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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 British Columbia, 1969 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in 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 advanced degree 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 and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r 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 my w r i t t e n p e r m i s s i o n . 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 Columbia Vancouver 8, Canada Date i i ABSTRACT Measurements of e l e c t r i c a l conductivity (a), thermoelectric power (6) and transport numbers in the temperature range 24 - 240°C have been made on CuCl in the pure state and after reaction with chlorine to varying extents. Attempts to measure the Hall Effect gave negative results for a l l samples. Data for pure CuCl confirm earlier reports that conduction is electronic (positive hole) at low temperatures and ionic (cation inter-s t i t i a l s ) at higher temperatures (above 160°C, for our samples). For the low-temperature range, the significance of various reported apparent activation energies of conduction (E 0) has been c l a r i f i e d in the present work in terms of an acceptor level at E. = 0.51 eV above the valance band A (cation vacancy as trapping s i t e ) . The purest samples show "compensated" behaviour, = E^. Less pure samples show "uncompensated" behaviour, E being close to E /2. % ionic conduction has been estimated in three ways: from the conductivity data, from classical 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 slightly-chlorinated CuCl (which conducts much better than pure CuCl) correlates with current interpretations of the conduction mechanism in NiO. Conduction is electronic (i.e. not ionic) at a l l temperatures (24 - 240°C). The 9 - T curves have a pronounced maximum at about 100°C. They can be explained, and correlated with a data, only on the basis of two conduction mechanisms in parallel, by holes i i i in the valence band and electrons "hopping" at the acceptor level with an activation energy of migration E^^ = 0.36 eV. At low temperatures, electron conduction predominates and E = E . Above 100 - 110°C, hole a yn ' conduction predominates and = E^ (as for the lower range in pure CuCl). An energy calculated from the rising 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 solid, but with E^ = 0.88 eV (high T, > 50% conversion) and 0.15 eV (low T, > 20% conversion). Conduction is by holes-(contradicting an earlier suggestion from this laboratory that the higher value was for cation i n t e r s t i t i a l s ) , and the higher value is assigned as another acceptor level, E^ = 0.88 eV, probably for anion i n t e r s t i t i a l s as hole traps. The lower value has not been f u l l y explained. The origin of the two different trap depths, E^ = 0.51 and 0.88 eV, is b r i e f l y considered, and i t is suggested that the difference between them, 0.37 eV, may represent approximately the crystal f i e l d s p l i t t i n g of Cu 3d t2 orbitals from Cu 3d e orbitals in the tetrahedral site 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 v l i i ACKNOWLEDGMENTS x 1. INTRODUCTION 1 1.1 E l e c t r i c a l Conductivity of Copper Chlorides 1 1.1.1 Previous Work in this Laboratory 1 1.1.2 The Need for Further Study of Ele c t r i c a l Conductivity in CuCl x Systems 6 1.1.3 Previous Work on Pure CuCl in Other Laboratories 8 1.1.4 Scope of the Present Work 11 1.2 Other Experiments Giving Information on the Nature of the Charge Carriers 13 Introductory page 1.2.1 The Hall Effect 14 1.2.2 Direct Determination of Transport Numbers 19 1.2.3 Injection or Suppression of Carriers at a Metal-Semiconductor Contact 21 1.2.4 Thermoelectric Power 27 1.3 Interpretation of Conductivity and Thermoelectric Data for an Impurity Semiconductor 31 1.3.1 Fermi Level and Concentration of Holes 31 1.3.2 Simultaneous Conduction by Valence-Band Holes and Electrons at E^ 33 1.3.3 Thermoelectric Power for a Mixed Ionic and Hole Conduction 37 1.4 Band Structure and Charge Carriers in Cuprous Halides 39 1.4.1 Band Structure 39 1.4.2 Charge Carriers 43 V 2. EXPERIMENTAL 46 2.1 Sample Preparation 46 2.1.1 Purification of CuCl 46 2.1.2 Reaction of Sublimed CuCl with C l 2 48 2.1.3 Preparation of Pellets 51 2.2 Conductivity Measurements 53 2.2.1 Conductivity Cell 53 2.2.2 Electric Circuits 55 2.2.3 Procedure 60 2.3 Transport Number Measurement 61 2.3.1 Gravimetric Method 61 2.3.2 Wagner's Method 64 2.4 Thermoelectric Power Measurements 65 2.4.1 Thermoelectric Power Cell 65 2.4.2 Thermoelectric Furnace 67 2.4.3 Procedure 69 2.5 Hall Effect Apparatus 70 2.5.1 Sample Holder and Heating Assembly 70 2.5.2 E l e c t r i c a l Circuit 72 2.5.3 Magnet 74 2.5.4 Sample Preparation 76 2.5.5 Procedure 76 3. RESULTS 78 3.1 E l e c t r i c a l Conductivity 78 3.1.1 Effects of Electrode Material, AC versus DC, and Surface Conductivity 78 3.1.2 Pure CuCl 80 3.1.3 Chlorinated CuCl 83 3.2 Thermoelectric Power 89 3.3 Transport Numbers 103 3.3.1 Gravimetric Method, and Data from Conductivity 103 3.3.2 The Wagner Method Suppressing Ionic Conduction 111 3.4 The Hall Effect 121 4. DISCUSSION 4.1 General Interpretation of Results 4.2 Models of the Acceptors 4.3 Positions of the Acceptor Levels 4.4 Summary of Proposed Defect Structures, Influence on E a 5. SUGGESTIONS FOR FURTHER WORK 5.1 Doping Experiments 5.2 Electron Paramagnetic Resonance 5.3 The Hall Effect 5.4 Thermoelectric Power 5.5 Calculations on Acceptor Levels REFERENCES 123 123 128 129 and Their 133 135 135 136 136 137 138 139 v i i LIST OF TABLES TABLE PAGE 1. D.C. Conductivity of Pressed Pellets of Partly Chlorinated C u C l 2 c 5 2. Comparison of Previous Results on Pure CuCl 10 3. Activation Energies and Specific Conductivities of Pure CuCl 82 4. Conductivity Results of Chlorinated CuCl 84 5. Transport Number of Pure CuCl (22.5 Volt Applied Voltage) 104 6. Transport Number of Pure CuCl (0.5 Volt Applied Voltage) 107 7. Transport Number (CuCl^ 0143^ 1 0 9 8. Conductivity of CuCl, n.,„ and CuCl, ,.c Estimated 1.0143 1.645 from Transport Number Data 110 9. Data for Non-ohmic Current Voltage Plot for Selected Temp. 112 10. Ionic Contribution Estimated by Wagner Method 116 v i l i LIST OF FIGURES FIGURE PAGE 1. Conductivity Data of Harrison and Ng 3 2. Activation Energies of d.c. Conduction in Partly Chlorinated CuCl (Harrison and Ng) 4 3. Summary of Previous Conductivity Results 9 4. Ionic Transport in CuCl 19 5. Cu 3d and CI 3p Levels 39 6. Splitting of d-Orbitals in Tetrahedral Field 39 7. Atomic Orbitals 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 Pellet Making Die 52 11. Conductivity Cell 54 12. Guard Ring 54 13. Circuit Diagram for Conductivity Measurement 56 14. Circuit Diagram for Low Sample Resistance 58 15. Circuit Diagram for the 200 CPS Oscillator 59 16. Current Versus Time Plot in CuCl 62 17. Thermoelectric Cell 66 18. Calibration Curves for Thermocouples (Thermoelectric Cell) 68 19. Hall Sample Holder \ 71 20. Hall Effect E l e c t r i c a l Circuit 73 21. Block Diagram of Magnetic Field Calibration Apparatus 75 ix 22. Conductivity Plot of Pure CuCl 81 23. Summary Conductivity Plot of Chlorinated CuCl 84 24. L o g 1 0 a g p Versus CuCl x Plot (1 i x i 1.65) 88 25. Thermoelectric Power of Pure CuCl 90 26. Thermoelectric Power Data of Chlorinated CuCl 91 27. Peltier Coefficient of Pure CuCl 93 28. (a) Peltier Coefficient of Chlorinated CuCl 94 (b) Peltier Coefficient of Chlorinated CuCl 95 29. Percentage of Ionic Conductivity in Pure CuCl 97 30. Comparison of Thermoelectric Power of CuCl (1 < x < 1.0675) with NiO x 99 31. Plot of Log 1 Q8T Versus 1/T 101 32. Change in Conductivity with Time at 222°C 106 33. Logio 1 V e r s u s Applied Voltage Plot 113 34. Conductivity of Pure CuCl by Wagner Method 114 35. Ohmic Current-Voltage Plot with Wagner Electrode at 24°C 117 36. Current-Voltage Plot of Pure CuCl with Wagner Electrode (high temperature, 236°C) 118 X ACKNOWLEDGEMENT S I wish to express my sincere thanks to Prof. L.G. Harrison for his continuing interest, guidance and inspiration 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 grateful 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 El e c t r i c a l Engineering, U.B.C., for his advice and assistance in setting up Hall Effect 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 thesis. Finally, I would like to extend my thanks to my wife for many assistances, especially in drawing the diagrams. 1. INTRODUCTION 1.1 ELECTRICAL CONDUCTIVITY OF COPPER CHLORIDES 1.1.1 Previous Work in This Laboratory The work reported in this thesis arises out of studies of the reactivity and catalytic activity of copper chlorides carried out 1 2 a b c in this laboratory by C.F. Ng ' ' ' ' . In that work, copper chloride prepared by reaction of CuCl with chlorine (overall composition repre-1 2b sented as CuCl x) was found ' to have anomalously high catalytic activity for the chlorination of propane from x = 1.5 to x = 1.85. Correlation of these results with kinetic data on the CuCl /CI? reaction x * led to a proposed mechanism for the catalytic effect involving the simultaneous presence of C u 2 + and Cu^ in a CuCl2 l a t t i c e . Studies in support of the kinetic work included x-ray diffraction and e l e c t r i c a l 2c conductivity . The former revealed that the only lattices present in CuCl x were those of CuCl and CuCl2, the CuCl2 l a t t i c e being slightly distorted in a manner attributable to a small fraction of displaced cations. While most of the interest in the CuCl system thus centred on x the CuCl2 phase, e l e c t r i c a l conductivity results were interpreted as relating principally to the CuCl phase. The conductivity of CuCl exceeded that of CuCl2 by a factor > 10 3, and even up to x = 1.7 the conductivity of a pressed pellet of CuCl x was at least 10 times that of CuCl2« The possibility of the defective CuCl2 phase having unusually high conductivity was rejected on the grounds that, although a variety 2 of activation energies for conduction was observed, none of the values correlated with the activation energy for cation diffusion (0.49 eV) found in studies of the CuCl / C l 0 reaction. The same diffusion data, x converted to ionic mobility by use of the Einstein relationship, would account for only 0.1 to 10% of the observed conductivity up to x = 1.75. The results 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, CuCl x (1 < x < 1.4, Fig. 1, Curve A) - In this case plots of log 1 Qo" sp versus 1/T were linear up to some ill-defined tempera-ture above which the slope decreases,and the activation energy in the linear part i s 0.34 eV. Specific 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 polarisation up to 30% reacted sample was similar to CuCl. Type II, CuCl x (1.4 < x < 1.75, Fig. 1, Curve B) - The conduc-t i v i t y plot showed two distinct regions of different slopes, the transi-tion being in the temperature range of about 120 - 130°C. The activation energy in the higher temperature region was the highest seen in his work and reached 0.92 eV in the composition range of about 65 - 75% reacted CuCl. The value of specific conductivity at 130° showed an increase in the composition range of 60% reacted CuCl but the data were rather scattered. In this composition range the activation energy showed an apparently continuous variation with composition as shown in Figure 2. 0.9H 0.8 H 0.7H 0.6 H 0 . 5 i 0.4 Figure 2 Activation Energies of D.C. 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 0.3 M, mechanical mixture 0.2 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 — I 2.0 x in CuCl x 5 TABLE 1 o D . C . C o n d u c t i v i t y o f P r e s s e d P e l l e t s o f P a r t l y - c h l o r i n a t e d C u C l l o g . _ a A c t i v a t i o n E n e r g y P o l a r i z a t i o n x i n C u C l (130°C) ' (eV) (%)* 1 . 0 0 0 - 5 . 3 4 0 . 2 7 7 1 6 0 . 0 1 . 0 4 8 - 5 . 1 6 0 . 3 6 8 1 5 0 . 0 1 . 1 0 0 - 4 . 8 4 0 . 3 2 8 1 5 0 . 5 1 . 2 0 7 - 4 . 7 1 0 . 3 5 2 1 5 0 . 0 1 . 3 2 5 - 5 . 6 3 0 . 3 0 6 1 4 4 . 0 1 . 3 9 6 - 5 . 9 0 0 . 3 7 8 7 2 . 0 1 . 5 0 3 - 6 . 8 2 0 . 5 7 5 and 0 . 4 0 1 3 8 . 5 1 . 5 7 3 - 6 . 7 6 0 . 6 4 0 and 0 . 3 4 8 3 0 . 0 1 . 6 0 8 - 6 . 2 7 0 . 7 6 1 and 0 . 4 0 9 4 5 . 5 1 . 6 3 1 - 7 . 1 2 0 . 7 7 6 and 0 . 5 4 2 1 0 . 5 1 .677 - 7 . 1 9 0 . 9 3 5 and 0 . 6 2 8 9 . 7 1 . 7 4 1 - 7 . 6 9 0 . 9 1 5 and 0 . 6 1 5 6 . 0 1 . 7 5 5 - 8 . 1 8 0 . 7 0 8 4 . 7 1 .757 - 8 . 1 2 0 . 7 0 3 4 . 6 1 .887 - 8 . 2 5 0 . 6 5 5 6 . 0 2 . 0 0 0 - 8 . 6 0 0 . 6 7 0 3 . 0 1 . 7 4 1 ( M ) - 7 . 6 2 0 . 6 0 2 and 0 . 3 7 6 7 8 . 0 P o l a r i z a t i o n e f f e c t c a l c u l a t e d a s change i n c o n d u c t i v i t y on change o f p o l a r i t y , as 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 . P o l a r i t y changed e v e r y 80 s . 6 Type III, CuCl x (1.75 < x < 2.0, Fig 1, Curve C) - In this range of composition the a plots were straight lines with an activation energy of 0.67 eV, similar to that of CuCl2« The numerical values of activation energies, specific conductance and polarisation effects are given in 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 in CuCl Systems x  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 restricted to temperatures below about 160°C. In consequence, when two regions of differing activation energy were observed, the higher range was often only just seen and not studied over a wide enough temperature range for the activation energy to be accurately established; and where an upper range was not observed, this might mean only that i t started slightly above the maximum temperature studied. (2) The apparently continuous variation of activation energy with composition in the composition range from x = 1.4 to x = 1.74 (Fig. 2) i s an unusual phenomenon and very d i f f i c u l t to explain mechanistically. In the light of the remarks under (1) above, repetition of these deter-minations over an extended temperature range is clearly desirable. (3) The CuCl starting material in Ng's work was reagent grade powder without further purification. At high x, this may not be significant; but close to the stoichiometric composition, the conductivity of CuCl is 7 known to be very sensitive to purity. It was,therefore considered desirable to repeat the work with starting material more highly purified and well characterized by conductivity so that i t s properties in this respect could be compared with those of previous reported studies on the conductivity of pure CuCl in other laboratories (see Section 1.1.3). (4) Again in relation to the known sensitivity of stoichiometric CuCl to impurities, i t should be noted, that Ng did not investigate any compo-sitions between x = 1 and x = 1.048. Many interesting changes could have occurred in the intervening 4.8% composition range. (5) Harrison and Ng gave a speculative interpretation of the activa-tion energies as follows:- Assuming that the conductivity below CuCl^ 7,_ is essentially that of CuCl component, there are three p o s s i b i l i t i e s for charge carriers: (i) positive holes, arising from the anion excess and requiring activation energy because of trapping by cation vacancies, as suggested by Vine and Maurer in Cul/l2 system; ( i i ) cation vacancies; ( i i i ) cationic Frenkel defects, as discussed in earlier studies^'~* of CuCl at higher temperatures. A l l these species may act as charge carriers in their samples and they have speculated that low activation energy of 0.34 eV is due to positive holes, the intermediate value to vacancies (perhaps complicated by interaction with impurities) and the higher value of 0.92 eV at x = 1.63 to Frenkel defects. Thus they have interpreted the transition at x = 1.63 as leading to a CuCl structure which i s more normal in the sense that i t contains fewer cation vacancies and holes. On the one hand, i t was necessary, in connection with (c), to know whether the activation energy of 0.92 eV observed in Ng's work was 8 clearly distinguishable from the value of 1.06 eV associated with cationic Frenkel defects in previous work on pure CuCl (see section 1.3.2). On the other hand, any additional types of experimental infor-mation throwing light on the nature of the charge carriers would be helpful in confirming or casting doubt on these speculative assignments of the nature of the charge carriers. 1.1.3 Previous Work on Pure CuCl in Other Laboratories Previously-reported data on the e l e c t r i c a l conductivity of CuCl are summarized in Fig. 3 and Table 2. When this work was started, the only data reported below 160°C were those of Ng from this laboratory. While the present work was in progress, Maidanovskaya^ reported a study going down to room temperature and showing an activation energy very close to that found by Ng (Table 1). That study also appears to have been on material of no greater purity than reagent grade; and the results at high temperatures dif 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: (a) sublimation (Tubandt et a l . ^ , the earliest study); (b) zone refining (Hsueh and Christy ); (c) preparation from g the elements (Wagner and Wagner ). Bradley et a l . prepared CuCl by reducing A.R. cupric chloride with sodium sulphite. Methods (b) and (c) give results very closely similar 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 activation 10 TABLE 2 Comparison of Previous Results on Pure CuCl Reference Tubandt et a l . (DC) Wagner et a l . (AC) Christy et a l . (AC) Bradley et a l . (AC) Harrison & Ng (DC) Maidanovskaya et a l . (DC & #1) Maidanovskaya et a l . (DC & #2) Activation Energies (eV)  Upper Range Lower Range 0.97 1.04 1.06 0.85 1.75 0.89 0.70 0.50 0.27 0.25 0.20 L°glO asp at 227°C -3.45 -3.96 -3.90 -3.86 -6.55 -7.60 11 energy of 1.06 eV continues linear 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 slightly lower activation energy (0.97 eV, Table %) at high temperatures, and the activation 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 this work, i t is convenient to consider sepa-rately three temperature ranges: (1) Above 220°C, an activation energy of 1.04 to 1.06 eV seems to be well established in the purest samples. (2) Between 220° and 100°C, a wide variety 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 Christy), the activation energy of 1.06 eV continues throughout this range, while for the least pure (Ng, Maidanovskaya) an activation energy of 0.20 to 0.25 eV i s observed. Bradley et a l . observed a knee in the conductivity plot at about 227°C. The activation energy in the high temperature region corresponded to 0.78 eV whereas in the lower region down to about 100°C a slope of 0.51eVwas identified. (3) Below 100°C, Ng and Maidanovskaya both found activation energies of 0.20 - 0.27 eV and there are no data for purer material. 1.1.4 Scope of the Present Work In his previous work in this laboratory, Ng tried to cover the whole range of composition from x = 1 to x = 2 as fu l l y as possible and 12 used the minimum temperature range which would cover a l l the conditions used in his catalytic and diffusion experiments. From the above discussion (particularly section 1.2) i t i s evident that a wider temper-ature 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) especially below 100°C where the behaviour of CuCl of good purity i s entirely unknown, but with attention also to extending the temperature range upwards to overlap substantially 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^ in the composition range from x = 1.4 to x = 1.74, to check the accuracy of the activation energy of 0.915 - 0.935 eV observed by Ng as the maximum in this range, and to determine whether changes in activation energy are continuous or discontinuous in the composition variable x and whether o shows a maximum at x ^ 1.6. The above discussion of conductivity data alone is adequate to show the composition and temperature regions which require further study; but to try to establish the nature of the charge carriers (which was Ng's original objective, in relation to the problem of identifying reaction intermediates and catalytically active sites) 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 this topic. 13 1 .2 OTHER EXPERIMENTS GIVING INFORMATION ON THE NATURE OF THE  CHARGE CARRIERS This section describes several types of measurement which are potentially capable of giving information on such points as the sign, concentration and mobility of the charge carriers, and whether they are electronic or ionic. Of these methods, the Hall Effect is the most powerful in circumstances in which a reasonably large and reproducible Hall EMF i s produced. The required conditions, however, (see Section 1 . 2 . 1 ) effectively exclude ionic conductors, samples containing large concentrations of impurities, defects or other scattering centres which limit mobility, and, by the same token, polycrystals. Thus, although attempts have been made to observe the Hall Effect in the samples studied in the present work, the amount of useful information obtained has not been large. Of the other methods described below, direct determination of transport numbers and the Wagner and Wagner electrolytic method of suppressing ionic conduction so as to observe the electronic component are readily applicable, and have been applied previously, to CuCl. Both these methods have been used again in the present work and have been successful in characterizing the starting material as similar to the samples used in the most reliable of previous investigations. Unfortun-ately, because of the requirement for a reducing environment (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 pellet assembly using Pt electrodes has been performed (see Section 2.3.1). 14 Thermoelectric power measurements can be made on the widest variety of samples, and w i l l usually give the sign of the charge carrier, whether i t is ionic or electronic. (In the case of vacancy conduction, i t i s the sign of the effective charge of the vacancy which is given by the sign of the Seebeck effect - see Section 1.2.4. There are also some complications in electronic conductors in which both electrons and holes are moving; the sign of the thermoelectric power is not always that of the majority carrier - see section 1.3.) If the conduction is known to be electronic, the mobility and concentration of carriers can be e s t i -mated from the thermoelectric EMF. But the Seebeck effect of i t s e l f w i l l not usually give a clear indication as to whether the conduction i s electronic or ionic; i t normally has similar magnitude in both cases. Nevertheless, the measurement of thermoelectric power has proved, for the present project, to be a very useful type of experiment to supplement the information obtained from conductivity studies. 1.2.1 The Hall Effect The Hall Effect i s the production of a potential difference by application of a magnetic f i e l d to a sample through which a current is flowing, as a result of deflection of the paths of the charge carriers in the magnetic f i e l d . Usually, the current and magnetic f i e l d are at right angles to each other, and the Hall P.D. is observed in the third direction at right angles to both current and magnetic f i e l d . The sign of the Hall P.D. gives the sign of the charge carrier; i f current and magnetic f i e l d are both in a horizontal plane, with current running to the right and f i e l d away from the observer, deflection of charge carriers i s 15 downwards, and the lower electrode in the ver t i c a l plane acquires the sign of the charge carrier. The Hall P.D. is proportional to both current density J x and magnetic f i e l d H^. The symbols which w i l l be used are:-^x> £y = linear dimensions of sample. A = cross-sectional area (yz plane). E . E = potential differences across £ ,£, . Hence fields are E ll x y x' y x x and E /£ . y y i , j = current, current density H z = magnetic f i e l d = a constant known as the Hall Coefficient The basic equation for the Hall Effect i s : ( V V = * H J * H z ( 1 ) where E„ = E /l and is called the Hall electric f i e l d . The Hall H y y elect r i c f i e l d builds up u n t i l i t balances the Lorentz force i.e. E T T e = e v H H z or E R = v H z ( 3 ) where v i s the velocity of the charge carriers. Assuming that a l l the charge carriers have the same velocity, the current density is given by the equation (4) 16 J = n e v ( 4 ) x where n is the concentration of charge carriers per cm 3 . Substituting the value of J x and from equation ( 4 ) and ( 3 ) respectively in equation ( 2 ) , one can write = v Hz/n e v H z = 1/n e ( 5 ) where and e are expressed in emu. In order to express R^ in cm3/ coulomb, this has to be multiplied by a factor 10 8. The physical s i g -nificance of the Hall coefficient can be understood in terms of the density of charge carriers. The Hall coefficient i s the reciprocal of the density of charge carriers; this means, larger the value of R^ , smaller the density of the charge carriers. In other words for smaller density of charge carriers the Hall voltage w i l l be larger and conversely the larger the density of charge carrier the smaller the Hall voltage. If one allows for a distribution of velocities, the smaller the Hall voltage. If one allows for a distribution of velocities, equation ( 5 ) must be corrected by a factor 3 T T / 8 . Thus once the Hall coefficient is known the density of charge carriers can be evaluated. Further the mobility of the charge carrier can be found by the relation = R^ o since a = neu. is usually called the Hall mobility, and a the conductivity. Sensitivity of a Hall Effect Apparatus The Hall coefficient R^  i s the reciprocal of the charge carrier concentration, (1/ne); but for a given applied voltage in the x direction, E X > the potential difference developed in the y direction as a result of 17 the Hall effect depends on the mobility of the charge carriers, as the following algebra indicates:-Current i = E a - E a (A/£ ). Hence j = i /A = E a /£ . (6) x x x sp x x x x sp x Now a g p = n e y = vf\, so that = E ^ / C A ^ ) . (7) Substituting (7) into ( l ) , ( E /£ ) = E u H /£ . (8) y y x z x v ' E £ Rearranging, = yH z = x x y / 9 1 - 1 ~ 1 \ /^ \ 1 erg cm sec G 1 -volt = -f- p(cm^volt sec ) H (G) § V O L L - L  x (10 coulomb) 10 7 erg coulomb-1 E _ a _Z = 1 0~8 _Z p (cn^ volt^ sec-1) H (gauss) (9) x x z For a given value of E , sensitivity of detection i s improved by X increasing £ /£ , i e . by using a short broad sample rather than a long y x narrow one. Consider H = 2000 G, £ /£ = 1. Then E /E = 2 x 10"5 y. z y x y x At E =3 volt, with minimum detectable E = 1 y V = 10~G V, x y minimum detectable y = 10 _ 17 (2 x 10~5) = 0.017 cm2 v o l t " 1 sec - 1, For a sample five times as long as i t is broad, i.e. £ /£ = 0.2, y x minimum detectable y = 0.085 cm2 v o l t - 1 sec" 1. To get a sensitivity better than 10 - 2 cm v o l t - 1 sec" 1, one must use at least 5 volt f o r _ E X across the sample with equal x and y dimensions, or at least 25 volts across the long narrow sample. (Because of shorting effects produced by the long current electrodes, the sensitivity of a square sample i s somewhat less than the above calculation indicates. Thus for accurate work a long narrow sample is preferred. But i f maximum sensitivity is important to detect the effect at a l l , the square sample is 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 sensitivity is about 70% of that calculated.) 19 1 . 2 . 2 Gravimetric Determination of Transport Numbers To find the transport numbers of anions, cations and electrons (t , t + and t g ) , i t is necessary to pass a known quantity of e l e c t r i c i t y between copper electrodes through three pellets or cystals of CuCl stacked together in series in good contact with each other allowing ionic transport across the boundaries. This is analogous to the Hittorf method for solutions. Figure 4  Ionic Transport in CuCl I transport, t Cu = Cu++e, (t ++t ) mole Net gain of Cu = t + + t _ - t + = t mole mole Cu transport, t mole CI . Cu++e = Cu (t ++t ) mole Net loss of Cu = t ++t_-t_ = t 71 araday If i t i s desired only to find the total fraction of the conductance which is ionic (t ++t_), a similar experiment with a single pellet or crystal of CuCl w i l l suffice, as the following analysis shows. As shown in Figure 4, for the passage of 1 faraday of e l e c t r i c i t y , the solid copper lost by anode or gained by cathode corre-sponds to total electrolytic conduction., t ++t . Thus the ionic and electronic conduction can be separated simply by finding the change in 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 is required. To separate t + and t , the change in weight of the l e f t and right hand pellets must be found. These changes should be equal and opposite, and should correspond to t moles of CuCl. 20 Transport number (electrolytic conduction) in chlorinated CuCl can be estimated by using inert (Pt) electrodes and three pellet assembly. Three pellets, (anode pellet - in contact with positive electrode, middle pellet and cathode pellet - in contact with cathode) could be stacked together and sandwiched between Pt electrodes. Assuming that only Cu cation is transported and since there is no supply + + of Cu at anode, any migration of Cu from anode pellet w i l l be observ-able in two ways; f i r s t l y , the weight loss in anode-pellet and secondly, the pellet composition approaches towards CuCl 2 near the electrode (brownish colour). The pellet i n the middle w i l l suffer no change since Cu + gained at this pellet is transported to the cathode-pellet. The gain of Cu + at cathode-pellet w i l l decrease CI |Cu+ ratio and the compo-siti o n approaches towards CuCl. Thus by observing the loss in weight at anode-pellet and gain at cathode pellet for a known amount of e l e c t r i c -i t y , the proportion of electrolytic conduction can be estimated. This method with inert electrode would be valid only i f passage of D.C. for a long time with inert electrode does not disturb defect structure and change conductivity (see Section 3 . 3 ) . 21 1.2.3 Injection or Suppression of Carriers at a Metal- Semiconductor Contact In certain circumstances, the concentrations of charge carriers 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 readily detectable effect, because the resistance of the sample becomes non-ohmic. Frequently, ohmic behaviour is replaced by a linear relationship between In I and applied voltage E , where I is the current. This type of dependence does not have a unique cause; two cases w i l l be discussed below. If the alteration in charge carrier concentrations can be carried out in a controlled manner, then the effect may be turned to good account in throwing some light on the nature of the carriers. This i s best accomplished by having a single non-ohmic contact (rectifying 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-it e or platinum) on one side and a copper electrode on the other. In the most general case, the sample may conduct partly by ionic migration ( i n t e r s t i t i a l cations) and partly electronically (elec-trons, or positive holes, or both). If ionic conduction predominates, a positive potential applied to the inert electrode may suppress the ionic conduction by repelling the charge carriers 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 linear plot of In I versus E. If, on the other hand, conduction i s almost completely electronic, with holes as majority carrier and electrons as minority carrier, the conductivity may be augmented by injection of minority carriers when the inert electrode i s made negative. This i s the normal behaviour of a rectifying contact between metal and p-type semiconductor, and also gives a linear plot of In I versus E. (a) Ionic carriers i n i t i a l l y in great excess: the Wagner method In this situation, as envisaged by Wagner and Wagner for the CuCl system, the migration of Cu + away from the inert electrode (while CuCl/Cu equilibrium i s maintained on the other side) produces a concen-tration gradient which eventually reaches a steady state because of back-diffusion of the Cu + i n t e r s t i t i a l s . There i s then no current of Cu +, 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 inert electrode - semiconductor contact. Under the influence of the concentration gradient of ionic defects, electrons and holes also acquire a concentration gradient, and i t is this which provides the driving force for the net current across the sample. The general theory of this effect takes into account the possibility of current being carried by both electrons and holes, with contributions to the conductivity in the undisturbed sample designated and respec-tively. Then the current I through a sample of cross-section A and 23 length L across which a potential difference E has been applied is given by I = (ART/LF) [ a n ( l - e ~ E e / k T ) + a p ( e 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 e E e / k T ] . ( 2 ) n p If the electron contribution is negligible, I = (ART/LF) a p e E e / k T and log I = log (apART/LF) + Ee/2.303kT. ( 3 ) A linear relation between log I and E i s then expected, with slope e/2.303kT. From the intercept of such a plot, 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 potential of CuCl; but there has been some con-q 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 in the undisturbed sample i s then less than 10 - 5 of the total conductivity. (b) Holes i n i t i a l l y in great excess: metal-semiconductor contact rec t i f i c a t i o n In the simplest theory of contact rectification, the effect should occur only when the difference in work functions between metal and semiconductor is such as to cause withdrawal of carriers from the 24 region of the semiconductor near to the metal, leading to the formation of a high-resistance "depletion layer" in the semiconductor. Most of the potential difference applied across the system then establishes i t s e l f across the depletion layer. In practice, i t has been found that surface states commonly exist which allow the re c t i f i c a t i o n effect to be produced in a manner largely independent of the difference in work function between metal and semiconductor''"? An applied potential E in the same sense (for a p-type carrier) of metal negative with respect to semiconductor w i l l then drop the potential barrier between metal and semi-conductor so that majority carriers (holes) can more easily escape across the depletion layer, while minority carriers (electrons) are injected into the sample from the metal electrode. The total current then rises non-ohmically with applied voltage according to I = I o ( e e E / k T - l ) . U Here E has the sign of the potential of the semiconductor relative to the metal, and the equation i s applicable to negative as well as positive values of E. The equation thus represents a current which for positive E increases exponentially without limit as E increases, while for 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 for an n-p junction r e c t i f i e r . (The significance of I is different in the two cases, but o the shape of the I - E characteristic w i l l not distinguish a metal-semiconductor rectifying contact from an n-p rectifying contact.) 25 At high positive values of E, for which eE >> kT, equation ( 4 ) reduces approximately to I = I q e e E ^ k T and hence log I = log I + eE/2.303kT. ( 5 ) Thus the plot of log I against E should be linear, with the same slope as in the previous case of suppression of ionic conduction. There are two important distinctions between the two cases:- (i) For suppression of ionic conduction, i f the current is followed continuously after application of the voltage E, i t should drop very markedly to reach i t s f i n a l steady value; but for the case of hole conduction, with positive E (forward-biased r e c t i f i e r ) , the current should rise to i t s f i n a l value. ( i i ) If both the ionic and the electronic charge carriers have positive sign, then opposite directions of the applied voltage are required to produce the effects described in ionic and electronic cases; i.e. the sign of E i s oppositely defined in sections (a) and (b) of the present account. Since the phenomenon is actually observed in the present work, i t i s useful to discuss what may be happening when, in the region without ionic conduction, a rectifying effect appears with high current passing for the "wrong" sign of E. There are two obvious explanations for this:-(i) the semiconductor sample may have been wrongly identified as p-type when i t is actually 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 distribution of defects within i t , and effectively contains a p - n junction inside i t . This would be the case, for example, i f a CuCl sample had been treated at high temperatures according to the 26 Wagner and Wagner method o f s u p p r e s s i n g i o n i c c o n d u c t i v i t y , w h i c h t e n d s t o b u i l d up a n i o n e x c e s s a t t h e i n e r t e l e c t r o d e end o f t h e s a m p l e , and s t o i c h i o m e t r i c c o m p o s i t i o n , o r p e r h a p s e v e n c a t i o n e x c e s s , a t t h e o t h e r e n d . I f t h i s d i s t r i b u t i o n o f i m p u r i t i e s i s f r o z e n on r e d u c i n g t he t e m p e r a t u r e , t h e s a m p l e may c o n t a i n a p - n j u n c t i o n w h i c h w o u l d behave a s a r e c t i f i e r , b u t w i t h f o r w a r d and r e v e r s e b i a s e s i n t h e o p p o s i t e s e n s e f r o m t h a t o f t h e m e t a l - p - t y p e s e m i c o n d u c t o r c o n t a c t d i s c u s s e d i n s e c t i o n (b) a b o v e . 27 1 . 2 . 4 T h e r m o e l e c t r i c Power The S e e b e c k e f f e c t i s t h e p r o d u c t i o n o f an EMF i n a s a m p l e by a t e m p e r a t u r e g r a d i e n t , and t h e t h e r m o e l e c t r i c power i s ( p o t e n t i a l g r a d i e n t ) / ( t e m p e r a t u r e g r a d i e n t ) . S i n c e t h e measurement o f t h e r m o e l e c t r i c power r e q u i r e s a c o m p l e t e c i r c u i t , u s u a l l y c o m p l e t e d w i t h c o p p e r w i r e , wha t i s a c t u a l l y m e a s u r e d i s t h e d i f f e r e n c e be tween t h e t h e r m o e l e c t r i c power o f t h e s a m p l e and t h a t o f c o p p e r ; b u t t h e l a t t e r i s u s u a l l y n e g l i -g i b l e i n c o m p a r i s o n w i t h t h e t h e r m o e l e c t r i c power o f a s e m i c o n d u c t o r s a m p l e . The t h e r m o e l e c t r i c power h a s s i m i l a r m a g n i t u d e i n i o n i c and e l e c t r o n i c c o n d u c t o r s , and c a n n o t u s u a l l y be u s e d t o d e t e r m i n e w h e t h e r t h e c h a r g e c a r r i e r s a r e i o n i c o r e l e c t r o n i c . F o r i o n i c c o n d u c t o r s , t h e a n a l y s i s o f t h e d a t a i s d i f f i c u l t ; t h e t h e r m o e l e c t r i c power depends on c e r t a i n q u a n t i t i e s known as " h e a t s o f t r a n s p o r t " , and no v e r y r e l i a b l e t h e o r y h a s y e t b e e n d e v e l o p e d t o show how t h e s e h e a t s o f t r a n s p o r t a r e r e l a t e d t o t h e t h e r m o d y n a m i c p r o p e r t i e s o f t h e l a t t i c e and i t s d e f e c t s . The t h e r m o e l e c t r i c power w i l l , h o w e v e r , u s u a l l y g i v e t h e s i g n o f t h e c h a r g e c a r r i e r s r e g a r d l e s s o f w h e t h e r t h e y a r e i o n i c o r e l e c t r o n i c , and t h i s i n f o r m a t i o n may i n i t s e l f be u s e f u l i n e l i m i n a t i n g some o t h e r w i s e p o s s i b l e c o n d u c t i o n m e c h a n i s m s . The s i g n o f t h e c h a r g e c a r r i e r s i s t h e s i g n o f t h e p o t e n t i a l a t t h e c o l d end o f t h e s a m p l e ; and i n t h e c a s e o f v a c a n c y c o n d u c t i o n , t h e s i g n o b t a i n e d i s t h a t o f t h e v a c a n c y , e . g . a n e g a t i v e s i g n f o r c a t i o n v a c a n c y c o n d u c t i o n . 28 (a) Electronic (Positive holes) Semiconductors: In electronic hole conductors thermoelectric power is related primarily to the Fermi energy by the simple relation ( l ) 6eT = E p + AkT. (1) where 0 is thermoelectric power in volt deg \ E is the Fermi energy r a, measured from the top of the valence band. T, k and e are the temperature, Boltzmann constant and electronic charge respectively. The quantity A originates from the kinetic energy of the charge carriers and the nature of scattering processes. A commonly has a value close to 2, and is often taken as 2 in the absence of precise information on scattering processes. The term AkT i s often small compared to E and is sometimes omitted^. r Circumstances can arise in which there i s a more serious disturb-12 ance of the relationship between Ep and e6T. Tsuji has shown that, for a "hopping" mechanism in which carriers are tightly bound to ions and an activation energy is needed for the jump from one ion to another, this activation energy must be added to the right hand side of equation (1 ). An important case of more general application is that in which two or more conduction mechanisms proceed in parall e l . For example, i f holes are supplied at the top of the valence band by ionisation of acceptor impurities, part of the current (fraction f ) may be carried by holes and part (f ) by electrons at the acceptor level (E^ above valence band). Then with kinetic energy term neglected, 9 e T = f p E F + f n ( E F - V & • E F - f n ' E A <3) 29 This topic i s further developed in Section 1.3, in which the relation of E„ to E. is discussed. This discussion w i l l show that, in this particular case of two mechanism conduction, 9 may remain positive even i f f << 1. Thus a positive 6 is indicative of hole conduction in P the valence band, but does not exclude the possibility that a greater part of the current is simultaneously carried by electrons in a special level (other than the conduction band). (b) Ionic Semiconductors The total thermoelectric power of an ionic conductor is made up of two parts, homogeneous thermoelectric power and heterogeneous thermo-ele c t r i c power. The homogeneous effect arises from the thermal diffusion of ions i n the crystal and the contribution resulting from the homogeneous effect in the lead wires may be considered negligibly small. The hetero-geneous part 0 arises essentially because of the variation with tempera-ture of the contact potential difference between the electrode and the crystal. The homogeneous thermoelectric power for a pure MX type ionic 13 crystal with Frenkel defects i s given by the expression (4) n l X l ( q i + 1 / 2 h ) " n2 X2 ( q2 + 1 / 2 h ) ®hom , , . eT ( n ^ + n 2A 2) where and 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 mobilities, 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 is the enthalpy of formation of a Frenkel defect. 30 No precise theory of the heats of transport exists. They are usually positive, but may be negative. To give a spurious indication of the sign of the carrier, however, a heat of transport would have to be unexpectedly negative with |q | > 1 /2 h. Provided that this does not happen, 6 ^ w i l l give a reliable indication of the sign of the charge carrier i f one carrier predominates. When both vacancies and inter-s t i t i a l s are important, 6 may have either sign. (In the present work, 0 has consistently been positive in a variety of different types of behaviour, one of them being the known Frenkel defect situation in pure CuCl at high temperature. In a l l other cases, the positive 8 gives some evidence against ionic conduction, in that i t is d i f f i c u l t to think of any other ionic carriers l i k e l y to be present which would have positive effective charge. But this is 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 Level and Concentration of Holes The equations presented here r e l a t e to a semiconductor with a band gap E , i n which holes are supplied by acceptor s i t e s at energy l e v e l E^ and may be p a r t l y "compensated" by electrons supplied from a donor at E^ ( a l l energies measured from the top of the valence band). In the present case, E i s s u f f i c i e n t l y large that electrons i n the conduction band cannot have a s i g n i f i c a n t concentration i n a system containing a s i g n i f i c a n t concentration of holes; hence the term f o r conduction band electrons i n equation ( 4 ) below i s thereafter completely dropped. In a l l cases of i n t e r e s t f o r the present work, E^, E^ and the Fermi l e v e l E are s u f f i c i e n t l y large i n comparison to kT that the low-r temperature l i m i t i n g forms should be applicable throughout. The approximation used throughout the following account i s that 1 4 used, f o r example, by Shive , i n which the valence band and conduction band are each replaced by a s i n g l e l e v e l (at E = 0 and E = E_ respect t i v e l y ) , with density of states (N , N n r e s p e c t i v e l y - L for "lower", U for "upper") given by the t r a n s l a t i o n a l p a r t i t i o n function N u L = ( 2 i r m J L k T / h 2 ) 3 / 2 = 2 . 4 2 x 1 0 1 5 T 3 / 2 cm - 3 i f mj L = in In the Fermi-Dirac s t a t i s t i c s , the p r o b a b i l i t y of occupation of any l e v e l i s completely determined by the distance of that l e v e l from the Fermi l e v e l E„. Thus i n a l l cases the concentration of holes at the top of the c valence band (E = 0) i s given by 32 p = 2NL [1 - 1/(1 + e " E F / k T ) ] . (2) In the present work, the lowest position which w i l l be considered for the Fermi level (except, perhaps, in the lower temperature range, heavily chlorinated) w i l l be E A/2 where = 0.53 eV. Thus we may always assume that E >> kT and approximate equation (2) by p = 2N e - E F / k T . (3) The complete expression showing how p is determined by ionization of acceptors, ionization into the conduction band, and compensation by electrons supplied from donors, i s p = [NA/(1 + e ( EA " E F ) / k T ] + [2^/(1 + e ( EG " E F ) / k T ] - t y i - 1/1 + e (V EF ) / k T}] In the present discussion, the band gap is so wide that' electrons in the upper band can be ignored; i.e. (E_ - E„)>> kT and the term in NIT effectively vanishes. If E_ remains well below the donor level, the r last term in equation ( 4 ) approximates to N Q, i.e. a l l the donors are ionized downwards so that their number is subtracted from the hole con-centration. Equation ( 4 ) f i n a l l y becomes: p = [NA/(1 + e EA " EF)/kT] - N D. (5) Equations (1), (3) and (5) permit the determination of expressions for p and E in a l l the cases of interest in the present account, r 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 level. 33 E p = (E A/2) + (kT/2) In (2N^/N^). (6) p = (2NL) N A e A (7) This i s the region analogous to slight ionization of a weak electrolyte: hole concentration proportional to square root of acceptor concentration, and governed by an energy E /2.. At greater extents of ionization, an improved approximation is E p = kT In t(N L/N A) - (1/2) + (1/2){(1 - 2N^/NA)2 C 8) + (8N L/N A)e EA / k T} 1 / 2] When E has been calculated from this equation, p may be found from r equation ( 3 ) . A condition of special importance is that at which the acceptors are just half-ionized. If the temperature f° r this condition is known, then the concentration af acceptors can be calculated according to NA = 4 N L/ ( 1 + eVkTl/2). ( 9 ) For the compensated case, the low-temperature approximation gives p = 2NL [(N A - N D)/N D] e~VkT, (10) and E p = E A - kT In [(N A - N D)/N D]. (11) 1.3.2 Simultaneous Conduction by Valence-band Holes and Electrons at E. A For a compensated semiconductor in which holes are the only charge carriers, the el e c t r i c a l conductivity should be = peu^ (12) 34 where p is given by equation ( 1 0 ) . Thus the apparent activation energy of a p should be E^, unless N^, N Q or u p (the hole mobility) is strongly temperature-dependent. If the holes move by a "hopping" or "polaron" mechanism, u p may be activated: o -E /kT , x yp = yp e yP ' 0.3) Then the expression for conductivity (simplified by assuming N. >> N ) A JJ becomes: i ° /•« it /x, \ -(E. + E )/kT .... a p = 2 e y p (\® A/\) e A yp y . (14) The apparent activation energy of conduction is then (E. + E ). A yp It sometimes happens (e.g. in NiO) that the thermoelectric power of a semiconductor (or the product e6T, which should be E , apart r from a small correction for kinetic energy) rises very rapidly with temperature in a range in which the conductivity shows normal activated behaviour. Such a result shows clearly that 6 is giving a spurious indication of the position of E„; for i f E^ increases rapidly with temper-r 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 is inconsistent with the behaviour of a. As Austin et a l . ^ indicate, i t is not very li k e l y that scattering processes could account for a correction to eOT (as a measure of E ) sufficient to account for the NiO data. If, however, the electrons r in the acceptor sites are able to contribute to conduction, e0T can 35 deviate drastically from E in accordance with equation (3) of r section 1.2.4: e6T = E — f E F n A where f i s the fraction of the current carried by the electrons. Sub-stitution of the expression for E„ given by equation (11), with r f + f =1, gives n p e6T = f E - kT ln(N 4/N ). (15) p A A D Now f = o /(a + a ) (16) p p p n where o is given by equation (14). o must now be evaluated similarly P n from the concentration and mobility of electrons at the acceptor level: o -E /kT o = n. e y = n. e y e yn . (17) n A n A n The electron concentration (called n to distinguish i t from n, a common symbol for electrons in the conduction band) is given by the f i r s t term on the right-hand side of equation (4): nA = V ( 1 +6< E a " Ep)/kT' (18) Substitution for E from equation (11) yields r nA = V [ 1 + ( NA / ND ) ] ( 1 9 ) or for the case N. >> N_, n. = N . (20) A D A D Substitution of equations (14), (17) and (2Q) into equation (16) yields: 3 6 * . ,//, , v (E - E + E.)/kT f = 1/ (1 + K e up yn A (21) where K = (1/2) ( N J / N J ) (y°/y°). D L A n p (22) For the case in which f << 1, equation (21) becomes: P - ,„v -(E - E + E.)/kT f = (1 /K) e yp yn A" . (23) Thus 9T, as given by equation (15), may behave approximately as an "activated" quantity, with "activation energy" (E - E + E A ) . This yp yn A is only very approximate since the term fpE^ may readily be comparable to the other term kT In (N /N ); but the latter may readily partly cancel with the neglected kinetic energy term. duction occur simultaneously (the latter involving an essentially constant cencentration of electrons in the acceptor level), and i f electron con-duction predominates at the bottom end of the temperature range studied, then e6T may rise rapidly with temperature from a value which may i n i t i a l l y be positive but << E_ towards a limiting value in which a "normal" r indication of E is given by this quantity when electron conduction has r become negligible. As the temperature is raised further, e0T should go through a maximum and start a slow linear decline in accordance with equation ( 1 1 ) . These equations i l l u s t r a t e that, when hole and electron con-37 1 . 3 . 3 T h e r m o e l e c t r i c Power f o r M i x e d I o n i c and H o l e C o n d u c t i o n I f c e r t a i n s i m p l i f y i n g a s s u m p t i o n s a r e v a l i d , a s i n d i c a t e d b e l o w , a c u r v e o f 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 c o m p l e t e l y e l e c t r o n i c t o c o m p l e t e l y 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 t h e % i o n i c c o n d u c t i o n i n t h e t r a n s i t i o n r e g i o n . I n t h e p r e s e n t w o r k , t h i s a n a l y s i s i s a p p l i e d t o t h e t h e r m o e l e c t r i c power d a t a f o r p u r e C u C l . I t w i l l be assumed t h a t , i n t h e r e g i o n o f e l e c t r o n i c c o n d u c -t i o n , t h e c a r r i e r s a r e h o l e s o n l y , f = 1 . ( T h i s a s s u m p t i o n i s p r o b a b l y c o r r e c t f o r p u r e C u C l , b u t no t f o r c h l o r i n a t e d s a m p l e s , i n 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 e l e c t r o n s . ) Then e q u a t i o n (15) o f S e c t i o n 1 . 3 . 2 g i v e s t h e c o n t r i b u t i o n o f h o l e s t o t h e P e l t i e r c o e f f i c i e n t as 6 0 h T = E A " k T l n ( N A / N D ) . (1 ) I n t h e r e g i o n o f h o l e c o n d u c t i o n , a p l o t o f eGT a g a i n s t T s h o u l d be a s t r a i g h t l i n e o f n e g a t i v e s l o p e , w i t h i n t e r c e p t E . I f t h i s l i n e i s e x t r a p o l a t e d t o h i g h e r t e m p e r a t u r e s , i n t o t h e t r a n s i t i o n r e g i o n t o i o n i c c o n d u c t i o n , t h e h o l e c o n t r i b u t i o n eS^T c a n be r e a d o f f a t any d e s i r e d t e m p e r a t u r e . I t w i l l f u r t h e r be assumed t h a t t h e i o n i c c o n t r i b u t i o n i s e n t i r e l y f r o m i n t e r s t i t i a l s . Then e q u a t i o n (4) o f S e c t i o n 1 . 2 . 4 c a n be s i m p l i f i e d t o ee ^ T = q * + ( l / 2 ) h = q x . (2) 38 At high temperatures, at which conduction becomes completely ionic, e6T should attain a constant value (eGT)^ = q^. In the region of mixed hole and ionic conduction, e6T = f e6 T + f.e9.T (3) P h i l when f and f. are fractions of the current carried by holes and p i ' i n t e r s t i t i a l s . From equations (1), (2) and (3), with f + = 1, the fractional ionic conductivity may be calculated as e0T e0, T £ = •- h ( 4 ) (eeT)^ - e6 hT where, as indicated above, (eOT)^ i s obtained as the limiting value at high T and e0^T i s obtained from the line of intercept and negative slope through the low-temperature points. 39 1.4 BAND STRUCTURE AND CHARGE CARRIERS IN CUPROUS HALIDES 1.4.1 Band Structure In CuCl, the highest valence bands may be formed from CI 3p and Cu 3d, the three fold degeneracy of the atomic p-orbital and five fold degeneracy of the d-orbital giving thus eight bands in a l l . Con-sidering f i r s t the isolated atom, we have thus two levels, one three fold degenerate and the other five fold degenerate, separated by about 3 eV, as given in 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 in tetra-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 . Splitting of d-orbitals in Tetrahedral Field d , d , d (t_ orbitals) xy yz xz 2 d 2 d 2 2 , . , z , x - y (e orbitals) CI 3p Figure 6 40 In the band structure of the crystal the degeneracies w i l l be further l i f t e d , although the situation of Figure 6 may s t i l l be found at special points in the Brillouin zone (which in fact correspond to the energy maxima of the bands). Also, the bands may be of mixed character, partly CI 3p and partly Cu 3d (the total number of bands, 8, remaining unchanged). The band structure of CuCl has been studied theoretically and 1 ft i 7 ip experimentally by several workers » * . According to Herman and McClure^ the lowest conduction band and the highest valence band arise from the 4s and 3d states of Cu + ion 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 Cu + ion and another between 3d Cu and 3p Cl bands. The optical energy gap is determined by the width of the former and the experimental value i s about 3 eV obtained from the absorp-tion spectrum"*"**. 1 7 Later Cardona experimentally estimated the fraction of the metal wave function in the valence band and suggested that only about 25% of the halogen wave function is involved in the valence band formation. These suggestions were made on the basis of exciton spectra studies. On. the basis of the theoretical calculation of band structure 18 of CuCl, Song" supported the previous arguments with the indication that the valence band has, at, a mixture of 79% of Cu + 3d and 21% of Cl 3p wave functions; The most recent calculation of band structure 1 9 of CuCl was done by Calabrese (Ph.D. thesis, Lehigh Univ. 1971) 41 (unpublished - this information is taken from the thesis abstract). According to his results, but contrary to the previous results, the contribution of 3p orbital of C l - to the top of the valence band i s larger than that of the 3d orbital of Cu +. He has also computed the effective mass of 0.23 m and 0.17 m with the corresponding energy gap e e of 1.0 eV and 0.3 eV for Slater exchange potential and screen exchange 20 * potential respectively. But i t has also been suggested that m at the top of the valence band i s about 20 xa^, a value similar to that for 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 in terms of atomic orbitals on tight binding approximation i s as follows. (1) The highest three bands. Each Cu + ion has 12 similar ions as second nearest neighbours, lying in the direction of 12 lobes of d ^ , d^ z and d . Corresponding orbitals on different atoms combine with each other xz as illustrated for the d orbitals in an (001) plane in Fig. 7. These xy orbitals w i l l also combine with P orbitals on CI i n the combinations fcl - C l d xy + C 2 P z C l d yz + Vx fc3 = C l d xz + C2 Py The arrangement of (+) and (-) signs shown in 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 Orbitals for Tight-binding Calculations on CuCl Tetrahedral sites, crystal f i e l d s p l i t t i n g Cu 3d Cl 3p 0.53 eV .d ,d ,d r xy yz zx d o d o o ^2.5 eV ( 9 Vi) (rJ^ % a C t f \ I i V , 1 I 1 ( \\ J 1 1 f Signs for top of band (greatest antibonding char-acter) It o ,/ Radial maxima (A) Cu 3d 0.32 Cl 3p 0.75 4 3 (2) The next two bands. The remaining d-orbitals of Cu (d 2, z d x2 ^2, the e-orbitals) are so oriented that they do not point directly towards any neighbouring cations. In this case, the formation of a band is l i k e l y to involve a larger contribution from the Cl 3p orbitals ( a l l three equally, as illustrated in Fig. 7. These two bands l i e at the bottom of the d-band distribution and are very narrow (about 0.1 eV). The top of the e-band is separated from the top of the t band by about 0.53 eV. Thus e = C, d 2 2 + C_ (P - P. - B ) 1 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 Cu + to another via the intervening Cl , in contrast to the t bands which have direct Cu-Cu interaction. (3) The lowest three bands. These w i l l be formed principally from Cl 3p orbitals. Because of the fact that the radius maximum of Cl 3p is o o 0.75 A in comparison with only 0.32 A for Cu 3d, this forms- a wider band. 1.4.2 Charge Carriers Except for the clear indication from transport number experi-ments (Tubandt et a l . ) Z that pure CuCl is an ionic conductor above 220°C and an electronic conductor below that temperature, suggestions on the nature of the charge carriers in CuCl have been largely speculative. No 44 theoretical calculations of the energy of defect formation has been reported. The suggestions of Harrison and Ng on the charge carriers in chlorinated CuCl have already been described (Section 1.1.2). There is no other report in the literature about the conductiv-i 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^. They observed that by addition of 2 mole % of CuC^ to CuCl the conductivity increases con-siderably and the knee in the a- plot tends to diminish. They believed that the considerable increase of conductivity upon doping throughout the whole temperature range, is due to the increase of electronic 2+ contribution, resulting from the presence of Cu (i.e. d-band holes) and the disappearance of the knee appears to suggest that the electronic component predominates throughout the whole temperature range. This suggestion i s based entirely on conductivity studies together with an indication from thermoelectric power that the charge carriers are positive. No details of thermoelectric power data are given. 3 Vine and Maurer have studied the Hall effect and el e c t r i c a l conductivity of Cul with excess iodine. Tubandt has shown earlier that there i s no ionic contribution to the conductivity below 200°C. Vine and Maurer thus interpret their data in terms of trapped holes. The mobil-2 - 1 - 1 i t i e s obtained from Hall effect data, being 6-14 cm volt sec at 102°C and generally decreasing with temperature, are compatible only with an electronic form of conduction, not an ionic form. 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 ratio 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 2 0 - 3 of ^10 cm Iodine concentration less than this does not give hole/ iodine atoms ratio close to unity. They suggest that during the absorp-tion of excess iodine by Cul, Cu + and an electron comes from the Cul l a t t i c e to combine with the iodine atom with the expansion of Cul l a t t i c e . The vacancy created by the migration of Cu + from the Cul l a t t i c e has an effective negative charge and can trap holes at low tem-eratures. In terms of the band picture an effect of introducing Cu + vacancies is to create a discrete level above the valence band. Such an energy level acts as an acceptor level 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 EA = E0 " 3 n <» —8 where a is a constant whose magnitude is of the order of 10 and -3 n (cm ) is the concentration of excess iodine atoms in this case. Vine 3 and Maurer have demonstrated that the above equation holds good up to 19 -3 1 9 - 3 n - 6 x 10 cm , but when n - 7 x 10 cm , E^ drops below the top of the valence band. / 46 2. EXPERIMENTAL 2.1 SAMPLE PREPARATION 2.1.1 Purification of CuCl The reagent grade CuCl (Fisher ACS) was dissolved in 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 crystalline CuCl was precipitated out. The precipitate was allowed to settle down. Addition of 10 - 15 ml of acetone helps settling down the precipitate. The bluish green supernatant liquid was decanted off. The white solid remaining in the bottom was washed with reagent grade acetone, three to four times. The clear white CuCl, free from any tinge of bluish green colouration was covered with acetone and was vacuum fi 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 solid thus obtained was dried at 40°C over night in oven. Drying in oven at 40°C or drying in desicca-tor did not produce any vi 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^ joint. The apparatus for the sublimation of CuCl i s shown in Fig. 8. It consists of an elec t r i c furnace F and a vacuum system (mercury diffusion 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 diffusion pump for about 8 - 1 0 hours. This was Figure 8 Apparatus for CuCl Sublimation 47 1 Stopcock B14 Joint Sublimation tube T Glass wool F (furnace) Mercury diffusion pump Pump 48 done to ensure the removal of any acetone vapour l e f t in the bulk of the material. In some cases less evacuation resulted i n the blackening of 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 P.D. from the variac was increased to about 52 volts and CuCl was sublimed at 450°C. This temperature was checked by thermocouple. After the completion of the sublimation, the solid CuCl was removed from the tube by breaking the tube. The f i r s t sublimed CuCl was slightly yellowish. It was then transferred to another similar tube. This process of sub-limation was repeated t i l l transparent white solid was obtained. Usually the fourth sublimation was found satisfactory. This sublimed CuCl was stored in a vacuum sealed tube for further use (though i t was observed that this material l e f t in air at room condition did not show any v i s i b l e change for about forty 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) joint, and electric furnace, pressure measuring system (pyrex spiral gauge scale) Hg manometer, chlorine purification and storage system. The whole apparatus is shown in Figure 9. Except for stopcock A a l l teflon stopcocks B, C, D, E, F, were used; for chlorine handling in the reaction apparatus the stopcock A was used with Kel-F grease. The spiral gauge calibration and chlorine purification were done in the same fashion as u-tube K^y i Ball Joint (S19) V H KJ Figure 9. Apparatus for Reaction of CuCl with Chlorine Chlorine purification system Glass wool Furnace >• Powder CuCl-W O O I S Hg Manometer Greaseless Joint L-shaped Reaction Tube V© >0 Thermometer 50 described previously by Ng . The temperature of the electric furnace was calibrated with variac reading and was checked by thermocouple (copper constantan) and Hg thermometer. Glass wool was used for the insulation between the furnace wall and the reaction tube. The powder sublimed CuCl was weighed into the reaction tube. It was then evacuated for two hours by rotary pump. The stopcock A was closed. The chlorine in the U-tube was frozen by liquid nitrogen and the a i r , i f any, was pumped off 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 spiral gauge scale was taken. Further readings were taken at timed intervals. From the calibration 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 (if any) was frozen in the side arm tube T by liquid nitrogen. The stopcock A was closed and the vacuum was broken after transferring 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 slightly chlorinated samples up to 2.38% were prepared at room temperature (24°C). The reaction was too fast for the kinetics to be followed. Heavily chlorinated CuCl (up to 64.5%) samples prepared at 130°C, showed remarkably slow reaction. One sample of 6.75% reacted was also prepared at 130°C. For pellet preparation the reacted CuCl 51 was finely powdered in a mortar and pestle. 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 during the grinding. This powder was stored in a vacuum desiccator and was used to make the pellets as described in the next section. 2.1.3 Preparation of Pellets The pellets of pure CuCl were prepared i n a Perkin Elmer KBr die model 186-0002 and hydraulic press assembly. The KBr die consists of a steel casing C and a steel barrel B in which the powdered sample can be introduced. A plunger P and the two dies E (upper) and F (lower) have been provided. Complete details have been given i n the self explanatory diagram shown in Figure 10. The various parts of the die assembly were cleaned with acetone. The barrel B was held upright and the lower die F was smoothly f i t t e d into i t . The barrel B, together with, the lower die f i t t e d into i t , was placed in the case C. Now the finely powdered sample,pure CuCl or reacted CuCl treated as described in the previous section 2.1.2,was introduced into the barrel B. Usually 1.5 - 2 gm of the powder was used except for the thermoelectric samples in which a larger amount of the sample ( 4 - 6 gm) was needed to give a pellet of length 1-1.5 cm. The powder was distributed evenly by shaking the die assembly. The upper die was then introduced into the barrel B and was pressed down tightly with the plunger P t i l l the upper die touched the sample. Then the assembly was completed with the larger 0-ring and top cap T. It was ' 52 Figure 10 Perkin Elmer KBr Pellet making die Plunger O-ring Top Cap O-ring Casing • (O Plunger P Top cap (T) Barrel (B) Upper die E Powder sample Vacuum pump •Lower die F Hose nipple O-ring 53 then evacuated for about five minutes and a pressure of 8000 psi was applied for three minutes. For removing the pellet 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 barrel by placing this assembly on the press ring and by applying the pressure. The pellet f e l l out on a plastic sheet placed previously to avoid contamination. The pellet was then transferred to a plastic bag and stored in a vacuum desiccator before use. The thickness and the weight of the pellet were measured in the plastic bag and the thickness and the weight of the plastic bag were subtracted to find out the actual thickness and the weight of the pellet. The area of the pellet is 1.326 cm2. 2.2 CONDUCTIVITY MEASUREMENTS 2.2.1 Conductivity Cell The conductivity c e l l consists of two bright platinum f o i l electrodes 0.26 mm thick and 1.55 cm in diameter. When silver 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 in the top electrode T, Figure 11. The top electrode was fixed on the bottom of a cylinder of fired lava. The bottom electrode s i t s in a cylindrical cavity (of the same material) which has threads inside matching with the threads on the top electrode. Whenever needed the bottom electrode is replaceable by a circular guard ring assembly to check the surface conductivity as shown in Fig. 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 Cell ? H H = metallic hook P = Pt wire T = Thermocouple wire B = Bottom electrode wire Cylinder of fired lava Figure 12 Guard Ring Top electrode -Sample •Bottom electrode 55 passes along the side of the cylinder. Further insulation of each wire was ensured by ceramic beads. At the top of the cylinder a metallic hook H was provided by means of which the weight of the cylinder together with the electrodes and sample assembly is supported on a horizontal glass rod fixed in a pyrex B-45 cone. This cone was connected with the vacuum system through a pyrex b a l l joint S-19 and a stopcock. The three wires P, T, and B and the fourth lead G for the guard ring assembly pass through teflon inserts in the glass cone and are vacuum sealed with highly insulating dekhotinski cement. For the operation the c e l l was placed in a large f l a t bottomed pyrex vessel, which contained a few pieces of f l a t uniform teflon in the bottom on which i t could rest firmly instead of hanging in the pyrex vessel. This conductivity c e l l was also used for transport number measurements (Section 2.3). This c e l l was heated by means of a small rion-inductively wound electric furnace. During DC measurements on high resistance samples, the furnace was 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 in Figure 13. The conductivity c e l l was connected in series with a Keithley Decade Shunt having the resistances 10 1 2 to 10 3 ohms and a potential difference of 1.2 volts was applied by a dry c e l l across the whole c i r c u i t . A reversing switch S was provided for the reversal of the current. The potential difference across the shunt was measured with a Keithley model 200B battery operated electrometer which has input r e s i s t -ance of 10ll* ohms. The entire apparatus was enclosed i n a grounded copper Figure 13 Circuit Diagram for Conductivity Measurement 1.5 volt • x Reversing switch S Shunt Box Keithley Electrometer 57 box with a window cut in i t to allow the meter to be read and extension rods to take the electrometer controls outside the box. (The apparatus was originally designed for very high resistance samples and this screening was not really necessary in 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 ci r c u i t as shown in Figure 14 was designed to measure the resistance of the sample when i t became quite small (y20 ohm, slightly chlorinated sample) around 230°C. In this c i r c u i t , the sample and a variable standard resistor (10 - 1000 ohms) are connected i n series with the source of both DC and AC. The DC current is supplied by a 1.5 volt battery built inside the chassis and AC by an oscillator of 200 cps, whose cir c u i t diagram is shown in Figure 15. Keithley electro-meter and Hewlett Packard AC voltmeter model 403A are connected alter-natively to measure the DC and AC potential difference accross the sample and resistor. The source switch S\ has been provided which can be used to apply either DC or AC current. The DC source is modulated by using a 10 turn 10 K potentiometer P and a reversing switch S 2 i s used to change the polarity. A three position switch S3 has been provided by means of which, the P.D.'s across the standard resistor, the sample and the total P.D. applied can be measured by using the position 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 106 ohms, since in this case no AC measurement could be made). Battery O •0-1-* OFF O — ZT 1.5 V Cell Figure 14 Circuit Diagram for Low Sample Resistance Source 10K 10 Turn $ Level DC P Source (S^) o— AC I Ext. -9 1 A'C external \ \ — & S 3 ° T Meter @ — O - X 0 -~Selector ] \ \ \ \ Electrometer / AC/DC / / O-/ / / -O—9O-Guard on 1 OFF 9 Guard ring I /77 \ Sample / / / Reference Resistor / \ \ • t o 09 3.9K >1K 7V Total current 1.55ma O.Olyf n H O C o i-h O H rt a> o o n -a CO c a> o o 0. 0 3. 5 meg O ,5V AC output 200 CPS 60 2.2.3 Procedure After the sample was introduced into the conductivity c e l l , i t was evacuated by a rotary o i l pump. The sample was heated to 200°C for about 15 hours (overnight). The conductivity readings were taken at temperature intervals of about 12 - 15°C and the usual time interval allowed for thermal equilibration at each temperature was about 3 - 4 hours. Occasional use of a longer time interval (overnight) did not cause any erratic behaviour. Measurements were sometimes started at 200°C after 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 results were reproducible but in certain samples reproducibility was obtained only by the second heating and cooling. Before measuring the conductivity, the applied voltage E\ (1.2 volts) was checked by an external meter (VT VM) for each reading. The ci r c u i t was completed, the potential difference E 2 across the shunt was measured immediately by the Keithley electrometer. The polarity was immediately reversed (within less than five seconds) and an E 2 reading was taken immediately with opposite polarity. For a l l samples i t was found that both E 2 values with positive and negative polarity were very similar (within 3 - 5%). The mean of the E 2 values was used to calculate the conductance of the sample using the following relation E 2 I ohm-1 0 - E, - E 2 ( 1 ) 61 where a i s the conductance in ohm"1 and I is the current range marked on the shunt in the amperes (the reciprocal of the shunt resistances). The specific conductivity a was calculated by the following equation a = o(£/s) ohm*"1 cm - 1 ( 2 ) where H is 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 variation of current with time i s shown in Figure 16 . The conductivity calculated from the mean current of positive and negative polarity did not show any significant deviation from the usual procedure. Blank Resistance Using a piece of teflon of about the pellet size the blank resistance of the apparatus was found to be 2.24 x 10 1 2 ohm cm at room temperature. This resistance i s at least about seventy times higher than the highest resistance measured for the samples and at a l l higher temperatures the ratio was even much larger. 2.3 TRANSPORT NUMBER MEASUREMENT 2.3.1 Gravimetric Method This experiment was performed gravimetrically using the con-ductivity apparatus described in 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 in diameter and 0.09 cm in thickness, and CuCl pellets were weighed separately. The Figure 16 Current Versus Time Plot in CuCl 62 7 1 6 - i 5 H 4 -A • Cu Electrode O Pt Electrode 2 -i 1 -J Polarity Change 4> Time (min.) 63 pellet was sandwiched between the pair of copper electrodes in the conductivity c e l l . This was then evacuated by a rotary pump for about twenty hours and the constant desired temperature was maintained by heating the pellet for 3 - 4 hours. A constant current was passed by applying a P.D. of 22.5 volts through this c e l l connected in 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% silver nit rate solution acidified with dilute n i t r i c acid. For operation, the cathode was weighed before dipping into the solution. On passing the current the electrolysis of silver nitrate solution took place and the fine dendritic silver was deposited at the cathode. The deposited silver at the cathode was washed carefully with d i s t i l l e d water and then with alcohol to avoid any contamination with silver nitrate remaining on the electrode. Care was taken to avoid any loss of deposited si l v e r . From the weight of the silver deposited the quantity of e l e c t r i c i t y was calculated using the relation that 1 coulomb of e l e c t r i c i t y is equivalent to 1.118 x l O - 3 gm of si l v e r . At the end of the experiment the CuCl pellet and both copper electrodes were weighed. From the loss of the copper at the anode and gain at the cathode or at the pellet, the amount of copper transported was calculated. Thus knowing the copper transported and the amount of el e c t r i c i t y consumed, the percentage of cationic conductivity was calcu-lated using the relation (1) 64 1 mg of copper = 1.515 coulombs of e l e c t r i c i t y % of cationic contribution = Wt of copper transported in mg x 1.515 coulombs ^ Total coulombs No attempt was made to detect anionic conduction, since ionic conduction in CuCl has been found^ to be completely cationic. -For chlorinated samples, the experiment was performed using a thermoelectric c e l l whose electrodes each contain (Pt. 10% Ph) thermo-couple. Three pellets of CuCl of comparable thickness were weighed and sandwiched between two Pt electrodes. The pellets and electrode assembly were heated overnight in vacuum at 200°C and cooled down to room temperature. The temperature was raised and after about 4 hours current was passed with either a 1.5 volt or a 22.5 volt 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 pellets 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 in Section (1.2.2). The experiment was performed at different temperatures. 2.3.2 Wagner's Method In this 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 in diameter and 0.9 mm thick inserted between the pellet and a pair of Pt electrodes. P.D.s of 0.4 volts to 0.8 volts were applied to the sample, tapped from a 1.5 volt 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 satisfactory for attainment of a steady reading. Usually the experi-ments were done with only one sign for the P.D. (Pt electrode positive, the direction required to suppress conduction by Cu + i n t e r s t i t i a l s . ) But in 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 substantially different results at low temperatures, as described in Section 3.3.2. 2.4 THERMOELECTRIC POWER MEASUREMENTS 2.4.1 Thermoelectric Power Cell 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 in diameter and has a thick-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 teflon cylinder 5.0 cm in length and 2.0 cm i n diameter. The bottom thermocouple electrode assembly, on the other hand, was fixed in a cylindrical cavity of teflon threaded inside matching with the top assembly as shown in 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 in the cylinder and the other two wires of the bottom electrode pass along the side of the assembly. The wires were insulated by teflon sleeves. Figure 17 Thermoelectric Cell 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 in a teflon cork which is fixed in a pyrex B-34 socket. These wires as well as the teflon cork are vacuum sealed with dekhotinski cement. The lower end of the socket B-34 is joined with a B-34 cone. In between socket and cone the side arm is joined with a two way stop cock whose rectangular end is connected to the vacuum system with a b a l l joint. For operation the c e l l was placed in a pyrex f l a t bottomed vessel with B-34 socket. Both thermocouples were calibrated (using melting ice at the reference junction) and calibration curves are given in Figure 18. 2.4.2 Thermoelectric Furnace The furnace is made of s i l i c a tube having the internal diameter of 4.2 cm and of length 14 cm. The tube i s wrapped in thin layer of asbestos paper. Then i t i s wound with heating element more closely towards the top and thinly at the bottom to produce a temperature gradient. The winding of the heating element is further insulated by several layers of asbestos paper. The bottom end of the furnace is insulated by glass wool. During the course of operation the loss of heat from the top is prevented by insulating the top with glass wool. The furnace was calibrated with variac reading. The temperature difference obtained between the ends of a pellet 1 - 1.5 cm long varied from 6° to 30°K. Figure 18 Top thermocouple Bottom thermocouple Temperature (°C) 00 69 2.4.3 P r o c e d u r e A f t e r i n t r o d u c i n g t h e s a m p l e i n t o t h e r m o e l e c t r i c c e l l , i t was e v a c u a t e d f o r a b o u t t w e n t y h o u r s , t h e n a n n e a l e d o v e r n i g h t a t 200°C and t h e n c o o l e d s l o w l y t o room t e m p e r a t u r e (abou t 3 - 4°C p e r h o u r c o o l i n g r a t e ) . 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 t o g e t r e p r o d u c i b i l i t y o f t h e r e s u l t s . The t e m p e r a t u r e was t h e n r a i s e d and a t an i n t e r v a l o f a b o u t 5 - 6 h o u r s , t h e t e m p e r a t u r e s o f b o t h ends o f t h e s a m p l e w e r e measu red b y t h e r m o c o u p l e s . The mean t e m p e r a t u r e T and g r a d i e n t AT w e r e c a l c u l a t e d . T h e r m a l e . m . f . was m e a s u r e d by a K e i t h l e y e l e c t r o m e t e r m o d e l 200B and t h e c o l d end was a l w a y s f o u n d t o be p o s i t i v e , i n d i c a t i n g t h e p o s i t i v e s i g n o f t h e c h a r g e c a r r i e r s . The r e s u l t s a r e t a b u l a t e d a s t h e S e e b e c k c o e f f i c i e n t , 8 = - A V / A T i n m i l l i v o l t p e r d e g r e e . The h e a t i n g and c o o l i n g r u n s we re r e p e a t e d t o g e t t h e r e p r o d u c i b l e 6 - T c u r v e . 70 2.5 HALL EFFECT APPARATUS 2.5.1 Sample Holder and Heating Assembly Since three shapes of samples (slotted circular, rectangular and square) were tried, separate sample holders were designed for each case. The sample holder was made with a piece of solid cylindrical teflon which was flattened at one end where the sample rests. On the flattened portion, a cavity of appropriate shape to accommodate the pellet was made. The electrical contacts were made by four platinum wires A, B, C, D attached to the sample as detailed later for each sample shape. A thermocouple wire T (Pt 10% Rh) was spot welded to one of the Pt wires (C). These five wires were insulated by passing through slots in the teflon terminating in holes d r i l l e d through the wider top of the teflon 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 in a pyrex vessel V which had two co-axial outer jackets. The extreme outer jacket was evacuated. The inner jacket was meant to pass the hot air to heat the. sample. The whole assembly of sample holder and pyrex vessel is shown in Figure 19. For the slotted circular samples, a l l four contacts may be large-area, and the Pt wires were attached to the sample with silver 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 Hall probes were Pt points on screws. D TC A B 2) / Figure 19 Hall Sample Holde < Pyrex vessel Teflon cylinder Hot air 72 The slotted circular samples (which remove problems of sensi-t i v i t y of the results to positions of the contacts) proved unsatisfactory because of mechanical d i f f i c u l t i e s in 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 positive results had been obtained with the simpler sample shapes.) The classical long rectangular shape was abandoned for the square in an effort to secure maximum sensitivity when a l l results had proved to be negative. 2.5.2 E l e c t r i c a l Circuit In the expectation that Hall EMF's of the order of 1 mV or more might sometimes be obtained, the ci r c u i t (Figure 20) was 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 Hall EMF. But for lower Hall EMF's, a more sensitive voltmeter could be connected at contacts F. The instrument used was a Hewlett Packard model 425-A D.C. microvoltmeter, with ranges down to 0.2 uV f u l l scale. I wish to thank Mr. J. Sallos of the Electronics Shop for lending me this instrument, which was part of the shop's own testing f a c i l i t i e s . Switch S 2 was used to connect the electrometer to the current leads or Hall probes. In the latter position, S3 was closed to complete the current-supplying c i r c u i t . S^  allowed any pair of electrodes to be selected for current or EMF measurement; this is needed for the van der Pauw method in which the slotted circular sample is used. Figure 20 73 Hall Effect Electrical Circuit o—o o—O 74 2.5.3 Magnet An electromagnet originally designed for use in a mass spectrometer was adapted for the present purpose. The pole pieces were 11 cm in diameter and 3 cm apart, and the windings were of many turns and high resistance, requiring a high voltage D.C. power supply delivering only a low current (up to 250 V and 200 milliamp). This power supply, operating off 110 V D.C. mains, was built (and rebuilt for the present purpose) by the Chemistry Department Electronics Shop. The circ u i t included a switch for reversing the f i e l d and coarse and fine 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 NMR probe. The apparatus (block diagram, Fig. 21) consists of a variable-frequency RF power supply, frequency counter, probe containing trans-mitting and receiving coils and a sample of lithium chloride solution and an RF detector with display on an oscilloscope. For protons in water, resonance is'at 4257.7 KHz for 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 calibrated i n both directions (forward and reverse) of the magnetic f i e l d with increasing and decreasing f i e l d . The maximum magnetic f i e l d obtainable from this magnet was about 2000 gauss. The calibration probe was placed in the centre of the f i e l d , as near as possible to the position normally occupied by the sample. Figure 21 Block Diagram of Magnetic Field Calibration Apparatus Frequency Counter Power Supply Magnet Probe Oscillator Detector Magnet Power Supply Oscilloscope 76 2.5.4 Sample Preparation 21 For the method of Van der Pauw which used slotted circular samples, circular pellets were prepared of both pure CuCl and CuCl x in the usual manner as described in Section (2.1.3). The pellets 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. At the middle of the circumference of each segment, the contacts were made using Ag-paint. The Ag-paint was dried carfully in a vacuum warmed by hot a i r . Rectangular samples were prepared from powder CuCl and CuCl^ in a steel die designed for this purpose using a pressure of 6000 psi by the hydraulic press mentioned in Section (2.1.3). The square sample was made by sawing from the circular pellet and the surfaces were polished on carborundum polishing paper. 2.5.5 Procedure In the Van der Pauw method, the conductivity and Hall 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 is known. Since no positive results were eventually obtained, the method w i l l not be described in detail. For rectangular samples, current and Hall EMF electrodes are distinct from each other, and current density and Hall f i e l d can be found from the e l e c t r i c a l data and sample dimensions in the obvious way. Since 77 the Hall probes may show a spurious Hall EMF because they are not positioned exactly opposite each other, readings were always taken with and without magnetic f i e l d . When i t was desired to search for very small Hall 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 Hall EMF's may arise from pick-up in the leads (which may be field-dependent i f the pick-up is from the magnet power supply) or from magnetoresistance (detectable at Hall probes only i f they are misaligned and so have a non-vanishing zero f i e l d P.D., and i f the sample has another resistance in series with i t ) . To eliminate such p o s s i b i l i t i e s , i t was necessary to check:- (a) that any observed effect did not recur i f the experiment was repeated with everything the same except that the sample was l i f t e d a short distance out of the f i e l d ; (b) that any observed "Hall EMF" reversed with f i e l d direction and was proportional to f i e l d (magnetoresistance is proportional to the square of the f i e l d ) . 78 3. RESULTS 3.1 ELECTRICAL CONDUCTIVITY 3.1.1 Effects of Electrode Material, AC versus DC, and Surface Conductivity For pure CuCl, three electrode materials have been used: Ag, Pt and Cu. 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 for pure CuCl below about 130°C. For a selection of samples, pure and chlorine-treated, the effect of surface conductivity was checked by using the guard-ring electrode assembly with the guard ring alternately grounded and joined to the remainder of the electrode. None of these possible disturbing influences was found to have any significant effect on the observed activation energies. Some of them, as detailed below, were found to change the absolute value of the conductivity by significant amounts - in the worst case, about 80% - but nothing was found which appeared to suggest that these factors were significantly affecting the conduction mechanism, except for a possible change in the ratio of ionic to electronic contribution in one case. The effect of electrode material was insignificant at lower temperatures (pure CuCl), but in the high temperature region above 190°C the conductivity was depressed by about 40% for Ag electrodes and 80% 79 for Pt electrodes relative to the value for Cu electrodes. This may arise from electrode polarization effects or from a slight tendency for ionic carriers (Cu*" i n t e r s t i t i a l s ) to be depleted when inert elec-trodes were used, as happens to a much greater extent when DC is passed for a long time with a Pt anode (the Wagner method of separating ionic and electronic conductivity, section 3.3.2). In either case, the effect would be expected to arise only in DC measurements, and this was in fact the case. No significant dependence on electrode material were found in AC measurements. AC conductivities were in general greater than DC conductivi-t i e s . The size of the discrepancy was dependent on the P.D. across the sample, and was a minimum (about 5 - 10% difference) for 0.2 - 0.3 V. The higher the P.D., the more serious the polarization effects became in DC measurements. I n i t i a l readings of DC conductivity, taken as rapidly as possible to attempt to f o r e s t a l l the polarization, often agreed very well with AC results. Measurements on a sample with the guard-ring electrode grounded commonly gave results for conductivity about 18% lower than with the guard ring joined to the rest of the electrode. This is the maximum possible effect of surface conductivity. Probably much of this decrease arises from effective 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, is appreciably smaller than the f u l l surface area of the sample. 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 variations, which was about 20%. 80 3.1.2 Pure CuCl No AC conductivity measurements were made below about 130°C in pure CuCl in CuCl^ f o r x > 1.46. Except for these, only AC data are given. The results showed two distinct regions, the one above 180°C with an apparent activation energy E^ = 1.03 eV and the other below 150°C with E^ = 0.55 eV. A typical set of data is plotted in Fig. 22. and activation energies and absolute values of conductivity at two temperatures are shown for several samples in Table 3 to show the repro-ducib i l i t y of the results. Between 180° and 150°C, the experimental points l i e dis t i n c t l y above either straight l i n e , but in fact correspond very closely to the sum of the conductivities given by the two straight lines, as shown by the dotted line in Fig. 22. Thus i t appears that the two conductivity mechanisms responsible for the two ranges are operating independently i n parallel between 150° and 180°C. In the upper range the present data agree very well with previous work on highly purified samples (Wagner and Wagner, Hsueh and Christy, see Fig. 3). The results of Bradley et a l . , whose sample was not as pure as those of former workers agree partly with present results. For instance, the absolute conductivity at 227° and the activa-tion energy in the lower region (which extends only down to about 97°C) are in agreement with the present results but the activation energy in the upper range is less by ^ 0.2 eV than the present result (see Table 2). The lower range represents behaviour previously reported only 103/T(°K) TABLE 3 Activation Energies and Specific Conductivities of Pure CuCl with Different Electrodes Activation Energies Eq (eV) Logi 0o at 103/T(°K) S P 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 Activation Energy E a Upper range 1.03 ± 0.01 eV Lower range 0.547 ± 0.01 eV Specification of electrodes: 1, 2 silver electrode 3, 5, 6, 7 copper electrode 4 Pt electrode. 83 by Bradley et a l . , activation energies observed in this region by other workers having usually been about half the value of 0.55 eV reported here. In the work of Bradley et a l . , 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 in overall composition from CuCl^ 000678 t 0 C u C 1 i 645 a r e P l o t t e d i n F 1S* 2 3 a n d tabulated i n Table 4. In a l l cases except for the samples with 0.0678% and 0.15% chlorination two distinct regions were found. In the samples with composition CuCl^ 000678 a n c* ^ u ^ - ' - i 0015 fc^e c o n d u c t : ' - v l t y data show only one region. The samples from 0.29% chlorination upwards dist i n c t l y show two regions with a break in the conductivity plot at 'v* 110°C. For nearly a l l samples the l o g i o 0 vs ——- plot is distinctly linear. The only possible sp J. 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 linear, but the data were rather scattered in the upper range. Data from this sample were excluded in calculating average values of activation energies. As the percentage chlorination increases, the samples show changes in activation energy, but these do not occur at the same percent-age chlorination for the upper and lower ranges. The activation energy TABLE 4 Conductivity Results of Chlorinated CuCl Activation Energies q (eV)_ Log a Sample Upper Range Lower Range 24°C 130°C 200°C C u C 1l.000678 0.38 -4.75 -3.12 -2.35 C U C 11.0015 0.38 -4.78 -3.12 -2.43 C u C 11.0029 0.43 0.38 -4.77 -3.02 -2.25 C u C 11.0102 0.52 0.28 -4.82 -3.52 -2.50 C U C 11.012 0.55 0.37 -4.88 -3.34 -2.37 C U C 11.0238 uncertain 0.47 -5.27 -3.12 -2.05 C u C 11.0675 0.43 0.31 -4.70 -3.25 -2.47 C u C 11.204 0.52 0.30 * -5.35 -3.84 -3.05 C u C 11.308 0.52 0.13 -5.65 -4.56 -3.60 C U C 11.461 0.47 0.13 -6.25 -5.52 -4.65 C u C 11.502 0.52 * 0.22 -7.30 -5.85 -4,85 C U C 11.545 0.79 0.12 -8.150 -7.32 -5.85 C U C 11.552 0.89 0.17 -8.50 -7.70 -5.90 C U C 11.604 0.930 0.25 -9.60 -8.30 -6.58 C u C 11.645 0.90 0.45 -10.50 -8.20 -6.50 * The lines indicate the compositions at which the activation energies show abrupt changes. 86 of 0.38 eV, which appears at the slightest extents of reaction with chlorine, i s maintained in the low temperature region up to 20.4%. Between that value and 30.8%, the lower range activation energy drops sharply. Best values for the activation energies in 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 activation energy again rises. An upper range did not appear in 0.0678% and 0.15% samples. It f i r s t appeared in the 0.29% sample, but with a rather low activation energy which was excluded from the average. Beyond this point, the upper range shows an activation energy which appears to match that of the lower range in pure CuCl. The best value, from pure CuCl and chlorinated samples from 1.02% to 50.2%, is 0.51 eV. This is in exact agreement with the lower range in the work of Bradley et a l . Their "pure" CuCl, prepared by solution reduction of A.R. CuCl 2, seems to l i e between the present "pure" and "slightly-chlorinated" samples in i t s absolute conductivity. A CuCl2~doped sample in their work, with 0.2 mole % CuCl 2, seems to match the present "slightly-chlorinated" samples f a i r l y closely for the range with activation energy 0.51 eV. Much of the work of Bradley et a l . was at very high pressures, and thus not directly comparable to the present data. At 40 kb pressure (but not at lower pressures) and with 2 mole % CuCl2 in the sample, they found an activation energy of 0.33 eV between 100° and 200°C. This resembles the present "lower-range" value. The significance of these comparisons w i l l be discussed in section 4. 87 Beyond 50.2%, the upper range activation energy rises abruptly. The average value from 54.5 to 64.5% i s 0.88 eV. In the previous work of Ng, the activation energy was found to rise contin-uously with composition towards the same maximum value. The discrepancy between the two sets of data arises because the temperature ranges used in 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% chlorination was investigated more extensively in the present work than in that of Harrison and Ng, whose f i r s t sample was at 4.8%. A feature not found at a l l in the earlier work is a rise in conductivity to about 1000 times that of pure CuCl at room temperature,' which takes place even at only 0.0678% chlorination. From there to about 1% chlorination, the room temperature conductivity remains constant, and thereafter i t f a l l s . The region around 60% chlor-ination, where Harrison and Ng found a not very well confirmed "bump" in the conductivity was re-investigated carefully and no evidence of a bump was found. The data on absolute values of conductivity are given in Table J|.. The conductivity after levelling off decreases with chlorination almost linearly as shown in l o g i Q O " ^ versus composition plot up to about CuCl^ 502' '^ ie decrease i n conductivity with higher compo-sition i s s t i l l seen and i t appears that the conductivity has levelled off at 60.4% chlorination (except at room temperature) (Fig. 24). 88 Figure 24 L o£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, slightly 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-electric power was positive. The results are shown as plots of thermoelectric power 9 against temperature in Figure 25 (pure CuCl) and Figure 26 ( a l l chlorinated samples). Figure 25 i l l u s t r a t e s : - (a) error limits in voltage measure-ments, marked for two series of points; these errors arise from fluctua-tions, probably caused by pick-up, which became increasingly serious as sample resistance rose; the ve r t i c a l lines i n Figure 25 indicate extreme limits of the fluctuations; (b) the approach to reproducible behaviour through successive cycles of heating and cooling; (c) the negligible effect of changing the electrode material from Cu to Pt. (The latter was used for a l l chlorinated samples.) For a l l the curves in Figure 26 up to x = 1.308, the error in voltage measurement is negligible, but another possible source of error is the approximation of the derivative 6 =-dV/dT by the ratio of f i n i t e differences AV and AT across the sample when the 0 - T curve is 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° in that region. 1.6 1.4 — Figure 25 Thermoelectric Power of Pure CuCl 60 > 6 1.2 — 1.0 — .8 — 6 4 t . ft 4 • • I + Cell Cu|CuCl|Cu, Cooling o> heating #, cooling A Cell Pt|CuCl|Pt, Cooling • Hsueh & Christy CuCl • Doped 0.01% CdCl 2 and 0.1% CdCl„ For f i t of the present data to a curve, see diagram of Peltier coefficient (Fig. 27), 40 80 120 160 Temperature (°C) 200 250 O 60 1 2.4' 2.0 1.6' 1.2 .8 Figure 26 Thermoelectric Power Data of Chlorinated CuCl • C u C 1l.000678 • C u C 11.0015 o C u C l1.0029 • C u C 1 1 . 0 l 0 2 A C u C 11.0238 • C u C l1.0675 o • CuCl CuCl 1.204 1.308 C u C l 1 < 5 4 5 CuCl 1.552 C u C 11.645 .4 40 80 120 160 200 240 Temperature (°C) 92 The possibility that the f i n i t e difference procedure might have distorted the positions and shapes of the maxima is best checked by comparing runs on similar samples in which the temperature intervals are displaced from each other, e.g. 90 - 100° and 101 - 111° in one run, but 95 - 105° and 106 - 116° in the other. Two such runs are those for x = 1.000678 and 1.0015 in Figure 26 (open and solid square displaced about 5% from each other near to the maximum). The reproducibility between these two runs seems to j u s t i f y the procedure for estimating 6. While the Seebeck effect i s the easiest thermoelectric effect to measure, the Peltier coefficient is easier to interpret, since i t indicates the energy transported by a charge carriers (roughly E for F positive holes), whenever there i s only a single species of c;.rrier; for mixed conduction mechanisms, i t gives the average energy transported by the carriers, weighted in proportion to the fraction of the current carried by each type of carrier, provided that the carriers are a l l of the same sign; contributions from carriers of opposite sign are subtracted. The Peltier coefficient is easily calculated from 9, being simply 9T. Values of this quantity are plotted against temperature in Figs. 27 (pure CuCl), 28(a) (chlorinated samples up to x = 1.0102) and 28(b) (more heavily chlorinated samples). The results show four types of behaviour, as follows:-(a) Pure CuCl: The thermoelectric power shows only a slight temperature dependence, but the dependence at low temperatures seems to be somewhat different from that above about 90°C; this i s seen most clearly in the I 1 40 80 120 160 200 240 Temperature (°C) Figure 28a Peltier Coefficient of Chlorinated CuCl 1.0 .8 .6 .4 - f .2 H O • A • CuCl 1.000678 CuCl 1.0015 CuCl 1.0029 C U C 11.0102 NiO (Austin et al) 40 80 120 160 200 T 240 Temperature (°C) 4S 1.0 — Figure 28b Peltier Coefficient of Chlorinated CuCl .8 > <u .6 .4 .2 O • CuCl 1.0238 CuCl 1.0675 CuCl 1.204 CuCl 1.308 O — 40 80 120 160 200 240 Temperature- (°C) to tn 96 plots of the Peltier coefficient (Fig. 27). In this sample, conduction i s changing from electronic (positive hole) to ionic (Frenkel defect, i n t e r s t i t i a l predominating, positive sign) over the temperature range studied. The way in which this changeover could give a variation of the form observed is shown by equations (1) - (4) of Section 1.3.3. The linear region, of negative slope, corresponds to conduction completely by positive holes (equation 1.3.3 (1)). Its intercept at T = 0, 0.53 eV, i s in good agreement with the proposal (Section 4.1) that there is an acceptor level at 0.51 eV. Departure of the curve upwards from this line should represent the appearance of a contribution from ionic conduction (equation 1.3.3 (2)). This is f i r s t noticeable at 80°C, according to the curve of e6T versus T. As the temperature increases, the Peltier coefficient should eventually become constant i f ionic conduction i s dominant. This condition has been achieved by about 180 - 200°C, and the limiting value of e6T is (eeT) r o = q ± = 0.439 eV. This value may be used in conjunction with equation 1.3.3 (4) to calculate from the values of eGT the % ionic conduction at any T. The results are shown as curve G of Fig. 29. Although the overall tem-perature range for the transition agrees well with that found by other methods, quantitative agreement on the form of the variation i s rather poor. In particular, the thermoelectric power results indicate that 50% ionic conduction is achieved just below 100°C, while a l l other methods indicate 130° - 160°C (the highest value, from the crossing-point of the linear In a versus 1/T plots, being probably the most rel i a b l e ) . Curves A - F of Fig. 29 are described in Section 3.3. Figure 29 % of Ionic Conductivity in Pure CuCl 100 80 60 40 20 80 120 160 200 240 Temperature (°C) 280 Previous work • Tubandt et a l - A A Maidanovskaya et a l This work Conductivity - C Gravimetric (22.5V) Gravimetric (0.5V) -Wagner's Method - F Thermoelectric Power 320 98 0 appears to be much more sensitive to slight changes in 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 in a data. (b) Chlorinated samples up to x = 1.0102: The thermoelectric power passes through a well-marked maximum at 100°C. This type of behaviour 14 has been reported in NiO by Austin et a l . , who pointed out that i t is 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 level) proposed for NiO w i l l be applied to these results. The phenomenological comparison between the CuCl and NiO data i s shown in Fig. 28(a) and Fig. 30 as plots of 9 against 1/T (as used by Austin et a l . ) ; the resemblance is quite striking and suggests that, once the 3d band has been somewhat depleted of electrons, CuCl behaves rather similarly to NiO in respect of electronic 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 - 75°C). (d) Chlorinated samples with x - 1.308: No maximum, 9 becoming rather insensitive to temperature but decreasing as x increases. Figure 30 Comparison of thermoelectric Power of CuCl x (1 < x < 1.0675) with NiO 2.0 1.8 60 •3 1.6 1 1.4 H 1.2 -\ 1.0 —4 CuCl 1.000678 CuCl 1.0675 103/T(°K) 100 There is a rough phenomenological correspondence between these types of behaviour and the kinetics of the CuCl/C^ reaction as studied by Harrison and Ng. An i n i t i a l l y very rapid reaction in 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 diffusion-controlled build-up of CuCl^ around each CuCl particle was somewhere between 20% and 30% chlorination. Evidently the changes at the surface reflected in this kinetic behaviour produces changes in defect equilibria in the CuCl phase which produce the thermoelectric power behaviour just described. The probable nature of the defect structure i s discussed in more detail in Section 4. The data for low temperatures in slightly-chlorinated samples, i.e. for the region in which 6 or 9T is rising rapidly towards the maximum, are later 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 in the manner of an "activated" quantity. Combining equations (15) and (23) in Section 1.3.2, we have e0T + kT ln(N A/N D) = (E^/K) e~ ( Eyp " Eyn + E A ) / k T (D In Fig. 31, data for the sample at x =1.000678 are plotted against 1/T in two ways:- (i) as log^ST, i.e. ignoring the correction for the donor-acceptor ratio; this gives a reasonably linear plot from 40° to 80°C with an "apparent activation energy" of 0.22 eV, ( i i ) as log^Q(e6T + —l\ 2 4.6x10 T), which corresponds to N A / N D ^ 10 • The plot is s t i l l linear, but now gives a slope corresponding to 0.17 eV. These values are further discussed in Section 4. 102 The high-temperature end of the 9T versus T curves for sl i g h t l y -chlorinated samples is also of interest. According to equation (11) in Section 1.3.1, this curve should be linear and should extrapolate to give at the absolute zero. The points in the present results are too scattered to give a very reliable extrapolation; values of E from 0.4 to 0.9 eV can be obtained from various ways of extrapolating the curves in Figs. 28(a) and (b). Probably the best value i s that obtained from the extrapolation of the combined results for samples at x = 1.000678 and x = 1.0015, for temperatures above 160°C, as shown in Fig. 28(a). This yields E. = 0.63 eV; but the uncertainties are such that error limits 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 in the "linear" 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 for further discussion in section 4, have thus been obtained from results 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 in this thesis, go above the linear extrapolation of the high-temperature data. No explanation has yet been found for this dis-crepancy. The data of Austin et a l . for NiO show a similar 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 after passage of a quantity of e l e c t r i c i t y measured by a silver 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 in the c i r c u i t . Results for the fraction of ionic conductivity (Table 5 and Fig. 29, curve D ) indicated that the conductivity i s almost completely electronic up to 200°C, and becomes 50% Ionic at about 265°C. These data are similar to those obtained half a century ago by Tubandt (Fig. 29, curve A ) in which conduction became 50% ionic at 230°C. Much more recently, Maidanovskaya found almost completely electronic conduction up to to 250°C (curve B ). But in the present work, the changeover in conduction mechanism as indicated by the crossing-point of the two linear portions of the log a versus 1/T plot (Section 3.1.2, Fig. 22) was at 160°C. If, as suggested in Section 3.1.2, the linear portions represent electronic and ionic conduction mechanisms which, in the transition region, are operating independently, in parallel, then the fraction of ionic conduction can be calculated at any temperature from the a - T data. For calculations covering the transition region, accurate data are not needed in that region. A l l that is required i s the slope and intercept of both linear portions of the log a versus 1/T plot, above and below the transition region. TABLE 5 Transport Number Wt. of Ag Wt. of Cu equiv. to T°C deposited (gm) wt. of Ag for 100% (gm) 24 2.5037 1.4770 170 0.4984 0.2940 196 0.5057 0.298 230 0.0815 0.0481 244 0.0284 0.01675 265 0.01667 . 0.00983 of Pure CuCl (.22.5 Volt Applied Voltage) Weight Change (mg) Pellet Anode Cathode Average % ionic 0.0 -5,70 +5.70 5.70 0.38 +0.2 -1.5 +0.80 1.15 0.78 +0.3 -4.97 +4.65 4.81 1.61 +1.75 -4.80 +4.10 4.45 9.25 +0.41 -3.19 +3.06 3.12 18.60 -1.35 -3.50 +4.55 4.02 41.00 o 105 The fraction of ionic conductivity calculated on this basis is plotted against T as curve C of Fig.29. Disagreement between this and the gravimetric data is very marked. It appears to be the latter 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 in the conductivity experiments of Section 3.1 (Table 3). When this was realized, conductivity measurements were made at various stages of a gravimetric experiment. It was found that the conductivity was at f i r s t close to the expected value, but later increased greatly and f i n a l l y decreased somewhat, remaining, however, far above the i n i t i a l value (Fig.32). Evidently the continuous passage of D.C. through the sample substantially 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 potential (0.77 V,for CuCl 2 production). The results (Table 6, Fig. 29, curve E) are markedly different from the previous data at high P.D. Conductivities are now in good agreement with those obtained in ordinary conductivity experiments, and the changeover from electronic to ionic conductivity occurs at a much lower temperature (160°C for 50%) in reasonable agreement with the calculation from conductivity plots, but in 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 electronic Time (hour) TABLE 6 Transport Number of Pure CuCl (0.5 Volt Applied Voltage) Wt. of Ag Wt. of Cu equiv. to Weight Change (mg) T°C deposited (mg) wt. of Ag for 100% (mg) Pellet 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 in that region with only 0.5 V applied. For chlorinated samples, which would be reduced by Cu electrodes, Table 7 shows the results of transport number measurements made by weighing the parts of a three-part assembly of pellets which was placed between Pt electrodes. For the slightly-chlorinated sample, no significant contribution from ionic conduction was found at any temperature. For the heavily-chlorinated sample, a l l pellets lost weight at 242°C. This could indicate up to about 5% ionic conduction, but more probably represents the loss of a very small amount of water from the CuCl component (CuCl 2* 2 H20 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 potential, but the conductivities 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 Wt. Cu equiv. to wt. Total E l e c t r i c i t y deposited (mg) of Ag for 100% (mg) (Coulombs) 50 47.60 28.08 42.60 70 31.60 18.65 28.30 102 ^40.05 23.60 35.80 135 42.25 25.07 37.80 200 39.10 23.06 35.00 Transport Number (CuCl^ 200 31.30 18.45 28.0 242 16.31 9.62 146.0 Weight Change (mg) Anode Middle Cathode Pellet Pellet Pellet -0.25 +0.05 +0.05 -0.15 +0.30 -0.10 +0.15 +0.15 -0.06 +0.70 +0.10 +0.45 +0.45 -0.05 +0.95 -0.18 -5.10 0.00 -1.70 +0.13 -1.80 110 TABLE 8 Conductivity of CuCl, . 0 and CuCl, ,,c 1.0143 1.645 Estimated from Transport Number Data C U C 11.0143 0 (ohm-1cm-1) a' (ohm - 1cm - 1) sp sp Temperature (°C) (from Transport Number) (from Conductivity Expt.) 50 2.12 x 10 - 5 3.56 x 10"5 70 5.13 x 10~5 6.30 x 10~5 .102 0.417 x 10~h 1.41 x 10~h 135 3.05 x 10-t* 3.98 x 10 - 4 200 1.26 x 10 - 3 3.16 x 10 - 3 C u C 11.645 200 3.05 x 10"7 3.16 x 10~7 242 1.07 x 10 - 6 1.78 x 10 - 6 I l l 3.3.2 The Wagner Method of Suppressing Ionic Conduction The Wagner method involves measuring the limiting current at long times for the c e l l Pt|CuCl|Cu with the Pt electrode positive. The method was tried 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 positive. The behaviour was then non-ohmic at a l l temperatures from 245°C down to 24°C (Table 9 and Fig. 3 3 ) and plots of logiol versus applied P.D. were linear. This is the expected behaviour (Section 1.2.3, equation (3)) for the higher temperatures, but is surprising at low temperatures, when the conduction is almost entirely 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 is the contribution to conduction from P P positive holes (in the c e l l Cu|CuCl|Pt) and A and L are cross-section and length of the sample. Fig. 34 shows the conductivities obtained from intercepts, as a logger versus 1/T plot, in comparison with the results of an ordinary conductivity experiment. At low temperatures, agreement is excellent. At high temperatures, this method gives values for the electronic component somewhat below the linear extrapolation of the low-temperature data. The slopes of the logic* versus E plots are, however, quantita-tively much less than the expected values, and they do not vary with 112 TABLE 9 Data for Non-ohmic Current Voltage Plot for Selected Temp. Voltage Current Log Current (volts) (amps) (amps) 0.4 6.76 x 10 - 9 -8.17 0.5 1.09 x 10~8 -7.96 0.6 2.24 x K T 8 -7.65 0.7 4.46 x 10~ 8 -7.35 0.8 8.91 x 10 - 8 -7.05 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 10 - 6 -5.95 0.6 2.24 x 10~6 -5.65 0.7 4.78 x 10 - 6 -5.32 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 -3.85 113 Conductivity of Figure 34 Pure CuCl by Wagner Method 115 temperature in the expected way. The slopes are shown in Table 10, together with the % ionic conduction calculated from the data plotted in Fig. 34. The % ionic conduction is also plotted as curve F of Fig. 29. The curve is in moderate agreement with other methods of determining the transport numbers. The non-ohmic behaviour of samples at low temperatures was rather surprising. At these temperatures, i n t e r s t i t i a l s should not be able to produce the effect because they contribute very l i t t l e to the conduction process. But the linear l o g ^ I versus E plots were s t i l l found for a positive sign of the Pt electrode. The linear plot is to be expected in the "forward bias" direction of a r e c t i f i e r , and the direction found is incorrect for a metal/p-type semiconductor r e c t i f i e r . In order to find out whether the history of the sample was important in determining i t s low-temperature behaviour, the following experiment was performed. A pellet was prepared as usual, and annealed at 196°C in the c e l l with Pt|CuCl|Cu electrode arrangement without  passing any current through i t . 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 results were obtained. The behaviour then found was ohmic (Fig. 35, points marked square). The temperature was changed to 236°C, and the same type of determination of current-voltage characteristic was repeated. The behaviour was non-ohmic (Fig. 36). This experiment was terminated with E positive (sign of Pt electrode) and measurements were made at two lower temperatures TABLE 10 Ionic Contribution Estimated by Wagner Method Temperature % (ionic) F/2.303RT Slope(volt" (T°C) 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 in 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 after determination of characteristic at high T o 00 119 (188°C and 140°C), but with only positive values of E used. The behaviour was non-ohmic at both temperatures. Finally the sample was brought back to room temperature, and the E - I characteristic redeter-mined with both positive and negative E. The behaviour was again ohmic, with the same resistance as before (Fig. 35, points marked triangles). The purpose of this experiment was to determine whether the sample at room temperature retained a "memory" of the polarization 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 distribution making i t , in effect, a p-n junction, and that defect distribution had become frozen-in at room temperature, then non-ohmic behaviour would be found after cooling. This did not happen in the experiment just described. In the earlier experiments, however, no cycling between positive and negative E was performed at a l l ; only positive E was used at a l l temperatures. This may have been enough to produce a non-uniform defect distribution. The explanation offered above for non-ohmic behaviour at room temperature is s t i l l a possibility. There are clearly a number of unresolved questions in regard to these complicated phenomena with an asymmetrical pair of electrodes. The procedure of the earlier experiments appears to give a correct indication of the % electronic conductivity, but for reasons which are obscure, since the calculation depends on extrapolation of l o g 1 0 I versus 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 side-line giving an additional method of finding data available in other ways, the study was not pursued further. 121 3.4 THE HALL EFFECT The Hall Effect 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 Bri t i s h Columbia) and indicated as containing a concentra-tion of acceptors of ^  7 x 10 1 5 cm - 3. The surface of the test sample was polished on Carborundum powder and silver paint was used to make the contacts. A Hall effect was found, of the appropriate sign for positive holes, and indicated a carrier concentration of about 3 x 10 1 5 cm - 3. This result was considered adequate to show that the apparatus was in working order, and the source of the discrepancy of a factor of about 2.4 between this value and the reported carrier concentration for the sample was not pursued. Measurements were made at room temperature on pure CuCl and on slightly chlorinated samples (x = 1.0061, 1.0074 and 1.0088) with applied voltages up to 3 V for the slightly chlorinated samples. For pure CuCl, which was considered the most l i k e l y sample to have an easily measurable Hall effect in view of the probably very low carrier concen-tration, measurements were f i n a l l y made with 22.5 V across a square sample, with a meter across the Hall probes capable of detecting 0.2 uV. No Hall EMF was found. This indicates either a carrier mobility ^ 10 - 3 cm 2volt - 1sec - 1 or a compensated semiconductor in which electrons and holes produce mutually opposed contributions to the Hall effect. 122 Since slightly chlorinated samples are believed to conduct electronically at a l l temperatures, with a changeover from predominantly electronic to predominantly positive 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 sensitivity of 0.2 yV. Again no Hall effect was found. 123 4. DISCUSSION 4.1 GENERAL INTERPRETATION OF RESULTS For pure CuCl in the upper part of the temperature range studied, the charge carriers are known to be i n t e r s t i t i a l cations. The present work has added nothing significant to knowledge on this already well-studied region, but merely confirmed that the present samples behave similarly to those used in the most reliable of previous studies. For the lower temperature range in pure CuCl, and for chlorine-treated samples at a l l temperatures covered in the present study, the charge carriers are electronic. The positive sign of the thermoelectric power shows that these must include positive holes, but does not prove that they are exclusively or even primarily positive holes in a l l cases. For a compensated semiconductor, in which both holes in the valence band and electrons at the acceptor level can conduct, 6 can be positive even when electron conduction predominates. This is established by equations (15) and (23) of Section 1.3.2, which were combined as equation ( 1 ) of Section 3.2. The apparent anomaly arises because each carrier contributes to the thermoelectric power (or the Peltier coefficient 6T) in proportion to the energy which i t transports. For the holes, this i s approximately the Fermi energy (measured from the valence band), but for the electrons i t is the difference between the Fermi energy and the acceptor level. This latter is 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_ is to E., which tends to cancel out the effect 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 correlation between the two must always lead one to suspect the presence of a double conduction mechanism, in which the two parts add differently in respect of energy transport and charge transport. Such a suspicion is greatly strengthened by the observation of a very rapid rise of 0 with temperature. Such a rise can be explained i n terms of the model of two charge carriers, with the aid of the equations cited above; and the phenomenon is very d i f f i c u l t to explain on any other basis; this point has been made by Austin et al.^"* in connection with data for NiO. They were primarily concerned, however, with the analysis of their results for Li-doped NiO, in which the 0 - T curves did not show a maximum in the neighbourhood of room temperature; they did not attempt a detailed analysis of the curves for pure NiO, which did have a maximum. Apparent activation energies derived from a and 0 data should be explicable in terms of three quantities: the acceptor level energy E , and the true activation energies for motion of holes and electrons, E ' yp and E . Of these, E i s li k e l y to be small; i t should differ from zero yn yp only i f the Cu 3d band is 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 in a situation in 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 of temperature (section 1.3.2, equation (20), n^ = N^). Then the apparent activation energy of conduction should be simply the true activation energy E • The value 0.36 eV, being the lower range apparent activation energy for ( slightly-chlorinated samples, w i l l be assigned to E • At higher tem-peratures, there should be a changeover to predominantly positive hole conduction, described by equation (14) in section 1.3.2. The apparent activation energy i s then (E^ + E ), and the value 0.51 eV w i l l be assigned to this. A correlation with thermoelectric power data may now be attempted. Equation ( 1 ) of section 3.2 shows that the apparent a c t i -vation energy of the Peltier coefficient (corrected for the term kT ln(N./lO) should be (E - E + E.). This should, therefore, be A D up yn A ' ' numerically equal to the difference between upper and lower range activation 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 definitively from the A yp present data. It is tempting to look at the whole range of conductivity data for chlorinated samples, and to suggest that the lowest activation energy observed corresponds to a situation with a fixed hole concentra-tion and represents E . This would yield the value 0.15 eV for E ^ yp yp (from the lower range data for highly-chlorinated samples) and hence 0.36 eV for the acceptor level E ; but these are in fact merely an upper 126 limit for E and a lower limit for E.. It is d i f f i c u l t to reconcile PP A such a low value of E^ with the thermoelectric power data for sli g h t l y -chlorinated samples. It has been pointed out in section 3.2 that the shape of the 0 - T curves has a puzzling feature, in that the maximum rises above the extrapolated line for high temperatures. The maximum also should not rise above E^; but i t does, even on the basis of the value 0.51 eV for E^. The discrepancy could be accounted for, in vague general terms, by the uncertain correction for scattering effects, which may be very complicated in a polycrystalline sample with complex surface structure. But i f E^ is 0.36 eV, the discrepancy i s altogether too big to account for i n any conventional manner. Hence i t i s suggested that E i s probably close to zero, giving E^ = 0.51 eV. The assignment of zero activation energy to E is consistent with the known situation in yp NiO, in which Hall Effect data were a v a i l a b l e ^ . It remains to consider the significance of the activation energies of highly-chlorinated samples, especially those above 50% chlorination, for which the activation energies in both temperature ranges are different from those of the slightly-chlorinated material. The more extensively-reacted material i s known to be formed in a d i f f e r -ent way, kinetically, from the material at lower extents of reaction. The work of Harrison and Ng showed that a layer of CuCl 2 began to build up on each CuCl particle somewhere between 20 and 30% reaction. This change seems to correspond to the disappearance of the maximum in the 0 - T plot and of the conduction behaviour with an activation 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 activation energy 0.51 eV which means, on the basis of the present interpretation, that the semiconductor is s t i l l compensated. An uncompensated system should show activation energy E A/2, not E ; var-A A ious previous reports^for not very well purified CuCl at low temperatures have, in fact, reported the activation energy as about one-half that found in the present work. Partial removal of donors at 20 - 30% reaction i s followed at a much later stage (> 50% reaction) by some process which gives rise to an activation energy of 0.88 eV. This w i l l be interpreted as E^ for a different type of acceptor (again including E i f i t differs from zero; 1^  P the holes s t i l l move in the same way - only the source of them is different). This interpretation i s on a much shakier basis than that for the phenomena at low extents of chlorination. The sample structure is much more complicated; i t is very heterogeneous, and the process of pressing a pellet converts a system of CuCl particles each coated with CuCl2 to one in which CuCl particles are in contact with each other. Scattering processes w i l l be very complex; and although the conductivity data are clearly related to what is happening in the CuCl phase, the same is not necessarily true of 0. As mentioned already, contributions to 0 and 9 do not add up in 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 activation energy of 0.88 eV is well-established, clearly distinct from the Frenkel defect activation 2c energy.of 1.03 eV (which Harrison and Ng had formerly tentatively identified 128 i t with), constant over a range of extents of reaction, and associated with positive hole conduction. It i s , furthermore, too large to be a value of E /2; an acceptor at 1.76 eV would not ionize significantly A at these temperatures. Thus the identification of 0.88 eV as E^ for an acceptor which appears only at high extents of reaction i s at least very plausible. 4.2 MODELS OF THE ACCEPTORS It is proposed that the hole-trapping site which gives acceptors with an ionization energy of 0.51 eV i s the most obvious one to postulate in slightly non-stoichiometric CuCl, v i z . the cation vacancy (as envisaged also by Vine and Maurer in iodine-doped Cul). The compensating donors in highly-purified samples are probably residual foreign material. In less well-purified samples, for which activation energies close to E^/2 have been observed, the chief difference i s probably not a greater concentration of foreign material but a much greater extent of oxidation, for which foreign donors can no longer compensate. In other words, the results are a l l consistent with the concept that purification of CuCl, whatever i t does by way of expelling foreign material, does much more towards achieving stoichiometric propor-tions of the host ions. On this basis, one of the most unusual features of the present results i s the occurrence in non-stoichiometric material of compensated behaviour. This suggests the formation of a special type of donor in the special conditions of C l 2 oxidation. It i s suggested that this i s a Cu + ion in some special surface position (and thus at the reaction 129 interface) in which i t can ionize to Cu in a localized form not incorporated into the valence band. This is consistent with the dis-appearance of some of the effects of a large donor concentration when surface conditions change drastically at 20 - 30% reaction. At that point, as already mentioned, CuCl2 starts to build up on each particle. As this reaction proceeds, the Cu originally present in CuCl must move to occupy eventually 66% more than i t s original volume; but the original Cl ends up occupying only 83% of i t s original volume. It is plausible to envisage a force tending towards inward movement of Cl, and to postulate injection of i n t e r s t i t i a l Cl as the source of the new acceptor with an ionization energy of 0.88 eV. 4.3 POSITIONS OF THE ACCEPTOR LEVELS For certain impurity levels in the group IV elemental semi-22 conductors, the "hydrogenlike" model of the state of the trapped elec-tron or hole has been very successful. In the simplest form of this model, the electron or hole is envisaged as being bound in an analogue of a hydrogen Is state, with binding energy (in eV) and Bohr radius o (in A) given by E = 13.6 m*/(m K 2) A e r = 0.528 K m /m* e where K is the dielectric constant of the host la t t i c e and m* is the effective mass appropriate, for acceptors, to a hole at the top of the valence band. The valid i t y of a model which represents the host la 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 effectively cover a region including a very large number of atoms of the host l a t t i c e . This condition is o satisfied in Si and Ge, in which r is found to be about 20 and 50 A respectively. Corresponding values of the binding energy are of order 10"2 eV. Vine and Maurer applied this model to the acceptor level produced by excess iodine in Cul, which was ascribed to a cation vacancy as trapping centre - the same model suggested here for the acceptors in "pure" and slightly chlorinated CuCl. They obtained f a i r l y close agree-ment between experiment and the hydrogenlike theory for an acceptor level with of the order of 0.4 eV (varying with acceptor concentra-tion). They hence estimated an effective mass for the hole only slightly smaller than the free electron mass; but they neglected to point out that, for such a high E , the Bohr radius is of order 2 A and hence A indicates localization 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 significance whatever. The corresponding calculation for CuCl, with m* = m , gives E = 0.98 eV e A and r = 1.97 A. A value of m >> m , such as has been reported for 20 CuCl (20 m ) would change the calculation to give E and r rather e A similar values to those i n the hydrogen atom i t s e l f ! The hydrogenlike model thus does not appear very f r u i t f u l for the present purpose, and any more sophisticated calculation of E^ for a localized model is beyond the scope of this thesis. Some more general features of the localized model may, however, be followed up. In the 131 f i r s t instance, for a binary compound in which a trapped hole resides principally on nearest neighbours of the trapping site, two values of are to be expected: one for the case in which those nearest neigh-bours are anions, and one for the case in which they are cations. Of the two acceptor sites postulated in 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 in a vacant tetrahedral site of the cation sublattice, and hence surrounded by cations. Thus two different values of E. are to be A expected. (If the hole were more highly localized, and therefore sensi-tive to the precise nature of the trapping centre rather than just i t s effective charge, there could of course be many more than two values of E , as is the case in the group IV elemental semiconductors for deep-lying acceptor levels produced by anything except group III impurities. In the present discussion, i t is supposed that the holes in CuCl are mainly localized on the nearest neighbours of the trapping site, so that E is sensitive 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% Cl 3p, according to Song ), trapping in 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", in that the hole, though localized, may s t i l l be described in terms of the same kind of orbital which predominantly constitutes the valence band. By the same token, trapping in the v i c i n i t y of a cation vacancy is "abnormal" in requiring promotion of the hole to the Cl 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 far been suggested in this account). The two values of E^, (0.51 - E^) and (0.88 - E^) eV, thus cannot be accounted for simultaneously on the basis of the present models i f a promotion to Cl 3p is needed for the former. There i s , however, another poss i b i l i t y . The proportion of Cl 3p mixed into the Cu 3d band is substantial and presumably increases down the band from the value of 21% quoted by Song for the top of the band. More specifically, the Cu 3d band system i s subdivided into a set of three (the t2 orbitals) broadened to about 0.6 eV wide and a set of two (the e orbitals) forming a very narrow band at the bottom of the broader one. This can be thought of as the normal crystal f i e l d s p l i t t i n g of d orbitals in a local tetrahedral environment, with broadening into bands superimposed on i t . While the t 2 orbitals are appropriately oriented to interact with the corresponding orbitals on neighbouring Cu +, the e bands are very l i k e l y to interact indirectly, through Cl 3p, and the bands formed from the e orbitals are li k e l y to contain a greater proportion of Cl 3p. (This qualitative picture could be investigated quantitatively with the aid of integrals tabulated in Song's paper.) It i s possible that the admixture of Cu and Cl orbitals in the e bands might be suitable to represent the state of a hole trapped in the vi 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, is to be compared with a promotion energy which i s basically the crystal f i e l d s p l i t t i n g , band top to band top, between t 2 and e orbitals. This i s 0.53 eV, according to Song's calcula-tions. 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 in very small number and are compensated by donors, which are probably impurities, so that the trap depth appears as E^. Less highly purified samples may be sufficiently non-stoichiometric to contain holes and cation vacancies i n concentrations which are not compensated by the chance presence of donors. E^ i s then one-half of the trap depth. Deliberate introduction of non-stoichiometry by reaction with chlorine (from C.07% to 20% conversion to CuCl 2) produces a high concentration of traps and holes, but also produces donors at the reaction interface. These latter are probably Cu + ions in a favourable 2+ location for a Cu to reside. Because of the presence of the donors, the semiconductor 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 level predominates below 100 - 110°C, and the true activation energy of this migration (E^ n = 0.36 eV) appears directly as E^. This correlates with the observation of Bradley g et a l . that an activation energy E^ = 0.33 eV appears in CuCl2~doped CuCl, which may be expected to contain holes and cation vacancies, and that the appearance of this value of E^ is favoured by high pressure, which should assist incipient band formation at the acceptor level. At about 20% conversion to CuCl2, the reaction mechanism of CuCl 2a with C l 2 i s known to undergo a change, the dominant feature of which i s that CuCl 2 now starts to build up on each CuCl particle. It is 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 essentially a long-lived intermediate in the mechanism which operates below 20% conversion. The decrease in donor concentration effectively destroys electron conduction at the acceptor level, but s t i l l allows compensation of hole conduction (which can occur at very low donor concentrations). Thus the activation energy E f f = 0.36 eV i s no longer found, but = 0.51 eV persists at higher temperatures. The origin of the very low value E^ = 0.15 eV which now appears at low temperatures is obscure; i t may arise from electron withdrawal from the CuCl producing holes without an adequate number of traps for them. Beyond about 50% conversion, another change takes place in the CuCl defect structure, which correlates with changes in chemical reactivity and catalytic activity previously observed ± n the CuCl2 component. The amount of copper diffusing through the latter (as Cu+) is now approaching a maximum. Simultaneously with the outward movement of copper, there should be an inward movement of chlorine. It is proposed that Cl inter-s t i t i a l s in the CuCl component now form hole traps with a depth of 0.88 eV, which is observed as E . 135 5. SUGGESTIONS FOR FURTHER WORK 5.1 DOPING EXPERIMENTS Probably the most widely-used method of attempting to introduce defects of known type in a controlled manner is by "doping" with foreign ions. Attempts to introduce cation vacancies into CuCl by doping with a divalent metallic chloride might be bery useful in the present case. If the orbitals 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 irradiation or, as in the present work, by chemical oxidation with chlorine. The properties of CuCl treated with chlorine are known from the work of Ng to be different from those of a mechanical mixture of CuCl and CuCl 2. No work has yet been done on attempting to introduce CuCl 2 in the manner of a dopant. (CuCl 2 was used as a dopant by Bradley et a l but considering the low purity of their CuCl, CuCl 2 should be further studied as dopant.) It might be very interesting to try the series of compounds N i C l 2 , CuCl 2, and ZnCl 2 as dopants. The 3d energy is similar in Ni and Cu, but much lower in Zn. Attempts should also be made to introduce guest ions on anion sites. A doubly-charged ion such as S 2 - would be suitable as a hole trap. A comparison of CuS and Cu2S as dopants might be very useful; the former should give holes and trapping sites simultaneously, while the latter 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 direct information on the location of a trapped electron or hole, because the spectrum shows hyperfine lines arising from the interaction of electron spins with the nuclear spins of the environment. In favourable cases, this can lead to quite unequivocal identification of the environment. CuCl contains two stable isotopes of each of the elements ( 6 3Cu, 6 5Cu, 3 5C1, 3 7C1) and they a l l have spin 3/2. The magnetic moments are, however, much larger for Cu than Cl, and hyper-fine splittings from the two elements should be.clearly distinguishable. Ng looked at the EPR signal of chlorine-treated CuCl, but found only the signal 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 in the CuCl phase could be observed. 5.3 THE HALL EFFECT Measurement of the Hall Effect i s the best way to make a defin-i t i v e separation of concentration and mobility of charge carriers. It seems unlikely that the Hall Effect in the present samples can be many orders of magnitude below the detection limit of the existing apparatus, and i t would be useful to continue attempts to detect the Hall Effect with modifications to the apparatus, and also with a greater variety of CuCl samples. The apparatus used in the present work was adequate in regard to the magnet and i t s power supply, and the current supply to the sample. It should, however, be redesigned as follows:-137 (a) Better shielding 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 Hall EMFs of a substantial fraction of a mV would be found. (The current leads and the EMF leads should be separated; at present they run in one bundle from the c e l l to a switching box, and they appear to be capable of picking up signals from each other in the yV region.) (b) A new voltmeter should be installed, capable of reading 0.1 yV or better. Part of the d i f f i c u l t y in obtaining a Hall Effect in these samples may arise from the strong and complicated scattering processes in a polycrystalline sample (in which the surface of each particle is a reaction interface in the CuCl/Cl 2 reaction). Single crystal experiments would be useful. Unfortunately, the features of most chemical interest -the defects formed during reaction - are l i k e l y to be much less well-developed in a single crystal than i n polycrystalline samples. For 23 example, in the work of Baijal xn this laboratory on the KI/CI2 reaction, polycrystalline samples reacted extensively and showed marked changes in conductivity, while single crystals were almost unreactive. Much infor-mation might, however, be obtained by trying to relate the conductivity behaviour of doped samples to that of chlorine-treated ones (as suggested in section 5.1) and then to study the Hall Effect in doped samples, for which purpose single crystals could probably be used. 5.4 THERMOELECTRIC POWER A l l that has been written in the preceding section about the nature of the sample, and what might be done about this in relation to 138 the strategy of a programme of Hall Effect work, applies equally to thermoelectric power. 5.5 CALCULATIONS ON ACCEPTOR LEVELS The least ambitious theoretical calculation which would be useful in support of the present interpretation is the estimation of the percentage of Cl 3p character in the Cu 3d (e) bands. This could be done with the aid of tabulated integrals in the papers of Song. A more extensive theoretical, project would be an attempt to calculate the bind-ing energy of a hole attracted to an effective charge located on either an anion or a cation s i t e . 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. ibid 1801 c. ib 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 Soc, 1969, 65_, 1912. 9. W. Hebb, J. Chem. Phys., 1952, 18, 62. 10. J.P. McKelvey, "Solid State Semiconductor Phys.", (Harper and Row, Pubs., 1966). 11. F.J. Morin, Phys. Rev., 1954, 9J3, H95. 12. Mikio Tsuji, J. Phys. Soc. Japan, 1959, 14, 1640. 13. R.E. Howard and A.B. Lidiard, 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. Soc, 1967, 90, 157. 16. F. Herman and D.S. McClure, Am. Phys. Soc. Bull., 1960, _5, 48. 17. M. Cardona, Phys. Rev., 1963, 12!9, 69. 18. a. M.K.S. Song, 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. Nikitine, J. Physique, 1967, 28., C3-48. 140 21. L.J. Van der Pauw, Philips Res. Repts., 1958, 13, 1. 22. W.C. Dunlap; "An Introduction to Semiconductors", (John Wiley & Sons Pubs. 1957). 23. M.D. Baijal, Ph.D. Thesis, The Univ. of B.C. (1964). 


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