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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 requirements Columbia, for  this  thesis  in p a r t i a l  f o r an a d v a n c e d  degree  at  I agree that  reference  tensive  presenting  the  and s t u d y .  copying of  this  Library I  s h a l l make  for  scholarly  o r by h i s  copying or p u b l i c a t i o n of  cial  not  Department  shall  of  /^Jj?  el  ,  Columbia  /?S7  freely  the  British available  permission for  p u r p o s e s may be  this  thesis  be a l l o w e d w i t h o u t my w r i t t e n  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, C a n a d a Date  it  of  representatives.  understood that gain  University  f u r t h e r agree that  thesis  by t h e Head o f my D e p a r t m e n t  the  f u l f i l m e n t of  for  It  exgranted  is  finan-  permission.  ABSTRACT The cubic fluorite-type solid solution of Z r ^ containing 0  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 i n t e r s t i t i a l oxygen ions from the." lattice or in terms of the inhomogeneous distribution of the CaO in the Zr0 lattice. 2  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 i s 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 i s gratefully acknowledged.  TABLE OF CONTENTS I.  Page 1  INTRODUCTION AND REVIEW OF LITERATURE (A)  Introduction  (B)  Review of Literature  . 1 3  1. Phase-Transformation and Stabilization of Zirconia .. 3 a.  Phase Transformation of Zr0  b.  Stabilization of Zr0  3  2  4  2  2. Crystalline Structure and Relationship of Lattice Parameter With Compositions in the Ca0-Zr0 System .. 7 2  a.  Crystalline Structure  •• 1  b.  Relationship, of Lattice Parameter With Compositions  3. Cation and Anion Diffusion i n the CaO-Zr0  2  a.  Anion.. (Oxygen ton) Diffusion  b.  Cation Diffusion  System •. • • • •  .. 11 '• 11 . 12  4.  Infrared Absorption Spectroscopy of Pure :Zr0 and CaO-stabilized.ZrOy  14  5.  Internal Friction in Zr0 Containing CaO  15  6.  Electrical Conductivity i n the CaOr-Zr0 Solid Solutions . ...........................  19  2  2  2  a.  II.  8  Electrical Conductivity Kinetics ..•  1 9  b. . Ionic Conductivity  20  c.  Electronic, Conductivity  22  d.  Relationship of Electrical Conductivity and Diffusion Coefficient  24  EXPERIMENTAL PROCEDURE (A) Materials and SpeciirtWl, Preparation 1. Materials Preparation  ........ 25 25 25  TABLE OF CONTENTS (cont'd) 2.  Page 25  .  (B)  Phase Identification  (C)  Annealing Procedure  26  (D)  Precise Lattice Parameter Measurement  27  1.  Experimental Procedure  27  2.  Lattice Parameter Calculation  28  ••••  (E)  Infrared Absorption Spectroscopy  (F)  Electrical Conductivity Measurement;.  (G) III.  Specimen Preparation  1.  Specimen Preparation  2.  Apparatus and Equipment  3.  Measurement Procedure  28 .....  ..  .30  (C)  32 33  Ca_ .. _ 0  Q c  X-ray Diffraction .....  . ...  33  .i  2. Infrared Absorption Spectra Precise Lattice Parameter of the Zr ' Solid Solution 1.  29  . . . . .•  Phase Identification of the Zr_  1.  29 29  Solid Solution  (B)  .  Porosity and True Density Measurements  EXPERIMENTAL RESULTS (A)  26  .. .33 35 Ca  o c  CL  c  Q C  ....... 38  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  Electrical Conductivity of the Z r Ca 0 Solid Solution \...... \ .... , \....... . Q  g 5  Q  1  g 5  1.  Electrical Conductivity as a Function of Temperature  46  2.  Calculation of the Oxygen Ion Diffusion Coefficients From Electrical Conductivity Data  53  46  TABLE OF CONTENTS (cont'd) (D)  Porosity and True Density of the Z r Solid Solution  Qg 5  Ca ^  , g  '.  58  1. Apparent Porosity of the Hot-pressed Specimens 2. True Density of the Zr„  o c  (E) IV.  Page  0^ ^  Q  Ca_ , 0. c  o c  .... 58  Solid  solution ;.,?:??.. eo Chemical Analysis of the Hot-pressed Ca0-Zr0 Specimens. 60 2  DISCUSSION (A)  62  Lattice Contraction or Shrinkage of the Cubic Unit Cell in the Z r Ca 0 Solid Solution -., 62 o g 5  (B)  0 - 1 5  Effect of Annealing on the Electrical Properties of the Zr„ Ca_ . _ 0. Solid Solution o c  U . oj  (C)  1 > g 5  i.0  1.  OJ  Effect bf Heat Treatment on the Oxygen Ion Diffusion in the CaO-Zr0 Solid Solution  . 77  2  V. VI. VII.  70  o c  U.  SUMMARY AND CONCLUSIONS  .  .  79  SUGGESTIONS FOR FUTURE WORK  81  APPENDICES  82  APPENDIX I APPENDIX II  : Experimental Data for Precise Lattice Parameter Measurements  82  : 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  : Derivation of the Nernst-Einstein Equation for Diffusion Coefficient Calculation from Electrical Conductivity Data  101  APPENDIX VI  TABLE OF CONTENTS (cont'd) APPENDIX VII : Apparent Porosity and Bulk Density Determination  Page .. 103  APPENDIX VIII : True Density Determination APPENDIX IX  VIII.  BIBLIOGRAPHY  : Theoretical Density Calculation of the CaO-ZrO Solid Solutions for the Oxygen Vacancy Model and the Oxygen Interstitial Model  104  105 106  LIST OF FIGURES No.  Page  1.  Phase equilibrium diagram for the Ca0-Zr0 system  6  2.  Fluorite-type structure of the Ca0-Zr0 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-Zr0 solid solutions ....  10  Infrared absorption spectra of monoclinic ZrO. and CaO-stabilized Zr0 7  16  Schematic diagram of the high temperature conductivity furnace and sample holder  31  2  2  2  5.  2  .6. 7.  electrical  X-ray diffraction patterns of the unreacted and reacted Ca0-Zr0 compositions.  34  Infrared absorption spectra of the monoclinic ZrO partially CaO-stabilized Zr0  36  2  8.  and  2  9.  Infrared absorption spectra of the completely CaO-stabilized Zr0 after heat treatment 2  10.  Typical X-ray diffraction pattern of powdered samples of the Zr_ Ca_ 0 „ solid solution o c  1 C  37 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 Zr0 solid solution after heat treatment  45  Decrease of lattice parameter as a function of annealing time.  47  2  14.  i  15.  Arrhenius  16i  Change of activation energy for electrical conduction with annealing temperature  17.  plot  of electrical conductivity and temperature.  48 49  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. 18.  19. 20. 21. 22. 23.  Page ' Variation of electrical conductivity as measured immediately and after 30-45 minutes of soaking at th,e same temperature  52  Change of electrical conductivity as measured during the heating and.cooling cycles (specimen annealed @900°C)  54  Change of electrical conductivity as measured during the heating and cooling cycles (specimen annealed @1400°C)....  55  Arrhenius plot and temperature  56  of oxygen ion diffusion coefficients  Change of activation energy for oxygen ion diffusion with annealing temperature Comparison  57  between the oxygen ion diffusion coefficient data  in the literature and the present data in the Ca0-Zr02 system 24.  Change of densities  25. 26.  Relative decrease of lattice parameter with annealing time.... Arrhenius plot of-the rate of relative decrease of lattice parameter and temperature  69  Change of excess energy for conduction with annealing temperature  74  27.  . with annealing temperatures  59 61 67  LIST QF TABLES  No. I  Page X-ray diffraction peaks of several compounds in the 27°-33° of 29 values '  33  v  II  Infrared absorption band frequencies of the monoclinic Zr0„ and CaO-stabilized Zr0  III IV  .... 38  2  Chemical analysis of the Ca0-Zr0 solid solutions ............  62  Energies of oxygen vacancy motion the Ca0-Zr0_ system  73  2  and dissociation in  I. (A)  INTRODUCTION AND REVIEW OF LITERATURE  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 has attracted the attention of both 2  the theoretical scientist and the.practical industrialist interested in high^temperature materials. most refractory oxides.  Zirconia (Zr02) is considered as one of the  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 neutron capture cross section. a complex crystal structure.  low  Zirconia also is polymorphic and possesses Thus, extensive research has been done in  studying i t s structure, polymorphism and refractory,properties. The application of pure Zr0 is limited due to the disruptive 2  volume change associated with i t s polymorphic transformation.  However, this  limitation can be.overcome,by the addition of certain foreign oxides with which Zr0 forms solid solutions. 2  (CaO)  The addition of a small amount of Calcia  to Zr0 results in the formation of stabilized.cubic solid solutions 2  which remain stable at temperatures up to 2000°C.  Because of the  stabilization, Zr0 ~based solid solutions have been used as a heat 2  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 h e a t i n g  CaO-ZrC^ c u b i c s o l i d p r o p e r t i e s , and  elements i n h i g h  temperature f u r n a c e s .  s o l u t i o n s a l s o possess r a t h e r unique  as a r e s u l t h a v e . c o n s i d e r a b l e  e l e c t r o l y t e s i n g a l v a n i c and  fuel cells.  usefulness  Electromotive  The  electrical as  solid  f o r c e measurements  on g a l v a n i c 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 v a l u e d  and  accepted  technique f o r o b t a i n i n g u s e f u l  thermodynamic d a t a , p a r t i c u l a r l y f o r the d e t e r m i n a t i o n  of  elevated-  temperature thermodynamic p r o p e r t i e s of m e t a l l i c o x i d e s .  The  solid  s o l u t i o n s 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 g e n e r a l l y custom-made p r o d u c t s . r e p o r t i n g the p r o p e r t i e s of these s o l i d  The  voluminous  literature  s o l u t i o n s , p a r t i c u l a r l y on  the  e l e c t r i c a l p r o p e r t i e s , f r e q u e n t l y show disagreement between workers. inconsistency i s generally inherent and  the t e c h n i q u e used i n p r e p a r a t i o n .  Ca0-Zr02 s o l i d Zr0  2  The  common method f o r  at temperatures between 1300-1400°C and  at low  material  preparing  s o l u t i o n s i s the method of p a r t i a l l y r e a c t i n g CaCO^ and  m a t e r i a l at h i g h e r  and  to the p u r i t y of the s t a r t i n g  This  temperature.  then s i n t e r i n g the  temperatures, f o l l o w e d by a l o n g p e r i o d of The  Ca0-Zr02 c u b i c s o l i d  s o l u t i o n s are  t h e i r e l e c t r i c a l p r o p e r t i e s are s t r u c t u r e s e n s i t i v e .  of specimen p r e p a r a t i o n and  subsequent a n n e a l i n g  may  reacted  annealing  nonstoichiometric  The  temperature  have a b e a r i n g  on  the  defect-structure.  The 1.  purpose of the p r e s e n t  to prepare a 15 mole % CaO  the h o t - p r e s s i n g  investigation is  + 85 mole % ZrO^  two-fold:  cubic s o l i d  s o l u t i o n by  t e c h n i q u e and.to anneal the specimens at v a r i o u s  temperatures;  and 2.  to observe any  change i n the c r y s t a l l i n e s t r u c t u r e and  the  electrical  - 3 conductivity with annealing composition, data  temperature  and t i m e .  The c h o i c e o f t h e  15 m o l e % CaO + 85 m o l e . % ZrO,,, i s d i c t a t e d b y t h e a v a i l a b l e  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 data f o r comparison.  (B)  Review of L i t e r a t u r e  (1).  Phase Transformation a.  Phase  and S t a b i l i z a t i o n o f Z i r c o n i a  Transformation  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 first  r e p o r t e d by Van A r k e l ^  inl924.  Several years  was  l a t e r R u f f and  2 Ebert  definitely  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  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 monoclinic forms.  constants  i n this  and d e n s i t i e s o f b o t h t h e  ( d e n s i t y = 5.68 gm/cc) a n d t e t r a g o n a l ( d e n s i t y = 6.10 gm/cc)  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  hexagonal  3 symmetry r e p o r t e d a decade l a t e r by Cohn r e v e r s i b l e r e a c t i o n of monoclinic Z r 0 observed  to occur  2  has never been c o n f i r m e d .  ^ r f ^  i n t h e r a n g e 1100-1200°C.  tetragonal Zr0 A l l attempts  2  The  has been to s t a b i l i z e  the high-temperature  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 quenching 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 1 9 6 2 , i t was g e n e r a l l y a s s u m e d 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 pure z i r c o n i a could not e x i s t ' ' . Recent d a t a h a v e i n d i c a t e d , h o w e v e r , t h a t a b o v e 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 of Z r 0 i s indeed p o s s i b l e ' 2  The m o n o c l i n i c at a d e f i n i t e  temperature  tetragonal transformation i n zirconia 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 heat  occurs  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 f i r s t 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 trans13  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  -518 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 w i l l form a solid solution with ZrO^ possessing cubic fluorite-type structure. An equal molar mixture of CaO and ZrO^ w i l l form a CaZrO^ compound rather than a solid solution. Duwez et a l 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 i n specimens prepared at 1500°C. Tien and Subbarao the cubic phase boundaries  delineated  by careful X-ray diffraction studies and observed  that the cubic phase existed from 12-13 mole % to 20-23 mole % CaO i n ?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.  Wt. %  8 12 16 20 2U 28 I  2500 2000  \  ^  \ i \  Qcubic t^Zr0 q| s . s .  6  -  n—'—rr  i  1  -  v 2  CaZrO, 1500 U -P cd  U  §•  1000  ,' monocl. / Z r 0 S.S.  EH  2  500  J  +  cubic Zr0 /S.S. 2  ) i i  i i  i  I  i  10 20  i i  1  •  •  1  •  1  1  •  50  kO  30  CaO (mole %) Figure 1. Phase E q u i l i b r i u m Diagram f o r the CaO^-ZrOg system, ( a f t e r Duwez and Odell^)  O ' Figure 2.  Zr or Ca  Fluorite-Type Structure of CaO-Zr0 Cubic S o l i d Solutions, 2  ( a f t e r Kingery53)  " 7~ In spite of these variations in the cubic phase boundaries, the composition of 15 mole % CaO and 85 mole % Zr0 is definitely within 2  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-Zr0 Cubic Solid Solutions 2  a.  Crystal Structure The Ca0-Zr0 solid solutions crystallize with the cubic 2  19 fluorite structure of the space group Fm3m  .  In the fluorite structure  the anions are in simple-cubic packing with half the interstices f i l l e d by cations. This gives rise to a unit c e l l iai which- a space at the. center of the unit c e l l 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 f i l l e d with Zr  and Ca  ions and that  enough oxygen vacancies were ..created to provide charge compensation distributed 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-Zr0 is assumed to be a random substitutional solid 4+ 2+ solution. The Zr ions are randomly replaced by the added Ca ions. 2  - 8 Recently, Diness and Roy  24  reported that there i s evidence  that the predominantly oxygen vacancy model changes to a cation i n t e r s t i t i a l 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 i n t e r s t i t i a l 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 f i r s t 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 model  •§°del  6.0  5.8 col •  al o S)| o  +>  •H CO  5.6  a  -p  CU Q  •H CO  a  CD Q  5.U  _° Calculated (X-ray. data) Pycnometrically.- determined i i I 5.2 10 20 25 15 CaO, Mole % Comparison o f d e n s i t i e s determined by X-ray and pycriometric methods f o r the CaO-ZrCv, c r y s t a l l i n e solutions quenched from 1600°C 1  Figure 3.  "oCalculated (X-ray data) BPycnometricaJLly determined 10  15 20 25 CaO, Mole % Comparison of D e n s i t i e s determined by X-ray and pyconometric methods f o r the CaO-ZrOg c r y s t a l l i n e s o l u t i o n s quenched from l800'€  Change of Densities with CaO Content i n the Ca0-Zr02 S o l i d S o l u t i o n s , a f t e r Annealing at High Temperatures Followed by Quenching. (After Diness and Roy **) 2  10  15  20  10  25  CaO, Mole %  CaO, Mole % a.  ( a f t e r Tien and Subbarao^^)  20  b.  ( a f t e r Hund ) 19  Figure h. Change of L a t t i c e Parameter with CaO Content i n the Ca0-Zr02 Cubic S o l i d 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 and the temperature used in 2  specimen preparation in these ..two studies may account for the different results.  Hund did not report the purity of his Zr0 and used ordinary 2  X-ray diffTactometer techniques, while Tien and Subbarao used 99.9% pure Zr0 and employed the back reflection region of the diffraction on 2  powder samples.  Zr0 of 99.9% purity and back reflection focusing camera 2  were used in the present investigation in order to check these.discrepancies . (3)  Cation and Anion (Oxygen Ion.) Diffusion in the Ca0-Zr0 System 2  a.  Anion (Oxygen Ion' ) Diffusion The oxygen ion mobility in the cubic solid solutions,of CaO25  Zr0 was f i r s t investigated by Kinergy, Pappis, Dotty and H i l l 2  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 Where C = ratio,, of at depth X at time t, 18  0  +  16  o C= 0  ratio of  o  18  rr  73— in the gas,  o + o 16  18  18  D = diffusion coefficient provided there is instantaneous equilibrium at,the solid-gas interface. The oxygen surface exchange coefficient can be defined by the expression:  Where C  s  is the surface ratio of  —  0 o  18  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: _ +0.098 D = 0.018 _ , n  rt1Q  0 > 0 1 5  , -31,200 - 4300, exp ( —• )  2, 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: +0.443 a-- 0.078 _ n  n n a  Q > 0 6 6  , -22,800 - 4400 exp (  .)  , cm/sec  in which the activation energy i s 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 i n i t i a l  studies and reported the following experimental data : D  L  - (Zr in Z r  0 > 8 8  C a ^  0 ^ ) - 2.95x10  D  L  = (Zr i n . Z r  0 > g 4  Ca  0 > 1 6  0^)  D  L  = (Ca in Z r  Q > 8 4  Ca  0 > 1 6  0  ±  3  82 900 exp ( — ^ - )  = 1.97 exp C " ^ 1 0  0 0 0  ^ y = 3.65 exp ( ^ | ^ )  )  2 cm /sec  cm /sec 2  cm /sec 2  ;  - 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 i t s 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. , Ca a  U.OH  ,, 0  n  n  U.  lb  0  . at 1000°Co„ 31  i.04  D_ 2+. Ca =  .--19 10  2. cm /sec  D„ 4+ Zr  10  -17  2 cm /sec  =  In a solid solution of Z ^ ^ g  Ca  2 7 0 > 1 4 2  —8 DQ2- (single crystal @960°C) = 7.8x10 D 2- (polycrystals @1002°C) = 5.9xl0~  cm /sec 8  Q  (4)  2  cm /sec. 2  Infrared Absorption Spectroscopy of Zirconia Infrared absorption spectroscopy is a powerful tool for study-  ing aqueous solutions. But in the past.few years i t s 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 i s lowered i f the unit cell of a,type C oxide  increases i t s dimensions. A linear  - 15 relationship .-. was  obtained from a plot of unit c e l l dimensions and the  peak band frequency. 'Later, they. . .: reported further experimental data on 34  pure ZrO^ and CaO-stabilized ZrC^ strongly in the 800-300 cm  . The monoclinic ZrO^ appeared to,absorb  region and the spectrum has six characteristic  absorption peaks with a broad,band shoulder,at about 620 cm \ Fig. 5A. In the low frequency region, 300-50 cm \ monoclinic Zr0 one at 230 cm  2  as shown in  the spectrum of the  show?s two absorption peaks, one at .270 cm-1  and the other  as shown,in Fig. 5B.  In sharp contrast to the monoclinic Zr0 solid solutions of CaO-stabilized Zr0  2  2  spectrum, the cubic  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-Zr0 in the, 2  low frequency region was quite transparent. This broad band i s , therefore, not contributed by any single Zr0 band or by the CaO band but a band with 2  several frequencies superimposed. This broad band may be considered as a characteristic absorption band for the CaO-stabilized Zr0 . From these 2  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 c e l l .  (5)  Internal,Friction in Zr0  2  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  -1 800  1  1  I  1  '  500 U00 300 Wave number. (cm~l)  700  600.  100 (B)  Lower Frequency Infrared Absorption Spectrum of Monoclinic Z r 0 (Nujol m u l l , C s l p l a t e s ) 2  300  2 8 0 260  2U0  220  200  Wave number.(cm ) -1  100  (C)  I n f r a r e d Absorption Spectrum of Cubic CaO-Stabilized.Zr0 (commercial material) 2  800  700  600  500  Uoo  300  Wave number (dm"*") -  Figure 5 .  Infrared Absorption Spectra of Monoclinic Z r 0 fefter Baun.and McDevitt^ ) 4  2  and CaO-Stabilized Z r 0  2  - 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 f i r s t found by Dew  in commercial  ZrO^ partially stabilized with CaO and i t s existence was confirmed in two 36 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 i t s maximum at about 300 G at 1 kHz;and in.the o  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 i n partially stabilized Zr0  2  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. Accordingly, 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 w i l l cause a preferred distribution so that this oxygen vacancy w i l l make no contribution to the frequency independent electrical conductivity but w i l l 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 C a  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 w i l l 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)  Electrical  a.  Conductivity  Electrical  i n t h e CaO-Zr0  Conductivity  Measured e l e c t r i c a l ionic  Cubic S o l i d  Solutions  Kinetics  conductivity i n oxide  systems i s the,sum o f  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  of excess electrons  and e l e c t r o n - h o l e s .  electrons or electron-holes bution vity  2  Even i f t h e c o n c e n t r a t i o n s o f .  a r e s m a l l , they s t i l l  make a s u b s t a n t i a l c o n t r i -  to the conductivity since their mobility i s high.  can therefore  The t o t a l  " °ion  where a  +  Ye e  F  c  = total  +  ....,....,..(1)  F  conductivity  a. ion  = 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  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 ) . -  CQ>CQ= concentration holes, F  =  the be  total  of the electrons  and e l e c t r o n -  Faraday  Constant i sa large concentration  o f oxygen  f i x e d by c o m p o s i t i o n and independent o f oxygen p r e s s u r e t h e  contribution w i l l  pressure  - 1  respectively.  In a system i n which there  ionic  conducti-  be e x p r e s s e d a s : 0  vacancies  consist  n o t be p r e s s u r e  dependent.  However, as t h e oxygen  i s c h a n g e d t h e r e may b e , a c h a n g e 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 conductivity.  expressed as f o l l o w s 0  2  The f o r m a t i o n 25  of conduction electrons  can then  :  (lattice) = VQ  2 _  +  3g .0 . . + 26 2(g)  '•(2)  2where 0  (lattice)=oxygen  VQ2°2(g) 9  i o n i n a normal l a t t i c e 1  = oxygen.ion vacancy =  o  x  v  £  e  n  = excess  l i b e r a t e d as gas electrons  site  - 20 Similarly electron-holes  one might f i l l  © according ^°2(g)  +  V  0  2  t o . the r e l a t i o n : ° ~(  _=  2  l a t t i c e  The c o n c e n t r a t i o n s . o f are or  therefore  equation f o r equations  = [%]  t h e excess electrons  • (3)  or electron-holes  Assuming that  at thelow concentrations,  t h e mass a c t i o n  ....(4)  2  (  5  )  2[ V 2 - ] a n d [0 ] a r e f i x e d b y t h e c o m p o s i t i o n , t h e n  of electrons  conductivity  expression  association  (2) and (3) c a n be expressed a s :  and e l e c t r o n - h o l e s  [8]  - k  W  = k  x  2  P P^  o  a r e given by:  (6)  2  (7)  0 2  i s then 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)  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 there  b.  •••••••  9  [0 ~]  2  2  concentrations  electronic  2  2  Since  This  +  = [e] P^IVQJLI  k  The t o t a l  )  dependent on t h e oxygen, p r e s s u r e .  i n t e r a c t i o n effects a r esmall  k  i nn o r m a l l y vacant s i t e s and form  i s an appreciable  c o n t r i b u t i o n from t h e  conduction.  Ionic  Conductivity 39  The w o r k s o f Wagner a n d K i u k k o l a electrical  conductivity of thecubic  due e n t i r e l y t o t h e m i g r a t i o n the  solid  have e s t a b l i s h e d  that the  solutions of Ca0-Zr0 i s  o f oxygen i o n v a c a n c i e s .  2  Subsequently,  e l e c t r i c a l , c o n d u c t i v i t y a s a f u n c t i o n o f t e m p e r a t u r e a n d 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 conductivity in the Ca0-Zr02 ceramics was also recently studied by Tien  47  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  a  = electrical conductivity  0  exp( j ~ )  (9)  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 4+ Zr  ion (0.99A) i s approximately 25% larger than the  ° ion (0.78A)., i t is expected that the energy required for an oxygen  - 22 - . ion  2+ Ca, i o n s would be the l a r g e s t , w h i l e t h a t f o r the  to pass between two 4+  case o f two surrounded  Zr  ions,would  by f o u r m e t a l  be the s m a l l e s t .  Each oxygen i o n i s  i o n s 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  c o n t e n t i n c r e a s e s from 13 to 20 Mole %, the p r o b a b i l i t y of h a v i n g  one  Ca  2+  to  i o n as a n e a r e s t neighbour  41% and  the p r o b a b i l i t y of h a v i n g two  an oxygen i o n i n c r e a s e s from 7.7% for  c o n d u c t i o n i n c r e a s e s and,  temperature c.  Ca.  to 17%.  to  energy  the c o n d u c t i v i t y at a g i v e n  content.  Electronic Conductivity e l e c t r o n i c c o n d u c t i v i t y i n an o x i d e system  p r e s s u r e dependent as i n d i c a t e d by  e = .  K  L  P  0  i s oxygen  the f o l l o w i n g two  -1/4  l)  34%  i o n s as n e a r e s t neighbours  T h e r e f o r e , the a c t i v a t i o n  consequently,  d e c r e a s e s w i t h i n c r e a s i n g CaO  The partial  to an.oxygen i o n i n c r e a s e s from 2+  equations:  1/4 2)  2  e = k p 2  0 2  39 K i u k k o l a and Wagner solid  i n t h e i r measurements on g a l v a n i c c e l l s  e l e c t r o l y t e s observed  e l e c t r o l y t e Zr_  o c  Ca»  U.OJ  partial  p r e s s u r e was  .. _ 0  U.1J  '  t h a t the . e l e c t r i c a l 1  was  Q C  virtually  involving  c o n d u c t i v i t y of the c o n s t a n t when the oxygen  1.oj  v a r i e d over a wide l i m i t . from 10^  to 10  2  2  *  48 atmospheres. W e i s s b a r t and Ruk-a r e p o r t e d t h a t the e l e c t r o n i c c o n t r i b u t i o n to the t o t a l c o n d u c t i v i t y i n t h i s system i s perhaps' l e s s than 2%. At -22 5 49 50 p < 10 atmosphere, S c h m a l z r i e d and A l c o c k and S t e e l e observed °2 t h a t the e l e c t r o n i c (n-type) c o n d u c t i o n becomes predominant, w i t h °e "^02 + 1.4  •  Vest and Tallan^"*" found  mole% A l g i v e s r i s e  partial  p r e s s u r e s up  n = 5.8  ±1.0.  to 10  t h a t i n c o r p o r a t i o n of 2 mole % vanadium  to dominant e l e c t r o n i c c o n d u c t i o n a t oxygen. -16  atmosphere, where  PQ  " 2  1  /  n  with  - 23 Very recently, Kroger  52  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„ Ca. , 0.. V 0.85 0.15 1.85 0.15 o r  r  o r  n  u  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  "zr  where  V  0 * — ^  (  C  a  Z r 0 > m V  X  (10)  oc = a Ca ion occupied a Zr ion site with effective double negative charge oxy = An An oxygen vacant • site with effective double positive charge  VQ" (Ca V ) with  m  m = 1 for pairs  Ca"^  Zr  +  Q  m  =.charged free, or associated neutral cluster k , , = P^" ' 1  [ C a  Zr 0 m V  (11)  3  z—  [Ca* ] [V'-] m  m  Zr  He also, considered the quasi chemical reactions which describe the u  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 w i l l 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 pressure of less than  P  -22.5  ' atmosphere in the cubic solid solutions.  rt  2  of CaO-Zr0 . 2  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 i j KT n  (  Z  e  (11)  )  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 a  =  f t-i k T N ( e) 2  Z i  *  (  1  2  )  Electrical conductivity measurement has been proved to be a reliable method of determining the oxygen diffusion coefficients in the , CaO-Zr0  2  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. actual reaction temperature is about 1750°C.  This implied that the  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 1 1  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. gradually withdrawing (D)  This was-done over a period of 30 minutes by  the alumina tube from the hot zone.of the furnace.  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: speci men  w a s  A small portion of each annealed  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 w i l l 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 Both m o n o c l i n i c Z r 0 first  passed  through  a 200  powder i n an a g a t e m o r t a r bromide.  The  agate mortar. prepared  and  2  CaO-stabilized Zr0  mesh s c r e e n and  D i s k s o f a b o u t 1.6  by v a c u u m p r e s s i n g a t a b o u t 1 0 , 0 0 0 p . s . i . .  The  or CaO-Zr0  2  m a t e r i a l i n the KBr.  2  cm  i n KBr.  D u p l i c a t e runs  p e l l e t w e r e made i n e a c h  (F)  Electrical  1.  Specimen,Preparation  circular  10 mm  i n length.  cylindrical Before  pellets  5 mm  ultrasonic d r i l l . leads.  After  platinum paste  s u r f a c e of each  i n diameter, on  3 mm  pellet  fine  deep  sand  and  t h e s u r f a c e o f t h e p e l l e t by  ( P l a t i n u m P a s t e No.  improved the e l e c t r i c a l the specimen.  The  o f e a c h s p e c i m e n w e r e measured by t e n m e a s u r e m e n t s was  m e a s u r e m e n t s was 2.  sample  and  These h o l e s were used t o house the m e a s u r i n g  l e a d w i r e s and  v a l u e over  i n diameter  g r i n d i n g wheel w i t h very  a p a r t were d r i l l e d  of t h i s platinum paste  diameter  with less  a b o u t ±0.1  A p p a r a t u s and The  6082).  The  of  application  c o n t a c t between  the  e l e c t r o d e s e p a r a t i o n and a m i c r o m e t e r and  used f o r c a l c u l a t i o n .  The  an  potential  annealing, these holes were.coated w i t h a t h i n l a y e r  Hanovia l i q u i d  potential  contained  c o n d u c t i v i t y measurements were,  o f a b o u t 10 mm  s m a l l h o l e s j a b o u t , 0 . 0 5 mm  approximately  disks  specimen.  a n n e a l i n g , t h e e n d s and  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 Two  t h i c k were  C o n d u c t i v i t y Measurement  Specimens used i n e l e c t r i c a l right  potassium  f u r t h e r g r i n d i n g i n the 1 mm  Zr0  finer  f o r about 5 minutes b e f o r e d i s p e r s i n g i n  p o w d e r s w e r e t h o r o u g h l y m i x e d by  wt.%  powders were  were then ground to a  i n , d i a m e t e r and  a b o u t 0.5  paper.  2  -  the  average  accuracy  mm.  Equipments  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  the  of  these  - 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 'i  G i•  ID  ;  C  High Temperature E l e c t r i c a l Conductivity Furnace A B C D E F G H I J K L M N  -  D e t a i l s of sample position  - Glo-bar furnace z e d alumina tube - Rpte c r-y sptt a l+ l i10$ thermocouple wires - Helium gas o u tRh let - Helium gas i n l e t - Water Cooling C o i l - 0.02" platinum wires as current leads -- 0.02" platinum wires as p o t e n t i a l leads - Steel-spring c o i l alumina p l a t e s - High-purity Platinum Thin p l a t e s -- R e c r y s t a l l i z e d alumina rod sample - 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  where  I L V A  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'* . The annealed specimens were ground to fine 7  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. (A)  EXPERIMENTAL RESULTS  Phase Identification of the Zr_.  o c  U.oj  Ca- , CL _ Solid Solution c  U.±_>  Q  l.oj  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 ZrO„ (monoclinic) ZrO„ (high-temp, tetragonal) Zr0„ (cubic solid-solution) CaC0„ "(calcite) CaZrO, (orthorhombic)  29  —  28.20 31.58 30.26 30.58 29.36 31.58  100 65 100 100 100 100  (hkl) (111) (111) (111) (111) (104) (220) (022)  The X-ray diffraction pattern for the unreacted mixtures of CaCO^ and Zr0 used in this study showed three diffraction peaks at 2  2 9 = 28.3°, 29.3°, and 31.5°, as shown in Fig. 7A. These peaks were identified as the two prominent monoclinic Zr0 peaks at (111) and (111) 2  and the most,intense peak of CaC0 at (104). 3  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 peaks. 2  This indicated that the Zr0 was not completely stabilized 2  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  - 34 (C)  (A)  (B)  -I  I  I  33 32 • 31  I  30  I  29  j  L  I  28  33 32  27  31  i  30  •  29  '  28  '  27  i  i  i  33  32  31  I  l  30- 29  I  28  L  27  Bragg Angle ( 26 ) i n Degrees (A) Monoclinic Zr0 +CaC0 Mixtures 2  Figure 7.  3  (B) P a r t i a l l y CaO-Stabilized ZrO, '2  (C) Completely CaO-Stabilized ZrO, 2  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. peak at (111).  This peak was identified as the cubic solid solution  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% Zr0 . 2  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. completely CaO-stabilized Zr0  2  The  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  -  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> S t a b i l i z e d Zr0o.  2  and  36  -  Partially  CaO-  - 37 -  s' \  B ^ Sample...Annealed @ 1500°C 2k h r s .  i 900  I  ,  800  I TOO  ,  L  i  600  I 500  S .!  I  U00  300  Wave Number (cm Figure 9.  I n f r a r e d Absorption Spectra of Completely CaO-Stabilized ZrO, A f t e r 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-Zr0 and CaOStabilized Zr0 2  2  Band Frequencies  Compound  Baun & McDevitt monoclinic ZrO,  commercial CaO-stabilized Zr0  -1 ( cm  Present Invest.  740  740  620  600  530  530  460  450  430  420  370  360  470  2  440-455  hot-pressed CaO-Zr0  2  (both CaO-ZrO^, materials are of the same composition 15 mole% CaO + 85 Mole% Zr0 > 2  (B)  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 c e l l of the Zv^ ^ temperature  Ca^ 15 ,°i g5  s o l i d  solution and the annealing  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. A l l <  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: series of samples. specimen.  for three separate  Each series of samples was. obtained from a single,  It is quite evident that the lattice parameter of the cubic  unit c e l l 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. values  However, these_lattice parameter  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 after hot-pressing.  treatment  Cu K,  V 2  (hkl)  9  Figure 10.  Typical  a =  =  X °# °X * a  (533)  (620)  (UU2)  (531)  8U.T  79.9  71-7  6U.3  62.6  86.8  80.7  TX.l  6U.6  62.7  (622)  X-Ray D i f f r a c t i o n P a t t e r n o f Powdered Sample o f Z r  Q  ^  Ca  Q  ^  Solid  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) Figure"-!!.  Decrease  1U00  1500  of L a t t i c e Parameter as a Function of Annealing Temperature  5.1370  5-1360 h  5.1350 H  5.1343  800  900  1000  1100  1200  Annealing ..Temperature Figure_L2L.  1300  lUOO  1500  ( °C)  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  Ca_ , 0..  Q c  c  solid solution, and these values vary widely.  Q c  cubic  For this composition,  25 Kingery et al reported that the lattice parameter is 5.131A. Their J  0  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. Subbarao  22  For the same composition, Tien and  ° 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 at about 1000°G per second.  i  The lattice parameter of the same-composition: o  obtained in the present ..study i s 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 c e l l of the Zr„  o c  Ca  n  ,  c  U.1J  U.OD  0  1  o c  solid solution significantly depends on the heat  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 Zr0 gave a broad band in 2  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 i s a least squares f i t plot which shows a linear relationship between lattice parameter and peak band frequency of the infrared absorption spectra for the Z r  n  o c  U.OJ  Ca_ , 0.. c  U.1J  o c  solid solution.  1.oj  It  is quite evident that the value of the peak band frequency is raised from 440 cm  -1  to 455 cm  -1  o  ° as the lattice parameter is reduced from 5.1369A to  ;  5.1344A. This observation is in accord with the postulation made by Baun 33 and McDevitt  , in which they stated that, as the unit c e l l 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 c e l l 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 c e l l i n the Zr^ g,. Ca  n  ,  c  3.  0.  solid solution after heat treatment.  o c  Effect of Annealing Time on the Lattice Parameter The effect of annealing time on the lattice parameter values  of the Zr_  o c  U.oO  Ca_ , 0.. c  U.lj  o c  solid solution has been studied at 1100°C,  l.oj  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,  i t 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) 1.  Electrical Conductivity of the Zr  Q  g 5  Ca  Q  1 5  Solid Solution  g 5  Electrical Conductivity as a Function of Temperature The electrical conductivity of the Zr  Q g 5  Ca  Q  ^  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 i s 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  O  1  1  • — i  1  1  Sperdm.en-J6.7_annealed.at 1100 °C -.Specii_en..#ii3-3_inealed-.at..l300 C Specime_L_#ii.6...annealed- at. l400°C o  m  A  Specimen #31 annealed at.l500°C  Annealing Time Figure lk.  (hrs.)  Decrease of L a t t i c e Parameter as a Function of Annealing Time.  •  1  1  1  •  r  (°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 o f A c t i v a t i o n Energy f o r E l e c t r i c a l . C o n d u c t i o n With A n n e a l i n g  Temperature.  - 50 This indicates that the electrical conductivity of the Cae*stabilized Zr0 solid solutions significantly depends on i t s thermal history. 2  The over-all electrical conductivity values obtained in the present investigation appeared to be in good agreement with those reported 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 % Zr0 obtained in the present investigation along 2  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)  10 -1  1300  1 2 0 0 i}oo  ispn  -51  -  20Ji  1 0 -2  10 -3  10  -1+  19.  Hund ( 1 9 5 2 ) 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 ) kl.  1 0 6.0  7.0  8.0  9.0 10  10.0  11.0  / T °K  Figure 1 7 - Comparison between the e l e c t r i c a l c o n d u c t i v i t y data from the l i t e r a t u r e and the present data f o r the Zr_  0 c  0.o5 solid solution.  Ca„ ,.- 0 , 0r  0.15 1.85  - 52 T  1  1  1  Measuring Temperature Figure  1  -  1  (°'C)  1 8 . V a r i a t i o n of E l e c t r i c a l Conductivity as Measured Immediately and A f t e r 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 Z r  n o c Ca„ , 0.. c  o c  data for the  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 i s 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  Measuring Temperature ('*C) 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)  1500  u. 1  Figure 20.  Change of E l e c t r i c a l Conductivity as Measured During (Specimen annealed at 1U00 °C )  the Heating and Cooling Cycles.  lUOO 1300 1200 1100 1000 -I-  1  1  900  - 56 -  (°c)  800  TOO  —i—  — r —  1  •  500  600  Annealed % 900°C  O Annealed % 1300°C A Annealed g 1500°C  a cu  .01  OJ V  s o  lQo" -p c cu •H  8  CJ •H CH CH OJ O  o  o  •H CO  Ifi  P.  o_ 9  10  10  0.60  0.70  0.80  1.0.0  0.90  1.1.0  1.20  10 /T°K 3  Figure 21.  Arrhenius "; p l o t and Temperatures.  of Oxygen Ion D i f f u s i o n C o e f f i c i e n t s  - 57 -  1-30  1.20 L  800  900  1000  1100  1200  Annealing Temperature Figure 22.  1300  ikoo  1500  (°C)  Change of A c t i v a t i o n Energy f o r Oxygenlon D i f f u s i o n 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 i s the summary  of experimental results obtained in the present study with the highest and lowest values as boundaries. (D) 1.  Porosity and Density of the Z r _ Ca Q g  Q  ,. 0.^ ,- Solid Solution g  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 determined 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 Z r  Q g  Ca ^ .0^  5  Q  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 i s 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 i n t e r s t i t i a l 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^check whether the annealing  In order to  treatment after hot-pressing has any effect  on the change of the chemical consti tuents ,  chemical analyses for CaO  and Zr0 contents in the sample have been carried out on four specimens. 2  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..  61 5 . TOO  oxygen i n t e r s t i t i a l model 5.650  o o 5.600 bO  -p •H  c R  5.550  oxygen vacancy model Q  0  o-  1  5.500 800  900  1000  1100  1200  1300  ikoo  Annealing Temperature (°C) Figure 2k.  Change of Density with Annealing Temperatures,  1500  - 62 by "Coast Eldr:idge Engineers and Chemists Ltd" i n Vancouver.  The  experimental results are given i n Table I I I . Table III Chemical Analysis of Ca0-Zr02 Solid Solutions Specimen, Annealing Zr0 CaO No. Temp. Time —... „, rrr; z T— ^ Wt.% Mole % Wt. % 2  T T  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.% Accepting this accuracy for analysis, i t appears  for CaO.  that annealing of the  specimens has no s i g n i f i c a n t effect on the change of the chemical 4+ content ( i . e . the amount of [Zr  2+ ] and [Ca  IV. (A)  ] i n the s o l i d solution).  DISCUSSION  L a t t i c e Contraction or Shrinkage of the Cubic Unit C e l l i n the Zr_ Ca- , 0. Solid Solution o c  U.03  c  U.1J  Q C  1.OJ  From the experimental results obtained i n the present i n vestigation, i t i s quite evident that annealing of the Zr^  Ca^ ^  0^  s o l i d solution after hot-pressing has a d e f i n i t e effect on i t s l a t t i c e parameter.  As the annealing temperature was  increased from  800 to 1500°C the l a t t i c e parameter of the s o l i d solution decreased correspondingly i n a l i n e a r . r e l a t i o n . 1100,  1300,  At a constant temperature  of  1400, and 1500°C, the l a 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 i s 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 ZrQ structure 2  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 i s assumed to be completely random and the distribution of CaO in the solid solution i s homogeneous.  The three models that have been  postulated to account for the formation of a homogeneous solid solution are : the cation i n t e r s t i t i a l model, the anion (oxygen) vancancy model, and the oxygen i n t e r s t i t i a l model. In the cation i n t e r s t i t i a l model i t is assumed that the Ca atoms f i r s t enter into the Zr0 lattice without replacing the Zr atoms 2  and : thus become,' :  interstitials.  If this mechanism i s operative the  lattice parameter of the cubic unit c e l l w i l l be slightly larger than the true cubic unit cell and the density of the material w i l l be increased. 24 Diness and Roy  have reported that there i s evidence indicating such  a,solid solution i s 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 i n t e r s t i t i a l solid solution having composition of 15 mole % CaO + 85 mole.% Zr0 would be in the order of about 6.00 2  grams/cc (see Fig. 3). In the anion (oxygen ion) vacancy model i t i s 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 i n t e r s t i t i a l model i t is assumed that the Ca . • atoms enter into the Zr0 lattice by replacing the Zr atoms with the 2  formation of oxygen vacancies and oxygen ion interstitals;  That i s ,  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 Zr0 /W system. If this mechanism is operative 2  the lattice parameter of the cubic unit c e l l 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 i n t e r s t i t i a l 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  U.OJ  Ca  n 1 C  0  U.XJ  o c  solid solution prepared in the present investigation  ±.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 i n t e r s t i t i a l  - 65 solid solution. CaQ ^- 0^  The calculated and measured densities of the Zr^ g,.  solid solution obtained in the present study are in good 2A  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 i n t e r s t i t i a l 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 Zr0 lattice can not be completely disregarded.  2  It is possible that the cubic  phase of Zr0 exists with some areas enriched in CaO and some areas 2  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 CaOZr0 solid solutions was very.small as compared with the dimension of the 2  cubic unit c e l l , (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 i s , 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 solid solutions.  ions upon heat treatment of specimens of the CaO-ZrC^ 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 can.be assumed to be a rate process. following empirical.relation a  The data were found to.fit best the  58 :  o - t a o a  temperature  , = kt  where a = the lattice parameter at time t t  a  Q  = the lattice parameter at time 0 (before annealing)  k  = rate constant  t  = annealing time  When ao-a.t versus t was plotted, f . t a linear relation was obtained, > as shown 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  F i g u r e 25.  (sec.)  R e l a t i v e Decrease o f L a t t i c e Parameter w i t h A n n e a l i n g  Time.  - 68 Using the rate constants, the temperature coefficients for 53 this process can be determined by an Arrhenius relation as follows :  where  k  =  A exp ( ^ j - )  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 i n 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 c e l l could tentatively be interpreted by either of the following two mechanisms: 1.  During the formation of the cubic solid solution of Zr0 with CaO 2  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 c e l l . 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  Zr  On the  0.85 0.15 °1.85 0 Ca  V  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 c e l l . (B)  Effect of Annealing on the Electrical Properties of the Zr_ Ca ,_ 0, Solid Solution. n  o c  The electrical conductivity of the Zr,-,  Q c  U i O j  Ca. , 0, c  U.IJ  o c  cubic 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 i s given for this variation. In the cubic fluorite-type structure each.cation has eight nearest neighbour oxygen.ions.  When Ca atoms diffuse into the ZrQ  2  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 i s 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 f i e l d .  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 NearestNeighbour Model for Th0 containing CaO, which is also a solid solution 2  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 Th0 solid solution containing 1.5 mole % CaO, he 2  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, F r a n k l i n ^ 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-Th0 and CaO-Zr0 solid solutions are of the 2  2  cubic fluorite-type structure and the volume conductivity i s 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-Zr0 system is very nearly the 2  same as that in the Ca0-Th0 system of 0.93 eVj any excess energy observed 2  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-ZrOSystem Annealing Temp erature (°C)  Observed E in conduction (eV)  E for oxygen vacancy motion (eV)  Total E for dissociation (eV)  800  1.14  900  1.07  0.28  1000  1.00  0.14  1100  0.92  0  1200  X.03  0.20  1300  1.04  0.22  1400  1.09  0.32  1500  1.14  0.42  0.93  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 i s necessary to remove a l l i n t e r s t i t i a l oxygen  - 74  -  1.50  E^ = energy f o r motion Eg = energy associated vacancies or with iated  1.40  of oxygen vacancy with c l u s t e r i n g of oxygen i n t e r s t i t i a l oxygen ions with order-disorder t r a n s i t ]  1.10  0.70 800  900  1000  1100  1200  Annealing Temperature Figure 27.  1300  1400  1500  (°C)  Change of Excess Energy f o r 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 i s 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-Th0 system. 2  This  52  postulation was also supported by Kroger model for the Zr„  o c  U.oj  Ca  , 0..  n  c  o c  V_  U . i j l.oj  in his propsed imperfection  solid solution:.  He maintained  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 ,i suggests that the majority of these 2  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, 46 38 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^ 0 ° 1 8 0 -'s0  id  2  which had been annealed at  1000°C  and that these superlattice lines dis<-  appeared when the specimens were reheated to that at temperatures below  1100°C,  solution  1400°C.  They also observed  those specimens heated at  a lower conductivity than those heated at  1400°C.  Beyond  1000°C  1100°C,  exhibited  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 plotfetsw^a straight line with a displacement of the curve to a higher conductivity at lower.temperatures and joined the f i r s t 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-Zr0 solid 2  solutions.  For Zr0 solid solutions containing 13 mole % or 16 mole % 2  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  V  5  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 Th0 solid solution containing 1.5 mole % CaO. 2  In view of the precious observations, i t is apparent that the oxygen vacancies and the substitutional Ca ions in.the CaO-Zr0 solid 2  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-Zr0 Cubic Solid Solution 2  The oxygen.ion diffusion coefficients calculated from the electrical conductivity data for the Zrg g5 ^ 0 15 ^1 85 ^^-^ solution a  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 » migration by way of the free vacancy centers m Zr  VQ  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-Zr0  2  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 i s 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, i f 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 % Zr0  o  (Zr_  Q c  Ca  n  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 CaOstabilized Zr0_ solid solution shifted depending on the heat treatment of the specimen.  6. The lattice contraction or shrinkage of the unit c e l l in the CaO-ZrO. solid solution was attributed to the removal of i n t e r s t i t i a l oxygen ions from the lattice or possibly  related..  to the existence of the  inhomogeneous distribution of Ca ions i n the solid solution. 7.  In the temperature range 500-1400°C, the electrical conductivity can -E be represented by an Arrhenius-type expression a = a  0  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 i s 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 ZrO would be 2  of interest to investigate using the reactive hot-pressing process for specimen preparation.  VII.  APPENDICES -  82 -  1  TABLE 1  APPENDIX I  Lattice Parameter-Annealing Temperature Data of the  Three  Separate Series of Samples  Annealing Expt.No.  Specimen No.  4 5  Temperatui e (°C)  Time (hrs.)  Lattice Parameter (A)  30  800  1  5.1369  it  1100  14  5.1361  6  M  1400  14  5.1354  7  II  1500  14  5.1346  17  29  800  1  5.1358  it  1200  17  5.1353  19  II  1300  24  5.1352  20  II  1400  10  5.135.1  42  73  800  1  5.1360  •>. 43  II  900  24  5.1358  44  II  1150  24  5.1355  45  II  1300  24  5.1353  1500  24  5.1350  18  46  it  APPENDIX I  TABLE 2 Lattice Parameter - Annealing Temperature Data of Most Measured Samples 0  Lattice Parsimeter  Annealing Temperatui e Time  Specimen No.  Measured  I  Mean  (A)  Mean  Standard  Values.  Values  Deviation  Deviation  29  5.1358  5.1363  -0.0005  + 0.0004  it  30  5.1369  +0.0006  M  31  5^1359  -0.0004  41  5.1365  +0.0002  43  5.1359  -0.0004  46  5.1363  52  5.1368  +0.0005  73  5.1360  -0.0003  14  30  5.1361  24  63  5.1354  17  29  5.1356  24  51  5.1357  24  57  5.1356  24  73  5.1355  24  29  5.1352  21  43  5.1353  +0.0001  24  51  5.1349  -0.0003  24  59  5.1353  +0.0001  24  73  5.1353  +0.0001  25  31  5.1344  24  40  5.1354  +0.0005  24  41  5.1344  -0.0005  24  65  5.1352  +0.0003  14 25 24 26 74  30 46 51 72 73  5.1346 5.1351 5.1350 5.1352 5.1350  (hrs.)  (°C) 800  1  II  II  II  II  it  1100 11  1200 II  II  II  1300 II  II  II  it  1400 II  II  II  1500 ii  ti ii II  .  0  5.1356  +0.0005  + 0.0004  -0.0002 5.1356  0  + 0.00002  +0.0001 0 -0.0001 5.1352  5.1349  5.1350  0  -0.0005  -0.0004 +0.0001 0 +0.0003 0  + 0.0001  + 0.0005  + 0.0002  APPENDIX I  - 84 -  TABLE 3  Lattice Parameter and Peak Band Frequency of the Infrared Absorption Spectra of the CaO-Stabilized ZrO.  Annealing  Specimen No.  Lattice  Temperatur< >, Time (°C)  31 30  0  Band Frequency (cm  800  1  5.1359 ( A )  445  II  1  5.1369  440  ii  41  (hrs.)  Parameter  1  5.1365  442'  II  1  5.1359  . 445  II  25  5.1359  444  60  900  25  5.1356  446  62  1000  25  5.1354  448  63  1100  25  5.1354  448  1200  24  5.1355  447  1300  24  5.1353  449  24  5.1353  449  15  5.1348  453  43 56  57 43 59  ,  II  31  1400  31  it  25  5.1344  455  30  1500  14  5.1346  454  51  II  24  5.1350  452  )  APPENDIX I  TABLE 4  - 85 -  Lattice Parameter - Annealing Time Data of Four Separate Series of Samples  Annealing Expt. No.  Specimen No.  Lattice Temperatui e  Time  Parameter 0  (°C)  (hrs.)  (  A  )  10 annealir g  o  5.1361  1100  5  5.1360  II  it  12  5.1358  II  II  21  5.1358  II  ii  48  5.1358  II  ti  69  5.1359  21  43  800  1  5.1359  22  II  1300  5  5.1355  23  f1  "  16  5.1355  24  If  21  5.1356  25  II  40  5.1356  26  II  61  5.1356  68  5.1355  800  1  5.1357  1400  59 60 61 62 63 64  27 28 29  67 II  "  11  46  4  5.1351  II  10  5.1350  II  14  5.1349  II  20  5.1345  33  II  25  5;1345  56  II  40  5.1345  30 31 32  II  II  "  65  5.1345  11  31  800  1  5.1359  12  it  1500  5  5.1352  13  II  10  5.1349  15  5.1348  II  20  5.1346  II  25  5,1344  57  ri  44  5.1344  58  ii  64  5.1344  55  14 15 16  II  "  APPENDIX I  TABLE  5  -86-  Relative Decrease o f L a t t i c e Parameter with Annealing Time  Lattice Specimen remperature  67  43  40  31  I  (A) 1100  1300  1400  1500  Tilme  Parameter 0  No.  Annea l i n g (hrs.) Jsec) xlO (  a  0  - a  Slope (k) fc  lO" *  a« xlD  • •.  5.1361  0  0  0  5.1360  5  1.80  0.1947  5.1358  12  4.32  0.5841  5.1358  21  7.56  0.5841.  5.1359  0  0  5.1356  5  1.80  0.5841  5.1355  16  5.76  0.7788  5.1355  21  7.56  0.7788  5.1357  0  0  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  5.1359  0  0  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  0  0  0  -1 (sec2.86  4.72  14.50  21.00  )  APPENDIX II  TABLE  1  _  8 7  Electrical Conductivity - Temperature Data Obtained at Equilibrated Temperatures During the Heating Cycle  El ectrical Conductivity (ohm •1-cm-1, )  Bulk Poro- /AnnealDensity sity ing Spec, Temp. (gm/cc) (%) No. (°C)  500°C  700°C  900°C  1100°C  1300°C  1400°C  61  4.466  17.0  800  •5 1.54x10" 2.84xl0~ I.83xl0  -3  •2 •2 •1 1.95x10" 7.66x10" 1.60x10"  58  4.478  19.1  900  •5 3.92x10" 4.23xl0 1.62xl0  -3  •2 •2 •1 1.17x10" 3.73x10" 0.70x10"  64  4.489  19.4  1000  •5 2.96x10" 5.53xl0~  -3  •2 •2 •1 3.olxl0" 6.12x10" 0.84x10"  66  4.504  18.8  1100  •5 .44x10" 6.75xl0" .65xl0  -3  •2 •2 •1 0.51x10" 3.92x10" 0.16x10"  69  4.429  18.8  1200  •5 .55x10" 1.34xl0~ ' .50xl0  -3  2 2 -1 1.68x10" 5.42x1-" 1.36x10"  70  4.500  18.3  1300  •5 •2 2 .98x10" 6.93xl0 i .70xl0~ 1.38x10" 5.70x10" 1.32x10"•1  74  i.593  17.8  1400  71  4.650  17.1  •5 1500 . .95x10" 1.32xl0" ] .13xl0  4  -4  .20xl0  4  5  4  _4  •  3  •5 2 1 •1 .74x10" 6.01xl0" f .22xl0" 4.37x10" ..48x10" 1.23x10" 4  3  3  -2  2 1 •1 3.38x10" ..65x10" 2.62x10"  APPENDIX I I  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 B e f o r e and A f t e r Soaking a t the Same Temperature  Spec. Anneal- •Soaking ing No. Temp. (°C) 61  800  1200  4  -3  1300  - 2  7 .66x10" 1.60x10"  1  2  2  1  2  3 . 9 2 x l 0 " 0.67x10"  2  3 . 7 2 x l 0 ~ 0.69x10"  3.23xl0  - 2  8 . 7 7 x l 0 " 0.77x10"  3.olxlO  - 2  6 . 1 2 x l 0 " 3.84x10"  - 2  1 .OOxlO" 3.16x10"  L.31xl0~  -5 -4 1.65xl0" 0.51xl0" 1. 44x10" 0 .67x10" 3  2  2  2  2  2  2  1.OlxlO  - 2  3.16x10"  1 1 1 1 1 1  - 2  2.01xl0  - 2  •1 5 . 5 0 x l 0 " L.34x10"  -4 •5 7.50xl0 1. 55x10" L .34x10"  - 3  L.68xl0  - 2  •1 5 • 4 2 x l 0 " L.36x10"  -5 -3 8.00xl0 b e f o r e 1. 76x10" L .43x10"  - 3  L.37xl0  - 2  -3 6.70xl0" L . 3 8 x l 0 1. 98x10"" D .67x10' 5  3  - 2  1400  •5 -3 6.47xl0 b e f o r e 4. 42x10" 0.50x10"  1500  -3 •5 -3 4.37xl0~ 2. 74x10" 3 .60x10" 6.22x10 -3 -5 1 . 1 8 x l 0 3.57xl0~ b e f o r e 1. 65x10" L .32x10"  - 3  4.54xl0  after  -2 -5 1.13xl0 1. 91x10" L .32x10"  - 2  3.38xl0"  2  2  6 . 4 7 x l 0 " L.44x10" 2  1  •1 5 . 7 0 x l 0 " L.32xl-" 2  1.81xl0  _ 1  •1 3.06x10"  2  1.48xl0  - 1  •1 L.23x10"  2  1.59xl0  - 1  •1 2.82x10"  2  1.65xl0  - 1  •1 2.62x10"  - 2  - 2  1  1400 °C  1300 °C  after  71  )  7 . 7 6 x l 0 " 1.55x10"  3  •5 2. 96x10" 5 .53x10"" ( ».20xl0  -Is  2  •4 •5 3.62xl0~ L.17xl0" 0. 92x10" 4 .23x10" - 3  -cm  -5 -4 1.42xl0 b e f o r e 1. 20x10" L .42x10"  after 74  - 3  3  after 70  3  •5 -4 1.71xlO" 0 . 5 2 x l 0 b e f o r e 0. 95x10" D.98x10"  1100  after 69  •5 •4 2.83x10" L . 9 5 x l 0 1. 54x10" 2 .84x10"  •4 •5 5.98xl0 b e f o r e 2. 79x10" 5 .08x10" after  66  1100 °C  900 °C  •5 •4 3.68xl0 b e f o r e 0. 87x10" 4 .32x10"  900  1000  700 °C  3  after 64  500 °C  (ohm ^  •4 •5 2.89xl0" L.92xl0" b e f o r e 1. 39x10" 2 .79x10" after  58  E l e c t r i c a l Conductivity  APPENDIX II  TABLE 3  - 89 -  Electrical,Conductivity - Temperature Data With Measurements ;  Made During the Heating and Cooling Cycles Anneal' ing Spec Temp. Cycle No; (°C)  61  58  64  66  69  70  800  900  1000  1100  1200  1300  Electrical Conductivity (ohm ^ - cm 500 °C  1400  1500  1300 °G  1400 °C  •5 I.84x10  2.83x10  Coplin 1.99x10  •5 3.76x10"  6.96x10' >.46xl0  •2 8.51x10-21.60x10-1  Heatin 0.92x10  •5 +.23x10"  3.62x10' L.17x10  •2 3.73x10  Coolin 1.71x10  -5 3.71x10"  7.43x10' 3.20x10  -2 4.90x10-23.70x10-1  Heatin 2.96x10  •5 5.53xlO  6.20x10' 3.01x10  -1 •2 6.12x10-2 "jb.84kl0  Coolin 0.53x10  •5 3.26x10"  4.74x10' D.82x10  r  •2  •2  -2 -1 7.66x10 L.60x10  t  -1 D.70x10  -2 -1 ,73x10 3.84x10  Cooling^ .20x10  •5 i.40x10"  Heating 1 .55x10  •5 L.34x10"  7.50x10' L.68x10  -2 5.42x10 tL.36xlO !  Coolingl .21x10  •5 L.40x10"  7.60x10' L.72x10  -2 -1: 5.94x10 1.36x10  i.93xl0"  6.70x10' L.38x10  -1 -2 5.70x10 1.32x10  L.61x10"  6.64x10' L.30x10  -2 5.20x10 1.32x10-1  •5 j.01x10"  6.22x10' 4.37x10  1.48x10-11.23x10-1  >.85x10"  5.47x10' 3.85x10  -1 -1 0.89x10 1.23x10  L.32x10"  1.13x10' 3.38x10  -1 -1 1.65x10 2.62x10  -5 Cooling 1 20x10 L.39x10"  0.86x10' 2.61x10  -1 1.24xl0u 2.62x10  Heating 1 .98x10  Heati :ing 2 .74x10  Heatin 1.95x10  •5  L.95x10  -1 -2,: -2 1.65x10' ).51x10 3.16x10 ro.9ixio -1 -2 2.58x10' ).50x10 1.01x10 3.16x10  Heatin 1.44x10  Coolin 0.50x10 71  1100 °C  Heating 1 54x10  Coolingjl .57x10 74  700 °C . 900 °C  ).67x10"  •5 •5  •5 -5  -1  1  APPENDIX II  TABLE  4  - 90 - ,  Activation Energies for Electrical Conduction and for Oxygen Ion Diffusion  in the Zr„  Q C  U.OJ  Ca n  c  0.  Q C  Solid Solution  U . l j l.o_>  Aptivation Energy for for Conduction (eV) Oxygen ion Diffusion Heating Cooling (eV)  Activation Energy Specimen No.  Annealing Temperatur( , Time (hrs.) (°C)  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  - 91 -  TABLE 5  APPENDIX II  Summary of Lattice Parameter, Electrical Conductivity, Activation Energy for Electrical.Conduction, and Method of Specimen Preparation of the Zr_ Ca_ , 0. Solid solution as .  j  ,  _,  o c  T  U.oO  Reported in the Literature  c  U.l_>  o c  l.OO  Electrical ActivaConductivity tion Parameter at 1000 °C Energy o (ohm - cm ^) (A) (eV) Lattice  Author  Hund  19  -3 2.2x10  41 Trombe & Foex.  4.0x10  Volechenkova,& 21  -3 2.7x10  Pal guev  21  2.3x10-2  1.21  Hathaway  Calcined ZrO. and CaC0„ mixtures at 1300 °C, then sintered at 2000 °C for 7 hours.  -2 5.0x10  1.17  Reacted 4.25 mole Zirconyl Chloride and 0.82 mole CaCl„ , precipitated solution and calcined at 870 °C for 3 hours.  2.0x10-2  1.30  Hot-pressed r0„ and CaCO. mixtures at 1400 °C and 3000-5000 psi pressure.  5.133  3.3x10-2  1.17  Calcined ZrO and CaCOmixtures at 1350 °C for 24 hours, then sintered at 2000 °C for 2 hours followed by one week annealing at 1400 °C.  5.135  -2 2.0x10  1.14  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  -2 2.6x10  20  43  Tien & Subbarao  Present study  22  Calcined ZrO. and CaCOmixtures at 1200 °C for 2 hours, then sintered at 1460 °C for 5 hours .  1.26  5.131  4 2  Dixon et a l .  Preparation  Calcined ZrO and CaCO, mixtures at 1300 °C.  Kingery et a l .  Rhodes & Carter  Method of Specimen  z  for  24 h o u r s .  APPENDIX  II  TABLE 6  Oxygen Ion Diffusion Coefficients Calculated from the Electrical Conductivity Data.  men No.  Anneal ing Temp. (°C)  500  61  800  92x10"  58  900  64  •11 8.68xl0 1000 3.69x10"  66  Speci  Diffusion Coefficients  -•  0  C  11  700 °C  900 °C  , 2 (cm - sec 1100 °C  1300 °C  4.46xl0 ° 5.38xl0~ 4.33xl0" _1  •11 15x10" 6.64xl0"  9  1G  8  6.88xl0" 2.60xl0" 9  1400  0  C  7 7 1 .95x10" 4 .34x10"  8  7 7 0 .95x10" 1 .89x10"  -8  6.68xl0  -8  7 7 1 .56x10" 2 .29x10"  •11 1100 L.80x10" 1.06xl0 ° 0.31xl0  -8  1 .14xl0  -8  7 7 0 .23x10" 0 .44x10"  69  •11 2.10xl0 1200 L.94x10"  1.42xl0  -8  3 .73xl0  -8  7 7 1 .38x10" 3.68x10"  70  •11 1.09xl0" 1300 2.47x10"  1.27xl0  -8  3 .06xl0  -8  7 7 1 .45x10" 3 .58x10"  74  •11 0.94xl0 1400 3.42x10"  1.18xl0" 9 .70xl0"  71  •11 2.07xl0~ 1500 2.38x10"  -10  1.18xl0  _1  -9  9  -9  9  8  2.15xl0" 7 •52xl0 8  8  7 7 3 .77x10" 3 .33x10"  -8  7 7 4 .40x10" 7.10x10"  APPENDIX III  TABLE  1  -11 -  Apparent Porosity and Bulk Density of the Hot-pressed Specimens  Annealing Specimen No.  *  Temperature(°C)  Time (hrs.)  Bulk Density (gm/cc) Before Heat Treatment  Apparent Porosity (%)  After Heat Before Heat After Heat Treatment  Treatment  Treatment  16.6  51  800  1  4.641  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  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  53  900 + 1400  24 + 22  55  1100 +  20 +  4.530  17.9  4.650 4.454  4.420  17.1 20.2  19.8  15.7 4.600 19.0 4.661 Besides annealing, these specimens had been heated from 500 °G to 1400 °C for about,16 hours in electrical conductivity measurements. 1400  ?n  APPENDIX III  TABLE 2 True Density of the Z r  Ca.  nQ C  n c  U. O J  - 94 0.  o c  Solid Solution  U . i j 1.OJ  Determined by the Pycnometric Method Using Distilled Water  Annealing Specimen Temp. Time No.  C) c  (hrs.)  True Density (grams/cc) Measured values  Mean value  Deviation from mean  Standard deviation  >  56 • . 800 ..  60  900  26  25  5.635  5.588  5.619  +0.031  5.553  -0.035  5.548  -0.040  5.596  5.563  5.530  63  57  59  65  72  1000  1100  1200  1300  1400  1500  25  24  24  24  25  24  5.542  +0.033  5.534  +0.008 +0.001  5.525  -0.009 5.545  +0.030  5.570  +0.025  5.524  -0.021  5.514  -0.031  5.583  5.566  +0.017  5.563  -0.003  5.552  -0.014  5.558  5.534  +0.020  5.533  -0.001  5.512  -0.022  5.609  5.545  +0.064  5.560  +0.015  5.554  +0.009  5.457  -0.088  5.592  - 0.026  -0.033  5.535  5.575  - 0.038  0  5.563  62  +0.047  5.551  +0.041  5.597  +0.046  5.510  +0.041  5.503  -0.048  - 0.007  - 0.027  - 0.013  - 0.017  - 0.041  - 0.044  APPENDIX III  TABLE  3  - 95 -  Theoretical Density Calculations from X-ray Data Assuming Oxygen Vacancy Model (Zr-,  o c  U .OJ  Ca_  1 C  Oxygen Interstitial Model (Zr Annealing Specimen No. •  Temp. (°C)  Lattice  Volume of  Parameter  Unit Cell  0  0  3  U .  n  0. ) and  1J  o c  1. O  J  Ca ., 0_ n  n n  )  Theoretical Density (gm/cc) Oxygen Vacancy Model  (A)  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 Estimation  1. L a t t i c e P a r a m e t e r  IV  - 96 -  of Error  Values  The l a t t i c e p a r a m e t e r v a l u e s o b t a i n e d calculated  according  t o Cohen's method,  ( s e e APPENDIX  complexity of 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 i n each step.  However, an e s t i m a t e . o f  computer p r i n t e d r e s u l t s . diffracted 0.05 mm  were c a l c u l a t e d u s i n g v a l u e s was a b o u t total  systematic  e r r o r has been o b t a i n e d  subtraction  0.0001 A. The d r i f t  0.0003 f o r a l l c o m p u t a t i o n s *•. Conductivity  Now  taking  error  the natural  through the  one w i t h  o f 0.05 mm  addition of  to a l l  readings,  The v a r i a t i o n o f p r i n t e d  c o n s t a n t w h i c h i s a measure o f the  i n the determination  varied  f r o m 0.0001 t o  . . Values  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 were c a l c u l a t e d a c c o r d i n g  uncertainty  the positions of the  t h e same c o m p u t e r programme.  error involved  2. E l e c t r i c a l  V ) . Because of the  Thus two s e t s o f d a t a ,  t o a l l r e a d i n g s and one w i t h  study.were  to determine the  The a c c u r a c y o f r e a d i n g  l i n e s was - 0.05 mm.  i n this  to the f o l l o w i n g equation:  logarithms  in.this  study  ( s e e p a g e 32 o f t h i 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  thesis)  the t o t a l  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  a The p o s s i b l e u n c e r t a i n t i e s  . 6 A  ~ ~ L ~  involved  +  A  . +  6 1. I  +  6 V V  i n t h e measurement o f t h e above p a r a m e t e r s  are: a) t h e e l e c t r o d e w i t h i n 0.1 mm  separation i n 5.0 mm  i n t h e s p e c i m e n . c o u l d be measured t o long,  hence  - 97 b)  the diameter o f the specimen c o u l d be measured t o w i t h i n 0.1 mm i n about 9.0 mm,  hence 6A A  c) the c u r r e n t p a s s i n g half  2JL_L  =  a d i v i s i o n i n 30 d i v i s i o n s , 0^.  I the v o l t a g e half  t o t a l uncertainty  >  Q  2  2  =  hence  o 017  the specimen c o u l d be measured t o w i t h i n  a d i v i s i o n i n 30 d i v i s i o n s , 6V  The  0  30  drop a c r o s s  ~  m  through the c i r c u i t c o u l d be measured to w i t h i n  -Jl  d)  2^1) 9.0  m  0.5 30~~  =  =  hence  . _ °-° m  1 7  i n 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  i s therefore  a p p r o x i m a t e l y 0.076 o r 7.6% i n e r r o r . 3.  Density  Values The  The  d e n s i t y o f the m a t e r i a l was determined i n grams/cc.  u n c e r t a i n t i e s i n v o l v e d i n the d e n s i t y measurement a r e t h e weight.and  the volume o f the m a t e r i a l . a)  The weight o f the m a t e r i a l c o u l d be o b t a i n e d  to w i t h i n .  0.001 gram i n 2.500 grams, hence ^W_ W b)  =  ^  l _ 2.500  =  the volume o f the m a t e r i a l c o u l d be determined to w i t h i n 0.005 c c i n about 0.450 c c , hence  V  The  t o t a l uncertainty  0.450  i n the.density  p  u  values  =.JSJL W  +  - "»-L U J  i s therefore  AJL_ V  =  approximately  c o n s o r 1.2%  APPENIDX V  " 98 -  Cohen's Method for Precise L a t t i c e Parameter Calculation (A)  Cohen's Method The precise l a t t i c e parameter of a cubic substance can  be.calculated i n accordance with the Cohen's method"*"*. If the X-ray d i f f r a c t i o n pattern was  made with a  symmetrical back-reflection focusing camera, the correct extrapolation function i s Ad — — By squaring  ^  = k a) tan a) the Bragg law and taking logarithms  of each  side and then d i f f e r e n t i a t i n g , the following r e s u l t i s obtained: Asin  2  sin^e  9  =  - 2 Ad  substituting equation 2„ A sin 9  ...  ...........(2)  d~  (l)into  (2), the following i s obtained:  „ , , . 2, = - 2 ko> s i n 0tano> 2 = - 2 kfl)cos a) tan<() =  Where D i s a new  Do) s i n 2<J>  (3)  constant 2  The true value of s i n 9 for any d i f f r a c t i o n l i n e i s given by the following  expression: sin 9 2  2 (true) = — ~ — ( 4 a  h +K +l ) 2  2  (4)  2  0  where a  O J  the true value of the l a t t i c e parameter, i s the  quantity to be determined, but 2  2  2  s i n 9(observed) - s i n 6 (true) =Asin 0  .(5)  For each l i n e on.the pattern, by combining equations (3), (4), and  ( 5 ) , the following i s obtained: 2 2 A s i n 0 (observed) = 5 4 at  2  2  2  (h +k +1 ) + Da) s i n 2a)  s i n c e s i n ^ G = cos <|)  ~  2  99  2 t h e r e f o r e cos where  C =  —  a -  (h  A6 The  <j) = Cot + A6  (6)  ^ a*  4 2  2  + k  + 1  2  )  ° 10 = 10(f) s i n 2$  experimental values of equation(6) are c a l c u l a t e d  e a c h 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 u s e d '. i n t h e The  two  normal equations  and  a r e g i v e n as  needed t o f i n d  E6  C v a l u e . The error  cos  2  <J>  The  from l i n e  is  +.AE  6  (6)  2  t h e r e f o r e be  computed from  c o n s t a n t which i s a measure of the  K^-  a r e of d i f f e r e n t wavelengths,. l i n e s  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  to l i n e , whereas i n e q u a t i o n  factor before The  from equation  + AEa6  can  0  d a t a m u s t t h e r e f o r e be n o r m a l i z e d  multiplying  A are found  the total  determination.  S i n c e Cu K ^ and  A.varies  = C Ea6  v a l u e of A i s a d r i f t  a p p e a r on  2  = C. Ea  l a t t i c e parameter a  i n v o l v e d i n the  consequently  determination.  follows: 2 Ea :cos <(>  The  C and  for  equation  c a n be u s e d f o r  for a l l lines  given as:  wavelength  i s t r e a t e d as a  t o any w a v e l e n g t h by u s e  (6)  normalizing factor  (6)X  constant.  of the  A  _ A  ' K „ a 1  proper  calculation.  t o t h e Cu K a ^  wavelength  2 Normalizing factor =  will  (1-54051) (1.54433)  0.99505  - 100 (B)  D e t e r m i n a t i o n o f the R e f l e c t i n g Photograph  Planes  ( h k l ) i n the X - r a y D i f f r a c t i o n  2 The diffraction  experimental values  of  a=  (h  2 + k  2 + 1 ) f o r each s e t o f  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 f o r m u l a :  2 2 cos cf. = s i n 9 =  \  2 (h  4 at  9  9  9  + k + 1 )  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). 2 cos <))  No.  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)  - 101 -.  APPENDIX VI  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 from thermal agitation is given by the following expression: u. k T i = -\T-  53 54 ' (1)  d  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 i t s macroscopic diffusion coefficient are given by.: * i D  =  i=  Z  i *  n  i  i  u  <-TT->  d  ( 2 )  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 a'  D i  =  N (Z e ) k  T  ±  2  obtained:  (4)  Since the macroscopic tracer diffusion coefficient D, as  - 102 determined from t r a c e r experiments, i s not  i d e n t i c a l to the macroscopic i o n i c  diffusion coefficient, a correlation factor " f " r e q u i r e d , which i s d e f i n e d  -  in diffusion is  therefore  as:  <5) 1  The  c o n d u c t i v i t y which i s u s u a l l y measured i s the  c o n d u c t i v i t y a, which i s r e l a t e d to the c o n d u c t i v i t y due o\  through a transport number t ^ . The  a.=  total  to motion of  r e l a t i o n i s expressed as  :  a t  I  (6) I  Combining e q u a t i o n s . ( 4 ) , n  (5), and  ( 6 ) , the f o l l o w i n g i s o b t a i n e d :  f t. k T  -5--—^2 e) N  (Z. l (B) Sample C a 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 C o n d u c t i v i t y Data f ( c o r r e l a t i o n f a c t o r f o r f l u o r i t e s t r u c t u r e ) = 0.65 t ^ ( t r a n s p o r t number f o r C a O - s t a b i l i z e d k  —16 (Boltzman's c o n s t a n t ) = 1.37x10  Z  (oxygen v a l e n c e ) = 2  N  (oxygen i o n s per solid  e  2  ions.  cm  ZrO^)  <->  =1  erg/°K  3  f o r the Z r . Ca_ .. 0, 22 U.OJ U . l j l.oj s o l u t i o n ) = 5.5x10 o c  c  o c  ( e l e c t r o n i c charge, i f c o n d u c t i v i t y i s expressed i n ohm the f a c t o r 10 must be i n t r o d u c e d to c o n v e r t from the e l e c t r o m a g n e t i c u n i t s ) ,«9 „ ,^-40 =. 10 x 2.5 x 10 F  r.  0. 6 5 x 1 x 1 . 3 7 x l 0 " = 22" 9 -40 5.5x10 x 4 x l 0 x 2 . 5 x 1 0  D =1.62  16  xlO  - 9  a T  cm -sec 2  _ 1  °  T  -1  -cm  -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 relationship of the volume of the open pores of the specimen to i t s exterior volume and is calculated as follows: P  W -D V  x 100%  Bulk Density,(B) The bulk density, in grams per cubic-centimeter of a specimen is the quotient of i t s dry weight divided by the exterior volume, including pores and is calculated as follows: B=  Where  W -S  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:  Sp  where  . . Gr  =  ______  (w  x  - P) - (W- -w)  P = weight of the stoppered-pycnometer W -weight of the stoppered.pycnometer and sample W^= weight of the stoppered pycnometer f i l l e d 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 -  T h e o r e t i c a l D e n s i t y C a l c u l a t i o n s of the  Ca0-Zr02  S o l i d S o l u t i o n s f o r the Oxygen Vacancy Model and the  Oxygen I n t e r s t i t i a l Model  The b a s i c d e n s i t y e q u a t i o n f o r a c u b i c s o l i d  s o l u t i o n i s expressed as  ^  1.66020 EA 3 a  P =  where . EA = n ^  + n  C a  A^  + n  Q  A  Q  n = number of atoms per u n i t  cell  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 c a t i o n s (Zr and Ca ) per u n i t c e l l structure i s 8 (-|-)  + 6  = 4  The t o t a l number of anions (oxygen i o n s ) per u n i t c e l l structure i s 4 x 2  i n the f . c . c .  i n the  fluorite  = 8  Atomic w e i g h t . o f Zr = 91.22, Ca = 40.08, 0 = For  16.00  the c o m p o s i t i o n 15 mole% CaO + 85 mole% ZrO^ assumed oxygen vacancy model ( Z r  0.85  C a  0 . 1 5 °1.85 >  EA = (4. (0.85))x91.22 + (4(0.15))x40.08 +  (4(1.85))xl6.00  = (3.4)x91.22 + (0.6)x40.08 + (7.4)xl6.00 =452.596 1.66020 x 452.596 (5.1359) For  = 5.5465 grams/cc  3  the same c o m p o s i t i o n assumed oxygen i n t e r s t i t i a l ( Z r  Z  0.85  C a  0.15  °2.00  model  )  A = (4(0.85))x91.22 + (4(0.15))x40.08 + ( 4 ( 2 . 0 0 ) ) x l 6 . 0 0 = (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.  - 106 -  BIBLIOGRAPHY  1.  A. E. Van A r k e l , P h y s i c a , 4__ 286  (1924).  2.  0. R u f f and F. E b e r t , Z. auorg. U. a l l g e m . chem.,180,  3.  W. M. Cohn, J . E l e c t r o c h e m . S o c , 68, 65 (1935).  4.  R. F; Domagala and D. J . McPherson, J . M e t a l s , 6_; Trans. AIME, 200, 238 (1954).  5.  C. T. Lynch, F. W. Vahdiek, and L. B. Robinson, J . Am. 4 4 ( 3 ) , 147 (1961).  6.  B. C. Weber and M. A. Schwartz,  7.  F. A. Mumpton and R. Roy, J . Am.  8.  P. Duwez and F. O d e l l , J . Am.  9.  D. K. Smith and C. F. 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