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Defect structure and electrical properties of CaO-stabilized ZrO2 Low, Norman Man-Pak 1967

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DEFECT STRUCTURE AND ELECTRICAL PROPERTIES OF CaO-STABILIZED ZrO„ BY NORMAN MAN-PAK LOW B. Sc., The University of British Columbia, 1961 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENT FOR THE DEGREE OF MASTER OF SCIENCE in the Department of METALLURGY We accept this thesis as conforming to the standard required from candidates for the degree of MASTER OF SCIENCE Members of the Department of Metallurgy THE UNIVERSITY OF BRITISH COLUMBIA April, 1967 In p r e s e n t i n g t h i s t h e s i s in 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 a t the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I ag ree 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 ag r ee 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 Depar tment 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 no t 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 . Depar tment o f The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, Canada Date / ^ J j ? el , /?S7 ABSTRACT The cubic fluorite-type solid solution of Zr 0^ containing 15 mole % CaO has been prepared by the hot-pressing process. The effects of annealing on the change.of lattice parameter, electrical properties, and density of the solid solution have been investigated. The lattice parameter of the cubic solid solution was found to depend on the heat treatment of the specimens. The decrease of lattice parameter with annealing temperature and time has been interpreted either in terms of the removal of interstitial oxygen ions from the." lattice or in terms of the inhomogeneous distribution of the CaO in the Zr02 lattice. The activation energy for conduction was also found to depend on,the heat treatment of the specimens. The variation of activation energy with annealing temperature has been interpreted in terms of pairing and clustering of the oxygen vacancies with the substitutional Ga ions in the solid solution. The minimum activation energy obtained in the present investigation corresponded to the theoretically predicted activation energy for the migration of oxygen vacancies. ACKNOWLEDGEMENT The author is grateful for the advice and encouragement . given by his research director, Dr. A. C D . Chaklader. Thanks are extended to Dr. E. Peters.for his criticisms and suggestions in the kinetic analysis, to Mr. A. G. Fowler of the Computing Centre, University of British Columbia for his assistance in setting up the FORTRAN computer programme, and to Mr. P. Bruin for his technical assistance. He also wishes to thank the various members of the faculty and fellow graduate students for many helpful discussions. Financial assistance which was provided by the National Research Council of Canada under Grant No. A-2461 is gratefully acknowledged. TABLE OF CONTENTS Page I. INTRODUCTION AND REVIEW OF LITERATURE 1 (A) Introduction . 1 (B) Review of Literature 3 1. Phase-Transformation and Stabilization of Zirconia .. 3 a. Phase Transformation of Zr0 2 3 b. Stabilization of Zr0 2 4 2. Crystalline Structure and Relationship of Lattice Parameter With Compositions in the Ca0-Zr02 System .. 7 a. Crystalline Structure •• 1 b. Relationship, of Lattice Parameter With Compositions 8 3. Cation and Anion Diffusion in the CaO-Zr02 System .. 11 a. Anion.. (Oxygen ton) Diffusion •. • • • • '• 11 b. Cation Diffusion . 12 4. Infrared Absorption Spectroscopy of Pure :Zr02 and CaO-stabilized.ZrOy 14 5. Internal Friction in Zr02 Containing CaO 15 6. Electrical Conductivity in the CaOr-Zr02 Solid Solutions . ........................... 19 a. Electrical Conductivity Kinetics ..• 1 9 b. . Ionic Conductivity 20 c. Electronic, Conductivity 22 d. Relationship of Electrical Conductivity and Diffusion Coefficient 24 II. EXPERIMENTAL PROCEDURE ........ 25 (A) Materials and SpeciirtWl, Preparation 25 1. Materials Preparation 25 TABLE OF CONTENTS (cont'd) Page 2. Specimen Preparation . 25 (B) Phase Identification • • • • 26 (C) Annealing Procedure 26 (D) Precise Lattice Parameter Measurement 27 1. Experimental Procedure 27 2. Lattice Parameter Calculation 28 (E) Infrared Absorption Spectroscopy 28 (F) Electrical Conductivity Measurement;. ..... . 29 1. Specimen Preparation 29 2. Apparatus and Equipment .. 29 3. Measurement Procedure .30 (G) Porosity and True Density Measurements 32 III. EXPERIMENTAL RESULTS . . . . .• 33 (A) Phase Identification of the Zr_ Q c Ca_ .. _ 0 Solid Solution . ..- 33 1. X-ray Diffraction ..... . .i .. .33 2. Infrared Absorption Spectra 35 (B) Precise Lattice Parameter of the Zr ' o c Ca c CL Q C Solid Solution ....... 38 1. Effect of Annealing-Temperature on the Lattice Parameter 38 2. Relationship Between Lattice. Parameter and Band Frequency of the Infrared Absorption Spectra 43 3. Effect of Annealing Time on the Lattice Parameter .. 44 (C) Electrical Conductivity of the Zr Q g 5 CaQ 0 1 g 5 Solid Solution \...... \ .... , \....... . 46 1. Electrical Conductivity as a Function of Temperature 46 2. Calculation of the Oxygen Ion Diffusion Coefficients From Electrical Conductivity Data 53 TABLE OF CONTENTS (cont'd) , Page (D) Porosity and True Density of the Zr Q g 5 CaQ ^ 0^ g^ Solid Solution '. 58 1. Apparent Porosity of the Hot-pressed Specimens .... 58 2. True Density of the Zr„ o c Ca_ , c 0. o c Solid solution ;.,?:??.. eo (E) Chemical Analysis of the Hot-pressed Ca0-Zr02 Specimens. 60 IV. DISCUSSION 62 (A) Lattice Contraction or Shrinkage of the Cubic Unit Cell in the Z r o g 5 C a 0 - 1 5 0 1 > g 5 Solid Solution -., 62 (B) Effect of Annealing on the Electrical Properties of the Zr„ o c Ca_ . _ 0. o c Solid Solution 70 U . o j U. i.0 1. O J (C) Effect bf Heat Treatment on the Oxygen Ion Diffusion in the CaO-Zr02 Solid Solution . 77 V. SUMMARY AND CONCLUSIONS . . 79 VI. SUGGESTIONS FOR FUTURE WORK 81 VII. APPENDICES 82 APPENDIX I : Experimental Data for Precise Lattice Parameter Measurements 82 APPENDIX II : Experimental Data for Electrical Conductivity Measurements 87 APPENDIX III : Experimental Data for Porosity and True Density Measurements 93 APPENDIX IV : Estimation of Error .., 96 APPENDIX V : Cohen's Method for Precise Lattice Parameter Calculation 98 APPENDIX VI : Derivation of the Nernst-Einstein Equation for Diffusion Coefficient Calculation from Electrical Conductivity Data 101 TABLE OF CONTENTS (cont'd) Page APPENDIX VII : Apparent Porosity and Bulk Density Determination .. 103 APPENDIX VIII : True Density Determination 104 APPENDIX IX : Theoretical Density Calculation of the CaO-ZrO Solid Solutions for the Oxygen Vacancy Model and the Oxygen Interstitial Model 105 VIII. BIBLIOGRAPHY 106 LIST OF FIGURES No. Page 1. Phase equilibrium diagram for the Ca0-Zr02 system 6 2. Fluorite-type structure of the Ca0-Zr02 cubic solid solutions. 6 3. Change of densities with CaO content in the CaO-ZrO^ solid solutions after annealinlgat high temperatures 9 4. Change of lattice parameter with CaO content in the CaO-Zr02 solid solutions .... 10 5. Infrared absorption spectra of monoclinic ZrO. and CaO-stabilized Zr02 7 16 .6. Schematic diagram of the high temperature electrical conductivity furnace and sample holder 31 7. X-ray diffraction patterns of the unreacted and reacted Ca0-Zr02 compositions. 34 8. Infrared absorption spectra of the monoclinic ZrO and partially CaO-stabilized Zr0 2 36 9. Infrared absorption spectra of the completely CaO-stabilized Zr02 after heat treatment 37 10. Typical X-ray diffraction pattern of powdered samples of the Zr_ o c Ca_ 1 C 0 „ solid solution 40 11. Decrease of lattice parameter as a function of annealing temperature 41 12. Decrease of lattice parameter as a function of annealing temperature (over-all data with mean values) 42 13. Relationship between lattice parameter and peak band frequency of the infrared absorption spectra for the CaO-stabilized Zr02 solid solution after heat treatment 45 14. Decrease of lattice parameter as a function of annealing time. 47 i 15. Arrhenius plot of electrical conductivity and temperature. 48 16i Change of activation energy for electrical conduction with annealing temperature 49 17. Comparison between the electrical conductivity data from the literature and the present data for the Zr^ g,. Ca^ ^ 0^  g,. solid solution .........! ! '. .... . 51 LIST OF FIGURES (cont'd) No. Page ' 18. Variation of electrical conductivity as measured immediately and after 30-45 minutes of soaking at th,e same temperature 52 19. Change of electrical conductivity as measured during the heating and.cooling cycles (specimen annealed @900°C) 54 20. Change of electrical conductivity as measured during the heating and cooling cycles (specimen annealed @1400°C).... 55 21. Arrhenius plot of oxygen ion diffusion coefficients and temperature 56 22. Change of activation energy for oxygen ion diffusion with annealing temperature 57 23. Comparison between the oxygen ion diffusion coefficient data in the literature and the present data in the Ca0-Zr02 system 59 24. Change of densities . with annealing temperatures 61 25. Relative decrease of lattice parameter with annealing time.... 67 26. Arrhenius plot of-the rate of relative decrease of lattice parameter and temperature 69 27. Change of excess energy for conduction with annealing temperature 74 LIST QF TABLES No. Page I X-ray diffraction peaks of several compounds in the 27°-33° of 29 values ' v 33 II Infrared absorption band frequencies of the monoclinic Zr0„ and CaO-stabilized Zr0 2 .... 38 III Chemical analysis of the Ca0-Zr02 solid solutions ............ 62 IV Energies of oxygen vacancy motion and dissociation in the Ca0-Zr0_ system 73 I. INTRODUCTION AND REVIEW OF LITERATURE (A) Introduction During the past ten years there have been numerous out-r standing developments in aircraft propulsion, nuclear systems, metallurgical research, and other closely allied fields. To meet the requirements of these fields, considerable efforts have been directed toward the. investigation and development of new refractory compounds and combinations. Over the years, the chemistry of Zr0 2 has attracted the attention of both the theoretical scientist and the.practical industrialist interested in high^temperature materials. Zirconia (Zr02) is considered as one of the most refractory oxides. It has not only a high melting point (2700°C) but also other distinctive properties, such as chemical inertness, corrosion resistance to oxidizing and reducing atmospheres and low neutron capture cross section. Zirconia also is polymorphic and possesses a complex crystal structure. Thus, extensive research has been done in studying its structure, polymorphism and refractory,properties. The application of pure Zr02 is limited due to the disruptive volume change associated with its polymorphic transformation. However, this limitation can be.overcome,by the addition of certain foreign oxides with which Zr0 2 forms solid solutions. The addition of a small amount of Calcia (CaO) to Zr02 results in the formation of stabilized.cubic solid solutions which remain stable at temperatures up to 2000°C. Because of the stabilization, Zr02~based solid solutions have been used as a heat exchanger of ceramic-heated blowdown jets and other aerodynamic devices, as potential fuels incorporated with urania and thoria for nuclear power - 2 - a p p l i c a t i o n , and as heating elements i n high temperature furnaces. The CaO-ZrC^ cubic s o l i d solutions also possess rather unique e l e c t r i c a l properties, and as a r e s u l t have.considerable usefulness as s o l i d e l e c t r o l y t e s i n galvanic and f u e l c e l l s . Electromotive force measurements on galvanic c e l l s which u t i l i z e the s o l i d e l e c t r o l y t e of Ca0-Zr02 have proved to be a valued and accepted technique for obtaining useful thermodynamic data, p a r t i c u l a r l y for the determination of elevated- temperature thermodynamic properties of m e t a l l i c oxides. The s o l i d solutions of Ca0-Zr02 used i n each p o t e n t i a l a p p l i c a  t i o n are generally custom-made products. The voluminous l i t e r a t u r e reporting the properties of these s o l i d s o lutions, p a r t i c u l a r l y on the e l e c t r i c a l properties, frequently show disagreement between workers. This inconsistency i s generally inherent to the p u r i t y of the s t a r t i n g material and the technique used i n preparation. The common method for preparing Ca0-Zr02 s o l i d solutions i s the method of p a r t i a l l y reacting CaCO^ and Z r 0 2 at temperatures between 1300-1400°C and then s i n t e r i n g the reacted material at higher temperatures, followed by a long period of annealing at low temperature. The Ca0-Zr02 cubic s o l i d solutions are nonstoichiometric and t h e i r e l e c t r i c a l properties are structure s e n s i t i v e . The temperature of specimen preparation and subsequent annealing may have a bearing on the defect-structure. The purpose of the present i n v e s t i g a t i o n i s two-fold: 1. to prepare a 15 mole % CaO + 85 mole % ZrO^ cubic s o l i d s o l u t i o n by the hot-pressing technique and.to anneal the specimens at various temperatures; and 2. to observe any change i n the c r y s t a l l i n e structure and the e l e c t r i c a l - 3 - c o n d u c t i v i t y w i t h a n n e a l i n g t e m p e r a t u r e and t i m e . The c h o i c e o f t h e c o m p o s i t i o n , 15 mole % CaO + 85 mole.% ZrO,,, i s d i c t a t e d by t h e a v a i l a b l e d a t a i n t h e l i t e r a t u r e on t h i s p a r t i c u l a r s o l i d s o l u t i o n as i t p r o v i d e s adequate d a t a f o r c o m p a r i s o n . (B) Review o f L i t e r a t u r e ( 1 ) . Phase T r a n s f o r m a t i o n and S t a b i l i z a t i o n o f Z i r c o n i a a. Phase T r a n s f o r m a t i o n The e x i s t e n c e o f two s t r u c t u r a l m o d i f i c a t i o n s o f z i r c o n i a was f i r s t r e p o r t e d by Van A r k e l ^ i n l 9 2 4 . S e v e r a l y e a r s l a t e r R u f f and 2 E b e r t d e f i n i t e l y e s t a b l i s h e d t h e phenomenon o f . p o l y m o r p h i s m i n t h i s m a t e r i a l by m e a s u r i n g t h e l a t t i c e c o n s t a n t s and d e n s i t i e s o f b o t h t h e m o n o c l i n i c ( d e n s i t y = 5.68 gm/cc) and t e t r a g o n a l ( d e n s i t y = 6.10 gm/cc) form s . The e x i s t e n c e . o f a m o d i f i c a t i o n o f z i r c o n i a w i t h h e x a g o n a l 3 symmetry r e p o r t e d a decade l a t e r by Cohn has ne v e r been c o n f i r m e d . The r e v e r s i b l e r e a c t i o n o f m o n o c l i n i c Z r 0 2 ^ r f ^ t e t r a g o n a l Z r 0 2 has been o b s e r v e d t o o c c u r i n t h e range 1100-1200°C. A l l a t t e m p t s t o s t a b i l i z e t h e h i g h - t e m p e r a t u r e t e t r a g o n a l m o d i f i c a t i o n by r a p i d q u e n c h i n g have been 4 5 u n s u c c e s s f u l t o d a t e ' . P r i o r t o 1962, i t was g e n e r a l l y assumed t h a t a 6 7 8 c u b i c m o d i f i c a t i o n o f . c h e m i c a l l y p u r e z i r c o n i a c o u l d n o t e x i s t ' ' . Recent d a t a have i n d i c a t e d , however, t h a t above 2200°C t h e r e v e r s i b l e f o r m a t i o n o f 9 10 a c u b i c form o f Z r 0 2 i s i n d e e d p o s s i b l e ' The m o n o c l i n i c t e t r a g o n a l t r a n s f o r m a t i o n i n z i r c o n i a o c c u r s a t a d e f i n i t e t e m p e r a t u r e and p r e s s u r e , p o s s e s s e s a l a t e n t h e a t of^endo- t h e r m i c ) r e a c t i o n , i n v o l v e s a change o f s t r u c t u r a l o r d e r i n g , and has a . l a r g e - 4 - disruptive volume change. This indicates that the monoclinic ~zzf tetragonal transformation is a phase transition "of the first order""'''''. 12 Furthermore, Wolten has pointed out that the.ZrC^ transformation is indeed both diffusionless, (ie., a l l atoms have the same neighbours in either phase,) and of the martensitic type. b. Stabilization of Zirconia The stabilization of ZrO^ has been an important subject of research for many years. Since the discovery of the reversible trans- 13 formation of ZrC^, Geller and Yavorsky confirmed and extended earlier findings which indicated that during the transformation a large and rapid volume change occurred and that the phase tranformation could be suppressed by the addition of certain oxides which resulted in the formation of solid solutions having a cubic lattice. A considerable amount of research work has been carried out in studying the reaction of ZrC^ with various 14 oxides. Roth has formulated a general set of rules which can be used for the reaction of ZrC^ in various binary oxide systems. These rules govern the solid-state reaction of ZrC^ with oxides of the divalent, trivalent, tetravalent, and pentavalent ions. Duwez, Odell and Brown^ were among the earlier researchers on the subject of stabilization of ZrC^ with other oxides. They established the phase diagram for the binary system of CaO—ZrC^, (Fig. 1), and the binary system of MgO-ZrO^ . Webber, Garrett, Mauer and Schwartz"^ later extended the earlier studies to cover more binary and ternary systems. Hoch and Mathur'^ have studied the formation of cubic ZrO^ with transition -5- 18 metals of group V and VI and their oxides. Smoot and Ryan have investigated the i n i t i a l temperatures of the ZrO^ phase change and the reactions for the formation of solid solution using X-ray diffraction. The study of the reaction of the.ZrO^ with other oxides or transition metals remains an open field in research. A small amount of CaO will form a solid solution with ZrO^ possessing cubic fluorite-type structure. An equal molar mixture of CaO and ZrO^ will form a CaZrO^ compound rather than a solid solution. Duwez et al showed that solid solutions containing 16 to 30 mole % CaO have cubic symmetry 19 when quenched from 2000°C. On the other hand, Hund found that the cubic phase existed only from 10 to 20 mole % CaO in specimens prepared at 1460°C. 20 Dietzel and Tober reported that cubic solid solutions of ZrO^ extended from 7 to 24 mole % CaO at 1800°C and from 14 to 20 mole % CaO at 1400°C. 21 A recent Russian investigation placed the cubic phase.field between .10 and 22 40 mole % CaO in specimens prepared at 1500°C. Tien and Subbarao delineated the cubic phase boundaries by careful X-ray diffraction studies and observed that the cubic phase existed from 12-13 mole % to 20-23 mole % CaO in ?3 • specimens prepared at 2000°C and quenched from 1400°C. Cocco has invest igated, by reflection microscopy, the composition limits at high temperature of the cubic phase of CaQ-Zr02 and reported a cubic phase composed of 5-10 mole % CaO and 90-95 mole % ZrO^. Thus, considerable disagreement exists concerning the cubic phase boundaries in the CaO-ZrO^  system. These variations can be.most probably attributed to the varying purity of the materials, the method of preparation, and finally to the reaction temperatures used in, preparing t h e solid solution. U -P cd U §• EH 2500 2000 1500 1000 500 Wt. % 8 12 16 20 2U 28 - 6 - I 1 i n—'—rr \ ^ v \ Qcubic i t^Zr0 2 \ q| s .s . ,' monocl. / Zr0 2 S.S. J + cubic Zr0 2/S.S. CaZrO, ) i i i i i I i i i 1 • • 1 • 1 1 • 10 20 30 CaO (mole %) kO 50 Figure 1. Phase Equilibrium Diagram for the CaO^ -ZrOg system, (after Duwez and Odell^) O Zr or Ca ' Figure 2. Fluorite-Type Structure of CaO-Zr02 Cubic S o l i d Solutions, (after Kingery53) " 7 ~ In spite of these variations in the cubic phase boundaries, the composition of 15 mole % CaO and 85 mole % Zr02 is definitely within the single cubic phase region. This is probably the determining factor which prompts most research workers.to choose this composition for their investigations. (2) Crystal Structure and Relationship with Compositions for the Ca0-Zr02 Cubic Solid Solutions a. Crystal Structure The Ca0-Zr02 solid solutions crystallize with the cubic 19 fluorite structure of the space group Fm3m . In the fluorite structure the anions are in simple-cubic packing with half the interstices filled by cations. This gives rise to a unit cell iai which- a space at the. center of the unit cell corresponding to unfilled interstices in the simple cubic anion lattice. The atomic arrangement in a fluorite-type structure is given in Fig. 2. 19 Hund established by density measurements that the cation 4+ 2+ lattice sites were completely filled with Zr and Ca ions and that enough oxygen vacancies were ..created to provide charge compensation dis tributed at random over the oxygen sites in order to preserve electrical 22 neutrality. Using X-ray intensity studies, Tien and Subbarao have 4+ 2+ confirmed the structural model with Zr and Ca ions.completely f i l l i n g the .cation lattice sites, and oxygen ion sites, equal in number to the mole % CaO added, being vacant. The formation of a cubic fluorite-type structure of Ca0-Zr02 is assumed to be a random substitutional solid 4+ 2+ solution. The Zr ions are randomly replaced by the added Ca ions. - 8 - 24 Recently, Diness and Roy reported that there is evidence that the predominantly oxygen vacancy model changes to a cation interstitial model,at higher temperatures. According to.their data, when the CaO-ZrC^ solid solutions were equilibrated at 1600°C and 1800°C respectively and were then quenched at about 1000°C/second, the pycnometer density measurements and X-ray data on the lattice parameter showed significantly different, results. In the 1600°C data, the measurements confirmed the classically accepted model for an effectively "pure" anion vacancy defect for that material. From the 1800°C data, i t was observed that in the low CaO concentration region (up to at least 15 mole%) the measured densities indicated a predominantly cation interstitial model, as shown in Fig. 3. However, they concluded that at this stage of the work the results had not defined the equilibrium concentration of defects.at any temperature with great precision since they could not,be sure that the "quenching" perfectly reproduced the high temperature defect character. No sub sequent work has been published to support.their observations. b. Relationship of Compositions with Lattice Parameter The relationship between the lattice parameter and compositions 19 of the cubic solid solutions of.Ca0-Zr02 was first investigated by Hund , who observed that the lattice parameter increased as the mole % of CaO added to mixture increased. A linear relationship was obtained in a plot between lattice parameter and mole % CaO with the lattice parameter increasing from 5.1137±0.0007A (10.3,mole.% CaO) to 5.1276±0.0005A (23.9 mole % CaO), 22 as shown in Fig. 4b. Tien and.Subbarao extended the earlier investigation and.also observed that a linear relationship existed between lattice parameter and mole% CaO in the cubic field as shown in Fig. 4a. The lattice parameter obtained in Tien and Subbarao's investigation varied from O 0 5.129 ± 0.005A (12 mole% CaO) to 5.143±0.005A (22 mole % CaO). It can be seen that although the change of lattice parameter between the 7 . 0 6 . 0 5 . 8 col • al o S)| o -p •H CO a CD Q 5 . 6 5.U 5 . 2 •§°del _° Calculated (X-ray. data) 1 Pycnometrically.- determined i i I 10 15 20 25 CaO, Mole % Comparison of densities determined by X-ray and pycriometric methods for the CaO-ZrCv, c r y s t a l l i n e solutions quenched from 1600°C +> •H CO a CU Q model "oCalculated (X-ray data) BPycnometricaJLly determined 10 25 15 20 CaO, Mole % Comparison of Densities determined by X-ray and pyconometric methods for the CaO-ZrOg c r y s t a l l i n e solutions quenched from l800'€ Figure 3. Change of Densities with CaO Content i n the Ca0-Zr02 So l i d Solutions,after Annealing at High Temperatures Followed by Quenching. (After Diness and Roy2**) a. 10 15 20 25 CaO, Mole % (after Tien and Subbarao^^) 10 20 CaO, Mole % b. (after Hund 1 9) Figure h. Change of Lattice Parameter with CaO Content i n the Ca0-Zr02 Cubic Solid Solutions. o i - 11 - phase boundaries in these two investigations was very similar, the position of the phase boundaries in these two cases was significantly different. For the composition 15 mole% CaO and 85 mole% Zr02, the o lattice parameter obtained in.Hund's work was about 5.119 A, whereas o that obtained in Tien and Subbarao's work.was about 5.133A. The experimental accuracy, the purity of the Zr0 2 and the temperature used in specimen preparation in these ..two studies may account for the different results. Hund did not report the purity of his Zr02 and used ordinary X-ray diffTactometer techniques, while Tien and Subbarao used 99.9% pure Zr02 and employed the back reflection region of the diffraction on powder samples. Zr0 2 of 99.9% purity and back reflection focusing camera were used in the present investigation in order to check these.dis crepancies . (3) Cation and Anion (Oxygen Ion.) Diffusion in the Ca0-Zr02 System a. Anion (Oxygen Ion' ) Diffusion The oxygen ion mobility in the cubic solid solutions,of CaO- 25 Zr02 was first investigated by Kinergy, Pappis, Dotty and Hi l l by direct measurement of the rate of exchange of oxygen between a gas phase and heated spherical particles assuming instantaneous equilibrium at the 18 solid surface. A decrease.of [0 ] in the constant volume gas phase was determined using an isotope ratio mass spectrometer. The temperature dependence of the oxygen iondiffusion coefficients between 700°C and 1100°C, can be -2 -1.22 expressed as: D = 1.0 x 10 exp ( — — — ), in which the activation energy K.I is 1.22 ev. They further claimed that the diffusion coefficients calculated from the electrical conductivity measurements were in good agreement with - 12 - 26 those determined by the isotoptLc exchange technique. Hagel redetermined the oxygen diffusion coefficients on well-spheroidized arc-melted specimens and obtained values appreciably lower than those calculated from the electrical conductivity data. Because of these discrepancies, Simpson and 27 Carter commented that the correlation factor in diffusion must be included when calculating diffusion coefficients from electrical conductivity data. The correlation factor in diffusion for the fluorite-type structure has been 28 calculated to be about 0.65 . Carter and Simpson extended their studies on the subject of oxygen diffusion to include oxygen exchange in the CaO-ZrO^ system by the conventional sectioning technique and employed a solid source mass spectrometer to determine the diffusion profile. They presented a theoretical model based on the observation that the large gas volume. maintained the boundary conditions at a constant composition of the gas' 29 phase , from which the diffusion profile could be expressed by the relation: C = Co erfc ( — ) 2/Dt 0 1 8 Where C = ratio,, of at depth X at time t, 0 1 6 + o 1 8 o 1 8 C0= ratio of r r 73— in the gas, o16+ o 1 8 D = diffusion coefficient provided there is instantaneous equilibrium at,the solid-gas interface. The oxygen surface exchange coefficient can be defined by the expression: 18 Where C is the surface ratio of 0 s — -~ o 1 6 + o 1 8 - 13 - From their experimental data over the temperature range 800-1097°C, the diffusion coefficients were expressed by the Arrhenius relation: _ n rt1Q +0.098 , -31,200 - 4300, 2, D = 0.018 _ 0 > 0 1 5 , exp ( —• ) cm /sec, in which the activation energy for diffusion is about 1.34 eV. They also reported that the diffusion coefficients are the same for both single crystal 30 and polycrystalline specimens, and were in good agreement with those results calculated from their electrical conductivity data. If correlation factor in diffusion was used, Kingery's result for the activation energy is about 1.32 eV in agreement with that obtained by Simpsonand Carter. The oxygen surface exchange coefficientg.in the same temperature range were found to f i t the relation as: n n n a +0.443 , -22,800 - 4400 , a-- 0.078 _ Q > 0 6 6 exp ( .) cm/sec in which the activation energy is about 0.99 eV, which is smaller than the activation energy for diffusion. b. Cation . Diffusion Investigations on the cation diffusion in the cubic solid solutions 31 of the Ca0-Zr02 system are limited. Carter and Rhode, have done some init i a l studies and reported the following experimental data : 3 82 900 2 DL - (Zr in Z r 0 > 8 8 C a ^ 0 ^ ) - 2.95x10 exp (—^-) cm /sec; DL = (Zr i n . Z r 0 > g 4 C a 0 > 1 6 0 ^ ) = 1.97 exp C " 1 0 ^ 0 0 0 ) cm2/sec DL = (Ca in Z r Q > 8 4 C a 0 > 1 6 0 ± ^ y = 3.65 exp ( ^ | ^ ) cm2/sec - 14 - Data on cation diffusion studies were also cited in the work 32 by Witzman, Molbius and Gerlach , who have investigated the cation diffusion and its temperature dependence by using radioisotopes. The cation diffusion in the CaO-ZrO^ system is considerably slower than the oxygen ion diffusion, as this can be seen from the following comparison of diffusion coefficients. In a solid solution of.Zr. a, Can ,, 0n 0. at 1000°C U.OH U . lb i.04 D_ 2+. .--19 2. Ca = 10 cm /sec -17 2 D„ 4+ = 10 cm /sec Zr In a solid solution of Z ^ ^ g C a 0 > 1 4 2 2 7 o„ 31 —8 2 DQ2- (single crystal @960°C) = 7.8x10 cm /sec D Q2- (polycrystals @1002°C) = 5.9xl0~8 cm2/sec. (4) Infrared Absorption Spectroscopy of Zirconia Infrared absorption spectroscopy is a powerful tool for study ing aqueous solutions. But in the past.few years its use has been extended 33 to solid state systems. Baun and McDevitt have reported infrared absorption data for some rare-earth oxides in the region 800-240 cm ^. They found that the rare-earth oxides give individualistic infrared absorption bands and that a l l type C (cubic) oxides give spectra which are different from the spectra obtained from type A (hexagonal) and type B (monoclinic) oxides. It was observed that the band.of the spectra is affected by changing the cation in the,lattice of type C oxides and that the peak frequency is lowered if the unit cell of a,type C oxide increases its dimensions. A linear - 15 - relationship .-. was obtained from a plot of unit cell dimensions and the peak band frequency. 'Later, they. . .: reported further experimental data on 34 pure ZrO^ and CaO-stabilized ZrC^ . The monoclinic ZrO^ appeared to,absorb strongly in the 800-300 cm region and the spectrum has six characteristic absorption peaks with a broad,band shoulder,at about 620 cm \ as shown in Fig. 5A. In the low frequency region, 300-50 cm \ the spectrum of the monoclinic Zr02 show?s two absorption peaks, one at .270 cm-1 and the other one at 230 cm as shown,in Fig. 5B. In sharp contrast to the monoclinic Zr02 spectrum, the cubic solid solutions of CaO-stabilized Zr0 2 gave only one broad band in the, 800-300 cm ^ region, as shown in Fig. 5C. This was obtained from a commercial cubic Zr0 2 sample which was stabilized with 15 mole % CaO. This broad band showed a peak frequency at about 470 cm \ When an equivalent amount of CaO was added in a KBr pellet, _they reported ,that no apparent absorption bands were found and that the,transmission spectrum of the cubic Ca0-Zr02 in the, low frequency region was quite transparent. This broad band is, therefore, not contributed by any single Zr0 2 band or by the CaO band but a band with several frequencies superimposed. This broad band may be considered as a characteristic absorption band for the CaO-stabilized Zr0 2. From these experimental results i t can be seen that the infrared absorption spectra of solids are strongly dependent on the crystal structure and also on the symmetry of the unit cell. (5) Internal,Friction in Zr02 Containing CaO A homogeneous stress or an electric field acting upon a point defect can, under certain conditions, cause reorientation of the defect - 16 - 100 -1 1 1 1 I ' 800 700 600. 500 U00 300 Wave number. (cm~l) 100 300 280 260 2U0 220 200 Wave number.(cm-1) (B) Lower Frequency Infrared Absorption Spectrum of Monoclinic Zr0 2 (Nujol mull, Csl plates) 1 0 0 (C) Infrared Absorption Spectrum of Cubic CaO-Stabilized.Zr0 2 (commercial material) 800 700 600 500 Uoo 300 Wave number (dm-"*") Figure 5 . Infrared Absorption Spectra of Monoclinic Zr0 2 and CaO-Stabilized Zr0 2 fefter Baun.and McDevitt^ 4) - 17 - and produce a.corresponding mechanical or electrical relaxation. Measurements of the internal friction peak or dielectric loss peak can,then be used to study the variation of point defect concentration with composition and heat treatment. 35 An internal friction peak was first found by Dew in commercial ZrO^ partially stabilized with CaO and its existence was confirmed in two 3 6 subsequent investigations, by Wachtman,Tefft, Lam and Stinchfield and by 37 Chang . Dew suggested plastic deformation as a possible cause; Chang suggested the motion of twin boundaries; and Wachtman et al suggested the 38 motion of oxygen vacancies. Recently, Wachtman and Corwin carried out a further investigation on the internal friction of ZrO^ containing CaO. In the cubic field of 10 to 20 mole % CaO added, they observed a symmetrical internal friction peak with its maximum at about 300oG at 1 kHz;and in.the two phase field, below 10 mole.% CaO, a' nonsymmetrical peak occurred at a somewhat higher temperature. The symmetrical peaks in as-sintered specimens were also observed to have the same dependence on CaO content as that reported for electrical conductivity at 1000°C. Wachtman and Corwin interpreted this observation to indicate that the nonsymmetrical internal friction peak in partially stabilized Zr02 might be associated with Chang's mechanism of twin boundary motion in tetragonal grains, but the symmetrical peak occurring in the cubic field could not be associated with tetragonal grains. The similarity of peak height dependence and electrical conductivity dependence on CaO content suggested that the symmetrical peak was associated with oxygen vacancy motion. Accord ingly, they have proposed three defect models to illustrate the motion of oxygen vacancies. - 18 - First, consider a single oxygen vacancy in an otherwise perfect fluorite structure. This vacancy would move,under an electric field but not under.homogeneous stress. It would therefore contribute to the frequency independent.part of the electrical conductivity but would not contribute to internal friction or dielectric relaxation. 2+ Second, consider an oxygen vacancy neighbouring a Ca ion at (0,0,0) and.constrained by electrostatic attraction to the eight nearest neighbour oxygen sites at (± 1/4,±1/4,±1/4). Either the homogeneous stress or the electric field will cause a preferred distribution so that this oxygen vacancy will make no contribution to the frequency independent electrical conductivity but will contribute both to internal friction and to dielectric relaxation. Third, consider two oxygen vacancies at (1/4j1/4y1/4) and (1/4,1/4,-1/4) neighbouring two Ca 2 + ions at (0,0,0) and (1/2,1/2,0). Two defects of the second.type should have electrostatic attraction of the dipoleTdipole type tending to.cause this defect to form. The oxygen vacancies in this defect will make no contribution to the frequency independent part of the electrical conductivity, the dielectric relaxation, or the internal friction. They concluded, however, that these models used to explain the motion of oxygen vacancies in the Ca0-Zr02 solid solutions were only partially correct, and that the detailed models are likely to be complex due to the fact that oxygen vacancies in the CaO-stabilized ZrO^ exist in several states of binding. It can,be seen that the dynamical behavior of oxygen vacancies in the cubic field of the Ca0-Zr02 system is a complicated subject. - 19 - (6) E l e c t r i c a l C o n d u c t i v i t y i n t h e CaO-Zr0 2 C u b i c S o l i d S o l u t i o n s a. E l e c t r i c a l C o n d u c t i v i t y K i n e t i c s Measured e l e c t r i c a l c o n d u c t i v i t y i n o x i d e systems i s the,sum o f i o n i c and e l e c t r o n i c c o n t r i b u t i o n s . The e l e c t r o n i c c o n t r i b u t i o n w i l l c o n s i s t o f e x c e s s e l e c t r o n s and e l e c t r o n - h o l e s . Even i f t h e c o n c e n t r a t i o n s o f . e l e c t r o n s o r e l e c t r o n - h o l e s a r e s m a l l , t h e y s t i l l make a s u b s t a n t i a l c o n t r i  b u t i o n t o t h e c o n d u c t i v i t y s i n c e t h e i r m o b i l i t y i s h i g h . The t o t a l c o n d u c t i  v i t y c an t h e r e f o r e be e x p r e s s e d a s : 0 " °ion + F Ye ce + F ....,....,..(1) where a = t o t a l c o n d u c t i v i t y a. = c o n d u c t i v i t y due t o m o t i o n o f i o n s i o n Ug ,u_ = . m o b i l i t y o f t h e e l e c t r o n s and e l e c t r o n - h o l e s , r e s p e c t i v e l y (cm. sec. --'- p e r v o l t c m - 1 ) . C Q > CQ = c o n c e n t r a t i o n o f t h e e l e c t r o n s and e l e c t r o n - h o l e s , r e s p e c t i v e l y . F = F a r a d a y C o n s t a n t I n a system i n w h i c h t h e r e i s a l a r g e c o n c e n t r a t i o n o f oxygen v a c a n c i e s f i x e d by c o m p o s i t i o n and in d e p e n d e n t o f oxygen p r e s s u r e t h e i o n i c c o n t r i b u t i o n w i l l n o t be p r e s s u r e dependent. However, as t h e oxygen p r e s s u r e i s changed t h e r e may be,a change i n t h e e l e c t r o n i c c o n t r i b u t i o n t o the t o t a l c o n d u c t i v i t y . The f o r m a t i o n o f c o n d u c t i o n e l e c t r o n s can t h e n 25 be e x p r e s s e d as f o l l o w s : 0 2 ( l a t t i c e ) = V Q 2 _ + 3g .0 . . + 26 2(g) ' • ( 2 ) 2 - where 0 ( l a t t i c e ) = o x y g e n i o n 1 i n a no r m a l l a t t i c e s i t e VQ 2 - = o x y g e n . i o n v a c a n c y ° 2 ( g ) = o x v £ e n l i b e r a t e d as gas 9 = e x c e s s e l e c t r o n s - 20 - S i m i l a r l y one might f i l l i n n o r m a l l y v a c a n t s i t e s and form e l e c t r o n - h o l e s © a c c o r d i n g t o . the r e l a t i o n : ^°2(g) + V 0 2 _ = ° 2 ~ ( l a t t i c e ) + 2 9 ••••••• • (3) The c o n c e n t r a t i o n s . o f t h e e x c e s s e l e c t r o n s o r e l e c t r o n - h o l e s a r e t h e r e f o r e dependent on t h e oxygen, p r e s s u r e . Assuming t h a t a s s o c i a t i o n o r i n t e r a c t i o n e f f e c t s a r e s m a l l a t t h e low c o n c e n t r a t i o n s , t h e mass a c t i o n e q u a t i o n f o r e q u a t i o n s (2) and (3) can be e x p r e s s e d a s : k = [ e ] 2 P ^ I VQ J L I ....(4) k 2 = [%]2 [02~] ( 5 ) 2- S i n c e [ V n 2 - ] and [0 ] a r e f i x e d by t h e c o m p o s i t i o n , t h e c o n c e n t r a t i o n s o f e l e c t r o n s and e l e c t r o n - h o l e s a r e g i v e n by: [8] - k x P o 2 (6) W = k 2 P ^ 0 2 (7) The t o t a l c o n d u c t i v i t y i s t h e n r e l a t e d t o t h e oxygen p r e s s u r e by o = °ion + k^ P- + k 2 P 0^ (8) T h i s e x p r e s s i o n i n d i c a t e s t h a t t h e t o t a l c o n d u c t i v i t y would be oxygen p r e s s u r e dependent i f t h e r e i s an a p p r e c i a b l e c o n t r i b u t i o n from t h e e l e c t r o n i c c o n d u c t i o n . b. I o n i c C o n d u c t i v i t y 39 The works o f Wagner and K i u k k o l a have e s t a b l i s h e d t h a t t h e e l e c t r i c a l c o n d u c t i v i t y o f t h e c u b i c s o l i d s o l u t i o n s o f C a 0 - Z r 0 2 i s due e n t i r e l y t o t h e m i g r a t i o n o f oxygen i o n v a c a n c i e s . S u b s e q u e n t l y , th e e l e c t r i c a l , c o n d u c t i v i t y as a f u n c t i o n o f t e m p e r a t u r e and o f CaO c o n t e n t - 21 - for this system has been extensively investigated by a large number . 19,22,25,30,31,40-46 _ ...,.„ . . . , of workers . The possibility of gram boundary 47 conductivity in the Ca0-Zr02 ceramics was also recently studied by Tien Most experimental results for the conductivity-temperature data oyer the temperature range 500-1800°C for the CaO-ZrO„ cubic solid solutions were / 2 . generally observed to follow an Arrhenius relation: a = a 0 exp( j ~ ) (9) a = electrical conductivity ao = Pre-exponential term E = activation energy K = Boltzman's constant T = Absolute temperature For a fixed composition, such as 15 mole % CaO and 85 mole % Zr02» the activation energy for conduction obtained by most investigators was in fair agreement. However, the conductivity values at a given temperature, such as at 1000°C, varied greatly between different workers. (See Table 5, APPENDIX II). The experimental results showed that with increasing CaO content the activation energy increased and the conductivity decreased 22 for a given temperature. Tien and Subbarao have proposed the following model to account for the observed dependence of conductivity on CaO content: The oxygen ion, which is the charge carrier, has to pass between two metal ions to reach an adjacent anion site. These .metal ions 4+ 4+ 2+ 2+ may be two Zr ions, one Zr ion and one,Ca ion or two Ca ions. 2+ ° Inasmuch as the Ca ion (0.99A) is approximately 25% larger than the 4+ ° Zr ion (0.78A)., i t is expected that the energy required for an oxygen - 22 - . 2+ ion to pass between two Ca, ions would be the l a r g e s t , while that for the 4+ case of two Zr ions,would be the smallest. Each oxygen ion i s surrounded by four metal ions i n the f l u o r i t e - t y p e l a t t i c e . As the CaO content increases from 13 to 20 Mole %, the p r o b a b i l i t y of having 2+ one Ca ion as a nearest neighbour to an.oxygen ion increases from 34% 2+ to 41% and the p r o b a b i l i t y of having two Ca. ions as nearest neighbours to an oxygen ion increases from 7.7% to 17%. Therefore, the a c t i v a t i o n energy for conduction increases and, consequently, the conductivity at a given temperature decreases with increasing CaO content. c. E l e c t r o n i c Conductivity The e l e c t r o n i c conductivity i n an oxide system i s oxygen p a r t i a l pressure dependent as indicated by the following two equations: -1/4 1/4 l) e = . K L P 0 2 2) e = k 2 p 0 2 39 Kiukkola and Wagner i n t h e i r measurements on galvanic c e l l s involving s o l i d e l e c t r o l y t e s observed that the . e l e c t r i c a l conductivity of the e l e c t r o l y t e Zr_ o c Ca» .. _ 0 1 Q C was v i r t u a l l y constant when the oxygen U . O J U .1J ' 1 .o j p a r t i a l pressure was varied over a wide l i m i t . from 10^ to 10 2 2 * 48 atmospheres. Weissbart and Ruk-a reported that the e l e c t r o n i c contribution to the t o t a l conductivity i n t h i s system i s perhaps' le s s than 2%. At -22 5 49 50 p < 10 atmosphere, Schmalzried and Alcock and Steele observed °2 that the e l e c t r o n i c (n-type) conduction becomes predominant, with °e "^02 • Vest and Tallan^"*" found that incorporation of 2 mole % vanadium + 1.4 mole% A l gives r i s e to dominant e l e c t r o n i c conduction at oxygen. -16 " 1 / n p a r t i a l pressures up to 10 atmosphere, where P Q 2 with n = 5.8 ±1.0. - 23 - 52 Very recently, Kroger has introduced the concept of charged, free, as opposed to associated neutral, imperfections to account for the observed variations of the electronic conductivity of stabilized ZrC^. He proposed two imperfection models, one for Zr„ o r Ca. , r 0.. o r Vn 0.85 0.15 1.85 u0.15 and one for donor-doped stabilized Zr02» In the former model, he suggested that most of the Ca is present in a neutral form. The doubly charged imperfections originally thought to be present might exist as neutral centers which are pairs or clusters formed according to.the following relation and only a small portion of them existed in the free, double charged form. m C a " z r + m V 0 * — ^ ( C a Z r V0 > mX (10) where m = 1 for pairs a Ca ion oc negative charge An oxy charge Ca"^ = cupied a Zr ion site with effective double VQ" = An oxygen vacant • site with effective double positive (Ca Z rV Q) m =.charged free, or associated neutral cluster with k , , = [ C aZr V0 3m (11) P^"1' z— [Ca* Z r] m[V'-] m He also, considered the quasiuchemical reactions which describe the formation and ionization of defects in the crystal and the incorporation or removal of oxygen into and from the crystal respectively, the' law of mass action to these relations, and .the complementary relations obtained with a neutrality condition and a calcium balance,equation, from which Kroger arrived at a schematic solution for the concentration of the various imperfections as a function of oxygen partial pressure at a . high temperature. Owing to the large concentration of oxygen vacancies - 24 - present in the neutral centers which increase the ionic current, he concluded. that electronic p-type or n-type conduction will become.noticeable only at extremely high.or extremely low oxygen,partial pressures. Since the extremely low pressures are more easily established than the extremely high oxygen pressures, only n-type conduction has been observed in a -22.5 pressure of less than Prt ' atmosphere in the cubic solid solutions. 2 of CaO-Zr02. d. Relationship Between Electrical Conductivity and Diffusion Coefficient When electrical conductivity is entirely due.to ionic mobility, the electrical conductivity and the transfer number (fraction of the total current carried by each.charged particle) are related to the ionic. 53 diffusion coefficient by the Nernst-Einstein .equation - : 2 ° - t o = D i n i ( Z j e ) (11) KT When the measured volume conductivity, the macroscopic tracer, diffusion coefficient, and the correlation factor in diffusion are combined, the Nernst-Einstein equation can be rearranged and expressed in the 54 following relation . (Derivations are given in APPENDIX VI) D f t-i k T a = N ( Z i e) 2 * ( 1 2 ) Electrical conductivity measurement has been proved to be a reliable method of determining the oxygen diffusion coefficients in the , CaO-Zr02 system and also in other oxide systems. - 25 - II. EXPERIMENTAL PROCEDURE (A) Materials and Specimen Preparation 1. Materials Preparation. Reagent grade calcium carbonate (Allied Chemical Co., U.S.A.) and 99.9% pure ZrO^ (Koch-Light Laboratory Ltd., England) were used to prepare the 15 mole% CaO and 85 mole % ZrO^  composition. The weighed mixtures were wet blended for two hours in a ball-mill with calcia-stabilized zirconia pebbles using acetone as the mixing agent. The blended mixtures were then filtered and dried in.an oven at,100°G for 20 hours. 2. Specimen Preparation The mixtures of CaCO^  and ZiO^ powders were loaded, into a right circular cylindrical graphite die (3/8" diameter in bore and 3" in length) with graphite plungers inserted from both sides. The graphite die- assembly was placed on a mechanical jack (the pressure.of which was controlled by a compressed gas cylinder) and -was heated by a LEPEL induction generator . The temperature was brought up rapidly to 1550°C in about 15 minutes. The powders inside the graphite die were allowed to heat at.ithis temperature under argon atmosphere for 15 minutes and were then hot-pressed at 4600 p.s.i. for another 15 minutes. The graphite die assembly was allowed to cool to room.temperature under.full pressure in the argon atmosphere in about 60 minutes before removing the specimen from the die assembly. The temperature was measured with a W-W + 26% Re thermocouple at a distance of .about 1/8" from the top level of the powder inside the graphite die. The true temperature of reaction - 26 - during hot-pressing was measured and found to be about 200°C higher than the.recorded temperature (1550°C) in the,plunger. This implied that the actual reaction temperature is about 1750°C. The ends and surface of each pellet were polished in a wet-belt .grinding wheel with very fine sand paper. The polished specimens were later heated in air in an oven at about 800°C for one hour. This short period of heating was intended to burn out any carbon remaining on the surface of the specimens. (B) Phase Identification The phases in each hot-pressed pellet wag" identified by X-ray diffraction. A Norelco diffraction unit using Ni-filtered Cu radiation was employed. A fast-^scan pattern, one.degree per minute, was made between 27° and.33° of 20 values. The diffraction pattern was limited to this narrow region because this interval includes the two most prominent monoclinic peaks ( 1 1 1 ) and Xl 11 the most intense tetragonal peak (1.1 1 ), and the solid-solution cubic peak (1 1 1) of ZrC^. T n e strongest peaks of the CaCO^  and CaZrO^ compounds also occur in this region. Thus, a.fast scan.of the diffraction pattern in this region indicated the phases present in the specimen. To check the, uniformity of the phase in the specimen, diffraction patterns were made on both ends of the pellet. (C) Annealing Procedure The annealing specimens were placed,in a high purity recrystallized alumina tube and were heated in air.in a Super-Kanthal furnace under,normal atmospheric conditions. The temperature was measured with a Pt-Pt+40 % Rh thermocouple, which was placed in contact with the annealing specimens inside the alumina tube. Thus, the recorded temperature was the true annealing - 27 - temperature. After annealing,the specimens were allowed to.cool. slowly to room temperature. This was-done over a period of 30 minutes by gradually withdrawing the alumina tube from the hot zone.of the furnace. (D) Precise Lattice Parameter Measurement 1. Experimental Procedure The precise lattice parameter measurement was made by obtaining X-ray diffraction photographs on powdered samples. A Norelco Precision Symmetrical Back Reflection Focus ing Camera was used. This camera has an effective camera diameter of 12 cm and provides excellent resolution between 9 =59° and 0 = 88.74°. The camera mounted with a powdered sample was exposed to Ni-filtered Cu radiation on,the standard Norelco diffraction unit. The (average exposure time for each diffraction photograph was about two hours at 35 Kv and .15 ma. The powdered sample used for the X-ray diffraction photograph was prepared by the following procedure: A small portion of each annealed speci men w a s ground to a fine powder in an agate mortar and subsequently passed through a 200 mesh screen. The screened powder was then dusted onto a piece of thick paper which has been covered with a layer of Dow-Corning silicone grease. The sample was then inserted into the camera with the powder,coating facing towards. "No-screen medical X-ray safety" films were used. On development the outer surface of the film was covered with a piece of flatback.paper tape, which was stripped off before the film was immersed in - 28 - the fixing solution. If this is not done, the lines will appear on both, sides of the film, with possible loss of apparent resolution and loss of . precision in determining the line positions. The positions of the Ka^a^ doublet diffracted lines and the camera knife-edge marks for film shrinkage corrections were measured using a Norelco Fdlm-Measuring device with accuracy to ±0.05 mm. .The true positions and observed positions,of the camera knife-edge marks were compared and the .necessary corrections for film shrinkage in each film were made through a FORTRAN computer programme. 2. Lattice Parameter Calculation The precise lattice parameter was calculated according to Cohen's method"' ~* (APPENDIX V) . A FORTRAN computer programme based on this calculation was written and a l l experimental data were computed by running this programme and the data in an IBM 7040 computer. The computer output printed the lattice parameter value and the drift-constant in 5 significant figures. The reproducibility was about ±0.0001 A and the drift-constant on a l l output results varied from 0.0001 to 0.0003. The drift-constant is a measure of the total systematic error involved in the determination. (E) Infrared Absorption Spectroscopy Measurement Infrared absorption spectra have been obtained for the 99.9% pure monoclinic Zr02» and the partially and completely CaO-stabilized ZrO^' The effect of annealing temperature on the infrared absorption spectra for completely CaO-stabilized ZrO^ has also been studied. A Perkin-Elmer Model 521 Grating Infrared Spectrophotometer was used for obtaining spectra in the region 1000 to 300 cm ^ in potassium bromide (KBr) pellets. - 29 - B o t h m o n o c l i n i c Z r 0 2 and C a O - s t a b i l i z e d Z r 0 2 powders were f i r s t p a s s e d t h r o u g h a 200 mesh s c r e e n and were t h e n ground t o a f i n e r powder i n an a g a t e m o r t a r f o r about 5 m i n u t e s b e f o r e d i s p e r s i n g i n p o t a s s i u m bromide. The powders were t h o r o u g h l y mixed by f u r t h e r g r i n d i n g i n t h e a g a t e m o r t a r . D i s k s o f about 1.6 cm i n , d i a m e t e r and 1 mm t h i c k were p r e p a r e d by vacuum p r e s s i n g a t about 10,000 p . s . i . . The d i s k s c o n t a i n e d about 0.5 wt.% Z r 0 2 o r CaO-Zr0 2 i n KBr. D u p l i c a t e r u n s w i t h l e s s sample m a t e r i a l i n t h e KBr. p e l l e t were made i n each specimen. (F) E l e c t r i c a l C o n d u c t i v i t y Measurement 1. S p e c i m e n , P r e p a r a t i o n Specimens used i n e l e c t r i c a l c o n d u c t i v i t y measurements were, r i g h t c i r c u l a r c y l i n d r i c a l p e l l e t s o f about 10 mm i n d i a m e t e r and 10 mm i n l e n g t h . B e f o r e a n n e a l i n g , t h e ends and s u r f a c e o f each p e l l e t were f u r t h e r p o l i s h e d i n a w e t - b e l t g r i n d i n g wheel w i t h v e r y f i n e sand p a p e r . Two s m a l l h o l e s j about,0.05 mm i n d i a m e t e r , 3 mm deep and a p p r o x i m a t e l y 5 mm a p a r t were d r i l l e d on the s u r f a c e o f t h e p e l l e t by an u l t r a s o n i c d r i l l . These h o l e s were used t o house t h e m e a s u r i n g p o t e n t i a l l e a d s . A f t e r a n n e a l i n g , t h e s e h o l e s w e r e . c o a t e d w i t h a t h i n l a y e r o f H a n o v i a l i q u i d p l a t i n u m p a s t e ( P l a t i n u m Paste No. 6082). The a p p l i c a t i o n o f t h i s p l a t i n u m p a s t e improved t h e e l e c t r i c a l c o n t a c t between t h e p o t e n t i a l l e a d w i r e s and t h e specimen. The e l e c t r o d e s e p a r a t i o n and t h e d i a m e t e r o f each specimen were measured by a m i c r o m e t e r and t h e a v e r a g e v a l u e o v e r t e n measurements was used f o r c a l c u l a t i o n . The a c c u r a c y o f t h e s e measurements was about ±0.1 mm. 2. A p p a r a t u s and Equipments The specimen h o l d e r used f o r e l e c t r i c a l c o n d u c t i v i t y - 30 - measurement was a four-terminal spring-loading device. The specimen was placed between two platinum plate electrodes to which a pair of 0.020" diameter platinum wires w&s attached serving as current leads. Two pieces of high-purity alumina plates were put on the platinum plates for protection,;' The platinum and alumina plates were held together under compression by a spring and an alumina rod. A second pair of 0.02" platinum wires was used as potential leads for measuring the voltage drop across the sample. The potential lead wires were securely inserted into the two small holes which have been coated with platinum paste. A schematic diagram is given in Fig. 6. An A-C source of 1000 cps was supplied from a Heatkit Oscillator. The voltage drop across the sample and across a standard resistor (Type 510 Decade-Resistance Unit) which was connected in series with the sample was measured by a Hewlett Packard Model.400D VTVM (Vacuum-Tube-Volt-Meter). The standard resistor connected in series with the specimen was used to measure the current passing through the specimen. 3. Measurement Procedure The conductivity measurement assembly was inserted into an open-end alumina tube and heated in a Glo-bar furnace. A steady stream of helium gas was always passed in order to maintain a neutral atmosphere during the entire period of measurement. A Pt-Pt+10% Rh thermocouple which was placed directly underneath the bottom alumina plate served as both,temperature-recording and temperature-controlling thermocouple. The rate of heating was about 8°G per minute in the 500-1000°C range and about 4°C per minute in the 1100-1400°C range. The voltage drop across the specimen and across the standard resistor was measured every two hundred degrees. Readings were taken immediately after - 31 - H G ' i i • ID ; C High Temperature E l e c t r i c a l Conductivity Furnace Details of sample posi t i o n A - Glo-bar furnace B - Recrystallized alumina tube C - pt - pt + 10$ Rh thermocouple wires D - Helium gas outlet E - Helium gas i n l e t F - Water Cooling C o i l G - 0.02" platinum wires as current leads H - 0.02" platinum wires as potential leads I - Steel-spring c o i l J - High-purity alumina plates K - Platinum Thin plates L - Recrystallized alumina rod M - sample N - Shielded molybdenum wires Figure 6. Schematic diagram of High-Temperature E l e c t r i c a l Conductivity Furnace and Sample Holder. - 32 - the desired temperature was reached and also after 30 to 45 minutes of soaking at the same -temperature. The conductivity of each specimen was measured both during the heating and cooling cyclesin the temperature range of 500-1400°C. 4. Electrical Conductivity Calculation The electrical conductivity was calculated according to the following relation"^. 0 I L V A where 0 =.Electrical conductivity (ohm ^ - cm ) I = Current.(Ampere) V = Voltage drop (volts) L = Electrode separation (cm) 2 A = Cross-sectional area of specimen (cm ) for a 4-terminal method of measurement voltage drop across standard resistor (volt) I (Amps) = Resistance in standard resistor (ohms) V = voltage drop across the specimen between potential leads (G) Porosity and Density Measurements The porosities of the hot-pressed and annealed specimens were determined by following the ASTM-C 20-46 water-absorption procedure"*7, The true specific gravity of a series of specimens which have been annealed at various temperatures for a fixed period of time was determined by following the ASTM-C135-47 pycnometer bottle procedure using powder . samples'*7 . The annealed specimens were ground to fine powders passing through a 100 mesh screen. A constant temperature bath of 25°C with fluctuation of about ±0.1°C was used and a l l weighings were carried out at room temperature of about 2€-22°C. - 33 - III. EXPERIMENTAL RESULTS (A) Phase Identification of the Zr_. o c Ca- , c CL Q_ Solid Solution U . o j U.±_> l . o j 1. X-Ray Diffraction In the interval 27°-33° of 29 values, six X-ray diffraction peaks can occur for thebinary system of CaO-ZrC^ as summarized in Table I: Table I X-ray Diffraction Peaks of Several Compounds in the 27°-33° Interval Compound 2 9 — (hkl) ZrO„ (monoclinic) 28.20 100 (111) 31.58 65 (111) ZrO„ (high-temp, tetragonal) 30.26 100 (111) Zr0„ (cubic solid-solution) 30.58 100 (111) CaC0„ "(calcite) 29.36 100 (104) CaZrO, (orthorhombic) 31.58 100 (220) (022) The X-ray diffraction pattern for the unreacted mixtures of CaCO^  and Zr02 used in this study showed three diffraction peaks at 2 9 = 28.3°, 29.3°, and 31.5°, as shown in Fig. 7A. These peaks were identified as the two prominent monoclinic Zr02 peaks at (111) and (111) and the most,intense peak of CaC03 at (104). After hot-pressing at 1500°C and under 46Q0 psi for 30 minutes, the,reacted material gave three peaks with a strongest peak at 2 0 = 30.4° and two small peaks at 28.2° and 31.5° asl shown in Fig. 7B. The strongest peak was identified as the cubic solid solution at (111), and the two small peaks were the monoclinic Zr0 2 peaks. This indicated that the Zr0 2 was not completely stabilized with CaO or completely converted into the cubic phase. However, when the mixtures were heated at a recorded temperature of 1550°C for 15 minutes, followed by further hot-pressing at 1550°C and 4600 psi pressure for another (A) - 34 - (C) (B) -I I I I I I L 33 32 • 31 30 29 28 27 (A) Monoclinic Zr02+CaC03 Mixtures j i • ' ' 33 32 31 30 29 28 27 Bragg Angle ( 26 ) i n Degrees i i i I l I L 33 32 31 30- 29 28 27 (B) P a r t i a l l y CaO-Stabilized (C) Completely CaO-Stabilized ZrO, ZrO, '2 2 Figure 7. X-Ray D i f f r a c t i o n Patterns of Unreacted and Reacted Ca0-Zr0 2 Compositions - 35 - 15 minutes, the reacted material gave only one diffraction peak at 2 9 = 30. as shown in Fig. 7C. This peak was identified as the cubic solid solution peak at (111). This indicated that the Zr©2 was completely stabilized with CaO at these reaction conditions. The possibility of the existence of tetragonal ZrO^ in the reacted material can be ruled out, since the tetragonal phase has never been detected previously at room temperature. The hot-pressed material was considered to be.a homogeneous cubic solid solution of Ca0-Zr02 having the composition of 15 mole% CaO + 85 mole% Zr02. 2. Infrared Absorption Spectra The 99.9% pure monoclinic Zr02 gave six bands in the region 800-300 cm ^ in the infrared absorption spectrum as shown in Fig. 8A. The strongest absorption band occurred at.530 cm ^. The partially CaO-stabilized Zr©2 gave similar absorption spectrum as the monoclinic Zr02« The strongest absorption band remained at the 530 cm ^ but the side bands showed gradual disappearance as shown in Fig. 8B. The completely CaO-stabilized Zr02 or cubic solid solution! of Ca0-Zr02 gave a single broad band which is completely different from the absorption spectrum of the monoclinic ZrO^, as shown in Fig. 9. The peak frequency of this broad band appeared to shift depending on the heat treatment of the specimen. For example, when the sample was annealed at 800°C for 1 hour, the peak frequency of the absorption band occurred at about 440 cm ^; whereas when the same sample was annealed at 1500°C for 24 hours, the peak frequency of the absorption band appeared at about 455 cm \ The shift of the peak frequency of the broad band may be due to the complexity of grouping the cations.and oxygen ions and vacancies in the - 36 - F i g u r e 8. I n f r a r e d A b s o r p t i o n S p e c t r a o f M o n o c l i n i c ZrC>2 and P a r t i a l l y CaO- S t a b i l i z e d Zr0 o. - 37 - B ^ Sample...Annealed @ 1500°C 2k hrs. s' \ i I , I , L i I S .! I 900 800 TOO 600 500 U00 300 Wave Number (cm Figure 9. Infrared Absorption Spectra of Completely CaO-Stabilized ZrO, After Heat Treatment. solid solution. In general, the infrared absorption spectra obtained in the present investigation are in good,agreement with those reported by Baun.and 34 McDevitt • This can be seen by comparing the data given in Figs. 5A,B,C and Fig. 9. The band frequencies of the infrared absorption spectra obtained in these two investigations are given in Table II• Table II Infrared Absorption Band Frequencies of Monoclinic-Zr02 and CaO- Stabilized Zr02 (B) Compound monoclinic ZrO, Band Frequencies ( cm -1 Baun & McDevitt 740 620 530 460 430 370 470 Present Invest. 740 600 530 450 420 360 440-455 commercial CaO-stabilized Zr02 hot-pressed CaO-Zr02 (both CaO-ZrO^ , materials are of the same composition 15 mole% CaO + 85 Mole% Zr02> Precise Lattice Parameter of the ZTQ g^ Ca^ ^  0^  g,. Cubic Solid Solution 1. Effect of Annealing Temperature on the Lattice Parameter - 39 - The relationship between.the lattice parameter of the cubic unit cell of the Zv^ ^ Ca^ 15 ,°i g5 s o l i d solution and the annealing temperature has been systematically investigated. More,than 60 X-ray diffraction photographs have been obtained and a typical example of the X-ray diffraction pattern of a powdered specimen is given in Fig. 10. The annealing temperatures ranged from 800°C to 1500°C. All < samples were heated and cooled under identical conditions. The experimental data are given in Tables 1 and 2, APPENDIX I. Figure 11 shows ithe linear relationship between the lattice parameter and the annealing temperature: for three separate series of samples. Each series of samples was. obtained from a single, specimen. It is quite evident that the lattice parameter of the cubic unit cell of the Ca0-Zr02 solid solution decreased as the annealing temperature increased from 800°C to 1500°C. The lattice parameter of three separate specimens before annealing at high temperature appeared to vary slighlty from one specimen to another. However, these_lattice parameter values seemed to,converge to an approximately constant value as specimens were annealed at temperatures higher than 1500°C. Figure 12 shows, the least.squares f i t plot of the mean values of the lattice.parameter of a l l samples measured as a.function of annealing temperature. The lattice parameter decreased from a mean o 0 value of 5.1363A at 800°G to a mean.value of 5.1349A at 1500°G. The experimental data of Figs. 11 ajnd 12,. therefore, indicate that a lattice contraction was experienced in the Zr. Q Ca_ , r 0.. o c cubic solid solution as the material was subjected to high temperature..heat treatment after hot-pressing. Cu K, V 2 = (hkl) = 9 ( 6 2 2 ) 8U.T 8 6 . 8 (533) 7 9 . 9 8 0 . 7 ( 6 2 0 ) 7 1 - 7 T X.l aX °# °X a* (UU2) (531) 6U.3 6 2 . 6 6 U . 6 6 2 . 7 Figure 1 0 . T y p i c a l X-Ray D i f f r a c t i o n Pattern of Powdered Sample of Z r Q ^ Ca Q ^ S o l i d Solution. -p-o 5.13TO C specimen #30 A specimen #73 O specimen #29 5.1360 5.1350 _L 800 900 1000. 1100 1200 1300 Annealing Temperature (°C) 1U00 1500 Figure"-!!. Decrease of Lattice Parameter as a Function of Annealing Temperature 5.1370 5-1360 h 5.1350 H 5.1343 800 900 1000 1100 1200 1300 Annealing ..Temperature ( °C) lUOO 1500 Figure_L2L. Decr.eas£_oiL Lattice^Parameter as..a.Function. of. Annealing Temperature. (over-rrall...data_.Hi±h...mean values). - 43 - Thus far in the literature, only a few workers have reported their lattice parameter values for the Zr A Q c Ca_ , c 0.. Q c cubic solid solution, and these values vary widely. For this composition, 25 J 0 Kingery et al reported that the lattice parameter is 5.131A. Their sample was prepared by calcining the CaCO^  and ZrC^ mixtures at 1300°Gito form solid solution. The reacted mixtures were then cold-pressed and sintered at 2000°C for 7 hours. For the same composition, Tien and 22 ° Subbarao reported a lattice parameter of 5.133A for their sample which was prepared by reacting the CaCO^  and ZrO^ mixtures at 1350°C for 24 hours. The reacted mixtures were then compacted and sintered at 2006°C in an oxygen atmosphere for 2 hours and later annealed at 1400°C for one week. Roy and 24 Diness have reported that the lattice parameter for the Zr^ g,. Cag ^ o . o C^ l g^ solid solution; changed from 5.144A to 5.134A when i t was-; heated to.l600°C and 1800°C respectively and then subsequently quenched i at about 1000°G per second. The lattice parameter of the same-composition: o obtained in the present ..study is 5.1350A when the sample was annealed at. 1500°C for 24.hours after hot-pressing. In view of the experimental results obtained in the present investigation together with those reported by'other workers, i t can be inferred that the lattice parameter of the cubic unit cell of the Zr„ o c Can , c 01 o c solid solution significantly depends on the heat U.OD U.1J l.OJ treatment,of the material. 2. Relationship Between Lattice Parameter and Band Frequency of the. Infrared Absorption Spectra The relationship between lattices-parameter and peak band frequency, of the infrared absorption spectra for the Zr^ g,. Ca^ ^ 0^  g,. - 44 - solid solution was obtained from X-ray diffraction and infrared absorption spectroscopy data which are given in Table 3j APPENDIX I. The solid solutions of CaO-stabilized Zr02 gave a broad band in the.infrared absorption spectra, as shown in Fig. 9. The peak frequency of the absorption bands was obtained by taking the intersecting point of two straight lines which were drawn parallel to the spectral tracing. Figure 13 is a least squares f i t plot which shows a linear re lationship between lattice parameter and peak band frequency of the infrared absorption spectra for the Zr n o c Ca_ , c 0.. o c solid solution. It U . O J U . 1 J 1.oj is quite evident that the value of the peak band frequency is raised from 440 -1 -1 ° cm to 455 cm as the lattice parameter is reduced from 5.1369A to o ; 5.1344A. This observation is in accord with the postulation made by Baun 33 and McDevitt , in which they stated that, as the unit cell of a. type C (cubic) oxide increases in size, the frequency of the band is lowered and a,linear relation can be obtained from plot of unit cell dimension and band frequency. From a l l these observations i t appeared that there ..is a definite lattice contraction or shrinkage.of the cubic unit cell in the Zr^ g,. Can , c 0. o c solid solution after heat treatment. 3. Effect of Annealing Time on the Lattice Parameter The effect of annealing time on the lattice parameter values of the Zr_ o c Ca_ , c 0.. o c solid solution has been studied at 1100°C, U . o O U . l j l . o j 1300°C, 1400°C, and 1500°C. Four series of samples from.four,separate specimens were used. The annealing time varied from 5 hours to 70 hours at each temperature. The experimental data are given in Table 4, APPENDIX I. I - 46 - Figure 14 shows the variation of lattice parameter values as a function of annealing time at each temperature. From these plots, it can be seen that the-lattice parameter values decreased rapidly with annealing time during the early stage of annealing. At 1100°C and 1300°C, the lattice parameter reached a constant value after 16 hours of annealing time and remained constant on further annealing; whereas at 1400°G and.l500°C, the lattice parameter decreased and reached a constant value after 24 hours of annealing. No further change of lattice parameter was observed when these .samples were subsequently annealed for a longer period at the same temperature. (C) Electrical Conductivity of the Zr Q g 5 CaQ 1 5 g 5 Solid Solution 1. Electrical Conductivity as a Function of Temperature The electrical conductivity of the Zr Q g 5 CaQ ^ 0^ g 5 cubic solid solution has been measured over the temperature range,of 500°-1400°C at,200°C intervals. The conductivity-temperature data are given in,Tables 1, 2, and 3, APPENDIX II. Figure 15 shows, the least . squares f i t of the Arrhenius relation for three of the eight measured specimens obtained at,the temperatures after 30-45 minutes of soaking during the heating cycle. The activation energy for conduction obtained from the Arrhenius relation is given-in Table 4, APPENDIX II. Figure 16 shows the relation between activation energy and annealing temperature for data obtained at the equilibrated temperatures during heating cycle. From this plot i t can be seen that the.relation between the activation energy for electrical conduction and annealing temperature shows a minimum value atllOO°C. 5.1366] > 1 • 1 1 1 • 1 • 1 1 1 • 1 1 1 • 1 1 1 1 1 1 1 • — i 1 1 • 1 1 1 • r O Sperdm.en-J6.7_annealed.at 1100 °C -.Specii_en..#ii3-3_inealed-.at..l300oC - m Specime_L_#ii.6...annealed- at. l400°C A Specimen #31 annealed at.l500°C Annealing Time (hrs.) Figure lk. Decrease of Lat t i c e Parameter as a Function of Annealing Time. (°C) - 48 - 1CT I T°k Figure 15. Arrhenius plot - of E l e c t r i c a l Conductivity and Temperature. - 49 - Figure l 6 . Change of A c t i v a t i o n Energy for Electrical.Conduction With Annealing Temperature. - 50 - This indicates that the electrical conductivity of the Cae*stabilized Zr02 solid solutions significantly depends on its thermal history. The over-all electrical conductivity values obtained in the present investigation appeared to be in good agreement with those re ported in the literature. For the purpose of comparison, the electrical conductivity data for the solid solution having composition; of 15 mole% CaO and 85 mole % Zr02 obtained in the present investigation along with those reported by other workers are shown in Fig. 17 and the electrical conductivity at 1000°C together with the activation energy reported in the literature are given in,Table 5, APPENDIX II. In general, the activation energy for conduction obtained in this £udy seemed to be slightly lower than most reported values. However, when specimens were , annealed at higher temperatures, e.g. 1500°C, the specimens appeared to give higher activation energy values which are more comparable with the reported values. The electrical conductivity of the specimens measured immediately after i t reached the desired temperature and also after soaking for 30-45 minutes at the same temperature was the same, as shown in Fig. 18. This indicates that the .30-45 minutes of heat treatment of the specimens at a given temperature did not significantly affect the conductivity. The structural change associated with the heat treatment as reported earlier in the present investigation was very small (see Fig. 14) and did not cause any significant'effect on the conductivity when carried out after 30-45 minutes of temperature equilibration. Cc) 1 0 - 1 1300 1 2 0 0 i } o o ispn 20Ji -51 - 1 0 - 2 1 0 - 3 1 0 -1+ 1 0 1 9 . Hund ( 1 9 5 2 ) kl. Trombe ( 1 9 5 3 ) 3 8 . Kiukkola ( 1 9 5 7 ) 2 5 . Kingery ( 1 9 5 9 ) h2. Hathaway ( 1 9 6 2 ) k3. Dixon et a l ( 1 9 6 3 ) 2 2 . Tien & Subbarao ( 1 9 6 3 ) S ^ T h i s study ( 1 9 6 6 ) 6 . 0 7 . 0 8 . 0 9 . 0 1 0 . 0 1 1 . 0 1 0 / T °K Figure 1 7 - Comparison between the e l e c t r i c a l conductivity data from the l i t e r a t u r e and the present data for the Zr_ 0 c Ca„ ,.- 0, 0r- 0 . o 5 0 . 1 5 1 . 8 5 s o l i d solution. - 52 - T 1 1 1 1 1 Measuring Temperature (°'C) Figure 1 8 . Variation of E l e c t r i c a l Conductivity as Measured Immediately and After 30-45 Minutes of Soaking at the Same Temperature. - 53 - The electrical conductivity measured during the heating and cooling cycles, however, showed some.variations, as shown in,Figs. 19 and 20 and also in Table 3, APPENDIX II. It was observed that when specimens were annealed at temperatures below 1000°C, the electrical conductivity values measured during the cooling cycle.were higher than those measured during the corresponding heating cycle; whereas when specimens were annealed at temperatures above 1300°C, the electrical conductivity values measured during the cooling cycle were lower than those measured during the corresponding heating cycle. 2. Calculation of Oxygen Ion Diffusion Coefficients From Electrical Conductivity Measurements As i t has been shown by previous workers that the electrical conductivity of the CaO-Zr02 cubic solid solutions at high temperatures is due entirely to the migration of oxygen ions, the oxygen ion diffusion coefficients can be calculated from the electrical conductivity data.by the Nernst-Einstein equation (see.APPENDIX VI). The diffusion coefficient-temperature data for the Z r n o c Ca„ , c 0.. o c solid solution calculated from the conductivity data obtained in the present study are given in Table 6, APPENDIX II. Figure 21 shows the least squares f i t of Arrhenius relation for threei of the 8 specimens measured. Figure 22 shows,the relationship between the activation energy for oxygen ion diffusion and annealing temperature. From this plot i t can,be seen that there is a minimum activation energy at 1100°G. A similar trend was also observed between the activation energy for electrical 500 ,600 700 800 900 1000 1100 1200 1300 ikOO 1500 u. Measuring Temperature ('*C) 1 Figure 19. Change of E l e c t r i c a l Conductivity as Measured During the Heating and Cooling Cycles . (Specimen annealed at 900 *C) Figure 20. Change of E l e c t r i c a l Conductivity as Measured During the Heating and Cooling Cycles. (Specimen annealed at 1U00 °C ) lUOO 1300 1200 1100 1000 - I - 1 1 1 900 ( ° c ) - 56 - 800 a cu .01 OJ s o V 8 lQo" -p c cu •H CJ •H CH CH OJ O o o •H CO P. Ifi  o_ 9 10 10 0.60 0.70 TOO — r — • Annealed % 900°C O Annealed % 1300°C A Annealed g 1500°C 600 — i — 500 0.80 0.90 10 3/T°K 1.0.0 1.1.0 1.20 Figure 21. Arrhenius "; plot of Oxygen Ion Diffusion Coefficients and Temperatures. - 57 - 1-30 1.20 L 800 900 1000 1100 1200 1300 Annealing Temperature (°C) ikoo 1500 Figure 22. Change of Activation Energy for Oxygenlon Diffusion with Annealing Temperature. - 58 - conduction versus annealing temperature, as shown.in Fig. 16. The oxygen ion diffusion coefficients calculated from the electrical conductivity, data obtained in the present investigation appeared 25 to be in good agreement with those reported by Kingery and by Carter 27 and Simpson , as shown in Fig. 23. However, the activation energy for oxygen ion diffusion obtained in.this study seemed to be slightly lower than the value of 1.34 eV reported by Carter and Simpson and of 1.32 eV (after correction for the correlation factor in diffusion,the published value being 1.22 eV) by Kingery. The highest activation energy for diffusion obtained in this study is about 1.25 eV for a specimen annealed at.l500°C for 24 hours. The band plotted in Fig. 23 is the summary of experimental results obtained in the present study with the highest and lowest values as boundaries. (D) Porosity and Density of the Zr Q g_ CaQ ,. 0.^  g,- Solid Solution 1. Apparent Porosity of the Hot-pressed Specimens. The apparent porosity, which is expressed as a percentage for the volume of the open pores of the specimen to the exterior volume of the hot-pressed specimens before and after heat treatment has been de termined by the water absorption procedure. The experimental data for the apparent porosity and bulk density of the measured specimens are given in Table 1, APPENDIX III. The bulk density of most specimens was found to vary from 4.34 to 4.60 grams/cc which did not change with any heat treatment below 1400°C. - 60 - 2. True Density of the Zr Q g 5 CaQ ^  .0^ g 5 Solid Solution The true density of the material was determined by the pycnometric method using ethyl alcohol, bromoform, and distilled water. The experimental data obtained from ethyl alcohol and bromoform were widely scattered and inconclusive. The data obtained from distilled water are given in Table 2, APPENDIX III. The theoretical density of the solid solution: assuming both oxygen vacancy and oxygen interstitial models calculated from X-ray data is given in Table 3, APPENDIX III. Figure 24 shows the relationship between the true density of the solid solution and the annealing temperature.. It is evident that the true density of the material was affected by the annealing treatment. When the specimens were annealed below lOOO^ C the true density appeared to be slightly higher than the theoretical density according to the oxygen vacancy model and lower than the oxygen interstitial model. When the specimens were annealed above 1000°C for 24 hours the true density appeared to be comparable with the theoretical density of the oxygen vacancy model. (E) Chemical Analysis of the Hot-pressed Ca0-Zr02 Solid Solution In the specimen preparation the solid solution was assumed to have the composition: of 15 mole % CaO and 85.mole,% ZrO^- In order to check whether the annealing treatment after hot-pressing has any effect on the change of the chemical consti tuents , chemical analyses for CaO and Zr02 contents in the sample have been carried out on four specimens. These four specimens have been annealed at 800°C, 1000°C, 1100°C, and 1400°C respectively for about 24 hours. The chemical analyses were carried out.. 5. TOO 5 . 6 5 0 61 - oxygen i n t e r s t i t i a l model o o bO 5 . 6 0 0 -p •H c R 5 . 5 5 0 oxygen vacancy model Q o - 0 5 . 5 0 0 1 800 900 1000 1100 1200 1300 ikoo 1500 Annealing Temperature (°C) Figure 2k. Change of Density with Annealing Temperatures, - 62 - by "Coast Eldr:idge Engineers and Chemists Ltd" in Vancouver. The experimental results are given in Table III. Table III Chemical Analysis of Ca0-Zr02 Solid Solutions Specimen, Annealing Zr0 2 CaO No. Temp. Time —... „, rrr; z T T T — ^ Wt.% Mole % Wt. % Mole % 56 800°C 26 hrs. 91.97 86.29 6.65 13.71 62 1000°C 25 hrs. 92.25 86.66 6.46 13.34 63 1100°C 24 hrs. 92.10 85.71 6.99 14.29 65 1400°C 25 hrs. 91.40 85.44 7.09 14.56 86.02±0.5 13.98±0.5 According to the analyst, i t was claimed that the accuracy of these analyses was about ± 1 wt.% for ZrO_ and about ±0.4 wt.% for CaO. Accepting this accuracy for analysis, i t appears that annealing of the specimens has no significant effect on the change of the chemical 4+ 2+ content (i.e. the amount of [Zr ] and [Ca ] in the solid solution). IV. DISCUSSION (A) Lattice Contraction or Shrinkage of the Cubic Unit Cell in the Zr_ o c Ca- , c 0. Q C Solid Solution U . 0 3 U . 1 J 1.OJ From the experimental results obtained in the present i n  vestigation, i t is quite evident that annealing of the Zr^ Ca^ ^ 0^ solid solution after hot-pressing has a definite effect on i t s lat t i c e parameter. As the annealing temperature was increased from 800 to 1500°C the la t t i c e parameter of the solid solution decreased correspondingly in a linear.relation. At a constant temperature of 1100, 1300, 1400, and 1500°C, the la t t i c e parameter decreased asymptotically with annealing time and approached a constant value which varied with the - 63 - temperature. From a literature survey i t is also apparent that there exists some,relationship between the lattice parameter and the temperature of specimen preparation. In the formation of the cubic phase solid solution of ZrC^ with CaO the Ca atoms are assumed to enter into the ZrQ2 structure by replacing the Zr atoms thus causing a rearrangement of the atoms resulting in a fluorite-type structure. The substitution for Zr atoms with Ca atoms is assumed to be completely random and the distribution of CaO in the solid solution is homogeneous. The three models that have been postulated to account for the formation of a homogeneous solid solution are : the cation interstitial model, the anion (oxygen) vancancy model, and the oxygen interstitial model. In the cation interstitial model it is assumed that the Ca atoms first enter into the Zr02 lattice without replacing the Zr atoms and ::thus become,' interstitials. If this mechanism is operative the lattice parameter of the cubic unit cell will be slightly larger than the true cubic unit cell and the density of the material will be increased. 24 Diness and Roy have reported that there is evidence indicating such a,solid solution is possible by heating.the material at 1800°C and then quenching at 1000°C/sec. According to their data, the theoretical density of a cation interstitial solid solution having composition of 15 mole % CaO + 85 mole.% Zr02 would be in the order of about 6.00 grams/cc (see Fig. 3). In the anion (oxygen ion) vacancy model i t is assumed that the Ca atoms enter into the Zr0„ lattice by replacing the Zr atoms with the - 64 - formation of an equal number of oxygen vacancies to maintain charge neutrality. This oxygen vacancy model is generally accepted by most 19 21 24 25 workers » » » a s t n e predominant point defect-type structure in the fluorite-type crystalline solution field of the CaO-ZrC^ system. According to the data by Diness and Roy for a composition of 15 mole % CaO +,.85 mole % ZrO,,, the theoretical density is in the order of about 5.54 grams/cc. (see Fig. 3). In the oxygen interstitial model i t is assumed that the Ca . • atoms enter into the Zr02 lattice by replacing the Zr atoms with the formation of oxygen vacancies and oxygen ion interstitals; That is, instead of oxygen ions diffusing out from the lattice they may remain as 41 interstitials. Buyers has mentioned that such a model is quite possible as indicated in his theoretical model for electrical conduction:in the Ta/CaO-stabilized Zr02/W system. If this mechanism is operative the lattice parameter of the cubic unit cell would be slightly larger than the value without.the oxygen interstitials. The density of the material would also be higher than that of the oxygen vacancy model but lower than that of the cation interstitial model, sinch the atomic weight of a Ca atom is much greater than that of an oxygen atom. According to the X-ray data, the theoretical density of the Zr n o c Can 1 C 0 o c solid solution prepared in the present investigation U . O J U . X J ±.O_> was calculated to be.in the range of .5.546-5.549 grams/cc for the pure oxygen vacancy model and in, the range of 5.664-5.666 grams/cc for the pure oxygen.interstitial model. The pycnometer measured density of the solid solution was found to be in the range 5.534-5.588 grams/cc which indicates that the cubic solid solution is conclusively not the cation interstitial - 65 - solid solution. The calculated and measured densities of the Zr^ g,. CaQ ^- 0^  solid solution obtained in the present study are in good 2 A agreement with those reported by Diness and Roy (see Fig. 3) for the oxygen vacancy model. However, the slightly higher density observed in the specimens annealed at low temperatures is indicative of the deviation from the pure oxygen vacancy model and could tentatively be interpreted as due to the presence of a small number of interstitial oxygen ions remaining in the lattice. The minimum amount of CaO required to stabilize ZrO- in the cubic phase has been agreed upon by various workers to be,in the range of 12-13 mole %. The solid solution prepared in this investigation con tained about 15 mole % CaO, which is just over the cubic phase boundary. Although in the literature no experimental observations have been reported on the existence of any inhomogeneity in a solid solution of the CaO-ZrO- system, the possibility of a. non-uniform distribution of CaO in the Zr02 lattice can not be completely disregarded. It is possible that the cubic phase of Zr02 exists with some areas enriched in CaO and some areas slightly "deficient in CaO because of the slow rate of this solid state 2+ reaction thus resulting in the inhomogeneous distribution of Ca ions; although the over-all solid solution remains in a stable cubic form. 22 19 It has been observed by both Hund and Tien and Subbarao , that the variation of lattice parameter with CaO content in the cubic field of CaO- Zr02 solid solutions was very.small as compared with the dimension of the cubic unit cell, (see Fig. 4). When the CaO content in the cubic field varied about,1 mole % the change of the lattice parameter was in the order . o of about,0.001A. The magnitude of change of the lattice parameter observed - 66 - in the present investigation was also in the same order. Thus, the possibility of the existence of inhomogenity in the solid solution is not. inconsistent with this observation. The results of the density measurements appeared to rule out the possibility of extensive formation of thermally-induced vacancies, that is, the formation of more,oxygen vacancies and cation vacancies (Schottky defects). Loss of Ca ions from the unit cell appeared to.be unfavorable since no,previous experimental observations have been reported 2+ on the loss of Ca ions upon heat treatment of specimens of the CaO-ZrC^ solid solutions. De-stabilization of the cubic CaO-ZrO^ solid solution was not observed from the X-ray diffraction measurements in this study. The decrease of lattice parameter with time at a fixed temperature can.be assumed to be a rate process. The data were found to.fit best the 58 following empirical.relation : ao - a t , = k t a o where a t = the lattice parameter at time t a Q = the lattice parameter at time 0 (before annealing) k = rate constant t = annealing time When a -a. versus t was plotted, a linear relation was obtained, as shown o t f . t > a o in Fig. 25. The slope of these lines is equal to the rate constant k. This empirical relation appeared to satisfy the kinetics of a "second order reaction". Time x 10 (sec.) Figure 25. Relative Decrease of L a t t i c e Parameter with Annealing Time. - 68 - Using the rate constants, the temperature coefficients for 53 this process can be determined by an Arrhenius relation as follows : k = A exp ( ^j-) where k = rate constant A = pre-exponenti/constant , E = activation energy K = Boltzman's constant T = absolute temperature When log (k) versus 1_ was plotted, a linear relation was obtained, as T shown in Fig. 26. The activation energy calculated from this Arrhenius plot was found to be about 1.30±0.20 eV. This value was observed to be in the same order of magnitutde as the activation energy for oxygen ion diffusion in the CaO-ZrC^ system or as the sum of energy for oxygen vacancy motion and.the energy for dissociation of an oxygen vacancy from 2+ pairing or clustering with a Ca ion. The lattice contraction or shrinkage of the cubic unit cell could tentatively be interpreted by either of the following two mechanisms: 1. During the formation of the cubic solid solution of Zr02 with CaO by the hot-pressing process, i t is possible that a very small fraction of the oxygen ions after being displaced to create the vacancies are trapped in the lattice as interstitials. As the hot-pressed specimens are subjected to further heat treatment, the oxygen ion interstitials are removed from the lattice thus causing a slight shrinkage of the unit cell. On the removal of a l l interstitials from the lattice, the solid solution would then be the final form of the oxygen vacancy material, i' e"' Zr0.85 Ca0.15 °1.85 V 0 Q * Figure 2 6 . Arrhenius pldt of the rate of relative decrease of lattice parameter and temperature. - 70 - 2. During the formation of the cubic solid solution of CaO-Zr02> the distribution of the CaO in the ZrO^ lattice might not be completely uniform thus resulting in an inhomogeneous effect in the solid solution. As the specimens are subjected to further heat treatment after hot-pressing the material then becomes homogenized and attains the final form containing 15 mole % CaO. In.both.mechanisms an.equilibrium condition is reached at each temperature after a sufficient annealing time but this equilibrium value is dependent on the temperature of heat treatment; Judging from the activation energy obtained from the kinetic analysis, i t appears that the lattice contraction of the cubic solid solution is controlled by a mechanism similar to that observed in the ionic.conduction of the CaO-ZrO 2 system. However, the present data are insufficient to conclude which of the two mechanisms is a decisive one for explaining the shrinkage of the cubic unit cell. (B) Effect of Annealing on the Electrical Properties of the Zr_ Can ,_ 0, o c Solid Solution. The electrical conductivity of the Zr,-, Q c Ca. , c 0, o c cubic U i O j U.IJ l.oD solid solution over the temperature range 500-1400°C obtained in the present investigation was found to be in good agreement with that reported in the literature. However, the activation energy for conduction obtained in.this study was found to be significantly different from that obtained by other workers. The activation energy for conduction appeared to be dependent on the annealing temperature of the specimens after hot-pressing. A minimum activation energy was observed when the hot-pressed specimens were annealed at 1100°C for 24 hoursi On the other hand, when the hot-pressed - 71 - specimens were annealed at 800°C and 1500°C for a similar period of time, the activation energy for conduction was observed to be slightly higher and comparable with those values reported by other workers. The following explanation is given for this variation. In the cubic fluorite-type structure each.cation has eight nearest neighbour oxygen.ions. When Ca atoms diffuse into the ZrQ2 lattice by replacing Zr atoms, an equal number of oxygen vacancies are formed. This is necessary to maintain electronic neutrality in the 59 system. Wachtman has calculated that each vacancy is so tightly bound to a Ca ion that, to a good approximation, i t can occupy only the eight nearest neighbour oxygen positions moving from one nearest [position to another. . Thus, each position is occupied with equal probability in the absence of a stress or electric field. On the other hand, a substitutional Ca ion can jump to an equivalent position only by interchanging with a Zr ion. Based on the proposed 8-position Nearest- Neighbour Model for Th02 containing CaO, which is also a solid solution of the.cubic fluorite-type structure, he observed that the electrostatic attraction between an oxygen vacancy and substitutional Ca ion should cause association and that there is a difference of electrostatic energy of about 0.34 eV between nearest neighbour and next-neighbour positions. Furthermore, he estimated that the energy required to free an oxygen vacancy completely from a Ca ion would be in the order of about 0.71 eV, but he pointed out. that the uncertainty in the electrostatic method of estimating the dissociation energy is so great that l i t t l e weight.should be attached to this value. From his study of the Th02 solid solution containing 1.5 mole % CaO, he calculated that the activation energy for the motion of an oxygen vacancy neighbouring a Ca ion is about 0.93 eV and the activation energy of free oxygen-vacancy motion might well be slightly larger than for the motion of an oxygen vacancy neighbouring a foreign ion. It is generally believed that the volume electrical conductivity could be attributed to oxygen vacancies with an activation energy for motion alone, because the number of oxygen vacancies is fixed by the CaO content. However, Franklin^ i has pointed out that while the total number of oxygen vacancies is presumably fixed by the CaO content, most of these are.bound to Ca ions and so do.not contribute to volume conductivity. The number of free oxygen vacancies should s t i l l be thermally activated and conductivity by oxygen-vacancy motion should s t i l l require an activation energy which is the sum of an energy of motion and one.half the energy of dissociation. Since both Ca0-Th02 and CaO-Zr02 solid solutions are of the cubic fluorite-type structure and the volume conductivity is based mostly on the motion of oxygen vacancies in.the material, i t is possible to interpret results obtained in the present investigation with the arguments outlined above. Assuming that the.energy required for the motion of oxygen vacancy in the CaO-Zr02 system is very nearly the same as that in the Ca0-Th02 system of 0.93 eVj any excess energy observed would be equal to one half of the energy of dissociation. The dissociation energy calculated from the observed activation energy for conduction is summarized in Table IV. - 73 - Table IV c Energies for Oxygen Vacany Motion and Dissociation in the CaO-ZrO- System Annealing Temp erature (°C) 800 900 1000 1100 1200 1300 1400 1500 Observed E in conduction (eV) 1.14 1.07 1.00 0.92 X.03 1.04 1.09 1.14 E for oxygen vacancy motion (eV) 0.93 Total E for dissociation (eV) 0.42 0.28 0.14 0 0.20 0.22 0.32 0.42 The relationship between the total energy and the heat treatment of the specimens is shown in Fig. 27. It can be seen that the activation energy for conduction obtained from specimens annealed at 1100°C is just the energy required for the motion of an oxygen vacancy, while the excess energy observed in the other specimens is one half the dissociation energy necessary for the vacancy-foreign ion to be dissociated before they could move under an electric .potential. The excess energy observed in the temperature range 800-1000°C can be considered in two aspects. It can be considered as the energy associated with the oxygen ion interstitials i f they do exist in the lattice. In order to facilitate the migration of the oxygen vacancies during ionic coiduction, i t is necessary to remove a l l interstitial oxygen - 74 - 1.50 1.40 1.10 0.70 E^ = energy for motion of oxygen vacancy Eg = energy associated with clustering of oxygen vacancies or with i n t e r s t i t i a l oxygen ions iated with order-disorder tr a n s i t ] 800 900 1000 1100 1200 1300 1400 1500 Annealing Temperature (°C) Figure 27. Change of Excess Energy for Conduction with Annealing Temperature. ions from the lattice because they might be blocking the vacancy migration path. Thus, an extra amount of energy in addition to the energy for vacancy motion is required. On the other hand, this excess energy can also be regarded as the energy associated with localized pairing or clustering 2+ of the oxygen vacancies and Ca ions due to the existence of an ingomogeneous distribution of CaO in the ZrO^ lattice. Thus, an extra amount of energy is required to dissociate them for ionic conduction. Wa-tchman. and Franklin have pointed out that the oxygen vacancies are mostly bound to Ca ions in the CaO-Th02 system. This 52 postulation was also supported by Kroger in his propsed imperfection model for the Zr„ o c Can , c 0.. o c V_ solid solution:. He maintained U.oj U . i j l . o j UQ that the imperfections may interact by short-range, forces through the .formation of associates. The high binding energy, expected, combined' with the high concentration in which Ca ions and oxygen vacancies are present in stabilized Zr0 2 ,i suggests that the majority of these imperfections are paired or clustered. The effect of the heat treatment of the CaO-ZrO~ solid solutions leading to the order-disorder transition of the Ca ions and 22 oxygen vacancies in the system has been observed by Subbarap and Tien, 4 6 3 8 Subbarao and Sutter , and also by Wachtman-and Corwin . Subbafaoand his co-workers have observed that superlattice lines appeared in the X-ray diffraction pattern for specimens of the Zr~_ -Q Ca^ 20 ° 1 8 0 s0-'-id solution which had been annealed at 1000°C and that these superlattice lines dis<- appeared when the specimens were reheated to 1400°C. They also observed that at temperatures below 1100°C, those specimens heated at 1000°C exhibited a lower conductivity than those heated at 1400°C. Beyond 1100°C, the - 76 - 1000°C heat treated specimens exhibited a change in slope of the Arrhenius plot and became more conductive. On reheating the same specimens, the Arrhenius plot fetsw^ a straight line with a displacement of the curve to a higher conductivity at lower.temperatures and joined the first curve at higher temperatures. They concluded that the ordered phase was less conductive and was transformed into the disordered phase at about 1100°C. Wachtman and Corwin have observed that there are variations in the internal friction peak height between unannealed specimens and specimens annealed at 1000°C for the CaO-Zr02 solid solutions. For Zr02 solid solutions containing 13 mole % or 16 mole % CaO, the internal friction peak height was decreased as the specimens were heated at 1000°G. These experimental observations have been interpreted as.a consequence.of the attraction of the oxygen vacancies to the Ca ions due to Coulombic forces. The total dissociation energy observed in the present investigation 5 V varied from 0.22 to 0.42 eV, which is in the same order of magnitude as the . energy calculated by Wachtman for the complete dissociation of an oxygen vacancy from the attraction of a- Ca ion. . A dissociation energy df 0.22 eV was also observed by Wachtman in his studies of the.mechanical and electrical relaxation in Th02 solid solution containing 1.5 mole % CaO. In view of the precious observations, i t is apparent that the oxygen vacancies and the substitutional Ca ions in.the CaO-Zr02 solid solution have a tendency to form pairs or clusters particularly at high temperatures. The true reaction temperature of the formation of solid solution during hot-pressing was found to be about 1750°C in the present investigation- Thus i t is quite possible that due to the inhomogeneous distribution of Ca ions, localized clustering effect in the solid solution would be predominant. As the specimens were annealed at about 1100°C, the clustering effect in the solid solution is minimized. The ionic conduction mechanism in the CaO-ZrC^ solid solution is due to.the migration of oxygen vacancies. In order to facilitate the migration of these vacancies, an extra amount of energy in addition to the energy of oxygen, vacancy motion is therefore.required to dissociate.any pairs of clusters. (C) Effect of Heat Treatment on the Oxygen,Ion Diffusion in the CaO-Zr02 Cubic Solid Solution The oxygen.ion diffusion coefficients calculated from the electrical conductivity data for the Zrg g5 ^a0 15 1^ 85 ^^-^ solution obtained in.the present investigation were found to be,comparable with those reported elsewhere. However, the activation energy for oxygen ion diffusion appeared to show a similar annealing temperature variation as.that observed in the electrical conductivity measurements. 52 Kroger has pointed out that ionic conduction and oxygen diffusion probably take place by migration of the oxygen vacancy V^'s x as neutral pairs (Ca Z r » migration by way of the free vacancy centers m V Q would introduce the association enthalpy into the activation energy of diffusion. For easy migration through the neutral defects to be possible, i t is essential that the associated Ca ions and oxygen vacancies form a random pattern, but with the Ca.ions near enough so that oxygen vacancies can jump from a.position next to a calcium ion to another one. If ordering of the Ca ions ..and oxygen vacancies exists in the Ca0-Zr02 solid solution i t would decrease the oxygen diffusion coefficients. - 78 - Kroger has estimated that the association enthalpy has the form (11^  / 2m). If the vibration entropy is not affected by the pairing- and m = 1 for pairs, the value of H^  =;-2.7 eV gives an association enthalpy of about -1.35 eV. However, if the ordering forms larger, associates, (clusters instead of pairs), the value of m would be greater than 1, thus reducing the association enthalpy. - 79 - V. SUMMARY AND CONCLUSIONS 1. The cubic fluorite-type solid solution having composition 15 mole.% CaO + 85 mole % Zr0o (Zr_ Q c Can 0 Q C) can be prepared by hot-pressing the mixture of ZrO. and CaC0_ powders at 17.50°C arid 4600 psi pressure for about 30 minutes. 2. The lattice parameter of the CaO-ZrO. cubic solid solution decreased in a linear relation with the annealing temperature as the specimens were annealed from 800°C to 1500°C. 3. At a constant temperature of 1100, 1300, 1400, and 1500°C, the lattice parameter of the cubic solid solution decreased rapidly with annealing time in the early stage and attained a constant value after sufficient time. 4. As the lattice parameter of the cubic solid solution decreased, the peak band frequency of the infrared absorption spectra of the same solid solution increased. A linear relationship between lattice parameter and band frequency was observed. 5. The peak band frequency of the infrared absorption spectra of the CaO- stabilized Zr0_ solid solution shifted depending on the heat treatment of the specimen. 6. The lattice contraction or shrinkage of the unit cell in the CaO-ZrO. solid solution was attributed to the removal of interstitial oxygen ions from the lattice or possibly related.. to the existence of the inhomogeneous distribution of Ca ions in the solid solution. 7. In the temperature range 500-1400°C, the electrical conductivity can -E be represented by an Arrhenius-type expression a = a0 exp (""j^—) where the activation energy E for electric conduction varied depending on the heat treatment of the specimens after hot-pressing. The activation energy for conduction decreased.as the specimens were annealed from 800°C - 80 - to 1100°C and increased as the specimens were annealed from.1200°C to 1500°C with a minimum activation energy for the specimens annealed at 1100°C. 8. Specimens annealed at 1100°C exhibited the lowest value of the activation energy for conduction. This value corresponded to the amount of energy required for the motion of the oxygen vacancy in the Ca0-Zr02 system. 9. The excess energy observed in specimens annealed in other temperatures was interpreted as the extra amount of energy required to dissociate the oxygen vacancies from Ca ions forming pairs or clusters. 10. The dependence of the activation energy for the oxygen ion diffusion (diffusion coefficients,, are calculated from the electrical conductivity data using the Nernst-Einstien equation) on the annealing temperature followed a trend similar to that observed in the electrical conductivity measurements. - 81 - VI. SUGGESTIONS FOR FUTURE WORK The results obtained in the present investigation have, to some extent, been exploratory in nature. The various models proposred'for explaining the experimental observations are hypotheses. In order to confirm these models or to extend the subject of this study, several topics are suggested. These topics include: 1. A more,precise density measurement is required in order to confirm the oxygen.interstitial model. 2. The annealing temperature can be extended up to 2000°C and substantiate the lattice contraction phenomenon observed in the temperature range of this study. 3. The effect of impurities on the kinetics of stabilization of Zr0 2 shouldbe investigated. 4. A study of the reaction kinetics between CaO and ZrO2 would be of interest to investigate using the reactive hot-pressing process for specimen preparation. VII. APPENDICES - 82 - 1 APPENDIX I TABLE 1 Lattice Parameter-Annealing Temperature Data of the Three Separate Series of Samples Annealing Expt.No. Specimen Temperatui e Time Lattice Parameter No. (°C) (hrs.) (A) 4 30 800 1 5.1369 5 it 1100 14 5.1361 6 M 1400 14 5.1354 7 I I 1500 14 5.1346 17 29 800 1 5.1358 18 it 1200 17 5.1353 19 I I 1300 24 5.1352 20 I I 1400 10 5.135.1 42 73 800 1 5.1360 •>. 43 I I 900 24 5.1358 44 I I 1150 24 5.1355 45 I I 1300 24 5.1353 46 it 1500 24 5.1350 APPENDIX I TABLE 2 Lattice Parameter - Annealing Temperature Data of Most Measured Samples Annealing Lattice Pars 0 imeter (A) Specimen I Temperatui e Time No. Measured Mean Mean Standard (°C) (hrs.) Values. Values Deviation Deviation 800 1 29 5.1358 5.1363 -0.0005 + 0.0004 it 30 5.1369 +0.0006 M 31 5^ 1359 -0.0004 I I 41 5.1365 +0.0002 I I 43 5.1359 -0.0004 I I 46 5.1363 0 I I 52 5.1368 +0.0005 it 73 5.1360 -0.0003 1100 14 30 5.1361 5.1356 +0.0005 + 0.0004 11 24 63 5.1354 -0.0002 1200 17 29 5.1356 5.1356 0 + 0.00002 I I 24 51 5.1357 +0.0001 II 24 57 5.1356 0 II 24 73 5.1355 -0.0001 1300 24 29 5.1352 5.1352 0 + 0.0001 II 21 43 5.1353 +0.0001 I I 24 51 5.1349 -0.0003 II 24 59 5.1353 +0.0001 it 24 73 5.1353 +0.0001 1400 25 31 5.1344 5.1349 -0.0005 + 0.0005 I I 24 40 5.1354 +0.0005 II 24 41 5.1344 -0.0005 II 24 65 5.1352 +0.0003 1500 14 30 5.1346 5.1350 -0.0004 + 0.0002 i i 25 46 5.1351 +0.0001 t i 24 51 5.1350 0 i i 26 72 5.1352 +0.0003 I I . 74 73 5.1350 0 APPENDIX I TABLE 3 - 84 - Lattice Parameter and Peak Band Frequency of the Infrared Absorption Spectra of the CaO-Stabilized ZrO. Specimen No. Annealing Lattice Parameter 0 ( A ) Band Frequency (cm ) Temperatur< (°C) >, Time (hrs.) 31 800 1 5.1359 445 30 I I 1 5.1369 440 41 ii 1 5.1365 442' 43 I I 1 5.1359 . 445 56 I I 25 5.1359 444 60 900 25 5.1356 446 62 1000 25 5.1354 448 63 1100 25 5.1354 448 57 , 1200 24 5.1355 447 43 1300 24 5.1353 449 59 II 24 5.1353 449 31 1400 15 5.1348 453 31 it 25 5.1344 455 30 1500 14 5.1346 454 51 I I 24 5.1350 452 APPENDIX I TABLE 4 Lattice Parameter - Annealing Time Data of Four Separate Series of Samples - 85 - Annealing Lattice Expt. Specimen No. No. Temperatui e Time Parameter 0 (°C) (hrs.) ( A ) 59 67 10 annealir g o 5.1361 60 I I 1100 5 5.1360 61 I I i t 12 5.1358 62 I I I I 21 5.1358 63 I I i i 48 5.1358 64 I I t i 69 5.1359 21 43 800 1 5.1359 22 I I 1300 5 5.1355 23 f 1 " 16 5.1355 24 I f 21 5.1356 25 I I 40 5.1356 26 I I " 61 5.1356 27 11 68 5.1355 28 46 800 1 5.1357 29 I I 1400 4 5.1351 30 I I 10 5.1350 31 II 14 5.1349 32 I I 20 5.1345 33 II 25 5;1345 56 I I 40 5.1345 55 I I " 65 5.1345 11 31 800 1 5.1359 12 i t 1500 5 5.1352 13 I I 10 5.1349 14 I I " 15 5.1348 15 I I 20 5.1346 16 I I 25 5,1344 57 r i 44 5.1344 58 i i 64 5.1344 APPENDIX I TABLE 5 - 8 6 - Relative Decrease o f Lattice Parameter with Annealing Time Specimen No. rempera- ture Lattice Parameter 0 (A) Annea Til ling me a 0 - afc a« xlD • •. Slope (k) lO" * -1 (sec- ) (hrs.) ( Jsec) xlO 67 1100 5.1361 0 0 0 2.86 5.1360 5 1.80 0.1947 5.1358 12 4.32 0.5841 5.1358 21 7.56 0.5841. 43 1300 5.1359 0 0 0 4.72 5.1356 5 1.80 0.5841 5.1355 16 5.76 0.7788 5.1355 21 7.56 0.7788 40 1400 5.1357 0 0 0 14.50 5.1351 4 1.44 1.1683 5.1350 10 3.60 1.3630 5.1349 14 • 5.04 1.5577 5.1345 25 9.00 2.3366 31 1500 5.1359 0 0 0 21.00 5.1352 5 1.80 1.3629 5.1349 10 3.60 1.9471 5.1348 15 5.40 2.1418 5.1346 20 7.20 2.5312 5.1344 25 9.00 2.9206 I APPENDIX II TABLE 1 _ 8 7 Electrical Conductivity - Temperature Data Obtained at Equilibrated Temperatures During the Heating Cycle Spec, No. Bulk Density (gm/cc) Poro- / sity (%) Anneal ing El ectrical Conductivity (ohm •1 -1, -cm ) Temp. (°C) 500°C 700°C 900°C 1100°C 1300°C 1400°C 61 4.466 17.0 800 1 .54x10" •5 2.84xl0~4 I .83xl0-3 1.95x10" •2 7.66x10" •2 1.60x10" •1 58 4.478 19.1 900 3 .92x10" •5 4.23xl0-4 1 .62xl0-3 1.17x10" •2 3.73x10" •2 0.70x10" •1 64 4.489 19.4 1000 2 .96x10" •5 5.53xl0~4 .20xl0-3 3.olxl0" •2 6.12x10" •2 0.84x10" •1 66 4.504 18.8 1100 .44x10" •5 6.75xl0"5 .65xl0-3 0.51x10" •2 3.92x10" •2 0.16x10" •1 69 4.429 18.8 1200 .55x10" •5 1.34xl0~4 ' .50xl0-3 1.68x10" 2 5.42x1-" 2 1.36x10" -1 70 4.500 18.3 1300 .98x10" •5 6.93xl0_4i .70xl0~3 1.38x10" 2 5.70x10" •2 1.32x10" •1 74 i.593 17.8 1400 • .74x10" •5 6.01xl0"4f .22xl0"3 4.37x10" 2 ..48x10" 1 1.23x10" •1 71 4.650 17.1 1500 . .95x10" •5 1.32xl0"3] .13xl0-2 3.38x10" 2 ..65x10" 1 2.62x10" •1 APPENDIX II TABLE 2 - 88 - E l e c t r i c a l , C o n d u c t i v i t y - Temperature^Data With Measurements Made Before and Aft e r Soaking at the Same Temperature Spec. Anneal ing •Soaking E l e c t r i c a l Conductivity (ohm ^ -Is -cm ) No. Temp. (°C) 500 °C 700 °C 900 °C 1100 °C 1300 °C 1400 °C 61 800 before 1. 39x10" •5 2 .79x10" •4 2.89xl0" 3 L.92xl0" 2 7 .76xl0" 2 1.55x10" 1 a f t e r 1. 54x10" •5 2 .84x10" •4 2.83x10"3 L.95xl0 - 2 7 .66x10"2 1.60x10" 1 58 900 before 0. 87x10" •5 4 .32x10" •4 3.68xl0 - 3 L.31xl0~ 2 3 .92xl0" 2 0.67x10" 1 a f t e r 0. 92x10" •5 4 .23x10" •4 3.62xl0~ 3 L.17xl0" 2 3 .72xl0~ 2 0.69x10" 1 64 1000 before 2. 79x10" •5 5 .08x10" •4 5.98xl0 - 3 3.23xl0 - 2 8 .77xl0" 2 0.77x10" 1 a f t e r 2. 96x10" •5 5 .53x10" " 4( ».20xl0 - 3 3 . o l x l O - 2 6 .12xl0" 2 3.84x10" 1 66 1100 before 0. 95x10" •5 D .98x10" -4 1.71xlO" 3 0.52xl0 - 2 1 .OOxlO"2 3.16x10" 1 a f t e r 1. 44x10" -5 0 .67x10" -4 1.65xl0" 3 0.51xl0" 2 1 . O l x l O - 2 3.16x10" 1 69 1200 before 1. 20x10" -5 L .42x10" -4 1.42xl0 - 2 2.01xl0 - 2 5 .50xl0" 2 L.34x10" •1 a f t e r 1. 55x10" •5 L .34x10" -4 7.50xl0 - 3 L.68xl0 - 2 5 •42xl0" 2 L.36x10" •1 70 1300 before 1. 76x10" -5 L .43x10" -3 8.00xl0 - 3 L.37xl0 - 2 6 .47xl0" 2 L.44x10" 1 a f t e r 1. 98x10" " 5 D .67x10' -3 6.70xl0" 3 L.38xl0 - 2 5 .70xl0" 2 L.32xl-" •1 74 1400 before 4. 42x10" •5 0 .50x10" -3 6.47xl0 - 3 4.54xl0 - 2 1 .81x l 0 _ 1 3.06x10" •1 a f t e r 2. 74x10" •5 3 .60x10" -3 -3 6.22x10 4.37xl0~ 2 1 .48x l 0 - 1 L.23x10" •1 71 1500 before 1. 65x10" -5 L .32x10" -3 1.18xl0 - 2 3.57xl0~ 2 1 .5 9 x l 0 - 1 2.82x10" •1 a f t e r 1. 91x10" -5 L .32x10" -2 1.13xl0 - 2 3.38xl0" 2 1 .65xl0 - 1 2.62x10" •1 1 APPENDIX II TABLE 3 - 89 - Electrical,Conductivity - Temperature Data;With Measurements Made During the Heating and Cooling Cycles Spec No; Anneal' ing Temp. (°C) Cycle Electrical Conductivity (ohm ^  - cm 500 °C 700 °C . 900 °C 1100 °C 1300 °G 1400 °C 61 58 64 66 69 70 74 71 800 900 1000 1100 1200 1300 1400 1500 Heating 1 Coplin Heatin Coolin Heatin Coolin Heatin Cooling^ Heating 1 Coolingl Heating 1 Coolingjl Heati Coolin Heatin :ing 2 Cooling 1 54x10 1.99x10 0.92x10 1.71x10 2.96x10 0.53x10 1.44x10 .20x10 .55x10 .21x10 .98x10 .57x10 .74x10 0.50x10 1.95x10 20x10 •5 •5 •5 -5 •5 •5 •5 •5 •5 •5 •5 •5 •5 •5 -5 -5 I.84x10 3.76x10" +.23x10" 3.71x10" 5.53xlOr 3.26x10" ).67x10" i.40x10" L.34x10" L.40x10" i.93xl0" L.61x10" j.01x10" >.85x10" L.32x10" L.39x10" 2.83x10 6.96x10' 3.62x10' 7.43x10' 6.20x10' 4.74x10' 1.65x10' 2.58x10' 7.50x10' 7.60x10' 6.70x10' 6.64x10' 6.22x10' 5.47x10' 1.13x10' 0.86x10' L.95x10 >.46xl0 L.17x10 3.20x10 3.01x10 D.82x10 ).51x10 ).50x10 L.68x10 L.72x10 L.38x10 L.30x10 4.37x10 3.85x10 3.38x10 2.61x10 •2 •2 •2 -2 •2 •2t -2,: 7.66x10 -2 L.60x10 -1 8.51x10 -2 1.60x10 -1 3.73x10 D.70x10 -1 4.90x10 -2 3.70x10 -1 -2 6.12x10 "jb.84kl0 -2 -1 ,73x10 3.84x10 -1 ro.9ixio -2 3.16x10 -1 1.01x10 -2 3.16x10 -1 5.42x10 -2 tL.36xlO-1! 5.94x10 -2 1.36x10 -1: 5.70x10 -2 1.32x10 -1 5.20x10 -2 1.32x10 -1 1.48x10 -1 1.23x10 -1 0.89x10 -1 1.23x10 -1 1.65x10 -1 2.62x10 -1 1.24xl0u 1 2.62x10 -1 APPENDIX II TABLE 4 - 90 - , Activation Energies for Electrical Conduction and for Oxygen Ion Diffusion in the Zr„ Q C Can - c 0. Q C Solid Solution U . O J U . l j l.o_> Specimen No. Annealing Activation Energy for Conduction (eV) Aptivation Energy for Oxygen ion Diffusion (eV) Temperatur( (°C) , Time (hrs.) Heating Cooling 34 800 1 1.14 1.28 61 800 25 1.14 1.08 1.25 58 900 24 1.07 1.03 1.18 64 1000 24 1.00 1.12 1.12 66 1100 24 0.92 1.12 1.04 69 1200 24 1.03 1.07 1.14 70 1300 26 1.04 1.02 1.15 74 1400 24 1.09 1.23 1.20 76 1500 26 1.14 1.17 1.25 APPENDIX II TABLE 5 - 91 - Summary of Lattice Parameter, Electrical Conductivity, Activation Energy for Electrical.Conduction, and Method of Specimen Preparation of the Zr_ o c Ca_ , c 0. o c Solid solution as . j , _, T U.oO U.l_> l . O O Reported in the Literature Author Lattice Parameter o (A) Electrical Conductivity at 1000 °C (ohm - cm )^ Activa tion Energy (eV) Method of Specimen Preparation Hund 19 41 Trombe & Foex. Volechenkova,& 21 Pal guev Kingery et al. 21 5.131 Rhodes & Carter Hathaway 4 2 20 Dixon et al. 43 Tien & Subbarao 22 5.133 Present study 5.135 2.2x10 -3 4.0x10 2.7x10 -3 2.3x10 -2 2.6x10 -2 5.0x10 -2 2.0x10 -2 3.3x10 -2 2.0x10 -2 1.21 1.26 1.17 1.30 1.17 1.14 Calcined ZrO. and CaCO- mixtures at 1200 °C for 2 hours, then sintered at 1460 °C for 5 hours . Calcined ZrO and CaCO, mixtures at 1300 °C. Calcined ZrO. and CaC0„ mixtures at 1300 °C, then sintered at 2000 °C for 7 hours. Reacted 4.25 mole Zirconyl Chloride and 0.82 mole CaCl„ , precipitated solution and calcined at 870 °C for 3 hours. Hot-pressed zr0„ and CaCO. mixtures at 1400 °C and 3000-5000 psi pressure. Calcined ZrO and CaCO- mixtures at 1350 °C for 24 hours, then sintered at 2000 °C for 2 hours followed by one week annealing at 1400 °C. Hot-pressed Zr0„ and CaC0„ at 1^ 50 °C and 5600 psi pressure for 30 minutes and then annealed at 1 5 0 0 °C f o r 24 h o u r s . APPENDIX II TABLE 6 Oxygen Ion Diffusion Coefficients Calculated from the Electrical Conductivity Data. Speci men Anneal ing Temp. Diffusion Coefficients , 2 (cm - sec No. (°C) 500 0 C 700 °C 900 °C 1100 °C 1300 °C 1400 0 C 61 800 92x10" 11 4.46xl0_1° 5.38xl0~9 4 .33xl0"8 1 .95x10" 7 4 .34x10" 7 58 900 -• 15x10" •11 6.64xl0"1G 6.88xl0"9 2 .60xl0"8 0 .95x10" 7 1 .89x10" 7 64 1000 3. 69x10" •11 8.68xl0 - 1 0 1.18xl0-8 6 .68xl0-8 1 .56x10" 7 2 .29x10" 7 66 1100 L. 80x10" •11 1.06xl0_1° 0.31xl0-8 1 .14xl0-8 0 .23x10" 7 0 .44x10" 7 69 1200 L. 94x10" •11 2.10xl0-9 1.42xl0-8 3 .73xl0-8 1 .38x10" 7 3 .68x10" 7 70 1300 2. 47x10" •11 1.09xl0"9 1.27xl0-8 3 .06xl0-8 1 .45x10" 7 3 .58x10" 7 74 1400 3. 42x10" •11 0.94xl0-9 1.18xl0"8 9 .70xl0"8 3 .77x10" 7 3 .33x10" 7 71 1500 2. 38x10" •11 2.07xl0~9 2.15xl0"8 7 •52xl0-8 4 .40x10" 7 7 .10x10" 7 APPENDIX III TABLE 1 -11 - Apparent Porosity and Bulk Density of the Hot-pressed Specimens Annealing Bulk Density (gm/cc) Apparent Porosity (%) Specimen No. Tempera- Time Before Heat After Heat Before Heat After Heat ture(°C) (hrs.) Treatment Treatment Treatment Treatment 51 800 1 4.641 16.6 61* 800 26 4.489 4.506 17.0 18.0 45 900 20 4,374 4.341 21.8 21.7 58* 900 24 4.478 4.593 19.1 !9.1 64* 1000 24 4.489 4.468 19.4 18.4 66* 1100 24 4.504 4.488 18.8 18.9 69* 1200 24 4.429 4.470 18.8 18.6 70* 1300 24 4.499 4.481 18.3 18.3 75 1300 23 4.530 17.9 37 1400 10 4.520 4.547 17.0 16.9 74* 1400 24 4.593 4.544 17.8 17.3 71* 1500 24 4.650 17.1 53 900 + 1400 24 + 22 4.454 4.420 20.2 19.8 55 1100 + 1400 20 + ?n 4.661 4.600 19.0 15.7 * Besides annealing, these specimens had been heated from 500 °G to 1400 °C for about,16 hours in electrical conductivity measurements. APPENDIX III TABLE 2 - 94 - True Density of the Zr n Q C Ca. n c 0. o c Solid Solution U. O J U . i j 1.OJ Determined by the Pycnometric Method Using Distilled Water Speci Annealing True Density (grams/cc) men Temp. Time Measured Mean Deviation Standard No. Cc) (hrs.) values value from mean deviation 56 • . 800 .. > 26 5.635 5.588 +0.047 - 0.038 5.619 +0.031 5.553 -0.035 5.548 -0.040 60 900 25 5.596 5.563 +0.033 - 0.026 5.563 0 5.530 -0.033 62 1000 25 5.542 5.534 +0.008 - 0.007 5.535 +0.001 5.525 -0.009 63 1100 24 5.575 5.545 +0.030 - 0.027 5.570 +0.025 5.524 -0.021 5.514 -0.031 57 1200 24 5.583 5.566 +0.017 - 0.013 5.563 -0.003 5.552 -0.014 - 0.017 59 1300 24 5.558 5.534 +0.020 5.533 -0.001 5.512 -0.022 65 1400 25 5.609 5.545 +0.064 - 0.041 5.560 +0.015 5.554 +0.009 5.457 -0.088 72 1500 24 5.592 5.551 +0.041 - 0.044 5.597 +0.046 5.510 +0.041 5.503 -0.048 APPENDIX III TABLE 3 - 95 - Theoretical Density Calculations from X-ray Data Assuming Oxygen Vacancy Model (Zr-, o c Ca_ 1 C 0. o c) and U . O J U . 1J 1. O J Oxygen Interstitial Model (Zr n Can ., 0_ n n) Specimen No. • Annealing Temp. (°C) Lattice Parameter 0 (A) Volume of Unit Cell 0 3 Theoretical Density (gm/cc) Oxygen Vacancy Model Oxygen Interstitial Model 56 800 5.1359 135.471 5.5465 5.6642 60 900 5.1356 135.450 5.5474 5.6651 62 1000 5.1354 135.432 5.5481 5.6658 63 1100 5.1354 135.432 5.5481 5.6658 57 1200 5.1354 135.432 5.5481 5.6658 59 1300 5.1353 135.424 5.5485 5.6661 65 1400 5.1352 135.416 5.5485 5.6661 72 1500 5.1352 135.4166 5.5485 5.6661 APPENDIX IV E s t i m a t i o n o f E r r o r - 96 - 1. L a t t i c e P a r a m e t e r V a l u e s The l a t t i c e p arameter v a l u e s o b t a i n e d i n t h i s s tudy.were c a l c u l a t e d a c c o r d i n g t o Cohen's method, (see APPENDIX V ) . Because o f t h e c o m p l e x i t y o f t h e , c a l c u l a t i o n , i t i s d i f f i c u l t t o d e t e r m i n e t h e u n c e r t a i n t y i n each s t e p . However, an e s t i m a t e . o f e r r o r has been o b t a i n e d t h r o u g h t h e computer p r i n t e d r e s u l t s . The a c c u r a c y o f r e a d i n g t h e p o s i t i o n s o f t h e d i f f r a c t e d l i n e s was - 0.05 mm. Thus two s e t s o f d a t a , one w i t h a d d i t i o n o f 0.05 mm t o a l l r e a d i n g s and one w i t h s u b t r a c t i o n o f 0.05 mm t o a l l r e a d i n g s , were c a l c u l a t e d u s i n g t h e same computer programme. The v a r i a t i o n o f p r i n t e d v a l u e s was a b o u t - 0.0001 A. The d r i f t c o n s t a n t w h i c h i s a measure o f t h e t o t a l s y s t e m a t i c e r r o r i n v o l v e d i n t h e d e t e r m i n a t i o n v a r i e d from 0.0001 t o 0.0003 f o r a l l c o m p u t a t i o n s *•. . . 2. E l e c t r i c a l C o n d u c t i v i t y V a l u e s The e l e c t r i c a l c o n d u c t i v i t y v a l u e s o b t a i n e d i n . t h i s s t u d y were c a l c u l a t e d a c c o r d i n g t o t h e f o l l o w i n g e q u a t i o n : (see page 32 o f t h i s t h e s i s ) Now t a k i n g t h e n a t u r a l l o g a r i t h m s and d i f f e r e n t i a t i n g b o t h s i d e s t h e t o t a l e r r o r i n t h e c o n d u c t i v i t y , w h i c h i s a d d i t i v e i s as f o l l o w s : _________ 6 L . 6 A . 6 1 . 6 V a ~ ~ L ~ + A + I + V The p o s s i b l e u n c e r t a i n t i e s i n v o l v e d i n t h e measurement o f t h e above pa r a m e t e r s a r e : a) t h e e l e c t r o d e s e p a r a t i o n i n t h e s p e c i m e n . c o u l d be measured t o w i t h i n 0.1 mm i n 5.0 mm l o n g , hence - 97 - b) the diameter of the specimen could be measured to within 0.1 mm i n about 9.0 mm, hence 6A = 2JL_-m 2 ^ 1 ) m 0 > Q 2 2 A L 9.0 c) the current passing through the c i r c u i t could be measured to within ha l f a d i v i s i o n i n 30 d i v i s i o n s , hence -Jl 0^. = o 017 I 30 d) the voltage drop across the specimen could be measured to within ha l f a d i v i s i o n i n 30 d i v i s i o n s , hence 6V 0.5 . m _ ~ = 30~~ = ° - ° 1 7 The t o t a l uncertainty i n the e l e c t r i c a l conductivity values i s therefore approximately 0.076 or 7.6% i n error. 3. Density Values The density of the material was determined i n grams/cc. The uncertainties involved i n the density measurement are the weight.and the volume of the material. a) The weight of the material could be obtained to within . 0.001 gram i n 2.500 grams, hence ^W_ = ^ l _ = W 2.500 b) the volume of the material could be determined to within 0.005 cc i n about 0.450 cc, hence V 0.450 u- U J"»-L The t o t a l uncertainty i n the.density values i s therefore approximately =.JSJL + AJL_ = c o n s or 1.2% p W V APPENIDX V " 98 - Cohen's Method for Precise Lattice Parameter Calculation (A) Cohen's Method The precise l a t t i c e parameter of a cubic substance can be.calculated in accordance with the Cohen's method"*"*. If the X-ray diffraction pattern was made with a symmetrical back-reflection focusing camera, the correct extrapolation function is Ad — — = k a) tan a) ^ By squaring the Bragg law and taking logarithms of each side and then differentiating, the following result is obtained: 2 Asin 9 - 2 Ad ... sin^e = d ~ . . . . . . . . . . . ( 2 ) substituting equation (l)into (2), the following is obtained: 2„ „ , , . 2, A sin 9 = - 2 ko> sin 0tano> 2 = - 2 kfl)cos a) tan<() = Do) sin 2<J> (3) Where D is a new constant 2 The true value of sin 9 for any diffraction line is given by the following expression: 2 sin 29 (true) = — ~ — ( h 2+K 2+l 2) (4) 4 a 0 where a O J the true value of the l a t t i c e parameter, is the quantity to be determined, but 2 2 2 sin 9(observed) - sin 6 (true) =Asin 0 . ( 5 ) For each line on.the pattern, by combining equations (3), (4), and ( 5 ) , the following is obtained: 2 2 A 2 2 2 sin 0 (observed) = 5 (h +k +1 ) + Da) sin 2a) 4 at s i n c e s i n ^ G = cos2<|) ~ 99 2 t h e r e f o r e cos <j) = Cot + A6 (6) where C = — ^ 4 a* 2 2 2 a - (h + k + 1 ) A - ° 10 6 = 10(f) s i n 2$ The e x p e r i m e n t a l v a l u e s o f e q u a t i o n ( 6 ) a r e c a l c u l a t e d f o r each o f t h e n b a c k - r e f l e c t i o n l i n e s used '. i n t h e d e t e r m i n a t i o n . The two n o r m a l e q u a t i o n s needed t o f i n d C and A a r e found from e q u a t i o n (6) and a r e g i v e n as f o l l o w s : 2 2 Ea :cos <(> = C. Ea + AEa6 2 2 E6 cos <J> = C Ea6 +.AE 6 The l a t t i c e p a r a m eter a 0 can t h e r e f o r e be computed from t h e C v a l u e . The v a l u e o f A i s a d r i f t c o n s t a n t w h i c h i s a measure o f t h e t o t a l e r r o r i n v o l v e d i n t h e d e t e r m i n a t i o n . S i n c e Cu K ^ and K^- a r e o f d i f f e r e n t w avelengths,. l i n e s w i l l c o n s e q u e n t l y appear on t h e d i f f r a c t i o n p a t t e r n , a s d o u b l e t s . The w a v e l e n g t h A . v a r i e s f r o m l i n e t o l i n e , whereas i n e q u a t i o n (6)X i s t r e a t e d as a c o n s t a n t . The d a t a must t h e r e f o r e be n o r m a l i z e d t o any w a v e l e n g t h by use o f t h e p r o p e r m u l t i p l y i n g f a c t o r b e f o r e e q u a t i o n (6) can be used f o r c a l c u l a t i o n . The n o r m a l i z i n g f a c t o r f o r a l l l i n e s t o t h e Cu Ka^ w a v e l e n g t h i s g i v e n a s : 2 N o r m a l i z i n g f a c t o r = A_ a 1 ' (1-54051) 0.99505 A K „ (1.54433) - 100 - (B) Determination of the R e f l e c t i n g Planes (hkl) i n the X - r a y D i f f r a c t i o n Photograph 2 2 2 The experimental values of a= (h + k + 1 ) for each set of d i f f r a c t i o n l i n e s i n the p a t t e r n were determined by the f o l l o w i n g formula: 2 2 2 \ 9 9 9 cos cf. = s i n 9 = (h + k + 1 ) 4 at 2 2 2 ct = (h + k + 1 ) = Using Tien and Subbarao's data for a 0 = 5.133 A , the reflecting planes obtained in the present investigation are given in the following Table, (results for Expt. # 2). No. 2 cos <)) a (hkl) 2 27°11.9' 0.79107 35.1=(35) (531) 4 25°32.7' 0.81398 36.1=(36) (442) (600) 6 17°59.9' 0.90451 40.1=(40) (620) 8 9°36.3' 0.97219 43.2=(43) (533) 10 3°28.1' 0.99634 44.2=(44) (622) APPENDIX VI - 101 -. Derivation of the Nernst-Einstien Equation for the. Relationship Between Electrical Conductivity and Diffusion Coefficient (A) Derivation The self-diffusion coefficient of an ion (or defect) i resulting 53 54 from thermal agitation is given by the following expression: ' u. k T d i = -\T- (1) where d. = microscopic diffusion coefficient of ion i l u^ = mobility (drift velocity per unit electric field) Z^  = valence e = electronic charge k = Boltzman's constant T = absolute temperature The conductivity of ion i and its macroscopic diffusion coefficient are given by.: * i = Z i * n i u i ( 2 ) D i = <-TT-> d i • • • • ' • ( 3 ) where a. = electrical conductivity due to motion of ion i l n^ = defect concentration (number of defects/unit vol.) N = concentration of the kind of atoms involved in the defect motion D. = macroscopic diffusion coefficient l Combining equations (1), (2), and (3), the following is obtained: D i = k T (4) a' N (Z ± e) 2 Since the macroscopic tracer diffusion coefficient D, as - 102 - determined from tracer experiments, i s not i d e n t i c a l to the macroscopic i o n i c d i f f u s i o n c o e f f i c i e n t , a c o r r e l a t i o n factor " f " i n d i f f u s i o n i s therefore required, which i s defined as: <5) 1 The conductivity which i s usually measured i s the t o t a l conductivity a, which i s related to the conductivity due to motion of ions. o\ through a transport number t^. The r e l a t i o n i s expressed as : a . = a t (6) I I Combining equations.(4), (5), and (6), the following i s obtained: n f t. k T -5--—^ -2 <-> N (Z. e) l (B) Sample Ca l c u l a t i o n of Oxygen Ion D i f f u s i o n C o e f f i c i e n t s from the E l e c t r i c a l Conductivity Data f ( c o r r e l a t i o n factor for f l u o r i t e structure) = 0.65 t^(transport number for CaO-stabilized ZrO^) = 1 —16 k (Boltzman's constant) = 1.37x10 erg/°K Z (oxygen valence) = 2 3 N (oxygen ions per cm for the Zr. o c Ca_ .. c 0, o c 22 U . O J U . l j l . o j s o l i d solution) = 5.5x10 2 -1 -1 e ( e l e c t r o n i c charge, i f conductivity i s expressed i n ohm -cm the factor 10 must be introduced to convert from the electromagnetic units) ,«9 „ F ,^-40 =. 10 x 2.5 x 10 r. 0. 65x1x1.37xl0" 1 6 = 22" 9 -40 ° T 5.5x10 x4xl0x2.5x10 D =1.62 x l O - 9 a T cm 2-sec _ 1 APPENDIX VII " 1 0 3 " Apparent Porosity and Bulk Density Determination (ASTM-C20-46)57 Apparent Porosity,(P) The apparent porosity expresses as a percentage the relation ship of the volume of the open pores of the specimen to its exterior volume and is calculated as follows: W - D P V x 100% Bulk Density,(B) The bulk density, in grams per cubic-centimeter of a specimen is the quotient of its dry weight divided by the exterior volume, including pores and is calculated as follows: B = W - S Where W = saturated weight S = suspended weight D = dry weight - 104 - APPENDIX VIII True Specific Gravity and True Density Determination (ASTM-C135-47)57 True Specific Gravity The true specific gravity of a refractory material determined by pycnometer bottle is calculated in accordance with the following formula: S p. G r. = ______ (w x - P) - (W- -w) where P = weight of the stoppered-pycnometer W -weight of the stoppered.pycnometer and sample W^= weight of the stoppered pycnometer filled with water W-= weight of the stoppered pycnometer, sample, and water True Density The true density in grams per cubic-centimeter of the sample is calculated in accordance with the following relation: True density = Specific Gravity x density of water APPENDIX IX - 105 - Theoretical Density Calculations of the Ca0-Zr02 So l i d Solutions for the Oxygen Vacancy Model and the Oxygen I n t e r s t i t i a l Model The basic density equation for a cubic s o l i d s o l u t i o n i s expressed as ^ 1.66020 EA P = 3 a where . EA = n ^ + n C a A ^ + n Q A Q n = number of atoms per unit c e l l A = atomic weight a = l a t t i c e parameter of the u n i t - c e l l 4+ 2+ The t o t a l number of cations (Zr and Ca ) per unit c e l l i n the f.c.c. structure i s 8 (-|-) + 6 = 4 The t o t a l number of anions (oxygen ions) per unit c e l l i n the f l u o r i t e structure i s 4 x 2 = 8 Atomic weight.of Zr = 91.22, Ca = 40.08, 0 = 16.00 For the composition 15 mole% CaO + 85 mole% ZrO^ assumed oxygen vacancy model ( Z r0.85 C a0.15 °1.85 > EA = (4. (0.85))x91.22 + (4(0.15))x40.08 + ( 4 ( 1 . 8 5 ) ) x l 6 . 0 0 = (3.4)x91.22 + (0.6)x40.08 + (7.4)xl6.00 =452.596 1.66020 x 452.596 (5.1359) 3 = 5.5465 grams/cc For the same composition assumed oxygen i n t e r s t i t i a l model ( Z r0.85 C a0.15 °2.00 ) ZA = (4(0.85))x91.22 + (4(0.15))x40.08 + (4(2.00))xl6.00 = (3.4)x91.22 + (0.6)x40.08 + (8.00)xl6.00 = 462.196 1.66020 x 462.196 (5.1359) 3 = 5.6642 grams/cc VIII. BIBLIOGRAPHY - 106 - 1. A. E. Van Arkel, Physica, 4__ 286 (1924). 2. 0. Ruff and F. Ebert, Z. auorg. U. allgem. chem.,180, 19 (1929). 3. W. M. Cohn, J . Electrochem. S o c , 68, 65 (1935). 4. R. F; Domagala and D. J . McPherson, J . Metals, 6_; Trans. AIME, 200, 238 (1954). 5. C. T. Lynch, F. W. Vahdiek, and L. B. Robinson, J . Am. Cerm. S o c , 44(3), 147 (1961). 6. B. C. Weber and M. A. Schwartz, Ber. .deut. Keram. Ges., 34, 3.91 (1957). 7. F. A. Mumpton and R. Roy, J . Am. Ceram. S o c , 43(5), 234 (1960). 8. P. Duwez and F. Odell, J . Am. Ceram. S o c , 33, 274 (1950). 9. D. K. Smith and C. F. Cl i n e , J . Am. Ceram. Soc., 45(5), 249 (1962). 10. G. M. Wolten, J. Am. Ceram. S o c , 46(9), 418 (1963). 11. E. Dow Whitney, J . Electrochem. S o c , 112(1), 91 (1965). 12. G. M. Wolten, J . Am. Ceram. S o c , 46(9), 420 (1963). 13. R. F. Ge l l e r and P. J . Yavorsky, J . Research Natl. Bur. Standards, 35(1), 87 (1945); RP 1662; Ceram. Abstr., 24(10), 191 (1945). 14. R. S. Roth, J . Am. Ceram. S o c , 39(7), 196 (1956). 15. P. Duwez, F. Odell, and F. H. Brown, J r . , J . Am. Ceram.. S o c , 35(5), 107 (1952). 16. B. C. Weber, H. J . Garrett, F. A. Mauer, and M. A. Schwartz, J. Am. Ceram. S o c , 39(6), 197 (1956). 17. M. Hoch and Mool-Ray Mathen, J . Am. Ceram. S o c , 45(8), 373 (1962). 18. T. W. Smoot and J . R. Ryan, J . Am. Ceram. Soc,, 46(12), 597 (1963). 19. F. Hund, Z. Physik. Chem., 199, 142 (1952). 20. A. D i e t z e l and H. Tober, Ber. Deut. Keram. Ges., 30(47), 71 (1953). 21. Z. S. Volchenkova and S. F. Pal'guev, Trans. Inst. Electrochem., 1, 97 (1961). 22. T. Y. Tien and E. C. Subbarao, J . Chem. Physics, 39(4), 1041 (1963). 23. A. Cocco, Chim. e.ind. (Miland), 41, 882 (1959). 24. A. M. Diness and Rusturn Roy, S o l i d State Communication, 3^, 123 (1965). 25. W.,D. Kingery, J . Pappis, M. E. Doty, and C. C. H i l l , J. Am. Ceram. S o c , 42(8), 393 (1959). 26. W. C. Hagel, "Oxygen D i f f u s i o n i n Glasses and Oxide Cr y s t a l s " , presented at the Pittsburgh Meeting of the Electrochemical Society, A p r i l 17, 1963; Abstract: J . Electrochem. Soc., 110(3), 63C (1963). 27. L. A. Simpson and R. E. Carter, J . Am. Ceram. Soc., 49(3), 139 (1966). 28. R. J. F r i a u f , J . Appl. Physics, 33(1), 494 (1962). - 107 - 29. John Crank, "Mathematics o f . D i f f u s i o n " , Oxford Univ. Press, N.Y., 1956. 30. R. E. Carter and W. L. Roth, General E l e c t r i c Report.No. 63-R1-3479M, 1963. 31. R. E. Carter and.W. H. Rhode, B u l l . Am. Ceram. Soc., 41, 283 (1962). 32. H. Witzmann, H. H. Molbius and D. Gerlach, Z. Chem., 4(4), 154 (1964). 33. . W. L.Baun and N. T. McDevitt, J . Am. Ceram. S o c , 46(6), 294 (1963). 34. W. L. Baun and.N. T. McDevitt, J . Am. Ceram. S o c , 47(12), 622 (1964). 35. R. J . Dew, J r . , "Damping Capacity of Refractory Oxides Under,Various Stress and Temperature Conditions", Sc. D. Thesis, MIT (1950), unpublished. 36. J . B. Watchman, J r . , W. E. Teft, D. G. Lam, J r . , and R..P. S t i n c h f i e l d , Wright Patterson A i r Development Center Technical Report 59-278 (1959). 37. Roger.Chang, "Mechanical Properties of Engineering Ceramics", edited by W. W. K r i e g e l and H. Palmour I I I , (Interscience Publ.N.Y.,1961),p209. 38. J . B. M ^ i ^ J r . , and W. C. Corwin, J . of Research of Natl. Bur. Standards -A, Physics and Chemistry 69A(5), 457 (1965). 39. K. Kiukkolafc C. Wagner, J. Electrochem. Soc., 104(6), 379 (1957). 40. J . Weissbart and R. Ruka, J . Electrochem. S o c , 109(8). 723 (1962). 41. A. G. Buyers, J . Am. Ceram. S o c , 48(3), 122 (1965). "42. F. Trombe and M. Foex, Compt. Rend., 236, 1783 (1953). 43. J . M. Dixon, L. D. LaGrange, U. Merten, C. F..;,Miller, and J . T. Porter,II, J . Electrochem. Soc,110(4), 276 (1963). 44. A. J . Hathaway, " E f f e c t . o f Oxygen.Vacancies on the E l e c t r i c a l Conductivity of Z i r c o n c i a S o l i d Solutions", M. Sc. Thesis, Niagara University, Niagara F a l l s , N. Y.,( 1962). 45. H. A. Johansen.and J . G. Cleary, J . Electrochem. Soc,111(1), 100 (1964). 46. E. C. Subbarao and P. H. Sutter, J . Phys. Chem. Soli d s , _25, 148 (1964). 47. T. Y. Tien, J. Appl. Physics, 35(1), 122 (1964). 48. J . Weissbart and R. Ruka, Electrochem. Soc. Extended Abstract, #44,Oct. 1961. 49. Hermann.Schmalzried, Z. Elektrochem., 66(7), 572 (1962). 50. C. B. Alcock and B. C. Steele, "Science i n Ceramics", Vol. 2, edited by G. H. Stewart, (Acamdemic Press, Inc., N. Y. 1965), p397. 51. R. W. Vest and N. M. T a l l a n , J . Appl. Physics, 36(2), 543 (1965). 52. F. A. Kroger, J . Am. Ceram. S o c , 49(4), 215 (1966). - 108 - 53. W. D. Kingery, "Introduction to Ceramics", (John Wiley, Inc.,N.Y.,1960),p647. 54. J . Bardeen and C. Herring, "Imperfections i n Nearly Perfect C r y s t a l s " , (John Wiley & Sons., Inc., N. Y., 1952), p261. 55. B. D. C u l l i t y , "Elements of X-ray D i f f r a c t i o n " , (Addison-Wesley Publishing Co., Inc., N. Y., 1956), p340. 56. K. Lark-Horovitz and V. A. Johnson, "Method of Experimental Physics, Vol. 6, part B, S o l i d State Physics", (Academic Press, Inc.,N.Y.,1959),p33. 57. ASTM Standard, part 13, (American Society fro Testing Materials, 1964 e d i t i o n ) , p36 and p39. 58. K. J . L a i d l e r , "Chemical K i n e t i c s " , (McGraw-Hill, Inc.,1965), p7. 59. J. B. Wafeetoaa-, J r . , Physical Review, 13(12), 517 (1963). 60. A. D. Fran k l i n , National Bureau of Standards, as c i t e d by J . B. Watchman, J r . , i n reference (59). 

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