  ( i ) p o s i t i v e holes, a r i s i n g from the anion excess and  requiring a c t i v a t i o n energy because of trapping by cation vacancies, as suggested by Vine and Maurer  i n Cul/l2 system; ( i i ) cation vacancies;  ( i i i ) c a t i o n i c Frenkel defects, as discussed i n e a r l i e r studies^'~* CuCl at higher temperatures.  of  A l l these species may act as charge  c a r r i e r s i n t h e i r samples and they have speculated  that low a c t i v a t i o n  energy of 0.34 eV i s due to p o s i t i v e holes, the intermediate value to vacancies  (perhaps complicated  by i n t e r a c t i o n with impurities) and the  higher value of 0.92 eV at x = 1.63 to Frenkel defects.  Thus they have  interpreted the t r a n s i t i o n at x = 1.63 as leading to a CuCl structure which i s more normal i n the sense that i t contains fewer cation and  vacancies  holes. On the one hand, i t was necessary, i n connection with (c), to  know whether the a c t i v a t i o n energy of 0.92 eV observed i n Ng's work was  8  c l e a r l y distinguishable from the value of 1.06  eV associated with  c a t i o n i c Frenkel defects i n previous work on pure CuCl (see section 1.3.2).  On the other hand, any a d d i t i o n a l types of experimental i n f o r -  mation throwing l i g h t on the nature of the charge c a r r i e r s would be h e l p f u l i n confirming or casting doubt on these speculative assignments of the nature of the charge c a r r i e r s .  1.1.3  Previous Work on Pure CuCl i n Other Laboratories  Previously-reported data on the e l e c t r i c a l conductivity of CuCl are summarized i n F i g . 3 and Table 2.  When this work was  started,  the only data reported below 160°C were those of Ng from t h i s laboratory. While the present work was  i n progress, Maidanovskaya^ reported a study  going down to room temperature close to that found by Ng  and showing an a c t i v a t i o n energy very  (Table 1).  That study also appears to have  been on material of no greater p u r i t y than reagent grade; and the r e s u l t s at high temperatures  d i f f e r from a l l reported studies on purer  material. Three methods have been used to prepare very pure CuCl for conductivity studies: study);  (a) sublimation (Tubandt et a l . ^ ,  (b) zone r e f i n i n g (Hsueh and Christy );  the elements (Wagner and Wagner ). reducing A.R.  the e a r l i e s t  (c) preparation from g  Bradley et a l . prepared CuCl by  cupric chloride with sodium sulphite.  Methods (b) and  give r e s u l t s very c l o s e l y s i m i l a r to each other above about 230°C (lowest temperature  of the Wagner and Wagner measurements), while the  Hsueh and Christy data show that the Arrhenius plot with a c t i v a t i o n  (c)  10  TABLE 2  Comparison of Previous Results on Pure CuCl  A c t i v a t i o n Energies (eV) Reference  Upper Range  L  °glO sp a  Lower Range  at 227°C  0.70  -3.45  Tubandt et a l . (DC)  0.97  Wagner et a l . (AC)  1.04  -3.96  Christy et a l . (AC)  1.06  -3.90  Bradley et a l . (AC)  0.85  Harrison & Ng (DC)  0.50  -3.86  0.27  Maidanovskaya et a l . (DC & #1)  1.75  0.25  -6.55  0.89  0.20  -7.60  Maidanovskaya et a l . (DC & #2)  11  energy of 1.06 eV continues l i n e a r down to 120°C.  Tubandt's data (for  material presumably of not quite such high purity, though probably much better than reagent grade) give a s l i g h t l y lower a c t i v a t i o n energy (0.97 eV, Table %) at high temperatures, and the a c t i v a t i o n energy decreases to about 0.7 eV below 200°C.  To summarize the state of knowledge on the conductivity of CuCl at the beginning of t h i s work, i t i s convenient to consider separ a t e l y three temperature ranges: (1)  Above 220°C, an a c t i v a t i o n energy of 1.04 to 1.06 eV seems to be  w e l l established i n the purest samples. (2)  Between 220° and 100°C, a wide v a r i e t y of behaviour has been  observed and i t seems probable that the behaviour can be correlated with impurity content.  For the purest samples (Hsueh and C h r i s t y ) , the  a c t i v a t i o n energy of 1.06 eV continues throughout this range, while f o r the least pure (Ng, Maidanovskaya) an a c t i v a t i o n energy of 0.20 to 0.25 eV i s observed.  Bradley et a l . observed a knee i n the conductivity  p l o t at about 227°C.  The a c t i v a t i o n energy i n the high temperature  region corresponded to 0.78 eV whereas i n the lower region down to about 100°C a slope of 0.51eVwas i d e n t i f i e d . (3)  Below 100°C, Ng and Maidanovskaya both found a c t i v a t i o n energies of  0.20 - 0.27 eV and there are no data for purer material.  1.1.4  Scope of the Present Work  In h i s previous work i n t h i s laboratory, Ng t r i e d to cover the whole range of composition from x = 1 to x = 2 as f u l l y as possible and  12  used the minimum temperature range which would cover a l l the conditions used i n h i s c a t a l y t i c and d i f f u s i o n experiments.  From the above  discussion ( p a r t i c u l a r l y section 1.2) i t i s evident that a wider temperature range should be used, and that the important questions to be resolved are concerned with three ranges of composition: (a)  pure CuCl (purer than Ng's  samples) e s p e c i a l l y below 100°C where  the behaviour of CuCl of good purity i s e n t i r e l y unknown, but with attention also to extending the temperature range upwards to overlap s u b s t a n t i a l l y the range of most of the data of Wagner and Wagner and also Hsueh and Christy. (b)  CuCl reacted with C l  2  to give compositions intermediate between  x = 1 and x = 1.048, a range of composition not previously studied. (c)  CuCl^ i n the composition range from x = 1.4  the accuracy of the a c t i v a t i o n energy of 0.915  to x = 1.74,  to check  - 0.935 eV observed by  Ng as the maximum i n t h i s range, and to determine whether changes i n a c t i v a t i o n energy are continuous or discontinuous i n the composition v a r i a b l e x and whether o shows a maximum at x ^  1.6.  The above discussion of conductivity data alone i s adequate to show the composition and temperature regions which require further study; but to t r y to establish the nature of the charge c a r r i e r s was Ng's  (which  o r i g i n a l objective, i n r e l a t i o n to the problem of i d e n t i f y i n g  reaction intermediates and c a t a l y t i c a l l y active s i t e s ) i t i s necessary to consider what information can be obtained, and what has already been obtained, from some other types of experiment  on e l e c t r i c a l properties.  The remaining sections of this introduction are devoted to t h i s topic.  13  1.2  OTHER EXPERIMENTS GIVING INFORMATION ON THE NATURE OF  THE  CHARGE CARRIERS  This section describes several types of measurement which are p o t e n t i a l l y capable of giving information on such points as the sign, concentration and mobility of the charge c a r r i e r s , and whether they are e l e c t r o n i c or i o n i c .  Of these methods, the H a l l E f f e c t i s the most  powerful i n circumstances i n which a reasonably large and reproducible H a l l EMF i s produced. 1.2.1)  The required conditions, however, (see Section  e f f e c t i v e l y exclude i o n i c conductors, samples containing large  concentrations of impurities, defects or other scattering centres which l i m i t mobility, and, by the same token, p o l y c r y s t a l s .  Thus, although  attempts have been made to observe the H a l l E f f e c t i n the samples studied i n the present work, the amount of useful information obtained has not been large.  Of the other methods described below, d i r e c t determination of transport numbers and the Wagner and Wagner e l e c t r o l y t i c method of suppressing i o n i c conduction so as to observe the electronic component are r e a d i l y applicable, and have been applied previously, to CuCl.  Both  these methods have been used again i n the present work and have been successful i n characterizing the s t a r t i n g material as s i m i l a r to the samples used i n the most r e l i a b l e of previous investigations. a t e l y , because of the requirement for a reducing environment  Unfortun(equili-  brium with Cu metal) at one electrode, Wagner's method cannot be extended to the CuCl^ compositions with x > 1.  But the transport number  method with three p e l l e t assembly using Pt electrodes has (see Section 2.3.1).  been performed  14  Thermoelectric  power measurements can be made on the widest  v a r i e t y of samples, and w i l l usually give the sign of the charge c a r r i e r , whether i t i s i o n i c or e l e c t r o n i c .  (In the case of vacancy  conduction,  i t i s the sign of the e f f e c t i v e charge of the vacancy which i s given by the sign of the Seebeck e f f e c t - see Section 1.2.4. complications  There are also some  i n e l e c t r o n i c conductors i n which both electrons and  holes  are moving; the sign of the thermoelectric power i s not always that of the majority c a r r i e r - see section 1.3.)  I f the conduction  i s known to  be e l e c t r o n i c , the mobility and concentration of c a r r i e r s can be e s t i mated from the thermoelectric EMF.  But the Seebeck e f f e c t of i t s e l f  w i l l not usually give a clear i n d i c a t i o n as to whether the conduction i s e l e c t r o n i c or i o n i c ; i t normally has s i m i l a r magnitude i n both cases. Nevertheless,  the measurement of thermoelectric power has proved, for the  present project, to be a very u s e f u l type of experiment to supplement the information obtained from conductivity studies.  1.2.1  The H a l l E f f e c t The H a l l E f f e c t i s the production of a p o t e n t i a l difference by  a p p l i c a t i o n of a magnetic f i e l d to a sample through which a current i s flowing, as a r e s u l t of d e f l e c t i o n of the paths of the charge c a r r i e r s i n the magnetic f i e l d .  Usually, the current and magnetic f i e l d are at  r i g h t angles to each other, and the H a l l P.D.  i s observed i n the t h i r d  d i r e c t i o n at r i g h t angles to both current and magnetic f i e l d . of the H a l l P.D.  The  sign  gives the sign of the charge c a r r i e r ; i f current and  magnetic f i e l d are both i n a h o r i z o n t a l plane, with current running  to the  right and f i e l d away from the observer, d e f l e c t i o n of charge c a r r i e r s i s  15  downwards, and the lower electrode i n the v e r t i c a l plane acquires the sign of the charge c a r r i e r . current density J  x  The H a l l P.D.  and magnetic f i e l d H^.  i s proportional  to both  The symbols which w i l l be  used are:^ > £y = l i n e a r dimensions of sample. x  A = cross-sectional  area  (yz plane). E . E = p o t e n t i a l differences y x  and i  , j H  across £ ,£, . x' y  Hence f i e l d s are E ll x x  E /£ . y y  = current, current density z  = magnetic f i e l d = a constant known as the H a l l Coefficient  The  basic equation f o r the H a l l E f f e c t i s :  (  V V  *H * z  =  J  H  (  where E„ = E /l and i s c a l l e d the H a l l e l e c t r i c f i e l d . H y y  1  )  The H a l l  e l e c t r i c f i e l d builds up u n t i l i t balances the Lorentz force i . e . E  or  H  TT  E  R  e  =  =  e v H z  vH  (3)  z  where v i s the v e l o c i t y of the charge c a r r i e r s .  Assuming that a l l  the charge c a r r i e r s have the same v e l o c i t y , the current density i s given by the equation ( 4 )  16  J  x  =  n e v  (4)  where n i s the concentration of charge c a r r i e r s per cm . 3  the value of J  x  and  Substituting  from equation ( 4 ) and ( 3 ) respectively i n  equation ( 2 ) , one can write = where  v H /n e v H z  and e are expressed i n emu.  coulomb, t h i s has to be multiplied nificance  =  z  1/n e  (5)  In order to express R^ i n cm / 3  by a factor 10 . 8  The physical  sig-  of the H a l l c o e f f i c i e n t can be understood i n terms of the  density of charge c a r r i e r s .  The H a l l c o e f f i c i e n t  i s the r e c i p r o c a l  of the density of charge c a r r i e r s ; t h i s means, larger the value of R^, smaller the density of the charge c a r r i e r s .  In other words f o r smaller  density of charge c a r r i e r s the H a l l voltage w i l l be larger and conversely the larger the density of charge c a r r i e r the smaller the H a l l voltage. If one allows f o r a d i s t r i b u t i o n of v e l o c i t i e s , the smaller the H a l l voltage.  I f one allows f o r a d i s t r i b u t i o n of v e l o c i t i e s , equation ( 5 )  must be corrected by a factor  3TT/8.  Thus once the H a l l c o e f f i c i e n t i s known the density of charge c a r r i e r s can be evaluated.  Further the mobility  can be found by the r e l a t i o n c a l l e d the H a l l mobility,  of the charge c a r r i e r  = R^o since a = neu.  i s usually  and a the conductivity.  S e n s i t i v i t y of a H a l l E f f e c t Apparatus  The  H a l l c o e f f i c i e n t R^ i s the r e c i p r o c a l of the charge c a r r i e r  concentration, (1/ne); but f o r a given applied voltage i n the x d i r e c t i o n , E  X >  the p o t e n t i a l difference  developed i n the y d i r e c t i o n as a r e s u l t of  17  the H a l l e f f e c t depends on the m o b i l i t y  of the charge c a r r i e r s , as the  following algebra i n d i c a t e s : Current i x Now a  g p  = E a x  - E a (A/£ ). Hence j = i /A = E a /£ . x sp x x x x sp x  = n e y = vf\,  = E^/CA^).  so that  Substituting (7) into ( l ) ,  ( E /£ ) y  E  (6)  = E  y  (7)  u H /£ .  x  (8)  z x  v  '  £  Rearranging,  = x  x  yH = z  / 9 1 - 1 ~ 1 \ /^\ 1 erg cm sec ) H ( G )  y  = -f- p(cm^volt  §  x  sec G  1 -volt V O L L  -  L  (10 c o u o lm b ) 10 erg coulomb 1-  7  _a  E  _Z  = ~ 8 _Z 10  x  (cn^volt^sec-) H  ( g a u s s )  1  p  x  (9)  z  For a given value of E , s e n s i t i v i t y of detection i s improved by X  increasing £ /£ , i e . by using a short broad sample rather than a long y narrow one. x  Consider H  z  = 2000 G, £ /£ = 1. y x  Then E / E = 2 x 10" y. y x 5  At E = 3 v o l t , with minimum detectable E = 1 y V = 10~ V, x y detectable y = 1 0 7 (2 x 10~ ) = 0.017 cm v o l t " s e c , minimum G  _1  5  2  1  -1  For a sample f i v e times as long as i t i s broad, i . e . £ /£ = 0.2, y x minimum detectable y = 0.085 cm v o l t sec" . 2  To get a s e n s i t i v i t y better than 1 0 least 5 v o l t f o r _ E  X  - 2  cm  volt  - 1  - 1  1  s e c " , one must use at 1  across the sample with equal x and y dimensions, or  at least 25 v o l t s across the long narrow sample.  (Because of shorting  e f f e c t s produced by the long current electrodes, the s e n s i t i v i t y of a square sample i s somewhat less than the above c a l c u l a t i o n indicates.  Thus f o r accurate work a long narrow sample i s preferred.  But i f  maximum s e n s i t i v i t y i s important to detect the e f f e c t at a l l , the square sample i s s t i l l much better than the one with £y/^  = x  0.2,  the correction for the square sample being that i t s s e n s i t i v i t y i s about 70% of that  calculated.)  19  1.2.2  Gravimetric Determination of Transport Numbers  To f i n d the transport numbers of anions, cations and electrons (t , t  +  and t ) , i t i s necessary to pass a known quantity of e l e c t r i c i t y g  between copper electrodes through three p e l l e t s or cystals of CuCl stacked together i n series i n good contact with each other allowing i o n i c transport across the boundaries.  This i s analogous  to the H i t t o r f  method for solutions. Figure 4 Ionic Transport i n CuCl Cu = Cu +e,  Cu +e = Cu  +  +  I  transport, t  (t +t ) mole  mole Cu  (t +t ) mole  Net gain of  transport, t  Net loss of Cu  mole CI .  = t +t_-t_  +  Cu = t + t _ - t +  = t  +  +  71araday  +  mole  = t  If i t i s desired only to f i n d the t o t a l f r a c t i o n of the conductance which i s i o n i c ( t + t _ ) , a s i m i l a r experiment +  with a single p e l l e t or  c r y s t a l of CuCl w i l l s u f f i c e , as the following analysis shows. As shown i n Figure 4,  for the passage of 1 faraday of  e l e c t r i c i t y , the s o l i d copper l o s t by anode or gained by cathode corresponds to t o t a l e l e c t r o l y t i c conduction., t + t . +  Thus the i o n i c and  e l e c t r o n i c conduction can be separated simply by finding the change i n weight of the electrodes for passage of a measured quantity of e l e c t r i c i t y . No measurement on the CuCl sample i s required.  To separate t  +  and t ,  the change i n weight of the l e f t and right hand p e l l e t s must be found. These changes should be equal and opposite, and should correspond to t moles of CuCl.  20  Transport number ( e l e c t r o l y t i c conduction) i n chlorinated CuCl can be estimated by using inert assembly.  Three p e l l e t s ,  (Pt) electrodes and three p e l l e t  (anode p e l l e t - i n contact with p o s i t i v e  electrode, middle p e l l e t and cathode p e l l e t - i n contact with cathode) could be stacked together and sandwiched between Pt electrodes. Assuming that only Cu cation i s transported and since there i s no  + of Cu  + at anode, any migration of Cu  from anode p e l l e t w i l l be observ-  able i n two ways; f i r s t l y , the weight loss i n anode-pellet and the p e l l e t composition (brownish colour). Cu  +  supply  approaches towards C u C l  2  secondly,  near the electrode  The p e l l e t i n the middle w i l l s u f f e r no change since  gained at this p e l l e t i s transported to the cathode-pellet.  gain of C u  +  at cathode-pellet w i l l decrease CI |Cu  s i t i o n approaches towards CuCl.  +  The  r a t i o and the compo-  Thus by observing the loss i n weight  at anode-pellet and gain at cathode p e l l e t for a known amount of e l e c t r i c i t y , the proportion of e l e c t r o l y t i c conduction can be estimated. method with i n e r t electrode would be v a l i d only i f passage of D.C.  This for a  long time with inert electrode does not disturb defect structure and change conductivity (see Section  3.3).  21  1.2.3  I n j e c t i o n or Suppression of C a r r i e r s at a MetalSemiconductor Contact  In c e r t a i n circumstances,  the concentrations of charge c a r r i e r s  can be profoundly altered by the passage of current across a semiconduc. tor between metal electrodes.  This can be a nuisance, since the experi-  ments intended to give information on defects are changing the defect structure of the sample.  But i t i s usually a r e a d i l y detectable e f f e c t ,  because the resistance of the sample becomes non-ohmic. ohmic behaviour  Frequently,  i s replaced by a l i n e a r r e l a t i o n s h i p between In I and  applied voltage E , where I i s the current.  This type of dependence does  not have a unique cause; two cases w i l l be discussed below.  If the a l t e r a t i o n i n charge c a r r i e r concentrations can be carried out i n a controlled manner, then the e f f e c t may be turned to good account i n throwing some l i g h t on the nature of the c a r r i e r s . best accomplished  This i s  by having a single non-ohmic contact ( r e c t i f y i n g  contact)  on one side of the semiconductor sample, and an ohmic contact on the other.  For example, CuCl may  be supplied with an inert electrode  (graph-  i t e or platinum) on one side and a copper electrode on the other. In the most general case, the sample may  conduct p a r t l y by  i o n i c migration ( i n t e r s t i t i a l cations) and p a r t l y e l e c t r o n i c a l l y trons, or p o s i t i v e holes, or both).  (elec-  I f i o n i c conduction predominates, a  p o s i t i v e p o t e n t i a l applied to the inert electrode may  suppress the i o n i c  conduction by r e p e l l i n g the charge c a r r i e r s which cannot be replenished from the electrode material.  The small electronic component can then be  22 observed by i t s e l f , although i t i s modified into non-ohmic behaviour which should give a l i n e a r plot of In I versus E.  I f , on the other hand, conduction i s almost  completely  e l e c t r o n i c , with holes as majority c a r r i e r and electrons as minority c a r r i e r , the conductivity may be augmented by i n j e c t i o n of minority c a r r i e r s when the inert electrode i s made negative.  This i s the normal  behaviour of a r e c t i f y i n g contact between metal and p-type semiconductor, and also gives a l i n e a r plot of In I versus E.  (a)  Ionic c a r r i e r s i n i t i a l l y i n great excess:  the Wagner method  In t h i s s i t u a t i o n , as envisaged by Wagner and Wagner f o r the CuCl system, the migration of C u away from the i n e r t electrode (while +  CuCl/Cu equilibrium i s maintained  on the other side) produces a concen-  t r a t i o n gradient which eventually reaches a steady state because of back-diffusion of the C u i n t e r s t i t i a l s . +  Cu , +  There i s then no current of  and the concentration gradient also cancels out the applied P.D.,  so that there i s very l i t t l e P.D. across the sample, most of the voltage drop occurring at the i n e r t electrode - semiconductor contact.  Under  the influence of the concentration gradient of i o n i c defects, electrons and holes also acquire a concentration gradient, and i t i s t h i s which provides the d r i v i n g force f o r the net current across the sample.  The  general theory of this e f f e c t takes into account the p o s s i b i l i t y of current being carried by both electrons and holes, with contributions to the conductivity i n the undisturbed tively.  sample designated  and  respec-  Then the current I through a sample of cross-section A and  23  length L across which a p o t e n t i a l difference E has been applied i s given by  I = (ART/LF) [ a ( l - e ~  E e / k T  n  ) + a (e p  E e / k T  - 1)].  ( i )  Commonly, Ee w i l l be much greater than kT, and the expression then reduces to I = (ART/LF) [a + a n p  E  e  /  k  ] .  T  e  (2)  I f the electron contribution i s n e g l i g i b l e ,  I = (ART/LF) a e  E e / k T  p  ( 3)  and log I = log (a ART/LF) + Ee/2.303kT. p  A l i n e a r r e l a t i o n between log I and E i s then expected, with slope e/2.303kT.  From the intercept of such a p l o t , a  p  can be evaluated.  According to Wagner and Wagner, the condition described above would  be established only when the P.D. across the sample i s kept  below the decomposition p o t e n t i a l of CuCl; but there has been some conq troversy over this point . Also, the method was applied by Wagner and Wagner only to CuCi above 250°C, and the electronic component of the conductivity i n the undisturbed sample i s then less than 1 0  - 5  of the  t o t a l conductivity. (b)  Holes i n i t i a l l y i n great excess:  metal-semiconductor contact  rectification In the simplest theory of contact r e c t i f i c a t i o n , the e f f e c t should occur only when the difference i n work functions between metal and semiconductor i s such as to cause withdrawal of c a r r i e r s from the  24  region of the semiconductor near to the metal, leading to the formation of a high-resistance "depletion l a y e r " i n the semiconductor.  Most of  the p o t e n t i a l difference applied across the system then establishes i t s e l f across the depletion layer.  In p r a c t i c e , i t has been found that  surface states commonly exist which allow the r e c t i f i c a t i o n e f f e c t to be produced i n a manner l a r g e l y independent of the difference i n work function between metal and semiconductor''"?  An applied p o t e n t i a l E i n  the same sense (for a p-type c a r r i e r ) of metal negative with respect to semiconductor w i l l then drop the p o t e n t i a l b a r r i e r between metal and semiconductor so that majority c a r r i e r s (holes) can more e a s i l y escape across the depletion layer, while minority c a r r i e r s (electrons) are injected into the sample from the metal electrode.  The t o t a l current then r i s e s non-  ohmically with applied voltage according to  I  =  I  o  ( e  e  E  /  k  T  - l ) .  U  Here E has the sign of the p o t e n t i a l of the semiconductor r e l a t i v e to the metal, and the equation i s applicable to negative as w e l l as p o s i t i v e values of E.  The equation thus represents a current which f o r p o s i t i v e E  increases exponentially without l i m i t as E increases, while f o r negative E i t reaches a saturation current I ; this i s the normal behaviour of a o r e c t i f i e r , and the equation has the same form as that f o r an n-p junction rectifier.  (The s i g n i f i c a n c e of I i s d i f f e r e n t i n the two cases, but o  the shape of the I - E c h a r a c t e r i s t i c w i l l not d i s t i n g u i s h a metalsemiconductor r e c t i f y i n g contact from an n-p r e c t i f y i n g contact.)  25  At high p o s i t i v e values of E, f o r which eE >> kT, equation  (4)  reduces approximately to  I = I  e E qe  ^  k T  and hence log I = log I  + eE/2.303kT.  (5)  Thus the plot of log I against E should be l i n e a r , with the same slope as i n the previous case of suppression of i o n i c conduction.  There are  two important d i s t i n c t i o n s between the two cases:- ( i ) For suppression of i o n i c conduction, i f the current i s followed continuously a f t e r a p p l i c a t i o n of the voltage E, i t should drop very markedly to reach i t s f i n a l steady value; but f o r the case of hole conduction, with p o s i t i v e E (forward-biased r e c t i f i e r ) , the current should r i s e to i t s f i n a l value.  ( i i ) I f both the i o n i c and the e l e c t r o n i c charge c a r r i e r s have  p o s i t i v e sign, then opposite directions of the applied voltage are required to produce the e f f e c t s described i n i o n i c and e l e c t r o n i c cases; i . e . the sign of E i s oppositely defined i n sections (a) and  (b) of the  present account.  Since the phenomenon i s a c t u a l l y observed i n the present work, i t i s useful to discuss what may  be happening when, i n the region without  i o n i c conduction, a r e c t i f y i n g effect appears with high current passing for the "wrong" sign of E. ( i ) the semiconductor  There are two obvious explanations for t h i s : -  sample may have been wrongly i d e n t i f i e d as p-type  when i t i s a c t u a l l y n-type;  ( i i ) the semiconductor  sample may have been  so disturbed by whatever previous treatment i t has received that i t does not have a uniform d i s t r i b u t i o n of defects within i t , and e f f e c t i v e l y contains a p - n junction inside i t .  This would be the case, f o r example,  i f a CuCl sample had been treated at high temperatures  according to the  26  W a g n e r a n d Wagner m e t h o d o f  suppressing ionic  t o b u i l d up a n i o n e x c e s s a t  the  stoichiometric end.  If  this  temperature,  inert  distribution the  of  impurities  s a m p l e may c o n t a i n a p but w i t h forward  sense from that  of  section  (b)  e l e c t r o d e end o f  the  c o m p o s i t i o n , or perhaps even c a t i o n e x c e s s ,  as a r e c t i f i e r ,  in  conductivity,  the metal -  above.  is  n junction  tends  s a m p l e , and at  f r o z e n on r e d u c i n g  the  other  the  which would behave  and r e v e r s e b i a s e s i n t h e  p-type  which  opposite  semiconductor contact discussed  27  1.2.4  Thermoelectric  Power  The S e e b e c k e f f e c t a temperature  gradient,  gradient)/(temperature power r e q u i r e s what i s  the production  of  and t h e  thermoelectric  power  gradient).  a complete  the  s a m p l e and t h a t  the of  i n comparison w i t h the  a n EMF i n is  a sample by  (potential  S i n c e the measurement of  circuit,  a c t u a l l y measured i s  power of gible  is  usually  thermoelectric  completed w i t h copper  difference  between the  copper; but  the  thermoelectric  latter  power o f  thermoelectric is  a  wire,  usually  negli-  semiconductor  sample.  The electronic the  thermoelectric  conductors,  charge c a r r i e r s  analysis certain theory  of  the  has yet  related  to  the  s i g n of  the of  sign for  at  itself  the  the  transport",  however,  the  ionic  and no v e r y  sign obtained  is  give  are i o n i c  in  the that  conduction.  the  reliable  transport  are  defects.  s i g n of  the  or e l e c t r o n i c , some  and  otherwise  charge c a r r i e r s  s a m p l e ; and i n of  whether  and i t s  the  eliminating the  and  power depends on  lattice  usually  The s i g n o f  c o l d end o f  c a t i o n vacancy  of  they  be u s e f u l  conduction mechanisms. the p o t e n t i a l  in  conductors,  show how t h e s e h e a t s o f  r e g a r d l e s s of whether may i n  For i o n i c  thermoelectric  properties  power w i l l ,  vacancy conduction, negative  electronic.  difficult;  thermodynamic  information  possible  or  been developed to  charge c a r r i e r s this  are i o n i c  known as " h e a t s  The t h e r m o e l e c t r i c  magnitude  and c a n n o t u s u a l l y b e u s e d t o d e t e r m i n e  data i s  quantities  power has s i m i l a r  the  is  the  case  the v a c a n c y , e . g .  a  of  28  (a)  E l e c t r o n i c (Positive holes) Semiconductors:  In e l e c t r o n i c hole conductors thermoelectric power i s related primarily to the Fermi energy by the simple r e l a t i o n ( l )  6eT = E  p  + AkT.  (1)  where 0 i s thermoelectric power i n volt deg \  E  i s the Fermi energy  r  a,  measured from the top of the valence band.  T, k and e are the temperature,  Boltzmann constant and e l e c t r o n i c charge respectively.  The quantity A  originates from the k i n e t i c energy of the charge c a r r i e r s and the nature of scattering processes.  A commonly has a value close to 2, and i s often  taken as 2 i n the absence of precise information on scattering processes. The term AkT i s often small compared to E  and i s sometimes o m i t t e d ^ .  r Circumstances can arise i n which there i s a more serious d i s t u r b 12 ance  of the r e l a t i o n s h i p between Ep and e6T.  Tsuji  has shown that,  for a "hopping" mechanism i n which c a r r i e r s are t i g h t l y bound to ions and an a c t i v a t i o n energy i s needed f o r the jump from one ion to another, t h i s a c t i v a t i o n energy must be added to the r i g h t hand side of equation (1 ). An important case of more general application i s that i n which two or more conduction mechanisms proceed i n p a r a l l e l .  For example, i f  holes are supplied at the top of the valence band by i o n i s a t i o n of acceptor impurities, part of the current (fraction f ) may be carried by holes and part (f ) by electrons at the acceptor l e v e l (E^ above valence band).  Then with k i n e t i c energy term neglected, 9  e  T  =  p  f  E  F  +  f  n  • F- n' A E  f  E  (  E  F - V  &  <3)  29  This topic i s further developed i n Section 1.3, i n which the r e l a t i o n of E„ to E. i s discussed.  This discussion w i l l show that, i n  t h i s p a r t i c u l a r case of two mechanism conduction, even i f f << 1. P  9 may remain p o s i t i v e  Thus a p o s i t i v e 6 i s i n d i c a t i v e of hole conduction i n  the valence band, but does not exclude the p o s s i b i l i t y that a greater part of the current i s simultaneously l e v e l (other than the conduction (b)  c a r r i e d by electrons i n a s p e c i a l  band).  Ionic Semiconductors  The t o t a l thermoelectric power of an i o n i c conductor i s made up of two parts, homogeneous thermoelectric power and heterogeneous thermoe l e c t r i c power.  The homogeneous e f f e c t arises from the thermal d i f f u s i o n  of ions i n the c r y s t a l and the contribution r e s u l t i n g from the homogeneous e f f e c t i n the lead wires may be considered n e g l i g i b l y small. geneous part  The hetero-  0 arises e s s e n t i a l l y because of the v a r i a t i o n with tempera-  ture of the contact p o t e n t i a l difference between the electrode and the crystal.  The homogeneous thermoelectric power f o r a pure MX type ionic 13 c r y s t a l with Frenkel defects i s given by the expression n  ®hom  l l  " 2 2 , , . eT ( n ^ + n A ) X  (  q  i  +  1  /  2  h  )  2  where  and  n  X  (q  2  +  1  /  2  h  (4)  )  2  are the defect concentration of i n t e r s t i t i a l and cation  vacancy, X's are the corresponding  defect m o b i l i t i e s ,  and  are the  heats of transport of i n t e r s t i t i a l and..cation vacancy respectively and h i s the enthalpy of formation of a Frenkel defect.  30  No precise theory of the heats of transport e x i s t s . usually p o s i t i v e , but may be negative.  They are  To give a spurious indication of  the sign of the c a r r i e r , however, a heat of transport would have to be unexpectedly negative with |q | > 1 / 2 h. happen, 6 ^  Provided that t h i s does not  w i l l give a r e l i a b l e i n d i c a t i o n of the sign of the charge  c a r r i e r i f one c a r r i e r predominates. s t i t i a l s are important, 6 may  When both vacancies and  inter-  have either sign.  (In the present work, 0 has consistently been p o s i t i v e i n a v a r i e t y of d i f f e r e n t types of behaviour, one of them being the known Frenkel defect s i t u a t i o n i n pure CuCl at high temperature.  In a l l other  cases, the p o s i t i v e 8 gives some evidence against i o n i c conduction, i n that i t i s d i f f i c u l t to think of any other i o n i c c a r r i e r s l i k e l y to be present which would have p o s i t i v e e f f e c t i v e charge.  But t h i s i s not  conclusive evidence; i t does not replace transport number determinations.)  31  1.3  INTERPRETATION OF CONDUCTIVITY AND THERMOELECTRIC POWER DATA FOR AN IMPURITY SEMICONDUCTOR  1.3.1  Fermi L e v e l and C o n c e n t r a t i o n o f Holes  The  e q u a t i o n s p r e s e n t e d here r e l a t e t o a semiconductor  with  a band gap E , i n which h o l e s a r e s u p p l i e d by a c c e p t o r s i t e s a t energy l e v e l E ^ and may be p a r t l y "compensated" by e l e c t r o n s s u p p l i e d from a donor a t E ^ ( a l l e n e r g i e s measured from t h e top of the v a l e n c e band). In t h e p r e s e n t case, E c o n d u c t i o n band cannot  i s s u f f i c i e n t l y l a r g e that e l e c t r o n s i n the have a s i g n i f i c a n t  containing a s i g n i f i c a n t  c o n c e n t r a t i o n o f h o l e s ; hence the term f o r  c o n d u c t i o n band e l e c t r o n s i n e q u a t i o n dropped. Fermi  c o n c e n t r a t i o n i n a system  ( 4 ) below i s t h e r e a f t e r c o m p l e t e l y  In a l l c a s e s of i n t e r e s t f o r the p r e s e n t work, E^, E ^ and the  level E  temperature  r  a r e s u f f i c i e n t l y l a r g e i n comparison  t o kT t h a t t h e low-  l i m i t i n g forms s h o u l d be a p p l i c a b l e throughout.  The  approximation  used  throughout  the f o l l o w i n g account  i s that  14  used,  f o r example, by S h i v e  , i n which t h e v a l e n c e band and c o n d u c t i o n  band a r e each r e p l a c e d by a s i n g l e l e v e l t i v e l y ) , w i t h d e n s i t y of s t a t e s (N , N  n  ( a t E = 0 and E = E_ r e s p e c t r e s p e c t i v e l y - L f o r "lower", U  f o r "upper") g i v e n by the t r a n s l a t i o n a l p a r t i t i o n f u n c t i o n N  = (2irmJ k T / h ) 2  u  L  In t h e F e r m i - D i r a c s t a t i s t i c s , i s c o m p l e t e l y determined l e v e l E„.  c  = 2.42x 10  3 / 2  L  1 5  T  3 / 2  cm  - 3  i f mj  L  = in  t h e p r o b a b i l i t y o f o c c u p a t i o n o f any l e v e l  by t h e d i s t a n c e o f t h a t l e v e l from the Fermi  Thus i n a l l cases t h e c o n c e n t r a t i o n of h o l e s a t the top o f the  v a l e n c e band  (E = 0) i s g i v e n by  32 p = 2N  [1 - 1/(1 + e " F E  L  / k T  )].  (2)  In the present work, the lowest p o s i t i o n which w i l l be considered f o r the Fermi l e v e l (except, perhaps, i n the lower temperature range, heavily chlorinated) w i l l be / 2 E  A  always assume that E  where  = 0.53 eV.  Thus we may  >> kT and approximate equation (2) by  p = 2N  e- F E  / k T  .  (3)  The complete expression showing how p i s determined by i o n i z a t i o n of acceptors, i o n i z a t i o n into the conduction band, and compensation by electrons supplied from donors, i s p = [N /(1 + e A ( E  A  " F E  ) / k T  ]  + [2^/(1 + e G  "  (E  E  F  ) / k T  - t y i - 1/1 + V F (  e  E  ]  ) / k T  }]  In the present discussion, the band gap i s so wide that' electrons i n the upper band can be ignored; i . e . (E_ - E„)>> kT and the term i n N e f f e c t i v e l y vanishes.  IT  If E_ remains well below the donor l e v e l , the r  l a s t term i n equation ( 4 ) approximates to N ,  i . e . a l l the donors are  Q  ionized downwards so that t h e i r number i s subtracted from the hole concentration.  Equation ( 4 ) f i n a l l y becomes: p = [N /(1 + e A " F)/kT] - N . E  A  (5)  E  D  Equations (1), (3) and (5) permit the determination of expressions for p and E  r  i n a l l the cases of interest i n the present account, For the uncompensated  p-type semiconductor,  = 0.  At low  temperatures, E^ l i e s roughly halfway between the top of the valence band and the acceptor l e v e l .  33  E =  (E /2) + (kT/2) In (2N^/N^).  p  p  (6)  A  = (2N )  N  L  e  A  A  (7)  This i s the region analogous to s l i g h t i o n i z a t i o n of a weak e l e c t r o l y t e : hole concentration proportional to square root of acceptor  concentration,  and governed by an energy E /2.. At greater extents of i o n i z a t i o n , an improved approximation i s  E  = kT In t(N /N ) - (1/2) + (1/2){(1 - 2N^/N )  p  L  A  +  When E  2  A  (8N /N )e A E  L  / k T  A  }  1 / 2  C 8  )  ]  has been calculated from this equation, p may be found from  r  equation  (3).  A condition of s p e c i a l importance i s that at which the  acceptors are j u s t h a l f - i o n i z e d .  If the temperature  f°  r  this  condition i s known, then the concentration af acceptors can be calculated according to  N  A  =  4 N / ( 1+ L  eV l/2). kT  ( 9 )  For the compensated case, the low-temperature approximation gives  p = 2N and 1.3.2  E  p  = E  A  L  [ ( N - N )/N ] A  D  D  e~V , kT  (10)  - kT In [ ( N - N ) / N ] . A  D  (11)  D  Simultaneous Conduction by Valence-band Holes and Electrons at E. A For a compensated semiconductor i n which holes are the only  charge c a r r i e r s , the e l e c t r i c a l conductivity should be  = peu^  (12)  34  where p i s given by equation ( 1 0 ) . of a  p  should be E^, unless N^, N  temperature-dependent. mechanism, u  p  Q  Thus the apparent a c t i v a t i o n energy or u  p  (the hole mobility) i s strongly  If the holes move by a "hopping" or "polaron"  may be activated:  y  p  =  y  p  o e  y  -E P  /kT '  , 0.3)  x  Then the expression for conductivity (simplified by assuming N. >> N ) A  JJ  becomes:  a  p  i  = 2 e y  °( \/ •« it , \ ® /\) e /x  p  A  -(E. + E A yp  )/kT .  y  .... (14)  The apparent a c t i v a t i o n energy of conduction i s then (E. + E ). A yp I t sometimes happens (e.g. i n NiO) that the thermoelectric power of a semiconductor  (or the product e6T, which should be E , apart r  from a small correction for k i n e t i c energy) r i s e s very rapidly with temperature  i n a range i n which the conductivity shows normal activated  behaviour.  Such a result shows c l e a r l y that 6 i s giving a spurious  i n d i c a t i o n of the position of E„; f o r i f E^ increases r a p i d l y with temperr  r  ature, then the hole concentration p, related to  E  by equation (3), r  must be f a l l i n g as the temperature  rises.  This i s inconsistent with the  behaviour of a. As Austin et a l . ^  indicate, i t i s not very l i k e l y that  scattering processes could account for a correction to eOT of E ) s u f f i c i e n t to account for the NiO data. r  (as a measure  I f , however, the electrons  i n the acceptor s i t e s are able to contribute to conduction, e0T can  35  deviate d r a s t i c a l l y from E  i n accordance with equation  (3) of  r  section 1.2.4: e6T = E F where f  —  fE n A  i s the f r a c t i o n of the current carried by the electrons.  s t i t u t i o n of the expression for E„ given by equation  Sub-  (11), with  r  f  n  + f = 1 , gives p e6T = f E - kT ln(N /N ). p A A D  (15)  f = o /(a + a ) p p p n  (16)  4  Now  where o i s given by equation P  (14). o must now be evaluated n  similarly  from the concentration and mobility of electrons at the acceptor  level:  o -E /kT o = n. e y = n. e y e yn . n A n A n The electron concentration (called n  (17)  to d i s t i n g u i s h i t from n, a common  symbol f o r electrons i n the conduction band) i s given by the f i r s t term on the right-hand side of equation (4):  A V  n =  Substitution f o r E  (1 +6 < E a  "  Ep)/kT  from equation  '  (18)  (11) y i e l d s  r  n  A  =  V  [1  +  or for the case N. >> N_, A D  ( N  A  / N  D  ) ]  n. = N . A D  Substitution of equations (16) y i e l d s :  (  1  9  )  (20)  (14), (17) and (2Q) into equation  36  * f where  . ,//, , v (E - E + E.)/kT = 1/ (1 + K e up yn A  K =  (1/2) (  N J / N J  D  L A  )  (21)  (y°/y°). n p  (22)  For the case i n which f << 1, equation (21) becomes: P f  ,„v -(E - E + E.)/kT = (1/K) e yp yn A" .  (23)  Thus 9T, as given by equation (15), may behave approximately as an "activated" quantity, with " a c t i v a t i o n energy" (E - E + E ). yp yn A A  This  i s only very approximate since the term fpE^ may r e a d i l y be comparable to the other term kT In (N /N ); but the l a t t e r may r e a d i l y p a r t l y cancel with the neglected k i n e t i c energy term. These equations i l l u s t r a t e that, when hole and electron conduction occur simultaneously (the l a t t e r involving an e s s e n t i a l l y constant cencentration of electrons i n the acceptor l e v e l ) , and i f electron conduction predominates at the bottom end of the temperature range studied, then e6T may r i s e r a p i d l y with temperature from a value which may i n i t i a l l y be p o s i t i v e but << E_ towards a l i m i t i n g value i n which a "normal" r  i n d i c a t i o n of E  r  i s given by this quantity when electron conduction has  become n e g l i g i b l e .  As the temperature i s raised further, e0T should go  through a maximum and s t a r t a slow l i n e a r decline i n accordance with equation ( 1 1 ) .  37  1.3.3  T h e r m o e l e c t r i c Power f o r  If below,  a c u r v e of  electronic % ionic this  certain  to  completely  analysis is  assumptions are v a l i d ,  the  transition the  i n the  are holes o n l y ,  for  pure CuCl,  region.  In  thermoelectric  w i l l be assumed t h a t ,  correct  as  completely  f  but  for  the P e l t i e r  (15)  0  the region of  straight  line  extrapolated ionic  of  chlorinated  T  =  hole  g i v e s the  CuCl.  conduc-  is  samples,  in  electrons.)  contribution  of  holes  to  as  E A  "  k  T  ln(N /N ). A  (1)  D  conduction, a p l o t of  eGT a g a i n s t T s h o u l d b e a  negative slope, with intercept temperatures,  the hole  into  contribution  E .  If  the t r a n s i t i o n  this  line  region  eS^T c a n be r e a d o f f  at  is  to any  temperature.  It entirely  h  to h i g h e r  conduction,  desired  Section 1.3.2  coefficient  6  In  of  pure  electronic  (This assumption  the  work,  power d a t a f o r  region of  = 1. not  the p r e s e n t  w h i c h t h e a c c e p t o r l e v e l becomes a c o n d u c t i o n l e v e l f o r Then e q u a t i o n  indicated  i o n i c c o n d u c t i o n c a n be a n a l y z e d t o g i v e  a p p l i e d to  the c a r r i e r s  probably  and H o l e C o n d u c t i o n  6T a g a i n s t T c o v e r i n g t h e r a n g e f r o m  conduction in  It tion,  simplifying  Mixed Ionic  will  f u r t h e r be assumed t h a t  from i n t e r s t i t i a l s .  simplified  the i o n i c  Then e q u a t i o n  (4)  of  contribution S e c t i o n 1.2.4  is can be  to  ee^T  = q* +  (l/2)h = q . x  (2)  38  At high temperatures, at which conduction becomes completely i o n i c , e6T should a t t a i n a constant value (eGT)^ = q^.  In the region of mixed hole and i o n i c conduction,  e6T = f e6 T + f.e9.T P h i l when f  p  (3)  and f. are f r a c t i o n s of the current carried by holes and i '  interstitials.  From equations (1), (2) and  (3), with f  +  = 1, the  f r a c t i o n a l i o n i c conductivity may be calculated as e0T £  =  e0, T •h (eeT)^ - e6 T  ( 4 )  h  where, as indicated above, (eOT)^ i s obtained as the l i m i t i n g value at high T and e0^T i s obtained from the l i n e of intercept slope through the low-temperature points.  and negative  39  1.4 1.4.1  BAND STRUCTURE AND  CHARGE CARRIERS IN CUPROUS HALIDES  Band Structure be formed from CI 3p  In CuCl, the highest valence bands may and Cu 3d,  the three f o l d degeneracy of the atomic p - o r b i t a l and  f o l d degeneracy of the d - o r b i t a l giving thus eight bands i n a l l . sidering f i r s t the isolated atom, we have thus two l e v e l s , one  five Con-  three  f o l d degenerate and the other f i v e fold degenerate, separated by about 3 eV, as given i n Figure 5. Cu 3d and CI 3p Levels Cu 3d  CI 3p  Figure 5  Considering next the Cu  +  and CI  ions each with four ligands i n t e t r a -  hedral symmetry, the 3p state should remain degenerate, while the  3d  state should be s p l i t into a group of three and a group of two as shown in Figure 6 . S p l i t t i n g of d - o r b i t a l s i n Tetrahedral F i e l d d d  CI 3p  Figure 6  xy 2  , d  z ,  d  yz x  2  , d  xz  - y  2  (t_ o r b i t a l s ) 2 ,  .  ,  (e o r b i t a l s )  40  In the band structure of the c r y s t a l the degeneracies w i l l be further l i f t e d , although the s i t u a t i o n of Figure 6 may s t i l l be found at s p e c i a l points i n the B r i l l o u i n zone (which i n fact correspond to the energy maxima of the bands).  Also, the bands may be of mixed  character, p a r t l y CI 3p and p a r t l y Cu 3d (the t o t a l number of bands, 8, remaining unchanged).  The band structure of CuCl has been studied t h e o r e t i c a l l y and  1 i 7 ip ft  experimentally by several workers  »  *  . According to Herman and  M c C l u r e ^ the lowest conduction band and the highest valence band a r i s e from the 4s and 3d states of C u i o n respectively, while the next lowest +  valence band arises from the 3p CI  state.  Thus there are two forbidden  gaps, one between 4s and 3d of C u i o n and another between 3d Cu and +  3p C l bands.  The o p t i c a l energy gap i s determined by the width of the  former and the experimental value i s about 3 eV obtained from the absorption  spectrum"*"**. 17  Later Cardona  experimentally estimated the f r a c t i o n of the  metal wave function i n the valence band and suggested that only about 25% of the halogen wave function i s involved i n the valence band formation. These suggestions were made on the basis of exciton spectra studies. On. the basis of the t h e o r e t i c a l c a l c u l a t i o n of band structure 18 of CuCl, Song"  supported the previous arguments with the i n d i c a t i o n  that the valence band has, at the.top, a mixture of 79% of C u of C l 3p wave functions;  +  3d and 21%  The most recent c a l c u l a t i o n of band structure 19  of CuCl was done by Calabrese  (Ph.D. t h e s i s , Lehigh Univ. 1971)  41  (unpublished - this information i s taken from the thesis a b s t r a c t ) . According to h i s r e s u l t s , but contrary to the previous r e s u l t s , the contribution of 3p o r b i t a l of C l to the top of the valence band i s -  larger than that of the 3d o r b i t a l of Cu . +  e f f e c t i v e mass of 0.23 m  and 0.17 m e  He has also computed the  with the corresponding energy gap  e  of 1.0 eV and 0.3 eV f o r Slater exchange p o t e n t i a l and screen exchange 20 p o t e n t i a l respectively.  But i t has also been suggested  * that m  at the  top of the valence band i s about 20 xa^, a value s i m i l a r to that f o r NiO, which i s another case of a 3d band system believed to be a few hundred mV wide. A simple picture of the probable composition of the bands i n terms of atomic o r b i t a l s on tight binding approximation i s as follows. (1)  The highest three bands.  Each C u  +  ion has 12 s i m i l a r ions as second  nearest neighbours, lying i n the d i r e c t i o n of 12 lobes of d ^ , d ^ and z  d  xz  .  Corresponding o r b i t a l s on d i f f e r e n t atoms combine with each other  as i l l u s t r a t e d f o r the d o r b i t a l s i n an (001) plane i n F i g . 7. These xy o r b i t a l s w i l l also combine with P o r b i t a l s on CI i n the combinations  fc  l -  fc  3  =  C  l  C  l  C  l  d xy d yz d xz  + 2 z + C  P  Vx  +  C  2 y P  The arrangement of (+) and (-) signs shown i n the diagram  corresponds  to the M.O. of greatest anti-bonding character, i . e . the top of the band. These bands are about 0.5 eV wide covering the f u l l width of the d-band.  42  Figure 7 Atomic O r b i t a l s for Tight-binding Calculations on CuCl  Tetrahedral s i t e s , crystal field splitting  0.53  Cu 3d  eV  Signs for top of band (greatest antibonding character)  (9  .d ,d ,d xy yz zx r  d  o  d  o  o  Vi)  (rJ^  % ^2.5  aC  eV  i V, ,/ It  t f  \ I 1I  C l 3p  \J\1  1( 1f  o  Radial maxima (A) Cu 3d 0.32 Cl 3p 0.75  43  (2)  The next two bands.  d2  The remaining d - o r b i t a l s of Cu  (dz 2,  ^2, the e - o r b i t a l s ) are so oriented that they do not point d i r e c t l y  x  towards any neighbouring cations.  In t h i s case, the formation of a band  i s l i k e l y to involve a larger contribution from the C l 3p o r b i t a l s ( a l l three equally, as i l l u s t r a t e d i n F i g . 7.  These two bands l i e at the  bottom of the d-band d i s t r i b u t i o n and are very narrow  (about 0.1 eV).  The top of the e-band i s separated from the top of the t band by about 0.53  eV.  Thus e 1  = C, d 2 2 + C_ (P - P. - B ) l x - y 2 x y z  e, = C. d 2 + C, (P - P - P ) 2 1 z 2 x y z In the e-band, the bonding i s carried from one C u intervening C l , i n contrast to the t  +  to another v i a the  bands which have d i r e c t Cu-Cu  interaction.  (3)  The lowest three bands.  C l 3p o r b i t a l s .  These w i l l be formed p r i n c i p a l l y from  Because of the fact that the radius maximum of C l 3p i s  o  o  0.75 A i n comparison with only 0.32 A for Cu 3d, t h i s forms- a wider band. 1.4.2  Charge Carriers Except f o r the clear i n d i c a t i o n from transport number experi-  ments (Tubandt et a l . )  Z  that pure CuCl i s an ionic conductor above 220°C  and an e l e c t r o n i c conductor below that temperature, suggestions on the nature of the charge c a r r i e r s i n CuCl have been l a r g e l y speculative.  No  44  t h e o r e t i c a l c a l c u l a t i o n s of the energy of defect formation has been reported. The suggestions of Harrison and Ng on the charge c a r r i e r s i n chlorinated CuCl have already been described (Section 1.1.2).  There i s no other report i n the l i t e r a t u r e about the conductivi t y of chlorine treated samples.  However, Bradley et a l . studied the  e l e c t r i c a l conductivity of CuCl doped with CuC^. addition of 2 mole % of CuC^  They observed that by  to CuCl the conductivity increases con-  siderably and the knee i n the a- plot tends to diminish.  They believed  that the considerable increase of conductivity upon doping throughout the whole temperature range, i s due to the increase of e l e c t r o n i c  2+ contribution, r e s u l t i n g from the presence of Cu  ( i . e . d-band holes)  and the disappearance of the knee appears to suggest that the e l e c t r o n i c component predominates throughout the whole temperature range.  This  suggestion i s based e n t i r e l y on conductivity studies together with an i n d i c a t i o n from thermoelectric power that the charge c a r r i e r s are positive.  No d e t a i l s of thermoelectric power data are given. 3 Vine and Maurer  have studied the H a l l e f f e c t and  conductivity of Cul with excess iodine.  electrical  Tubandt has shown e a r l i e r that  there i s no i o n i c contribution to the conductivity below 200°C.  Vine  and  Maurer thus i n t e r p r e t t h e i r data i n terms of trapped holes. The mobil2 - 1 - 1 i t i e s obtained from H a l l e f f e c t data, being 6-14  cm  volt  and generally decreasing with temperature, are compatible e l e c t r o n i c form of conduction, not an i o n i c form.  sec  at 102°C  only with an  They observed that the  concentration of holes increases with increase of iodine pressure at a fixed temperature.  However, the concentration of holes appears to  45  decrease with temperature at a fixed iodine pressure.  The r a t i o of free  holes to iodine approaches unity as the concentration of iodine increases and the concentration of free holes equals iodine atoms at about iodine 1  2  pressure of 10  - 10  mm Hg which corresponds to the hole concentration  20-3 of ^ 1 0  cm  Iodine concentration less than t h i s does not give hole/  iodine atoms r a t i o close to unity. t i o n of excess iodine by Cul, Cu  +  They suggest that during the absorpand an electron comes from the Cul  l a t t i c e to combine with the iodine atom with the expansion of Cul lattice.  The vacancy created by the migration of C u  +  from the Cul  l a t t i c e has an e f f e c t i v e negative charge and can trap holes at low eratures.  In terms of the band picture an effect of introducing  vacancies i s to create a d i s c r e t e l e v e l above the valence band.  temCu  +  Such an  energy l e v e l acts as an acceptor l e v e l and i s denoted by the symbol E . For small concentration of impurities E^ i s  constant  but  decreases with increasing concentration of impurities as given by the equation  (1) 1/3 E  A  =  E  0  "  3  <»  n  —8 where a i s a constant whose magnitude i s of the order of 10  and  -3 n (cm  ) i s the concentration of excess iodine atoms i n this case.  Vine  3 and Maurer have demonstrated that the above equation holds good up to 19 -3 19-3 n - 6 x 10 cm , but when n - 7 x 10 cm , E^ drops below the top of the valence band. /  46  2.  2.1 2.1.1  EXPERIMENTAL  SAMPLE PREPARATION P u r i f i c a t i o n of CuCl The reagent grade CuCl (Fisher ACS) was dissolved i n 6M HC1  to a dark greenish solution.  The solution was poured into a large  beaker containing d i s t i l l e d water; thereby white c r y s t a l l i n e CuCl was p r e c i p i t a t e d out. The p r e c i p i t a t e was allowed to s e t t l e down. Addition of 10 - 15 ml of acetone helps s e t t l i n g down the p r e c i p i t a t e . The b l u i s h green supernatant l i q u i d was decanted o f f . The white s o l i d remaining i n the bottom was washed with reagent grade acetone, three to four times.  The clear white CuCl, free from any tinge of b l u i s h  green colouration was covered with acetone and was vacuum f i l t e r e d using Buchner funnel.  During f i l t r a t i o n CuCl was washed three to  four times with acetone.  The white s o l i d thus obtained was dried at  40°C over night i n oven.  Drying i n oven at 40°C or drying i n desicca-  tor d i d not produce any v i s i b l e difference.  The white powder of CuCl so obtained was transferred to a pyrex tube T and connected to the vacuum pump by B ^ j o i n t .  The  apparatus f o r the sublimation of CuCl i s shown i n F i g . 8.  I t consists  of an e l e c t r i c furnace F and a vacuum system (mercury d i f f u s i o n pump). After connecting the sublimation tube T to vacuum, the stopcock 1 was opened slowly to prevent the sucking up of powder CuCl into the system. It was then evacuated f i r s t with rotary pump and then with mercury d i f f u s i o n pump f o r about 8 - 1 0 hours.  This was  Figure 8  47  Apparatus for CuCl Sublimation  Mercury diffusion pump  1 Stopcock  B14 Joint  Pump  Sublimation tube T Glass wool  F (furnace)  48  done to ensure the removal of any acetone vapour l e f t i n the bulk of the of  material.  In some cases less evacuation resulted i n the blackening  the whole material.  Then the furnace was switched on.  The gap  between the wall of the furnace and the tube was insulated with glass wool and also a portion of the tube close to the furnace.  The  from the v a r i a c was increased to about 52 volts and CuCl was at 450°C.  This temperature was checked by thermocouple.  P.D. sublimed  After the  completion of the sublimation, the s o l i d CuCl was removed from the tube by breaking the tube.  The f i r s t sublimed CuCl was s l i g h t l y yellowish.  I t was then transferred to another s i m i l a r tube.  This process of sub-  limation was repeated t i l l transparent white s o l i d was obtained. Usually the fourth sublimation was found s a t i s f a c t o r y .  This sublimed  CuCl was stored i n a vacuum sealed tube for further use (though i t was observed that this material l e f t i n a i r at room condition did not show any v i s i b l e change for about f o r t y hours),  2.1.2  Reaction of Sublimed CuCl with Chlorine  The apparatus consisted of an L shaped reaction tube with a greaseless 14/35  (west glass) j o i n t , and e l e c t r i c furnace,  pressure measuring system (pyrex s p i r a l gauge scale) Hg manometer, chlorine p u r i f i c a t i o n and storage system. shown i n Figure 9.  The whole apparatus i s  Except f o r stopcock A a l l teflon stopcocks B, C, D,  E, F, were used; f o r chlorine handling i n the reaction apparatus the stopcock A was used with Kel-F grease.  The s p i r a l gauge c a l i b r a t i o n  and chlorine p u r i f i c a t i o n were done i n the same fashion as  Figure 9. Apparatus for Reaction of CuCl with Chlorine Chlorine p u r i f i c a t i o n system u-tube  K^y  B a l l J o i n t (S19)  i  V  H  KJ  Hg Manometer Greaseless Joint  Glass wool WOOIS Furnace  >•  Powder CuCl-  L-shaped Reaction Tube >0 Thermometer  V©  50  described previously by Ng . The temperature of the e l e c t r i c furnace was c a l i b r a t e d with v a r i a c reading and was checked by (copper constantan) and Hg thermometer.  thermocouple  Glass wool was used for the  i n s u l a t i o n between the furnace wall and the reaction tube.  The powder sublimed CuCl was weighed into the reaction tube. It was closed.  then evacuated f o r two hours by rotary pump.  The stopcock A was  The chlorine i n the U-tube was frozen by l i q u i d nitrogen and  the a i r , i f any, was pumped o f f by opening the stopcock C.  Now  the  stopcock D was closed (this disconnects the vacuum pump) and chlorine gas was allowed to come i n . Then the stopcock C was closed and A was opened.  The timer was started and the i n i t i a l reading of the s p i r a l  gauge scale was taken.  Further readings were taken at timed i n t e r v a l s .  From the c a l i b r a t i o n the decrease of chlorine pressure with time was determined and plotted.  After the completion of the reaction as  indicated by pressure reading, the excess chlorine ( i f any) was i n the side arm tube T by l i q u i d nitrogen. The stopcock A was  frozen closed  and the vacuum was broken after t r a n s f e r r i n g the chlorine of tube T to the U-tube.  The reaction tube was weighed and from the weight  increase, the composition of the reacted CuCl was  determined.  The s l i g h t l y chlorinated samples up to 2.38% were prepared at room temperature be followed.  (24°C).  The reaction was too fast for the k i n e t i c s to  Heavily chlorinated CuCl (up to 64.5%) samples prepared  at 130°C, showed remarkably slow reaction. was also prepared at 130°C.  One sample of 6.75% reacted  For p e l l e t preparation the reacted CuCl  51  was  f i n e l y powdered i n a mortar and p e s t l e .  The powder was  immediately  transferred to the reaction tube and heated under vacuum at 100°C for 5—6  hours, to remove any moisture contamination  This powder was  during the grinding.  stored i n a vacuum desiccator and was  used to make the  p e l l e t s as described i n the next section.  2.1.3  Preparation of P e l l e t s The p e l l e t s of pure CuCl were prepared  die model 186-0002 and hydraulic press assembly.  i n a Perkin Elmer KBr The KBr die consists  of a s t e e l casing C and a s t e e l b a r r e l B i n which the powdered sample can be introduced. have been provided.  A plunger P and the two dies E (upper) and F (lower) Complete d e t a i l s have been given i n the s e l f  explanatory diagram shown i n Figure 10. The various parts of the die assembly were cleaned with acetone.  The b a r r e l B was held upright and the lower die F was  f i t t e d into i t . i t , was  smoothly  The b a r r e l B, together with, the lower die f i t t e d into  placed i n the case C.  Now  the f i n e l y powdered sample,pure CuCl  or reacted CuCl treated as described i n the previous section 2.1.2,was introduced into the b a r r e l B.  Usually 1.5 - 2 gm of the powder was used  except for the thermoelectric samples i n which a larger amount of the sample ( 4 - 6 gm) was needed to give a p e l l e t of length 1 - 1 . 5  cm.  The powder was  The  upper die was  d i s t r i b u t e d evenly by shaking the die assembly.  then introduced into the b a r r e l B and was pressed down  t i g h t l y with the plunger P t i l l the upper die touched the sample. the assembly was  completed with the larger 0-ring and top cap T.  Then It was  ' 52  Figure 10 Perkin Elmer KBr  P e l l e t making die  Plunger P Plunger O-ring Top cap (T) Top Cap O-ring  Barrel (B)  Casing  • (O  Upper d i e E Powder sample  Vacuum pump  •Lower die F Hose nipple O-ring  53  then evacuated f o r about f i v e minutes and a pressure of 8000 p s i was applied f o r three minutes.  For removing the p e l l e t from the assembly  the vacuum was broken, then the top cap, plunger and larger 0-ring were removed.  The plunger was s l i d back into the b a r r e l by placing t h i s  assembly on the press ring and by applying the pressure. f e l l out on a p l a s t i c sheet placed previously to avoid  The p e l l e t contamination.  The p e l l e t was then transferred to a p l a s t i c bag and stored i n a vacuum desiccator before use.  The thickness and the weight of the p e l l e t were  measured i n the p l a s t i c bag and the thickness and the weight of the p l a s t i c bag were subtracted to find out the actual thickness and the weight of the p e l l e t .  2.2 2.2.1  The area of the p e l l e t i s 1.326 cm . 2  CONDUCTIVITY MEASUREMENTS Conductivity C e l l The conductivity c e l l consists of two bright platinum  electrodes 0.26 mm thick and 1.55 cm i n diameter.  foil  When s i l v e r and copper  electrodes were required, they were simply placed between the platinum electrodes and the sample.  To measure the sample temperature, a thermo-  couple wire (Pt 10% Rh) was spot welded i n the top electrode T, Figure 11. The top electrode was fixed on the bottom of a cylinder of f i r e d lava.  The bottom electrode s i t s i n a c y l i n d r i c a l c a v i t y (of the  same material) which has threads inside matching with the threads on the top electrode.  Whenever needed the bottom electrode i s replaceable  by a c i r c u l a r guard ring assembly to check the surface conductivity as shown i n F i g . 12. The two leads of the top electrode P and T pass through two holes i n the cylinder and the lead to the bottom electrode B  Figure 11 Conductivity C e l l  ? H  H = m e t a l l i c hook P = Pt wire T = Thermocouple wire B = Bottom electrode wire  Cylinder of f i r e d lava  Figure 12 Guard Ring  Top electrode  -Sample •Bottom electrode  55  passes along the side of the cylinder. was  ensured by ceramic beads.  H was  provided  Further  i n s u l a t i o n of each wire  At the top of the cylinder a m e t a l l i c hook  by means of which the weight of the cylinder together with  the electrodes and sample assembly i s supported on a horizontal glass rod fixed i n a pyrex B-45  cone.  This cone was  system through a pyrex b a l l j o i n t S-19  connected with the vacuum  and a stopcock.  The  three wires  P, T, and B and the fourth lead G for the guard r i n g assembly pass through t e f l o n i n s e r t s i n the glass cone and are vacuum sealed with highly i n s u l a t i n g dekhotinski  cement.  For the operation  the c e l l  placed i n a large f l a t bottomed pyrex v e s s e l , which contained  a  was  few  pieces of f l a t uniform t e f l o n i n the bottom on which i t could rest firmly instead of hanging i n the pyrex v e s s e l .  This conductivity c e l l was  used for transport number measurements (Section 2.3). heated by means of a small  rion-inductively  This c e l l  also  was  wound e l e c t r i c furnace.  DC measurements on high resistance samples, the furnace was  During  the only  AC  device inside the copper case which screened the whole apparatus.  2.2.2  Electric Circuits The e l e c t r i c a l c i r c u i t for most DC conductivity measurements i s  shown i n Figure 13.  The  conductivity c e l l was  Keithley Decade Shunt having the resistances 1 0 p o t e n t i a l difference of 1.2 whole c i r c u i t . current.  v o l t s was  connected i n series with a 12  to 10  provided  Keithley model 200B battery operated electrometer  the  for the reversal of the  The p o t e n t i a l difference across the shunt was  ll  ohms and a  applied by a dry c e l l across  A reversing switch S was  ance of 10 * ohms.  3  measured with a  which has input r e s i s t -  The entire apparatus was enclosed  i n a grounded copper  Figure 13 C i r c u i t Diagram f o r Conductivity Measurement  1.5 v o l t  • x Reversing switch S  Shunt Box  Keithley Electrometer  57  box with a window cut i n i t to allow the meter to be read and extension rods to take the electrometer controls outside the box.  (The  was o r i g i n a l l y designed for very high resistance samples and  apparatus this  screening was not r e a l l y necessary i n the present work except for pure CuCl and highly chlorinated CuCl below 100°C.)  Apart from the previous conductivity measuring c i r c u i t  (high  impedance) a simple c i r c u i t as shown i n Figure 14 was designed to measure the resistance of the sample when i t became quite small (y20 s l i g h t l y chlorinated sample) around 230°C.  In this c i r c u i t , the sample  and a v a r i a b l e standard r e s i s t o r (10 - 1000 ohms) are connected with the source of both DC and AC.  ohm,  i n series  The DC current i s supplied by a  1.5 v o l t battery b u i l t inside the chassis and AC by an o s c i l l a t o r of 200 cps, whose c i r c u i t diagram i s shown i n Figure 15.  Keithley e l e c t r o -  meter and Hewlett Packard AC voltmeter model 403A are connected  alter-  n a t i v e l y to measure the DC and AC p o t e n t i a l difference accross the sample and r e s i s t o r .  The source switch S\ has been provided which can be used  to apply either DC or AC current.  The DC source i s modulated by using a  10 turn 10 K potentiometer P and a reversing switch S the p o l a r i t y .  2  i s used to change  A three p o s i t i o n switch S3 has been provided by means of  which, the P.D.'s across the standard r e s i s t o r , the sample and the t o t a l P.D.  applied can be measured by using the p o s i t i o n 1, 2, and 3 respect-  ively.  AC and DC conductivities were measured simultaneously on each kind of sample wherever  possible, ( i . e . except where the resistance of  the sample becomes greater than 10 measurement could be made).  6  ohms, since i n this case no AC  Figure 14 C i r c u i t Diagram f o r Low Sample Resistance  Battery  O  Guard on  •0-1-* OFF S  O—  ZT 1.5 V C e l l  Source 10K 10 Turn $ Level DC P  -9  AC I Ext.  1 A'C  external \ \  —  Guard r i n g OFF  Source (S^) o—  @  Meter  —O-X0-  ~Selector \ \  1  3 ° T  ]  9  I  /77 \  \  Sample  \ Electrometer / AC/DC /  /  &  O-  /  /  /  /  / / -O—9O-  Reference Resistor \  /  \ • t o  09  O.Olyf  n  H O C o  i-h O  H  rt a> o o  n -a CO o o  3.9K >1K O  7V  Total current 1.55ma  0.5 meg 0 3.,5V AC output 200 CPS  c a>  60  2.2.3  Procedure  After the sample was introduced into the conductivity c e l l , i t was evacuated for  by a rotary o i l pump.  about 15 hours (overnight).  The sample was heated to 200°C  The conductivity readings were taken  at temperature i n t e r v a l s of about 12 - 15°C and the usual time i n t e r v a l allowed for thermal e q u i l i b r a t i o n at each temperature was about hours.  3-4  Occasional use of a longer time i n t e r v a l (overnight) did not  cause any e r r a t i c behaviour.  Measurements were sometimes started at  200°C a f t e r the overnight heating, but sometimes the sample was allowed to cool down slowly (3 - 4°C per hour) and measurements were started at room temperature.  In either case, the measurements were made through  two cycles of heating and cooling.  Usually the f i r s t heating and cooling  r e s u l t s were reproducible but i n c e r t a i n samples r e p r o d u c i b i l i t y was obtained only by the second heating and cooling.  Before measuring the conductivity, the applied voltage E\ (1.2 v o l t s ) was checked by an external meter (VT VM) for each reading. The c i r c u i t was completed, the p o t e n t i a l difference E was measured immediately immediately  2  by the Keithley electrometer.  across the shunt The p o l a r i t y was  reversed (within less than f i v e seconds) and an E  was taken immediately found that both E  2  with opposite p o l a r i t y .  2  reading  For a l l samples i t was  values with p o s i t i v e and negative p o l a r i t y were very  s i m i l a r (within 3 - 5%).  The mean of the E  2  values was used to c a l c u l a t e  the conductance of the sample using the following r e l a t i o n E 0  -  2  I ohm  E, - E  -1  ( 2  1  )  61  where a i s the conductance i n ohm"  and I i s the current range marked  1  on the shunt i n the amperes (the r e c i p r o c a l of the shunt resistances). The s p e c i f i c conductivity a  a  =  was calculated by the following equation  o(£/s) ohm*" cm 1  ( 2 )  -1  where H i s the thickness of the sample and s i s the area of the sample.  In some samples the current was measured with respect to time and such v a r i a t i o n of current with time i s shown i n Figure 16 . The conductivity calculated from the mean current of p o s i t i v e and negative p o l a r i t y did not show any s i g n i f i c a n t deviation from the usual procedure.  Blank Resistance Using a piece of t e f l o n of about the p e l l e t size the blank resistance of the apparatus was found to be 2.24 x 1 0 temperature.  1 2  ohm cm at room  This resistance i s at l e a s t about seventy times higher  than the highest resistance measured f o r the samples and at a l l higher temperatures the r a t i o was even much l a r g e r .  2.3 2.3.1  TRANSPORT NUMBER MEASUREMENT Gravimetric Method This experiment was performed gravimetrically using the con-  d u c t i v i t y apparatus described i n Section 2.2.1 and a coulometer device. For pure CuCl  the c e l l  configuration  of  Cu/CuCl/Cu was used.  Both  copper electrodes, made of 98% pure copper, of 1.32cm i n diameter and 0.09  cm i n thickness, and CuCl p e l l e t s were weighed separately.  The  62 Figure 16 Current Versus Time Plot i n CuCl  7  1  6-i  Polarity Change  4>  5 H  4 -A  2  -i  1 -J  Time (min.)  •  Cu Electrode  O  Pt Electrode  63  p e l l e t was sandwiched between the pair of copper electrodes i n the conductivity c e l l .  This was then evacuated by a rotary pump f o r about  twenty hours and the constant desired temperature was maintained by heating the p e l l e t f o r 3 - 4  hours.  A constant current was passed by  applying a P.D. of 22.5 v o l t s through t h i s c e l l connected i n series with a coulometer.  The coulometer consists of two bright platinum f o i l  electrodes, one serving as cathode and the other as anode dipped into 10% s i l v e r n i t rate solution a c i d i f i e d with d i l u t e n i t r i c a c i d .  For  operation, the cathode was weighed before dipping into the s o l u t i o n . On passing the current the e l e c t r o l y s i s of s i l v e r n i t r a t e solution took place and the f i n e d e n d r i t i c s i l v e r was deposited at the cathode.  The  deposited s i l v e r at the cathode was washed c a r e f u l l y with d i s t i l l e d water and then with alcohol to avoid any contamination with s i l v e r n i t r a t e remaining on the electrode. of deposited s i l v e r .  Care was taken to avoid any loss  From the weight of the s i l v e r deposited the  quantity of e l e c t r i c i t y was calculated using the r e l a t i o n that 1 coulomb of e l e c t r i c i t y i s equivalent to 1.118 x l O  - 3  gm of s i l v e r .  At the end of the experiment the CuCl p e l l e t and both copper electrodes were weighed.  From the loss of the copper at the anode and  gain at the cathode or at the p e l l e t , the amount of copper transported was calculated.  Thus knowing the copper transported and the amount of  e l e c t r i c i t y consumed, the percentage of c a t i o n i c conductivity was calculated using the r e l a t i o n (1)  64  1 mg of copper  =  1.515  coulombs of e l e c t r i c i t y  % of c a t i o n i c contribution = Wt of copper transported i n mg x 1.515 coulombs ^ Total coulombs  No attempt was made to detect anionic conduction, since ionic conduction i n CuCl has been found^  to be completely c a t i o n i c . -  For chlorinated samples, the experiment was performed using a thermoelectric c e l l whose electrodes each contain couple.  Three p e l l e t s of CuCl  (Pt. 10% Ph) thermo-  of comparable thickness were weighed and  sandwiched between two Pt electrodes.  The p e l l e t s and electrode  assembly were heated overnight i n vacuum at 200°C and cooled down to room temperature.  The temperature was raised and a f t e r about 4 hours  current was passed with e i t h e r a 1.5 v o l t or a 22.5 v o l t battery. The constant temperature was recorded from the thermocouples.  After  passing an appreciable amount of e l e c t r i c i t y the p e l l e t s were weighed separately at room temperature.  The amount of e l e c t r i c i t y was determined  as described previously i n Section (1.2.2).  The experiment was performed  at d i f f e r e n t temperatures. 2.3.2  Wagner's Method In t h i s case the conductivity apparatus was used with the  c e l l configuration of Cu|CuCl|Pt.  The copper electrode was a copper  disc of 1.33 cm i n diameter and 0.9 mm p e l l e t and a p a i r of Pt electrodes.  thick inserted between the  P.D.s  of 0.4 v o l t s to 0.8 v o l t s  were applied to the sample, tapped from a 1.5 v o l t battery using a 10 turn 5 K potentiometer.  The current was followed with time using a  65  Keithley electrometer (model 200B) and usually 15 minutes was found s a t i s f a c t o r y f o r attainment of a steady reading. ments were done with only one sign f o r the P.D.  Usually the experi(Pt electrode positive,  the d i r e c t i o n required to suppress conduction by C u  +  interstitials.)  But i n one case, the P.D. was cycled between ± l . o V a number of times at 236.0° and 24°C.  The two procedures gave s u b s t a n t i a l l y d i f f e r e n t  r e s u l t s at low temperatures, as described i n Section 3.3.2.  2.4  THERMOELECTRIC POWER MEASUREMENTS  2.4.1  Thermoelectric Power C e l l This c e l l (similar to conductivity c e l l ) consists of two  bright platinum f o i l electrodes of 1.55 cm i n diameter and has a t h i c k ness of 0.26 mm.  Two thermocouples, Pt 10% Rh were spot welded to each  electrode to measure the temperature of each end of the sample. The top thermocouple-electrode was fixed on the bottom of a small threaded t e f l o n cylinder 5.0 cm i n length and 2.0 cm i n diameter.  The bottom  thermocouple electrode assembly, on the other hand, was fixed i n a c y l i n d r i c a l cavity of t e f l o n threaded inside matching with the top assembly as shown i n Figure 17 .  The top electrode can be screwed  into  the bottom one to ensure good contact between the electrodes and the sample.  The two top wires pass through two holes made i n the cylinder  and the other two wires of the bottom electrode pass along the side of the assembly.  The wires were insulated by t e f l o n sleeves.  Figure 17 Thermoelectric C e l l  Top  electrode  Bottom electrode  67  The weight of the whole assembly and the sample was supported by these four wires, since the weight was not large enough to make i t necessary to provide a hook to support the weight.  Each wire passed  through a separate hole made i n a t e f l o n cork which i s fixed i n a pyrex B-34  socket.  These wires as well as the t e f l o n cork are vacuum sealed  with dekhotinski cement. with a B-34 cone.  The lower end of the socket B-34 i s joined  In between socket and cone the side arm i s joined  with a two way stop cock whose rectangular end i s connected to the vacuum system with a b a l l j o i n t .  For operation the c e l l was placed i n  a pyrex f l a t bottomed v e s s e l with B-34 socket.  Both thermocouples were calibrated (using melting i c e at the reference junction) and c a l i b r a t i o n curves are given i n Figure 18. 2.4.2  Thermoelectric Furnace The furnace i s made of s i l i c a tube having the i n t e r n a l diameter  of 4.2 cm and of length 14 cm. asbestos paper.  The tube i s wrapped i n thin layer of  Then i t i s wound with heating element more c l o s e l y  towards the top and t h i n l y at the bottom to produce a temperature gradient.  The winding of the heating element i s further insulated  by several layers of asbestos paper. insulated by glass wool.  The bottom end of the furnace i s  During the course of operation the loss of  heat from the top i s prevented by i n s u l a t i n g the top with glass wool. The furnace was calibrated with variac reading.  The temperature  difference obtained between the ends of a p e l l e t 1 - 1.5 cm long varied from 6° to 30°K.  Figure 18 Top thermocouple Bottom thermocouple  Temperature  (°C)  00  69  2.4.3  Procedure  After  introducing  was e v a c u a t e d f o r  about  and t h e n c o o l e d s l o w l y  the  sample i n t o  twenty h o u r s ,  thermoelectric  cell,  then annealed overnight  t o room t e m p e r a t u r e  (about  3 -  it  at  4°C p e r  200°C  hour  cooling rate).  The p r o c e d u r e o f  a n n e a l i n g was f o u n d u s e f u l  reproducibility  of  T h e t e m p e r a t u r e was t h e n r a i s e d a n d  at  an i n t e r v a l  of  the r e s u l t s . about  5 - 6  hours,  the  temperatures  the sample were measured by t h e r m o c o u p l e s . gradient  AT w e r e c a l c u l a t e d .  electrometer indicating tabulated  as the  T curve.  of b o t h ends  The mean t e m p e r a t u r e  s i g n of  c o l d e n d was a l w a y s f o u n d the charge c a r r i e r s .  Seebeck c o e f f i c i e n t ,  8=-AV/AT  The h e a t i n g a n d c o o l i n g r u n s w e r e r e p e a t e d t o 6 -  get  of  T and  T h e r m a l e . m . f . was m e a s u r e d b y a K e i t h l e y  m o d e l 200B and t h e  the p o s i t i v e  to  to be  The r e s u l t s  in millivolt  get  the  positive,  per  are degree.  reproducible  70  2.5  HALL EFFECT APPARATUS  2.5.1  Sample Holder and Heating Assembly  Since three shapes of samples (slotted c i r c u l a r , rectangular and square) were t r i e d , separate sample holders were designed f o r each case.  The sample holder was made with a piece of s o l i d c y l i n d r i c a l  t e f l o n which was  flattened at one end where the sample r e s t s .  On the  flattened portion, a cavity of appropriate shape to accommodate the p e l l e t was made. The e l e c t r i c a l contacts were made by four platinum wires A, B, C, D attached to the sample as detailed l a t e r for each sample shape.  A thermocouple wire T (Pt 10% Rh) was  Pt wires (C).  spot welded to one of the  These f i v e wires were insulated by passing through  slots  i n the t e f l o n terminating i n holes d r i l l e d through the wider top of the t e f l o n support, which was  shaped to f i t a B19 socket.  This sample  holder was vacuum-sealed (using dekhotinski cement) to the socket, which had a side arm to be connected  to the vacuum system.  For operation the  sample holder was placed i n a pyrex vessel V which had two outer jackets.  The extreme outer jacket was evacuated.  jacket was meant to pass the hot a i r to heat the. sample.  co-axial  The inner The whole  assembly of sample holder and pyrex v e s s e l i s shown i n Figure 19. For the s l o t t e d c i r c u l a r samples, a l l four contacts may  be  large-area, and the Pt wires were attached to the sample with s i l v e r paint.  For rectangular samples (11 x 3 x 1 mm),  four Pt points were  spot-welded to the Pt wires and mounted on screws by means of which they could be pressed firmly against the sample.  For square  (9.4 mm)  samples,  large-area current contacts of Pt f o i l were used, and the H a l l probes were Pt points on screws.  D  TC  A  B  /  2)  Figure 19 H a l l Sample Holde  <  Pyrex vessel  Teflon cylinder  Hot a i r  72  The s l o t t e d c i r c u l a r samples (which remove problems of s e n s i t i v i t y of the r e s u l t s to positions of the contacts) proved unsatisfactory because of mechanical d i f f i c u l t i e s i n f i t t i n g them into the available space.  (A smaller size of this type of sample would have been used i f  any p o s i t i v e r e s u l t s had been obtained with the simpler sample shapes.)  The c l a s s i c a l long rectangular shape was  abandoned for the  square i n an e f f o r t to secure maximum s e n s i t i v i t y when a l l r e s u l t s had proved to be negative.  2.5.2  Electrical Circuit  In the expectation that H a l l EMF's of the order of 1 mV more might sometimes be obtained, the c i r c u i t  (Figure 20) was  or  provided  with switching arrangements to allow a single Keithley model 200B electrometer (connected at E contacts, Figure 20) to be used successively to measure current and H a l l EMF.  But for lower H a l l EMF's, a more  s e n s i t i v e voltmeter could be connected at contacts F. used was  a Hewlett Packard model 425-A D.C.  down to 0.2 uV f u l l scale.  The  instrument  microvoltmeter, with ranges  I wish to thank Mr. J . Sallos of the  E l e c t r o n i c s Shop for lending me t h i s instrument, which was part of the shop's own  testing  Switch S  facilities.  2  was  leads or H a l l probes.  used to connect  the electrometer to the current  In the l a t t e r p o s i t i o n , S3 was  the current-supplying c i r c u i t .  closed to complete  S^ allowed any pair of electrodes to be  selected for current or EMF measurement; this i s needed for the van der Pauw method i n which the s l o t t e d c i r c u l a r sample i s used.  Figure 20  73  Hall Effect E l e c t r i c a l C i r c u i t  o—o  o—O  74  2.5.3  Magnet  An electromagnet spectrometer  o r i g i n a l l y designed f o r use i n a mass  was adapted for the present purpose.  The pole pieces were  11 cm i n diameter and 3 cm apart, and the windings were of many turns and high resistance, r e q u i r i n g a high voltage D.C. power supply d e l i v e r i n g only a low current (up to 250 V and 200 milliamp).  This  power supply, operating o f f 110 V D.C. mains, was b u i l t (and r e b u i l t f o r the present purpose) by the Chemistry Department E l e c t r o n i c s Shop.  The  c i r c u i t included a switch f o r reversing the f i e l d and coarse and f i n e current controls, allowing the current to be adjusted between 0 and 200 milliamp to an accuracy of about 0.04 milliamp. The magnetic f i e l d was calibrated by means of a proton probe.  NMR  The apparatus (block diagram, F i g . 21) consists of a v a r i a b l e -  frequency RF power supply, frequency  counter, probe containing trans-  m i t t i n g and r e c e i v i n g c o i l s and a sample of lithium chloride solution and an RF detector with display on an o s c i l l o s c o p e . water,  For protons i n  resonance i s ' a t 4257.7 KHz f o r a f i e l d of 1000 G, and resonance  frequency i s proportional to f i e l d .  The magnetic f i e l d was c a l i b r a t e d i n both d i r e c t i o n s (forward and reverse) of the magnetic f i e l d with increasing and decreasing  field.  The maximum magnetic f i e l d obtainable from t h i s magnet was about 2000 gauss.  The c a l i b r a t i o n probe was placed i n the centre of the f i e l d , as  near as possible to the p o s i t i o n normally occupied by the sample.  Figure 21 Block Diagram of Magnetic F i e l d C a l i b r a t i o n Apparatus  Magnet Frequency Counter  Probe  Power Supply  Oscillator Detector  Magnet Power Supply  Oscilloscope  76  2.5.4  Sample Preparation 21 For the method of Van der Pauw  which used slotted  c i r c u l a r samples, c i r c u l a r p e l l e t s were prepared CuCl  x  of both pure CuCl and  i n the usual manner as described i n Section (2.1.3).  The p e l l e t s  were cut about 5 mm deep into four equal segments by a fine mechanical saw with the help of a clamping device made of brass. the circumference  At the middle of  of each segment, the contacts were made using  Ag-paint.  The Ag-paint was dried c a r f u l l y i n a vacuum warmed by hot a i r . Rectangular  samples were prepared  i n a s t e e l die designed  from powder CuCl and CuCl^  for this purpose using a pressure of 6000 p s i  by the hydraulic press mentioned i n Section (2.1.3).  The square sample  was made by sawing from the c i r c u l a r p e l l e t and the surfaces were polished on carborundum polishing  2.5.5  paper.  Procedure  In the Van der Pauw method, the conductivity and H a l l c o e f f i cient of the irregularly-shaped sample can be found from various combinations of measurements of current between two electrodes and P.D. between two others with and without magnetic f i e l d , provided that the electrodes are a l l on the circumference  of the sample (not penetrating  i t ) and the thickness of sample i s known.  Since no p o s i t i v e  results  were eventually obtained, the method w i l l not be described i n d e t a i l . For rectangular samples, current and H a l l EMF electrodes are d i s t i n c t from each other, and current density and H a l l f i e l d can be found from the e l e c t r i c a l data and sample dimensions i n the obvious way.  Since  77  the H a l l probes may  show a spurious H a l l EMF because they are not  positioned exactly opposite each other, readings were always taken with and without magnetic  field.  When i t was desired to search f o r  very small H a l l EMF's, the electrode positions were adjusted by t r i a l and error to reduce the P.D.  between them at zero f i e l d below 0.2 yV.  Spurious H a l l EMF's may  a r i s e from pick-up i n the leads  (which may be field-dependent i f the pick-up i s from the magnet power supply) or from magnetoresistance (detectable at H a l l probes only i f they are misaligned and so have a non-vanishing zero f i e l d P.D., i f the sample has another resistance i n series with i t ) . such p o s s i b i l i t i e s , i t was necessary to check:-  and  To eliminate  (a) that any observed  e f f e c t d i d not recur i f the experiment was repeated with everything the same except that the sample was (b)  l i f t e d a short distance out of the f i e l d ;  that any observed " H a l l EMF"  proportional to f i e l d of the f i e l d ) .  reversed with f i e l d d i r e c t i o n and  was  (magnetoresistance i s proportional to the square  78  3.  3.1 3.1.1  RESULTS  ELECTRICAL CONDUCTIVITY E f f e c t s of Electrode Material, AC versus DC, and Surface Conductivity  For pure CuCl, three electrode materials have been used: Pt and Cu.  Ag,  For chlorine-treated samples, Pt electrodes were used  throughout because of the danger that the other materials would reduce the sample.  In most cases, both AC and DC measurements have been made;  but the low conductivity precluded AC measurements f o r pure CuCl below about 130°C.  For a s e l e c t i o n of samples, pure and chlorine-treated,  the e f f e c t of surface conductivity was checked by using the guard-ring electrode assembly with the guard r i n g a l t e r n a t e l y grounded and joined to the remainder of the electrode.  None of these possible disturbing influences was found to have any s i g n i f i c a n t e f f e c t on the observed a c t i v a t i o n energies.  Some  of them, as detailed below, were found to change the absolute value of the conductivity by s i g n i f i c a n t amounts - i n the worst case, about 80% - but nothing was found which appeared to suggest that these factors were s i g n i f i c a n t l y a f f e c t i n g the conduction mechanism, except for a possible change i n the r a t i o of i o n i c to e l e c t r o n i c contribution i n one case.  The e f f e c t of electrode material was i n s i g n i f i c a n t at lower temperatures (pure CuCl), but i n the high temperature region above 190°C the conductivity was depressed by about 40% for Ag electrodes and 80%  79  for Pt electrodes r e l a t i v e to the value f o r Cu electrodes.  This  may  a r i s e from electrode p o l a r i z a t i o n e f f e c t s or from a s l i g h t tendency for i o n i c c a r r i e r s (Cu*" i n t e r s t i t i a l s ) to be depleted when inert e l e c trodes were used, as happens to a much greater extent when DC i s passed for a long time with a Pt anode (the Wagner method of separating ionic and e l e c t r o n i c conductivity, section 3.3.2).  In either case, the e f f e c t  would be expected to a r i s e only i n DC measurements, and fact the case.  this was  in  No s i g n i f i c a n t dependence on electrode material were  found i n AC measurements.  AC c o n d u c t i v i t i e s were i n general greater than DC conductivities.  The size of the discrepancy was  sample, and was  dependent on the P.D.  across  a minimum (about 5 - 10% difference) for 0.2 - 0.3  The higher the P.D., DC measurements.  the V.  the more serious the p o l a r i z a t i o n e f f e c t s became i n  I n i t i a l readings of DC conductivity, taken as r a p i d l y  as possible to attempt to f o r e s t a l l the p o l a r i z a t i o n , often agreed very well with AC r e s u l t s .  Measurements on a sample with the guard-ring electrode grounded commonly gave r e s u l t s for conductivity about 18% lower than with the guard r i n g joined to the rest of the electrode. possible e f f e c t of surface conductivity.  This i s the maximum  Probably much of this decrease  arises from e f f e c t i v e removal of part of the bulk of the sample, as well as the surface, away from the c i r c u i t , since the inner electrode, without guard-ring, sample.  i s appreciably smaller than the f u l l surface area of the  The 18% decrease, which could be measured simply by changing  e l e c t r i c a l connections  without touching the sample, was  a significant  change, but lay within the range of sample-to-sample v a r i a t i o n s , which was  about  20%.  80  3.1.2  Pure CuCl  No AC conductivity measurements were made below about 130°C i n pure CuCl i n CuCl^ f o  x > 1.46.  r  Except for these, only AC data are  given.  The r e s u l t s showed two d i s t i n c t regions, the one above 180°C with an apparent a c t i v a t i o n energy E^ = 1.03 150°C with E^ = 0.55  eV.  eV and the other below  A t y p i c a l set of data i s plotted i n F i g . 22.  and a c t i v a t i o n energies and absolute values of conductivity at two temperatures  are shown for several samples i n Table 3 to show the repro-  d u c i b i l i t y of the r e s u l t s .  Between 180° and 150°C, the experimental  points l i e d i s t i n c t l y above either straight l i n e , but i n fact correspond very closely to the sum of the conductivities given by the two straight l i n e s , as shown by the dotted l i n e i n F i g . 22. Thus i t appears that the two conductivity mechanisms responsible for the two ranges are operating independently i n p a r a l l e l between 150° and 180°C.  In the upper range the present data agree very w e l l with previous work on highly p u r i f i e d samples (Wagner and Wagner, Hsueh and Christy, see F i g . 3).  The r e s u l t s of Bradley et a l . , whose sample  was not as pure as those of former workers agree p a r t l y with present results.  For instance, the absolute conductivity at 227° and the a c t i v a -  t i o n energy i n the lower region (which extends only down to about 97°C) are i n agreement with the present r e s u l t s but the a c t i v a t i o n energy i n the upper range i s less by ^ 0.2 eV than the present result 2).  The lower range represents behaviour previously  (see Table  reported only  10 /T(°K) 3  TABLE 3  Activation Energies and S p e c i f i c Conductivities of Pure CuCl with Different  A c t i v a t i o n Energies q E  Electrodes  ( V) e  Logi o  at 10 /T(°K) 3  0  SP  Samples  Upper Range  Lower Range  2.0  3.36  1  1.02  0.55  -4.07  -8.70  2  1.02  0.53  -4.05  -8.56  3  1.05  0.55  -3.85  -8.38  4  1.03  0.51  -4.55  -8.34  5  1.00  0.59  -3.80  -8.47  6  1.03  0.57  -3.82  -8.22  7  1.08  0.53  -3.98  -8.49  Average A c t i v a t i o n Energy E a Upper range 1.03  ± 0.01  Lower range 0.547 ± 0.01  S p e c i f i c a t i o n of electrodes: 1, 2  s i l v e r electrode  3, 5, 6, 7 copper electrode 4  Pt electrode.  eV eV  83  by Bradley et a l . ,  a c t i v a t i o n energies observed i n t h i s region by other  workers having usually been about half here.  In the work of Bradley et a l . ,  the value of 0.55 eV reported however, the room temperature  conductivity was about a hundred times greater than the present value, and the upper temperature range started at about 230°C and had an a c t i vation energy of only 0.78 eV.  3.1.3  Chlorinated CuCl  Data for samples ranging i n o v e r a l l composition from CuCl^ 000678 In  all  t  0  C  u  C  1  i  645  a  r  P  e  l o t t e d  i  n  F 1  S*  2  3  a  n  tabulated i n Table 4.  d  cases except f o r the samples with 0.0678% and 0.15% c h l o r i n a t i o n  two d i s t i n c t regions were found. CuCl^ 000678  anc  * ^ ^ - ' - i 0015 ^ u  fc  e  In the samples with composition  c o n d u c t :  ' - l y data show only one region. v  t  The samples from 0.29% c h l o r i n a t i o n upwards d i s t i n c t l y show two regions with a break i n the conductivity plot at 'v* 110°C. the  logio  vs ——- plot i s d i s t i n c t l y l i n e a r . J.  0  sp  For nearly a l l  samples  The only possible  exception was the 20.4% chlorinated samples, for which i t would be possible to  draw a continuous curve through the points. For  the 2.38% sample, the lower range was l i n e a r , but the data  were rather scattered i n the upper range.  Data from t h i s sample were  excluded i n c a l c u l a t i n g average values of a c t i v a t i o n energies.  As the percentage c h l o r i n a t i o n increases, the samples show changes i n a c t i v a t i o n energy, but these do not occur at the same percentage c h l o r i n a t i o n for the upper and lower ranges.  The a c t i v a t i o n energy  TABLE 4 Conductivity Results of Chlorinated CuCl  A c t i v a t i o n Energies Sample  CuC1  l.000678  CUC1  1.0015  CuC1  1.0029  CuC1  1.0102  C U C 1  1.012  CUC1  1.0238  CuC1  1.0675  CuC1  1.204  C u C 1  1.308  C U C 1  1.461  CuC1  1.502  C U C 1  1.545  C U C 1  1.552  C U C 1  1.604  C u C 1  1.645  Upper Range  q (eV)_  Lower Range  Log  a  24°C  130°C  200°C  0.38  -4.75  -3.12  -2.35  0.38  -4.78  -3.12  -2.43  0.43  0.38  -4.77  -3.02  -2.25  0.52  0.28  -4.82  -3.52  -2.50  0.55  0.37  -4.88  -3.34  -2.37  0.47  -5.27  -3.12  -2.05  0.43  0.31  -4.70  -3.25  -2.47  0.52  0.30  -5.35  -3.84  -3.05  uncertain  * 0.52  0.13  -5.65  -4.56  -3.60  0.47  0.13  -6.25  -5.52  -4.65  0.52  0.22  -7.30  -5.85  -4,85  0.79  0.12  -8.150  -7.32  -5.85  0.89  0.17  -8.50  -7.70  -5.90  0.930  0.25  -9.60  -8.30  -6.58  0.90  0.45  -10.50  -8.20  -6.50  *  * The l i n e s indicate the compositions at which the a c t i v a t i o n energies show abrupt changes.  86  of 0.38 eV, which appears at the s l i g h t e s t extents of reaction with chlorine, i s maintained i n the low temperature region up to 20.4%. Between that value and 30.8%, the lower range a c t i v a t i o n energy drops sharply.  Best values f o r the a c t i v a t i o n energies i n the lower range  are 0.36 eV up to 20.4%  (average of a l l samples from 0.0678%, with  2.38% excluded) and 0.15 eV from 30.8% to 55.2%; thereafter the low range a c t i v a t i o n energy again r i s e s .  An upper range did not appear i n 0.0678% and 0.15%  samples.  It f i r s t appeared i n the 0.29% sample, but with a rather low a c t i v a t i o n energy which was excluded from the average.  Beyond this point, the  upper range shows an a c t i v a t i o n energy which appears to match that of the lower range i n pure CuCl.  The best value, from pure CuCl and  chlorinated samples from 1.02% to 50.2%, i s 0.51 eV.  This i s i n exact  agreement with the lower range i n the work of Bradley et a l .  Their  "pure" CuCl, prepared by solution reduction of A.R. C u C l , seems to l i e 2  between the present "pure" and " s l i g h t l y - c h l o r i n a t e d " samples i n i t s absolute conductivity.  A CuCl2~doped sample i n their work, with 0.2  mole % C u C l , seems to match the present " s l i g h t l y - c h l o r i n a t e d " samples 2  f a i r l y c l o s e l y for the range with a c t i v a t i o n energy 0.51 eV.  Much of  the work of Bradley et a l . was at very high pressures, and thus not d i r e c t l y comparable to the present data.  At 40 kb pressure (but not  at lower pressures) and with 2 mole % CuCl2 i n the sample, they found an a c t i v a t i o n energy of 0.33 eV between 100° and 200°C. the present "lower-range" value. w i l l be discussed i n section 4.  This resembles  The significance of these comparisons  87  Beyond 50.2%, the upper range a c t i v a t i o n energy r i s e s abruptly.  The average value from 54.5 to 64.5% i s 0.88 eV.  In the  previous work of Ng, the a c t i v a t i o n energy was found to r i s e continuously with composition towards the same maximum value.  The discrepancy between the two sets of data arises because the temperature ranges used i n Harrison and Ng's work was i n many cases only just enough to permit the beginning of the upper range to be observed, while the range has been covered much more widely i n the present work.  The region from 0 to 6.75% c h l o r i n a t i o n was investigated more extensively i n the present work than i n that of Harrison and Ng, whose f i r s t sample was at 4.8%.  A feature not found at a l l i n the e a r l i e r  work i s a r i s e i n conductivity to about 1000 times that of pure CuCl at room temperature,' which takes place even at only 0.0678% c h l o r i n a t i o n . From there to about 1% c h l o r i n a t i o n , the room temperature conductivity remains constant, and thereafter i t f a l l s .  The region around 60% chlor-  i n a t i o n , where Harrison and Ng found a not very w e l l confirmed "bump" i n the conductivity was re-investigated c a r e f u l l y and no evidence of a bump was found. i n Table J|..  The data on absolute values of conductivity are given  The conductivity a f t e r l e v e l l i n g o f f decreases with  c h l o r i n a t i o n almost l i n e a r l y as shown i n l o g i Q O " ^ versus composition plot up to about CuCl^ 502'  '^  ie  decrease i  n  conductivity with higher compo-  s i t i o n i s s t i l l seen and i t appears that the conductivity has l e v e l l e d o f f at 60.4% c h l o r i n a t i o n (except at room temperature) ( F i g . 24).  88  Figure 24 Lo  £lO°sp  v e r s u s  C u C 1  x  O < x i 1.65)  89  3.2  THERMOELECTRIC POWER  Thermoelectric  power measurements were made on a l l types of  sample (pure, s l i g h t l y chlorinated, and heavily chlorinated) except where the sample resistance exceeded about 10^ ohm;  this happened only  for pure CuCl below about 50°C and for heavily chlorinated sampes (> 54.5%  chlorinated) below 120°C.  In a l l cases the sign of the thermo-  e l e c t r i c power was p o s i t i v e .  The r e s u l t s are shown as plots of thermoelectric power 9 against temperature i n Figure 25 (pure CuCl) and samples).  Figure 25  Figure 26 ( a l l chlorinated  i l l u s t r a t e s : - (a) error l i m i t s i n voltage measure-  ments, marked for two series of points; these errors a r i s e from f l u c t u a tions, probably  caused by pick-up, which became increasingly serious as  sample resistance rose; the v e r t i c a l l i n e s i n Figure 25 l i m i t s of the f l u c t u a t i o n s ;  indicate extreme  (b) the approach to reproducible behaviour  through successive cycles of heating and cooling; (c) the n e g l i g i b l e e f f e c t of changing the electrode material from Cu to Pt.  (The l a t t e r  was  used for a l l chlorinated samples.)  For a l l the curves i n Figure 26 up to x = 1.308, the error i n voltage measurement i s n e g l i g i b l e , but another possible source of error i s the approximation of the d e r i v a t i v e 6 =-dV/dT by the r a t i o of f i n i t e differences AV and AT across the sample when the 0 - T curve i s very non-linear.  AT was  about 6° at the lowest temperatures and about 30° at  the highest temperatures.  The most doubtful range i s , however, that near  to the maxima on the curves, and AT was  from 8 to 13° i n that region.  1.6 Figure 25 1.4  —  1.2  —  Thermoelectric Power of Pure CuCl  4 1.0  —  4  6  t.  60  •  ft  •  I+  .8 — >  6 Cell  Cu|CuCl|Cu,  Cooling o>  Cell  Pt|CuCl|Pt,  Cooling  Hsueh & Christy  CuCl  •  •  Doped 0.01% and  heating #, cooling A  0.1%  CdCl  2  CdCl„  For f i t of the present data to a curve, see diagram of P e l t i e r c o e f f i c i e n t  40  ( F i g . 27),  O 80  120  160 Temperature (°C)  200  250  60  1  Figure 26  •  Thermoelectric Power Data of Chlorinated CuCl  2.4'  • o  • A  2.0  •  C u C 1  CuC1  l.000678  o  •  1.0029  C u C 1  1.0l02  CuC1  1.0238  CuCl  1.0675  1.204  CuCl 1.308  1.0015  CuCl  CuCl  CuCl  1 < 5 4 5  CuCl 1.552 C u C 1  1.645  1.6'  1.2  .8  .4  40  80  120  160 Temperature (°C)  200  240  92  The p o s s i b i l i t y that the f i n i t e difference procedure might have d i s t o r t e d the positions and shapes of the maxima i s best checked by comparing runs on s i m i l a r samples i n which the temperature intervals are displaced from each other, e.g. 90 - 100° and 101 - 111° i n one run, but 95 - 105° and 106 - 116° i n the other.  Two such runs are those for x = 1.000678 and  1.0015 i n Figure 26 (open and s o l i d square displaced about 5% from each other near to the maximum).  The r e p r o d u c i b i l i t y between these two runs seems  to j u s t i f y the procedure for estimating 6.  While the Seebeck e f f e c t i s the easiest thermoelectric e f f e c t to measure, the P e l t i e r c o e f f i c i e n t i s easier to i n t e r p r e t , since i t indicates the energy transported by a charge c a r r i e r s (roughly E  for F  p o s i t i v e holes), whenever there i s only a single species of c;.rrier; f o r mixed conduction mechanisms, i t gives the average energy transported by the c a r r i e r s , weighted i n proportion to the f r a c t i o n of the current carried by each type of c a r r i e r , provided that the c a r r i e r s are a l l of the same sign; contributions from c a r r i e r s of opposite sign are subtracted. The P e l t i e r c o e f f i c i e n t i s e a s i l y calculated from 9, being simply 9T. Values of this quantity are plotted against temperature i n Figs. 27 (pure CuCl), 28(a) (chlorinated samples up to x = 1.0102) and 28(b) (more heavily chlorinated samples). The r e s u l t s show four types of behaviour, as follows:(a)  Pure CuCl:  The thermoelectric power shows only a s l i g h t  temperature  dependence, but the dependence at low temperatures seems to be somewhat d i f f e r e n t from that above about 90°C; this i s seen most c l e a r l y i n the  40  80  120  160 Temperature (°C)  200  I  1  240  Figure 28a P e l t i e r Coefficient of Chlorinated CuCl  O  1.0  CuCl CuCl  •  .8  A •  CuCl CUC1  1.000678 1.0015 1.0029  1.0102  NiO  (Austin et a l )  .6  .4 - f  .2  H  40  80  120  160  200  T 240  Temperature (°C)  4S  Figure 28b 1.0  — P e l t i e r Coefficient of Chlorinated CuCl O  .8  CuCl •  >  <u  CuCl  CuCl CuCl  .6  1.0238 1.0675 1.204 1.308  O—  .4  .2  40  80  120  160  200  240  Temperature (°C) -  to tn  96  plots of the P e l t i e r c o e f f i c i e n t (Fig. 27).  In this sample, conduction  i s changing from e l e c t r o n i c (positive hole) to i o n i c (Frenkel defect, i n t e r s t i t i a l predominating, p o s i t i v e sign) over the temperature studied.  The way  range  i n which this changeover could give a v a r i a t i o n of  the form observed i s shown by equations (1) - (4) of Section 1.3.3.  The  l i n e a r region, of negative slope, corresponds to conduction completely by p o s i t i v e holes (equation 1.3.3  (1)).  I t s intercept at T = 0, 0.53  i s i n good agreement with the proposal (Section 4.1) acceptor l e v e l at 0.51  eV.  eV,  that there i s an  Departure of the curve upwards from t h i s  l i n e should represent the appearance of a contribution from i o n i c conduction (equation 1.3.3  (2)).  This i s f i r s t noticeable at 80°C,  according to the curve of e6T versus T.  As the temperature increases,  the P e l t i e r c o e f f i c i e n t should eventually become constant i f i o n i c conduction i s dominant.  This condition has been achieved by about  180 - 200°C, and the l i m i t i n g value of e6T i s (eeT)  ro  = q  ±  = 0.439 eV.  This value may be used i n conjunction with equation 1.3.3  (4)  to calculate from the values of eGT the % i o n i c conduction at any T. The r e s u l t s are shown as curve G of F i g . 29.  Although the o v e r a l l tem-  perature range for the t r a n s i t i o n agrees w e l l with that found by other methods, quantitative agreement on the form of the v a r i a t i o n i s rather poor.  In p a r t i c u l a r , the thermoelectric power r e s u l t s indicate that 50%  i o n i c conduction i s achieved just below 100°C, while a l l other methods indicate 130° - 160°C (the highest value, from the crossing-point of the l i n e a r In a versus 1/T p l o t s , being probably the most r e l i a b l e ) . A - F of F i g . 29 are described i n Section 3.3.  Curves  Figure 29 Previous work  % of Ionic Conductivity i n Pure CuCl  •  Tubandt et a l - A  A  Maidanovskaya et a l  This work 100  Conductivity - C  80  Gravimetric  (22.5V)  Gravimetric  (0.5V) -  Wagner's Method - F Thermoelectric Power 60  40  20  80  120  160  200  Temperature (°C)  240  280  320  98  0 appears to be much more s e n s i t i v e to s l i g h t changes i n conditions than does a.  Disagreement between the present  9 data and  those of Hsueh and Christy (Fig. 25) contrasts strongly with the good agreement found i n a data.  (b)  Chlorinated samples up to x = 1.0102:  The  passes through a well-marked maximum at 100°C.  thermoelectric power This type of behaviour  14 has been reported i n NiO by Austin et a l .  ,  who  pointed out that i t  i s d i f f i c u l t to explain on the basis of a single conduction mechanism. In section 4, the model of two mechanisms (holes, and electrons at the acceptor  l e v e l ) proposed for NiO w i l l be applied to these r e s u l t s .  The  phenomenological comparison between the CuCl and NiO data i s shown i n Fig.  28(a) and F i g . 30 as p l o t s of  9 against 1/T  (as used by Austin et  a l . ) ; the resemblance i s quite s t r i k i n g and suggests that, once the 3d band has been somewhat depleted  of electrons, CuCl behaves rather  s i m i l a r l y to NiO i n respect of e l e c t r o n i c properties. (c)  Chlorinated samples from x = 1.0238 to x = 1.204:  Similar behavior  to type (b), but with a less pronounced maximum at a lower temperature (70 (d)  75°C). Chlorinated samples with x - 1.308:  i n s e n s i t i v e to temperature but decreasing  No maximum, 9 becoming rather as x increases.  Figure 30 Comparison of thermoelectric Power of C u C l  x  (1 < x < 1.0675) with NiO CuCl  2.0  CuCl  1.8  60  •3  1  1.6  1.4  H  1.2 -\  1.0 —4  10 /T(°K) 3  1.000678 1.0675  100  There i s a rough phenomenological  correspondence between  these types of behaviour and the k i n e t i c s of the CuCl/C^  reaction as  studied by Harrison and Ng.  An i n i t i a l l y very rapid reaction i n the  f i r s t 5% of chlorination was  followed by a slower zero-order process  up to about 20%.  The onset of a d i f f u s i o n - c o n t r o l l e d build-up of CuCl^  around each CuCl p a r t i c l e was  somewhere between 20% and 30% c h l o r i n a t i o n .  Evidently the changes at the surface r e f l e c t e d i n this k i n e t i c behaviour produces changes i n defect e q u i l i b r i a i n the CuCl phase which produce the thermoelectric power behaviour just described.  The probable nature  of the defect structure i s discussed i n more d e t a i l i n Section 4.  The data for low temperatures  in slightly-chlorinated  samples,  i . e . f o r the region i n which 6 or 9T i s r i s i n g rapidly towards the maximum, are l a t e r to be related to a model of two-level conduction by holes and electrons.  In Section 1.3.2, equations have been presented  which show that 6T should change with, temperature approximately i n the manner of an "activated" quantity.  Combining equations (15) and  (23)  i n Section 1.3.2, we have  e0T + kT ln(N /N ) = (E^/K) e ~ y p " y n (E  A  E  D  +  E  )  /  k  (D  T  A  In F i g . 31, data for the sample at x =1.000678 are plotted against 1/T i n two ways:- ( i ) as l o g ^ S T , i . e . ignoring the correction for the donoracceptor r a t i o ; this gives a reasonably l i n e a r plot from 40° to 80°C with an "apparent a c t i v a t i o n energy" of 0.22  —l\ 4.6x10 T), which corresponds to but now  N A  /  N D  2 ^ 10 •  gives a slope corresponding to 0.17  discussed i n Section 4.  eV,  ( i i ) as log^Q(e6T +  The plot i s s t i l l  eV.  linear,  These values are further  102  The high-temperature  end of the 9T versus T curves f o r s l i g h t l y -  chlorinated samples i s also of i n t e r e s t .  According to equation  (11) i n  Section 1.3.1, this curve should be l i n e a r and should extrapolate to give  at the absolute zero.  The points i n the present r e s u l t s are too  scattered to give a very r e l i a b l e extrapolation; values of E  from 0.4 to  0.9 eV can be obtained from various ways of extrapolating the curves i n Figs. 28(a) and (b).  Probably the best value i s that obtained from the  extrapolation of the combined r e s u l t s for samples at x = 1.000678 and x = 1.0015, f o r temperatures  above 160°C, as shown i n F i g . 28(a).  This  y i e l d s E. = 0.63 eV; but the uncertainties are such that error l i m i t s of A about ± 0.2 eV should be set on this quantity.  No s t a t i s t i c a l analysis  has been attempted, because the greatest source of error i s the choice of the range to be included i n the " l i n e a r " portion, which i s a subjective matter and not amenable to s t a t i s t i c a l analysis. Quantitative or semi-quantitative data, as required f o r further discussion i n section 4, have thus been obtained from r e s u l t s below 80°C and above 160°C; the range between those two temperatures  i s puzzling.  The values of 6T should not, on the basis of the type of explanation being developed high-temperature crepancy.  i n this thesis, go above the l i n e a r extrapolation of the data.  No explanation has yet been found f o r this d i s -  The data of Austin et a l . for NiO show a s i m i l a r discrepancy,  which has not been pointed out or discussed at a l l by those authors.  103  3.3  TRANSPORT NUMBERS  3.3.1  Gravimetric Method, and Data from Conductivity  For pure CuCl, transport number measurements were made by weighing the copper electrodes before and a f t e r passage of a quantity of e l e c t r i c i t y measured by a s i l v e r coulometer  (Section 2.3.1). In  the f i r s t experiments, a c e l l of EMF 22.5 V was used i n the c i r c u i t . Results f o r the f r a c t i o n of i o n i c conductivity (Table 5 curve  D ) indicated that the conductivity i s almost  and F i g . 29,  completely  e l e c t r o n i c up to 200°C, and becomes 50% Ionic at about 265°C.  These  data are s i m i l a r to those obtained half a century ago by Tubandt ( F i g . 29, curve A ) i n which conduction became 50% i o n i c at 230°C.  Much more  recently, Maidanovskaya found almost completely e l e c t r o n i c conduction up to to 250°C (curve B ).  But i n the present work, the changeover i n conduction mechanism as indicated by the crossing-point of the two l i n e a r portions of the log a versus 1/T plot (Section 3.1.2, F i g . 22) was at 160°C.  I f , as  suggested i n Section 3.1.2, the l i n e a r portions represent e l e c t r o n i c and i o n i c conduction mechanisms which, i n the t r a n s i t i o n region, are operating independently, i n p a r a l l e l , then the f r a c t i o n of i o n i c conduction can be calculated at any temperature  from the a - T data.  For c a l c u l a t i o n s  covering the t r a n s i t i o n region, accurate data are not needed i n that region.  A l l that i s required i s the slope and intercept of both l i n e a r  portions of the log a versus 1/T p l o t , above and below the t r a n s i t i o n region.  TABLE 5 Transport Number of Pure CuCl  T°C  Wt. of Ag deposited (gm)  Wt. of Cu equiv. to wt. of Ag f o r 100% (gm)  Pellet  24  2.5037  1.4770  0.0  170  0.4984  0.2940  196  0.5057  230  (.22.5 Volt Applied Voltage)  Weight Change (mg) Anode Cathode  Average  % ionic  -5,70  +5.70  5.70  0.38  +0.2  -1.5  +0.80  1.15  0.78  0.298  +0.3  -4.97  +4.65  4.81  1.61  0.0815  0.0481  +1.75  -4.80  +4.10  4.45  9.25  244  0.0284  0.01675  +0.41  -3.19  +3.06  3.12  18.60  265  0.01667  . 0.00983  -1.35  -3.50  +4.55  4.02  41.00  o  105  The f r a c t i o n of i o n i c conductivity calculated on this basis i s plotted against T as curve  C  of Fig.29.  and the gravimetric data i s very marked.  Disagreement  between t h i s  I t appears to be the l a t t e r  which are suspect, because the quantities of e l e c t r i c i t y  passing  through the gravimetric samples indicate conductivities much greater than those found i n the conductivity experiments of Section 3.1 (Table 3). When this was r e a l i z e d , conductivity measurements were made at various stages of a gravimetric experiment. was at f i r s t  I t was found that the conductivity  close to the expected value, but l a t e r increased greatly  and f i n a l l y decreased somewhat, remaining, however, f a r above the i n i t i a l value (Fig.32). Evidently the continuous passage of D.C. through the sample s u b s t a n t i a l l y changes i t s properties.  This might be because the P.D.  across the sample i s more than adequate to decompose CuCl into Cu and either CuCl2 or_ C l . 2  Consequently, some of the gravimetric experiments  were repeated with an applied P.D. of only 0.5 V across the sample and coulometer.  This i s less than the lowest decomposition p o t e n t i a l  (0.77 V,for C u C l  2  production). The r e s u l t s (Table  6, F i g . 29, curve E)  are markedly d i f f e r e n t from the previous data at high P.D.  Conductivities  are now i n good agreement with those obtained i n ordinary conductivity experiments, and the changeover  from e l e c t r o n i c to i o n i c conductivity  occurs at a much lower temperature  (160°C for 50%) i n reasonable  agreement with the c a l c u l a t i o n from conductivity p l o t s , but i n marked contrast to the high P.D. data and to Tubandt's.  The low P.D. experiments  could not be extended down into the region of primarily e l e c t r o n i c  Time (hour)  TABLE 6 Transport Number of Pure CuCl (0.5 Volt Applied Voltage)  T°C  Wt. of Ag deposited (mg)  Wt. of Cu equiv. to wt. of Ag for 100% (mg)  Pellet  Weight Change (mg) Anode Cathode  Average  % ionic  224  13.85  8.17  -8.65  -7.60  +5.95  6.78  83.0  198  13.10  7.73  -3.45  -7.20  +5.65  6.43  83.0  181  7.55  4.55  0.90  -4.30  +2.90  3.60  80.9  162  3.50  2.06  1.25  -0.71  +0.25  0.48  23.3  108  conductivity below 160°C, because of the excessively long time needed for experiments i n that region with only 0.5 V applied.  For chlorinated samples, which would be reduced by Cu electrodes, Table 7  shows the r e s u l t s of transport number measurements  made by weighing the parts of a three-part assembly of p e l l e t s which was placed between Pt electrodes.  For the s l i g h t l y - c h l o r i n a t e d  sample,  no s i g n i f i c a n t contribution from i o n i c conduction was found at any temperature.  For the heavily-chlorinated sample, a l l p e l l e t s l o s t  weight at 242°C.  This could indicate up to about 5% i o n i c conduction,  but more probably represents the loss of a very small amount of water from the CuCl  component (CuCl * 2 H 0 2  2  dehydrates at about  100°C).  In a l l the experiments on chlorinated samples, the applied P.D.  (22.5 V)  was above the decomposition p o t e n t i a l , but the c o n d u c t i v i t i e s as calculated from the transport number data agree well with those from ordinary conductivity experiments (Table  8).  TABLE 7 Transport Number (CuCl. , ,.,) n  T°C  Wt. of Ag deposited (mg)  Wt. Cu equiv. to wt. of Ag for 100% (mg)  Total E l e c t r i c i t y (Coulombs)  Anode Pellet  Weight Change (mg) Middle Cathode Pellet Pellet  50  47.60  28.08  42.60  -0.25  -0.10  +0.10  70  31.60  18.65  28.30  +0.05  +0.15  +0.45  102  ^40.05  23.60  35.80  +0.05  +0.15  +0.45  135  42.25  25.07  37.80  -0.15  -0.06  -0.05  200  39.10  23.06  35.00  +0.30  +0.70  +0.95  Transport Number (CuCl^  200  31.30  18.45  28.0  -0.18  0.00  +0.13  242  16.31  9.62  146.0  -5.10  -1.70  -1.80  110  TABLE 8  Conductivity of CuCl, . and CuCl, ,, 1.0143 1.645 Estimated from Transport Number Data 0  CUC1  0  Temperature (°C)  c  1.0143  (ohm cm ) sp (from Transport Number) -1  -1  50  2.12 x 1 0  70  5.13 x 10~  - 5  5  a' (ohm cm ) sp (from Conductivity Expt.) -1  -1  3.56 x 10"  5  6.30 x 10~  5  .102  0.417 x 10~  135  3.05 x 10 *  3.98 x 1 0  - 4  200  1.26 x 1 0  3.16 x 1 0  - 3  -t  C u C 1  - 3  h  1.41 x 10~  h  1.645  200  3.05 x 10"  242  1.07 x 1 0  7  - 6  3.16 x 10~ 1.78 x 1 0  7  - 6  Ill  3.3.2  The Wagner Method of Suppressing Ionic Conduction  The Wagner method involves measuring the l i m i t i n g current at long times f o r the c e l l Pt|CuCl|Cu with the Pt electrode p o s i t i v e . The method was  t r i e d only for pure CuCl, because CuCl|Cu equilibrium  i s established on one side.  For three samples, P.D.'s were applied across the sample only in the sense of Pt electrode p o s i t i v e . at a l l temperatures  from 245°C down to 24°C (Table 9  p l o t s of l o g i o l versus applied P.D. behaviour  The behaviour was  were l i n e a r .  then non-ohmic  and F i g .  3 3 ) and  This i s the expected  (Section 1.2.3, equation (3)) f o r the higher temperatures,  but  i s s u r p r i s i n g at low temperatures, when the conduction i s almost e n t i r e l y electronic.  According to equation (3) of Section 1.2.3, the slope of a plot of l o g i o l against applied P.D.  should be (F/2.303 RT), and the intercept  should be a (ART/LF) where a i s the contribution to conduction from P P p o s i t i v e holes ( i n the c e l l Cu|CuCl|Pt) and A and L are cross-section and length of the sample.  F i g . 34 shows the conductivities obtained  from intercepts, as a logger versus 1/T p l o t , i n comparison with the r e s u l t s of an ordinary conductivity experiment. agreement i s excellent. for  At high temperatures,  At low  temperatures,  this method gives values  the e l e c t r o n i c component somewhat below the l i n e a r extrapolation of  the low-temperature data. The slopes of the l o g i c * versus E p l o t s are, however, quantitat i v e l y much less than the expected values, and they do not vary with  112  TABLE 9 Data f o r Non-ohmic Current Voltage Plot for Selected Temp. Voltage (volts)  Current (amps)  Log Current (amps)  0.4  6.76 x 1 0  0.5  1.09 x 10~  0.6  2.24 x K T  0.7  4.46 x 10~  0.8  8.91 x 1 0  0.4  1.07 x 10~  7  -6.97  0.5  2.40 x 10"  7  -6.65  0.6  4.46 x 10~  7  -6.35  0.7  8.91 x 10~  7  -6.05  0.4  5.01 x 10"  7  -6.30  0.5  1.12 x 1 0  0.6  2.24 x 10~  0.7  4.78 x 1 0  0.4  1.40 x 10~  6  -5.85  0.5  3.16 x 10"  6  -5.50  0.6  7.94 x 10"  6  -5.10  0.7  1.78 x 10~  5  -4.75  0.4  7.07 x 10"  6  -5.15  0.5  1.76 x 10"  5  -4.75  0.6  5.01 x 10~  5  -4.30  0.7  1.42 x 10"  4  -3.85  - 9  8  -7.96 -7.65  8  8  - 8  - 6  6  - 6  -8.17  -7.35 -7.05  -5.95 -5.65 -5.32  113  Figure 34 Conductivity of Pure CuCl by Wagner Method  115  temperature  i n the expected way.  The slopes are shown i n Table  10,  together with the % i o n i c conduction calculated from the data plotted i n F i g . 34. Fig.  29.  The % i o n i c conduction i s also plotted as curve F  of  The curve i s i n moderate agreement with other methods of  determining the transport numbers.  The non-ohmic behaviour of samples at low temperatures rather s u r p r i s i n g .  At these temperatures,  was  i n t e r s t i t i a l s should not be  able to produce the e f f e c t because they contribute very l i t t l e to the conduction process.  But the l i n e a r l o g ^ I versus E plots were s t i l l  found for a p o s i t i v e sign of the Pt electrode.  The l i n e a r plot i s to  be expected i n the "forward b i a s " d i r e c t i o n of a r e c t i f i e r , and the d i r e c t i o n found i s incorrect for a metal/p-type  semiconductor  rectifier.  In order to find out whether the h i s t o r y of the sample was important i n determining i t s low-temperature behaviour, the following experiment at  was performed.  A p e l l e t was prepared as usual, and  196°C i n the c e l l with Pt|CuCl|Cu  passing any current through i t .  annealed  electrode arrangement without  After cooling to room  temperature,  E - I measurements were made, the sample being held at constant E u n t i l I became constant (^ 15 min.)  and values of E from +1.0  V to  -1.0 V being used c y c l i c a l l y u n t i l reproducible r e s u l t s were obtained. The behaviour then found was ohmic ( F i g . 35, points marked square). temperature was  changed to 236°C, and the same type of determination of  current-voltage c h a r a c t e r i s t i c was ohmic ( F i g . 36).  The  This experiment  repeated. was  The behaviour was  terminated with E p o s i t i v e  of Pt electrode) and measurements were made at two lower  non(sign  temperatures  TABLE 10  Ionic Contribution Estimated by Wagner Method  Temperature (T°C)  % (ionic)  F/2.303RT  Slope(volt"  24  2.53  17.0  3.00  40  4.70  16.1  3.50  65  17.75  14.9  3.11  80  5.41  16.3  2.95  90  18.23  13.9  3.00  100  14.90  13.5  2.95  125  37.50  12.6  3.32  144  62.00  12.1  3.34  160  90.80  11.6  3.59  181  97.25  11.4  4.53  197  98.00  10.7  4.40  217  99.20  10.3  4.47  245  99.60  9.7  4.60  Figure 35 Ohmic Current-Voltage Plot with Wagner Electrode at 24°C  Limits of scatter of experimental points i n 4 cycles of changing E (A: E decreasing. B: E increasing) In cycle 1 only negative values of E were used. Cycles 2B and beginning of 3A Cycle 4B Measurements a f t e r determination of c h a r a c t e r i s t i c at high T  o  00  119  (188°C and 140°C), but with only p o s i t i v e values of E used. behaviour was non-ohmic at both temperatures.  The  F i n a l l y the sample was  brought back to room temperature, and the E - I c h a r a c t e r i s t i c redetermined with both p o s i t i v e and negative E.  The behaviour was again ohmic,  with the same resistance as before (Fig. 35, points marked t r i a n g l e s ) . The purpose of t h i s experiment was to determine whether the sample at room temperature retained a "memory" of the p o l a r i z a t i o n which i t had acquired at high temperature, and therefore behaved non-ohmically at low temperature.  As mentioned at the end of Section 1.2.3, i f the  sample had acquired a defect d i s t r i b u t i o n making i t , i n e f f e c t , a p-n junction, and that defect d i s t r i b u t i o n had become frozen-in at room temperature, then non-ohmic behaviour would be found a f t e r cooling. This did not happen i n the experiment j u s t described.  In the e a r l i e r  experiments, however, no cycling between p o s i t i v e and negative E was performed at a l l ; only p o s i t i v e E was used at a l l temperatures.  This  may have been enough to produce a non-uniform defect d i s t r i b u t i o n .  The  explanation offered above f o r non-ohmic behaviour at room temperature is s t i l l a possibility. There are c l e a r l y a number of unresolved questions i n regard to these complicated phenomena with an asymmetrical pair of electrodes. The procedure of the e a r l i e r experiments appears to give a correct i n d i c a t i o n of the % e l e c t r o n i c conductivity, but for reasons which are obscure, since the c a l c u l a t i o n depends on extrapolation of l o g I versus 1 0  E curves the slopes of which are inexplicable on the basis of the theory  120  used to handle the intercepts.  Since these experiments were only a  s i d e - l i n e giving an additional method of finding data a v a i l a b l e i n other ways, the study was not pursued further.  121  3.4  THE HALL EFFECT  The H a l l E f f e c t apparatus was tested with the aid of a piece of p-type s i l i c o n obtained from Mr. K.L. Bhatia (Dept. of Physics, The University of B r i t i s h Columbia) and indicated as containing a concentrat i o n of acceptors of ^ 7 x 1 0 was  1 5  cm . -3  The surface of the test sample  polished on Carborundum powder and s i l v e r paint was used to make  the contacts.  A H a l l e f f e c t was found, of the appropriate sign for p o s i t i v e holes, and indicated a c a r r i e r concentration of about 3 x 1 0  1 5  cm . -3  This result was considered adequate to show that the apparatus was i n working order, and the source of the discrepancy of a factor of about 2.4 between this value and the reported c a r r i e r concentration for the sample was not pursued. Measurements were made at room temperature on pure CuCl and on s l i g h t l y chlorinated samples (x = 1.0061, 1.0074 and 1.0088) with applied voltages up to 3 V for the s l i g h t l y chlorinated samples. For pure CuCl, which was considered the most l i k e l y sample to have an e a s i l y measurable H a l l e f f e c t i n view of the probably very low c a r r i e r concent r a t i o n , measurements were f i n a l l y made with 22.5 V across a square sample, with a meter across the H a l l probes capable of detecting 0.2 uV. No H a l l EMF was found. ^ 10  - 3  cm volt sec 2  - 1  - 1  This indicates either a c a r r i e r mobility or a compensated semiconductor  i n which electrons  and holes produce mutually opposed contributions to the H a l l e f f e c t .  122  Since s l i g h t l y chlorinated samples are believed to conduct e l e c t r o n i c a l l y at a l l temperatures, with a changeover from predominantly e l e c t r o n i c to predominantly p o s i t i v e hole conduction as the temperature i s raised, a high temperature measurement on such a sample was desirable. Accordingly, a sample of CuCl 1.0074 was tested at 170°C, with an applied P.D.  of 1.5 V and detection s e n s i t i v i t y of 0.2 yV.  H a l l e f f e c t was  found.  Again no  123  4.  4.1  DISCUSSION  GENERAL INTERPRETATION OF RESULTS  For pure CuCl i n the upper part of the temperature range studied, the charge c a r r i e r s are known to be i n t e r s t i t i a l cations.  The  present work has added nothing s i g n i f i c a n t to knowledge on this already well-studied region, but merely confirmed that the present  samples  behave s i m i l a r l y to those used i n the most r e l i a b l e of previous studies.  For the lower temperature range i n pure CuCl, and for c h l o r i n e treated samples at a l l temperatures covered i n the present study, the charge c a r r i e r s are e l e c t r o n i c . The p o s i t i v e sign of the thermoelectric power shows that these must include p o s i t i v e holes, but does not prove that they are exclusively or even primarily p o s i t i v e holes i n a l l cases. For a compensated semiconductor, i n which both holes i n the valence band and electrons at the acceptor l e v e l can conduct, 6 can be p o s i t i v e even when electron conduction (15) and  predominates.  This i s established by equations  (23) of Section 1.3.2, which were combined as equation  Section 3.2.  ( 1 ) of  The apparent anomaly arises because each c a r r i e r contributes  to the thermoelectric power (or the P e l t i e r c o e f f i c i e n t 6T) i n proportion to the energy which i t transports.  For the holes, t h i s i s approximately  the Fermi energy (measured from the valence band), but for the electrons i t i s the difference between the Fermi energy and the acceptor  level.  This l a t t e r i s rather small, and hence each electron contributes much less to the thermoelectric phenomena than does each hole.  (Further, up to  a high value of the electron concentration, the larger that concentration,  124  the nearer E_ i s to E., which tends to cancel out the e f f e c t of the F A increased concentration.)  Thus, since thermoelectric data give information on energy transport while conduction data give information on charge transport, a lack of obvious c o r r e l a t i o n between the two must always lead one to suspect the presence of a double conduction mechanism, i n which the two parts add d i f f e r e n t l y i n respect of energy transport and charge transport. Such a suspicion i s greatly strengthened by the observation of a very rapid r i s e of 0 with temperature.  Such a r i s e can be explained i n terms  of the model of two charge c a r r i e r s , with the a i d of the equations cited above; and the phenomenon i s very d i f f i c u l t to explain on any other basis; this point has been made by Austin et a l . ^ " * i n connection with data for NiO.  They were primarily concerned, however, with the analysis of  their r e s u l t s for Li-doped NiO, i n which the 0 - T curves did not show a maximum i n the neighbourhood of room temperature;  they did not attempt a  d e t a i l e d analysis of the curves for pure NiO, which d i d have a maximum.  Apparent  a c t i v a t i o n energies derived from a and 0 data should  be explicable i n terms of three q u a n t i t i e s :  the acceptor l e v e l energy E ,  and the true a c t i v a t i o n energies for motion of holes and electrons, E ' yp and E . Of these, E i s l i k e l y to be small; i t should d i f f e r from zero yn yp only i f the Cu 3d band i s narrow enough to require either a "hopping" mechanism or' a f a i r l y extreme case of a "polaron" mechanism.  The electrons,  on the other hand, are i n a s i t u a t i o n i n which a "hopping" mechanism i s very probable, and so one expects E >E yn yp  125  At low temperatures,  electron conduction should predominate,  and the electron concentration should be independent (section 1.3.2, equation (20), n^ = N^).  of  temperature  Then the apparent  activation  energy of conduction should be simply the true a c t i v a t i o n energy E The value 0.36 (  •  eV, being the lower range apparent a c t i v a t i o n energy for  s l i g h t l y - c h l o r i n a t e d samples, w i l l be assigned to E  •  At higher tem-  peratures, there should be a changeover to predominantly p o s i t i v e hole conduction, described by equation (14) i n section 1.3.2. a c t i v a t i o n energy i s then (E^ + E  ), and the value 0.51  The  apparent  eV w i l l be  assigned to t h i s .  A c o r r e l a t i o n with thermoelectric power data may now attempted.  Equation  be  ( 1 ) of section 3.2 shows that the apparent  acti-  vation energy of the P e l t i e r c o e f f i c i e n t (corrected for the term kT l n ( N . / l O ) should be (E - E + E.). AD up yn A  This should, therefore, be ' '  numerically equal to the difference between upper and lower range a c t i v a t i o n energies from the a data, i . e . 0.51 - 0.36  eV = 0.15  eV.  This i s to be compared with the values from plots of the thermoelectric data (Fig. 31), 0.22  eV without correction for kT In(N^/N^) and 0.17  eV  with a reasonable guesswork value for- that correction. Separation of the value 0.51  eV (for the upper range a data)  into i t s two components E. and E cannot be made d e f i n i t i v e l y from the A yp present data.  I t i s tempting to look at the whole range of conductivity  data for chlorinated samples, and to suggest that the lowest a c t i v a t i o n energy observed corresponds to a s i t u a t i o n with a fixed hole concentrat i o n and represents E . ^ yp  This would y i e l d the value 0.15  eV for E yp  (from the lower range data for highly-chlorinated samples) and hence 0.36  eV for the acceptor l e v e l E ; but these are i n fact merely an upper  126  l i m i t for E and a lower l i m i t for E.. PP A  I t i s d i f f i c u l t to reconcile  such a low value of E^ with the thermoelectric power data for s l i g h t l y chlorinated samples.  I t has been pointed out i n section 3.2 that the  shape of the 0 - T curves has a puzzling feature, i n that the maximum r i s e s above the extrapolated l i n e for high temperatures.  The maximum  also should not r i s e above E^; but i t does, even on the basis of the value 0.51 eV for E^.  The discrepancy could be accounted f o r , i n vague  general terms, by the uncertain correction for scattering e f f e c t s , which may be very complicated structure.  i n a p o l y c r y s t a l l i n e sample with complex surface  But i f E^ i s 0.36 eV, the discrepancy i s altogether too b i g  to account f o r i n any conventional manner. E  Hence i t i s suggested that  i s probably close to zero, giving E^ = 0.51 eV.  The assignment of  zero a c t i v a t i o n energy to E i s consistent with the known s i t u a t i o n i n yp NiO, i n which H a l l E f f e c t data were a v a i l a b l e ^ . I t remains to consider the s i g n i f i c a n c e of the a c t i v a t i o n energies of highly-chlorinated samples, e s p e c i a l l y those above 50% c h l o r i n a t i o n , f o r which the a c t i v a t i o n energies i n both temperature ranges are d i f f e r e n t from those of the s l i g h t l y - c h l o r i n a t e d material. The more extensively-reacted material i s known to be formed i n a d i f f e r ent way, k i n e t i c a l l y , from the material at lower extents of reaction. The work of Harrison and Ng showed that a layer of C u C l  2  began to build  up on each CuCl p a r t i c l e somewhere between 20 and 30% reaction. change seems to correspond  This  to the disappearance of the maximum i n the  0 - T plot and of the conduction behaviour with an a c t i v a t i o n energy of 0.36  eV.  Apparently  the concentration of donors has been suppressed -  but not to zero, because the upper temperature range s t i l l displays the  127  a c t i v a t i o n energy 0.51 eV which means, on the basis of the present i n t e r p r e t a t i o n , that the semiconductor  i s s t i l l compensated.  An  uncompensated system should show a c t i v a t i o n energy E /2, not E ; varA  A  A  ious previous reports^for not very well p u r i f i e d CuCl at low temperatures have, i n f a c t , reported the a c t i v a t i o n energy as about one-half that found i n the present work. P a r t i a l removal of donors at 20 - 30% reaction i s followed at a much l a t e r stage (> 50% reaction) by some process which gives r i s e to an a c t i v a t i o n energy of 0.88 eV.  This w i l l be interpreted as E^ for a  d i f f e r e n t type of acceptor (again including E i f i t d i f f e r s from zero; 1^ P the holes s t i l l move i n the same way - only the source of them i s different). for  This i n t e r p r e t a t i o n i s on a much shakier basis than that  the phenomena at low extents of c h l o r i n a t i o n .  The sample structure  is much more complicated; i t i s very heterogeneous, and the process of pressing a p e l l e t converts a system of CuCl p a r t i c l e s each coated with CuCl2 to one i n which CuCl p a r t i c l e s are i n contact with each other. Scattering processes w i l l be very complex; and although the conductivity data are c l e a r l y related to what i s happening i n the CuCl phase, the same i s not n e c e s s a r i l y true of 0.  As mentioned already, contributions  to 0 and 9 do not add up i n the same way.  No attempt w i l l be made to  correlate the conductivity data for highly-chlorinated samples with the very low (and composition-dependent) thermoelectric power. Nevertheless, the high-temperature  a c t i v a t i o n energy of 0.88 eV  i s well-established, c l e a r l y d i s t i n c t from the Frenkel defect a c t i v a t i o n 2c energy.of 1.03 eV (which Harrison and Ng  had formerly tentatively i d e n t i f i e d  128  i t with), constant over a range of extents of r e a c t i o n , and associated with p o s i t i v e hole conduction.  I t i s , furthermore, too large to be a  value of E /2; an acceptor at 1.76 eV would not ionize s i g n i f i c a n t l y A  at these temperatures.  Thus the i d e n t i f i c a t i o n of 0.88 eV as E^ for  an acceptor which appears only at high extents of reaction i s at least very p l a u s i b l e . 4.2  MODELS OF THE ACCEPTORS  I t i s proposed that the hole-trapping s i t e which gives acceptors with an i o n i z a t i o n energy of 0.51 eV i s the most obvious one to postulate i n s l i g h t l y non-stoichiometric CuCl, v i z . the cation vacancy (as envisaged also by Vine and Maurer i n iodine-doped C u l ) . The compensating donors i n h i g h l y - p u r i f i e d samples are probably residual foreign material.  In less w e l l - p u r i f i e d samples, f o r which a c t i v a t i o n  energies close to E^/2 have been observed, the chief d i f f e r e n c e i s probably not a greater concentration of foreign material but a much greater extent of oxidation, f o r which foreign donors can no longer compensate.  In other words, the r e s u l t s are a l l consistent with the  concept that p u r i f i c a t i o n of CuCl, whatever i t does by way of expelling foreign material, does much more towards achieving stoichiometric proportions of the host ions.  On this b a s i s , one of the most unusual features of the present r e s u l t s i s the occurrence behaviour.  i n non-stoichiometric material of compensated  This suggests the formation of a s p e c i a l type of donor i n  the s p e c i a l conditions of C l Cu  +  2  oxidation.  I t i s suggested  that this i s a  i o n i n some s p e c i a l surface p o s i t i o n (and thus at the reaction  129  interface) i n which i t can ionize to Cu incorporated into the valence band.  i n a l o c a l i z e d form not  This i s consistent with the d i s -  appearance of some of the e f f e c t s of a large donor concentration when surface conditions change d r a s t i c a l l y at 20 - 30% r e a c t i o n .  At that point, as already mentioned, CuCl2 s t a r t s to b u i l d up on each p a r t i c l e .  As t h i s reaction proceeds, the Cu o r i g i n a l l y present  i n CuCl must move to occupy eventually 66% more than i t s o r i g i n a l volume; but the o r i g i n a l C l ends up occupying only 83% of i t s o r i g i n a l volume.  I t i s p l a u s i b l e to envisage a force tending towards inward  movement of C l , and to postulate i n j e c t i o n of i n t e r s t i t i a l C l as the source of the new acceptor with an i o n i z a t i o n energy of 0.88 eV.  4.3  POSITIONS OF THE ACCEPTOR LEVELS  For c e r t a i n impurity l e v e l s i n the group IV elemental semi22 conductors, the "hydrogenlike" model of the state of the trapped e l e c tron or hole has been very successful. In the simplest form of this model, the electron or hole i s envisaged as being bound i n an analogue of a hydrogen Is state, with binding energy (in eV) and Bohr radius o  (in A) given by E  A  = 13.6 m*/(m  K ) 2  e  r = 0.528 K m /m* e where K i s the d i e l e c t r i c constant of the host l a t t i c e and m* i s the e f f e c t i v e mass appropriate, for acceptors, to a hole at the top of the valence band.  The v a l i d i t y of a model which represents the host l a t t i c e  130  only by the use of the single numerical constant K requires that the state of the trapped hole should e f f e c t i v e l y cover a region including a very large number of atoms of the host l a t t i c e .  This condition i s o  s a t i s f i e d i n S i and Ge, i n which r i s found to be about 20 and 50 A respectively. 10"  2  eV.  Corresponding values of the binding energy are of order  Vine and Maurer applied this model to the acceptor l e v e l  produced by excess iodine i n Cul, which was ascribed to a cation vacancy as trapping centre - the same model suggested here for the acceptors i n "pure" and s l i g h t l y chlorinated CuCl.  They obtained f a i r l y close agree-  ment between  experiment  l e v e l with  of the order of 0.4 eV (varying with acceptor concentra-  tion).  and the hydrogenlike theory for an acceptor  They hence estimated an e f f e c t i v e mass f o r the hole only s l i g h t l y  smaller than the free electron mass; but they neglected to point out that, f o r such a high E , the Bohr radius i s of order 2 A and hence A  indicates l o c a l i z a t i o n of the hole on the nearest neighbours of the vancancy.  This invalidates the use of K to represent the host l a t t i c e ,  and suggests that the calculated E^ may have no s i g n i f i c a n c e whatever. The corresponding c a l c u l a t i o n for CuCl, with m* = m , gives E e and r = 1.97  A.  A value of m  = 0.98  eV  A  >> m , such as has been reported for  20 ) would change the c a l c u l a t i o n to give E and r rather e A similar values to those i n the hydrogen atom i t s e l f ! CuCl (20  m  The hydrogenlike model thus does not appear very f r u i t f u l for the present purpose, and any more sophisticated c a l c u l a t i o n of E^ for a l o c a l i z e d model i s beyond the scope of this thesis. features of the l o c a l i z e d model may,  Some more general  however, be followed up.  In the  131  f i r s t instance, for a binary compound i n which a trapped hole resides p r i n c i p a l l y on nearest neighbours of the trapping s i t e , two values of are to be expected:  one for the case i n which those nearest neigh-  bours are anions, and one f o r the case i n which they are cations.  Of  the two acceptor s i t e s postulated i n the present work, the cation vacancy i s surrounded by anions, and the anion i n t e r s t i t i a l i s most l i k e l y to be i n a vacant tetrahedral s i t e of the cation s u b l a t t i c e , and hence surrounded by cations.  Thus two d i f f e r e n t values of E. are to be A  expected.  (If the hole were more highly l o c a l i z e d , and therefore sensi-  t i v e to the precise nature of the trapping centre rather than just i t s e f f e c t i v e charge, there could of course be many more than two values of E , as i s the case i n the group IV elemental semiconductors for deepl y i n g acceptor l e v e l s produced by anything except group I I I impurities. In the present discussion, i t i s supposed that the holes i n CuCl are mainly l o c a l i z e d on the nearest neighbours of the trapping s i t e , so that E  i s s e n s i t i v e primarily to the nature and arrangement of those  neighbours.)  ,  Since the valence band of CuCl i s composed primarily of cation 18 orbitals  (at the top, 79% Cu 3d, 21% C l 3p, according to Song  ), trapping  i n the v i c i n i t y of an i n t e r s t i t i a l anion may be regarded as "normal", i n that the hole, though l o c a l i z e d , may  s t i l l be described i n terms of the  same kind of o r b i t a l which predominantly constitutes the valence band. By the same token, trapping i n the v i c i n i t y of a cation vacancy i s "abnormal" i n requiring promotion of the hole to the C l 3p band.  Song's  calculations of the band structure indicate about 3 eV for the promotion  132  energy.  This would indicate that a cation vacancy cannot trap a hole  (unless the binding energy, apart from promotion, i s much greater than has so f a r been suggested i n this account).  The two values of E^, (0.51 - E^) and (0.88 - E^) eV, thus cannot be accounted f o r simultaneously on the basis of the present models i f a promotion to C l 3p i s needed f o r the former. another p o s s i b i l i t y .  There i s , however,  The proportion of C l 3p mixed into the Cu 3d band  i s s u b s t a n t i a l and presumably increases down the band from the value of 21% quoted by Song for the top of the band.  More s p e c i f i c a l l y , the  Cu 3d band system i s subdivided into a set of three (the t2 o r b i t a l s ) broadened to about 0.6 eV wide and a set of two (the e o r b i t a l s ) forming a very narrow band at the bottom of the broader one. This can be thought of as the normal c r y s t a l f i e l d s p l i t t i n g of d o r b i t a l s i n a l o c a l tetrahedral environment, with broadening into bands superimposed on i t . While the t  2  o r b i t a l s are appropriately oriented to interact with the  corresponding o r b i t a l s on neighbouring Cu , the e bands are very l i k e l y +  to interact i n d i r e c t l y , through C l 3p, and the bands formed from the e o r b i t a l s are l i k e l y to contain a greater proportion of C l 3p.  (This  q u a l i t a t i v e picture could be investigated quantitatively with the a i d of i n t e g r a l s tabulated i n Song's paper.) It i s possible that the admixture of Cu and C l o r b i t a l s i n the e bands might be suitable to represent the state of a hole trapped i n the v i c i n i t y of a cation vacancy.  On that basis, the difference of the two  E^ values, 0.88 - 0.51 = 0.37 eV, i s to be compared with a promotion energy which i s b a s i c a l l y the c r y s t a l f i e l d s p l i t t i n g , band top to band top, between t tions.  2  and e o r b i t a l s .  This i s 0.53 eV, according to Song's c a l c u l a -  133  4.4  SUMMARY OF PROPOSED DEFECT STRUCTURES, AND THEIR INFLUENCE ON E .  Pure CuCl contains holes and cation vacancies which act as hole traps (depth 0.51 eV).  These are present i n very small number and  are compensated by donors, which are probably impurities, so that the trap depth appears as E^.  Less highly p u r i f i e d samples may be s u f f i c i e n t l y  non-stoichiometric to contain holes and cation vacancies i n concentrations which are not compensated by the chance presence of donors. one-half of the trap depth.  E^ i s then  Deliberate introduction of non-stoichiometry  by reaction with chlorine (from C.07% to 20% conversion to CuCl ) produces 2  a high concentration of traps and holes, but also produces donors at the reaction i n t e r f a c e .  These l a t t e r are probably Cu  +  ions i n a favourable  2+ l o c a t i o n f o r a Cu semiconductor  to reside.  Because of the presence of the donors, the  i s compensated and the trap depth appears as E^ when hole  conduction predominates.  Eut the acceptors are now so close together that  "hopping" conduction of electrons at the acceptor l e v e l predominates below 100 - 110°C, and the true a c t i v a t i o n energy of this migration ( E ^ = 0.36 eV) n  appears d i r e c t l y as E^. g et a l .  This correlates with the observation of Bradley  that an a c t i v a t i o n energy E^ = 0.33 eV appears i n CuCl2~doped  CuCl, which may be expected  to contain holes and cation vacancies, and that  the appearance of this value of E^ i s favoured by high pressure, which should a s s i s t i n c i p i e n t band formation at the acceptor l e v e l . At about 20% conversion to CuCl2, the reaction mechanism of CuCl 2a with C l i s known 2  that CuCl  2  to undergo a change, the dominant feature of which i s  now s t a r t s to b u i l d up on each CuCl p a r t i c l e .  I t i s possible  that this suppresses the donor concentration at the surface, by allowing a  134  more direct, transfer of copper from the CuCl to the CuC1.2 l a t t i c e , the donors being e s s e n t i a l l y a long-lived intermediate i n the mechanism which operates below 20% conversion.  The decrease i n donor concentration  e f f e c t i v e l y destroys electron conduction at the acceptor l e v e l , but s t i l l allows compensation of hole conduction (which can occur at very low donor concentrations). found, but  Thus the a c t i v a t i o n energy E  = 0.36 eV i s no longer  ff  = 0.51 eV p e r s i s t s at higher temperatures.  The o r i g i n of the very low value E^ = 0.15 eV which now  appears  at low temperatures i s obscure; i t may a r i s e from electron withdrawal from the CuCl producing holes without an adequate number of traps for them. Beyond about 50% conversion, another change takes place i n the CuCl defect structure, which correlates with changes i n chemical r e a c t i v i t y and c a t a l y t i c a c t i v i t y previously observed  ±  n  the CuCl2 component.  amount of copper d i f f u s i n g through the l a t t e r (as Cu ) +  a maximum.  The  i s now approaching  Simultaneously with the outward movement of copper, there  should be an inward movement of chlorine.  I t i s proposed that Cl  inter-  s t i t i a l s i n the CuCl component now form hole traps with a depth of 0.88 which i s observed as E .  eV,  135  5.  5.1  SUGGESTIONS FOR FURTHER WORK  DOPING EXPERIMENTS  Probably the most widely-used method of attempting to introduce defects of known type i n a controlled manner i s by "doping" with foreign ions.  Attempts to introduce cation vacancies into CuCl by doping with a  divalent m e t a l l i c chloride might be bery useful i n the present case.  If  the o r b i t a l s of the guest metal would not combine with the Cu 3d bands, introduction of holes by a separate method would be necessary.  This  might be done either by i r r a d i a t i o n or, as i n the present work, by chemical oxidation with c h l o r i n e .  The properties of CuCl treated with  chlorine are known from the work of Ng to be d i f f e r e n t from those of a mechanical mixture of CuCl and C u C l . 2  attempting to introduce C u C l  2  No work has yet been done on  i n the manner of a dopant.  (CuCl  2  was  used as a dopant by Bradley et a l but considering the low purity of t h e i r CuCl, C u C l  2  should be further studied as dopant.)  It might be  very i n t e r e s t i n g to t r y the series of compounds N i C l , CuCl , and Z n C l 2  as dopants.  2  2  The 3d energy i s similar i n Ni and Cu, but much lower i n Zn.  Attempts should also be made to introduce guest ions on anion sites. trap.  A doubly-charged  ion such as S  2 -  would be suitable as a hole  A comparison of CuS and Cu S as dopants might be very useful; the 2  former should give holes and trapping s i t e s simultaneously, while the l a t t e r would give electron and hole traps - but a separate process would then be needed to produce electrons or holes.  136  5.2  ELECTRON PARAMAGNETIC RESONANCE  EPR  can often give very d i r e c t information on the l o c a t i o n of  a trapped electron or hole, because the spectrum shows hyperfine l i n e s a r i s i n g from the i n t e r a c t i o n of electron spins with the nuclear spins of the environment.  In favourable cases, this can lead to quite  i d e n t i f i c a t i o n of the environment. each of the elements ( C u , C u , 63  65  35  unequivocal  CuCl contains two stable isotopes of  C1,  37  C1)  and they a l l have spin  3/2.  The magnetic moments are, however, much larger for Cu than C l , and hyperf i n e s p l i t t i n g s from the two elements should be.clearly distinguishable. Ng looked at the EPR s i g n a l of chlorine-treated CuCl, but found only the s i g n a l to be expected from the CuCl2 l a t t i c e .  This material would have  to be removed by treatment with a suitable solvent before signals from defects i n the CuCl phase could be observed.  5.3  THE HALL EFFECT  Measurement of the H a l l E f f e c t i s the best way  to make a d e f i n -  i t i v e separation of concentration and mobility of charge c a r r i e r s .  It  seems u n l i k e l y that the H a l l E f f e c t i n the present samples can be many orders of magnitude below the detection l i m i t of the e x i s t i n g  apparatus,  and i t would be useful to continue attempts to detect the H a l l E f f e c t with modifications to the apparatus, CuCl samples.  and also with a greater v a r i e t y of  The apparatus used i n the present work was  regard to the magnet and i t s power supply, and sample.  I t should, however, be redesigned  adequate i n  the current supply to the  as follows:-  137  (a)  Better s h i e l d i n g should be provided around the sample c e l l and  on  the leads between sample c e l l and meters to permit measurements below 1 uV.  The present apparatus was  designed  on the assumption that H a l l  EMFs of a s u b s t a n t i a l f r a c t i o n of a mV would be found. leads and the EMF  (The current  leads should be separated; at present they run i n one  bundle from the c e l l to a switching box, and they appear to be of picking up signals from each other i n the yV (b)  A new  capable  region.)  voltmeter should be i n s t a l l e d , capable of reading 0.1 yV or  better.  Part of the d i f f i c u l t y samples may  i n obtaining a H a l l Effect i n these  a r i s e from the strong and complicated  s c a t t e r i n g processes  i n a p o l y c r y s t a l l i n e sample (in which the surface of each p a r t i c l e i s a reaction i n t e r f a c e i n the C u C l / C l would be u s e f u l .  2  reaction).  Single c r y s t a l experiments  Unfortunately, the features of most chemical i n t e r e s t -  the defects formed during reaction - are l i k e l y  to be much l e s s w e l l -  developed i n a s i n g l e c r y s t a l than i n p o l y c r y s t a l l i n e samples.  For  23 example, i n the work of B a i j a l xn this laboratory on the KI/CI2 reaction, p o l y c r y s t a l l i n e samples reacted extensively and showed marked changes i n conductivity, while single c r y s t a l s were almost unreactive.  Much i n f o r -  mation might, however, be obtained by t r y i n g to r e l a t e the conductivity behaviour of doped samples to that of chlorine-treated ones (as suggested i n section 5.1)  and then to study the H a l l E f f e c t i n doped samples, for  which purpose single c r y s t a l s could probably be used. 5.4  THERMOELECTRIC POWER  A l l that has been written i n the preceding section about the nature of the sample, and what might be done about t h i s i n r e l a t i o n to  138  the strategy of a programme of H a l l Effect work, applies  equally to  thermoelectric power. 5.5  CALCULATIONS ON ACCEPTOR LEVELS  The  least ambitious t h e o r e t i c a l c a l c u l a t i o n which would be  useful i n support of the present interpretation percentage of Cl 3p character i n the Cu 3d  i s the estimation of  (e) bands.  the  This could be  done with the aid of tabulated integrals i n the papers of Song.  A more  extensive theoretical, project would be an attempt to calculate the binding energy of a hole attracted an anion or a cation  site.  to an e f f e c t i v e charge located  on  either  139  REFERENCES  1.  C.F. Ng, Ph.D. Thesis, The Univ. of B.C. (1969).  2.  a. L.G. Harrison and C.F. Ng, Trans. Faraday Soc., 1971, 67_, 1787 b. i b i d 1801 c. i b i d 1810.  3.  B.H. Vine and R.J. Maurer,z. Physik Chem. 1951, 198, 147.  4.  J.B. Wagner and C. Wagner, J . Chem. Phys., 1957, 26^, 1597.  5.  Y.W. Hsueh and R.W. Christy, J . Chem. Phys., 1963, 3519.  6.  L.G. Maidanovskaya, I.A. Kirovskaya, and G.L. Lobanova, Inorganic Materials, 1967, 3, 839.  7.  C. Tubandt et a l , "JHandbuch der Experimental Physik", 1932, 12_, Part I, 383.  8.  R.S. Bradley, D.C. Munro and P.N. Spencer, Trans. Faraday S o c , 1969, 65_, 1912.  9.  W. Hebb, J . Chem. Phys., 1952, 18, 62.  10.  J.P. McKelvey, " S o l i d State Semiconductor Phys.", (Harper and Row, Pubs., 1966).  11.  F.J. Morin, Phys. Rev., 1954, 9J3, H95.  12.  Mikio T s u j i , J . Phys. Soc. Japan, 1959, 14, 1640.  13.  R.E. Howard and A.B. L i d i a r d , Rep. Progr. Phys., 1964, 27.* 161.  14.  J.N. Shive, "The Properties, Physics and Design of Semiconductor Devices", D. Van Nostrand Co., INC., 1959.  15.  I.G. Austin, A.J. Springthorpe, B.A. Smith and C.E. Turner, Proc. Phys. S o c , 1967, 90, 157.  16.  F. Herman and D.S. McClure, Am. Phys. Soc. B u l l . , 1960, _5, 48.  17.  M. Cardona, Phys. Rev., 1963, 12!9, 69.  18.  a. M.K.S. Song, De Jour.de Physique, 1967, 28, 195. b. K.S. Song, J . Phys. Chem. Solids, 1967, 28.> 2003.  19.  E. Calabrese, Ph.D. Thesis, Lehigh Univ. (1971).  20.  J . Ringeissen and S. N i k i t i n e , J . Physique, 1967, 28., C3-48.  140  21.  L.J. Van der Pauw, P h i l i p s Res. Repts., 1958, 13, 1.  22.  W.C. Dunlap; "An Introduction to Semiconductors", (John Wiley & Sons Pubs. 1957).  23.  M.D.  B a i j a l , Ph.D. Thesis,  The Univ. of B.C.  (1964).  

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