High-Temperature Defect Structure Of Cobalt Doped Alpha-Alumina

PDF

Download

Open document

Flip pages

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content INFORMATION TO USERS This material was produced from a microfilm copy of the original document. While the most advanced technological moans to photograph and reproduce this document have been used, the quelity is heavily dependent upon the quality of the original submitted. The following explanation of techniques is provided to help you understand markings or patterns which may appear on this reproduction. 1. The sign or "target" for pages apparently lacking from the document photographed is "Missing Page Is)". If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting thru an imago and duplicating adjacent pagas to insure you complete continuity. 2. When an image on the film is obliterated with a large round black mark, it is an indication that the photopapher suspected that the copy may have moved during exposure and thus cause a blurred imago. You will find a good image of the page in the adjacent frame. 3. Whan a map, drawing or chart, etc., was part of the material being photographed the photographer followed a definite method in "sectioning" the material. It is customary to begin photoing at the upper left hand corner of a large diset and to continue photoing from left to right in equal sections with a small overlap. If necessary, sectioning is continued again — beginning below the first row and continuing on until complete. 4. The majority of users indicate that the textual content is of greatest value, however, a somewhat higher quality reproduction could be made from "photographs" if essential to the understanding of the dissertation. Silver prints of "photographs" may be ordered at additional charge by writing the Order Department, giving the catalog number, title, author and specific pagas you wish reproduced. 6. PLEASE NOTE: Some pages may have indistinct print. Filmed as received. Xerox University Microfilms 900 North Zm S Road Ann A fter, MICtMgan 49106 74-14,435 DUTT, Bulusu Venkateswara, 1939- HIGH TEMPERATURE DEFECT STRUCTURE OF COBALT DOPED * -ALUMINA. U n iv e rsity o f Southern C a lif o r n ia , P h.D ., 1974 M aterials Science University Microfilms, A X E R O X Company, Ann Arbor, Michigan THIS DI88ERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED. HIGH TEMPERATURE DEFECT STRUCTURE OF COBALT DOPED a-ALUMINA by Bulusu V. Dutt A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Materials Science) January 1974 UNIVERSITY O F SO U TH ERN CALIFORNIA THE ORADUATESCHOOL UNIVERSITY PARK LOS ANOKLSS. CALIFORNIA SOOOT This dissertation, written by ..B u lu su V en k a ta »wa_ra D utt under the direction of A X ?..... Dissertation Com mittee, and approved by all its members, has been presented to and accepted by The Graduate School, in partial fulfillment of requirements of the degree of DOCTOR OF P H IL O SO P H Y DISSERTATION COM M ITTEE ABSTRACT Room temperature optical absorption spectra, elec tron spin resonance at 15 - 18°K, high temperature (1620°C) electrical conductivity and emf measurements are correlated to determine the high temperature defect structure of ■ cobalt-doped a-alumina. Proposals of defect models by others based on the three kinds of measurements are review ed and in some cases, a reinterpretation is offered. A disorder model based on charge compensation of divalent cobalt by native aluminum interstitials and a foreign donor is proposed. Cobalt-doped alumina is found to be a mixed (ionic + electronic) conductor at high temperatures. At 1620°C, the conductivity is predominantly ionic, with triply charged Al-interstitial ions as charge - 8 "3 carriers in the range 10 < pt^^O atm and predominantly electronic, with holes as charge carriers in the range _ 3 10 <pC>2<l atm. The mobilities and activation energies of ions and holes and a set of equilibrium constants are estimated. The level positions of Co^+ and Fe^+ in the bandgap are determined. The standard free energy of incorporation of CoO in A^Oj forming the defects CoA1 and Al^‘ is estimated. ii This is used to calculate the solubility of cobalt in as a function of pO^ at 1620°C. iii ACKNOWLEDGEMENTS The author is deeply indebted to Professor F. A* Kroger for his guidance, encouragement and invaluable advice during the course of this work. The author gratefully acknowledges the many invalu able discussions he had with Professor J. P. Hurrell on optical and ESR spectra. He would like to thank Professors Jan Smit and S. P. S. Porto for their interest in this work and the helpful discussions he had with them. Appreciation is expressed to fellow graduate students for the helpful discussions the author had with them. Technical assistance provided by Mr. J. C. Emerson of the Glass Shop and Mr. H. B. Lloyd of the Engineering Workshop is very much appreciated. Financial assistance provided by the Air Force Office of Scientific Research under contract number AF-AFOSR-68-1405 is gratefully acknowledged. Finally, I would like to thank my wife, Radha, for her patience and understanding during the course of this work. iv TABLE OF CONTENTS ABSTRACT ii ACKNOWLEDGEMENTS iv LIST OF TABLES vii LIST OF FIGURES viii I. INTRODUCTION 1 II. STRUCTURE AND PROPERTIES 4 III. THEORY 8 A. Crystal Field Theory of Transition 8 Ion Spectra B. Optical Absorption Spectra of Coz+ 19 Ion in A1203 C. Electron Spin Resonance of Co£ Ion in AI^Ot D. Electrical Conductivity and 27 Transference Numbers E. Defect Equilibria 33 IV, EXPERIMENTAL RESULTS REPORTED IN THE 4S LITERATURE A. Optical Absorption Spectra 45 B. Electron Spin Resonance Spectra 47 C. Conductivity and Transference 50 Numbers V. EXPERIMENTAL TECHNIQUES AND RESULTS 52 A. Sample Preparation 52 B. Annealing, Color Change and Blackening 54 C. Optical Absorption Measurements and 56 Results D. ESR Experiments and Results 63 E. Coz+ and Co3+ Concentrations as a 71 Function of Oxygen Partial Pressure F. Electrical Measurements and Results 73 v TABLE OF CONTENTS (Continued) VI. DISCUSSION 83 A. General 83 B. Optical Absorption Spectra 85 C. ESR Spectra of Co2+ ion in 90 A120- D. Electrical Conductivity and tion 94 Determination E. Disorder Model 100 F. An Alternative Interpretation of 112 Pappis and Kingery's Conductivity Data G. Determination of Thermodynamic Parameters 117 H. Ternary Al-O-Co System and Solubility 121 of Co as a Function of Oxygen Partial Pressure SUMMARY 131 vi 1 2 3 4 3 6 7 8 9 10 11 12 13 14 5 14 15 17 22 35 41 42 46 48 53 60 72 86 LIST OF TABLES Properties of A^Oj Character table for the groups Td and 0 States arising in octahedral field from the t* e£ Zg * Color properties of Transition Metal ions in Corundum Selection and polarization rules for electric dipole transitions for ions in Corundum Defect formation reactions for AI2O3 and the corresponding mass action relations Oxygen partial pressure dependence of defect concentrations; pure AI2O3 Oxygen partial pressure dependence of defect concentrations; Co-doped AI2O3 Data from optical absorption spectrum of Co3 iA^Oj (ref. 1 ). ESR spectra of Co^rA^Oj (ref. 7) Spectrographic analysis of Czochralski grown Co:Al203 sample Relative concentrations of Co^+, Co3+ as a function of p0£ Concentrations of Co^+ and C034 as a function of p02 at 1620°C Absorption band intensity as f (PO2) vii LIST OF FIGURES Figure 1 Portion of Al^O^ lattice 2 Pattern of octahedral sites 3 The arrangement of atoms in a rhombohedral unit cell 4 Contours of t2g and eg orbitals 5 eg and t2g orbitals inscribed in a cube 6 The effect of octahedral crystal field in lifting the orbital degeneracy of D and F state ions. 7 Energy levels as a function of the strength of the crystal field for d and d7 ions according to Tanabe and Sugano 8 Splitting of the free ion levels of d^ and d by an octahedral field with a superimposed trigonal component A ^ x 9 Energy level splitting of F term for Co4 in crystaline electric and strong magnetic fields. 10 Arbitrary level positions of defect centers in the bandgap 11 A set of defect isotherms based on compen sation of Co^j by AIJ'for CoiA^Oj 12 Room temperature absorption spectra 13 Optical absorption band intensities Vs. pOj 14 Room temperature absorption spectra of Ti, CoiA1^0j Page 6 6 7 10 11 13 20 21 25 40 43 57 58 59 viii Figure Page 15 ESR spectra at x-band frequencies 68 16 ESR measurements of relative intensity 69 of Co*+ concentration 17 Schematic arrangement of the electrical 74 cell assembly 18 (a) Circuit arrangement 75 (b) Equivalent circuit 19 Conductivity as a function of temperature 77 20 Electrical conductivity as a function of 78 p02 21 Emf as a function of pC^ at 1620°C 80 22 The ionic transference number t, as a 81 function of p02 at 1620°C 23 Modified version of Fig. 20 98 24 A set of defect isotherms based on the 99 model suggested 25 Energy level positions of unknown donors Dx 106 CoJ^i in the bandgap 26 Pappis and Kingery's conductivity data Vs. 114 our model 27 Schematic ternary Al-O-Co system 125 28 (a) Concentration of defect Vs. p02 128 (b) a- and acO0 as a function of oxygen ix I. INTRODUCTION Aluminum oxide doped with different metal ions, particularly the transition ions, has been the subject of a large number of investigations with a view to understand the defect centers responsible for the physical properties observed, namely, the color (optical absorption and luminescence), electrical conductivity, paramagnetic resonance, diffusion and creep etc. These physical prop erties depend on the presence of small concentrations of crystal imperfections in the form of vacancies, intersti tials and foreign atoms and their charged state. The concentration of these imperfections is governed by the conditions prevailing during growth and/or subsequent treatment of the crystals. The most extensive work to date on the optical absorption spectra of all the trivalent ions of the first transition row in corundum was that of McClure. (1) Miiller and Gunthard studied absorption spectra of divalent cobalt and nickel in reducing the trivalent ions to divalent form using hydrogen. The crystals with hydrogen were analyzed by infrared spectra. The location of the protons appears to depend on the transition ion substi tuting for Al-ion, indicating that transition metal ion- 2 hydrogen paiis are formed. Gttnthard and his associates have extended their work on in a series of publica tions (3-5) to include other transition metal ions and some doubly doped systems (Fe-Ti) to study the phenomenon of non-additive colors. Keig (6) gave optical absorption spectra of Co:Al*0 , Ti:Al,0., and Co, Ti:Al_0, systems. L 3 £ J 2 5 Cr^+ ion in A^O^ (ruby) is the most extensively studied system because of its importance as laser material. The work on other ions is motivated mainly because of the color properties (use as gemstones) and evaluation of the doped corundum as a working material for paramagnetic ampli fiers. The work reported here is mainly concerned with cobalt doped alumina. It is known that cobalt has valence states of Co2+ and Co^+ and more recently Townsend and Hill (9) could prove the presence of tetravalent cobalt 2 + ion, when cobalt is present along with Mg with charge compensation [Co* ] ■ [Mg' ] in A1,0». The paramagnetic A1 A1 L J resonance experiments of Zverev and Prokhorov (7) and Townsend and Hill (9) show the same two types of spectra, but with different intensity ratio, 2:1 and 10:1 respec tively. Zverev and Prokhorov suggest that these two spectra to be arising from substitutional and interstitial cobalt centers (Co*^ and Cop, while Townsend and Hill explain that these spectra could be due to free substitu tional Co’, and associates of Col, with native defects 3 Al3;forming (Co4 Al,)'*. 1 Al l Electrical conductivity and self diffusion of aluminum and oxygenwere studied in a series of publications (see references cited in Brook et al. (11)). The recent measurements of Yee (12) indicate that the plausible native defect responsible for electrical conductivity is Al;?'. Clearly, there appears to be lacking a well under stood disorder model to explain all the differences observed in electrical, optical and magnetic properties. The present work is an attempt to establish the defect structure of CorA^O^ with the aid of electron spin resonance, optical absorption, electrical conductivity and emf measurements as a function of the partial pressure of oxygen at a fixed temperature and electrical conductiv ity as a function of temperature at fixed partial pressures of oxygen. The results are analyzed in the framework of the quasichemical approach of Kroger and Vink (13) to arrive at a disorder model. II. STRUCTURE AND PROPERTIES In this chapter, a brief summary of the structure(14) and properties of a-alumina is presented (15). Figure 1 shows the corundum lattice, a-alumina (space group R "3 c). The AZ-ion is in octahedral oxygen coordination, the oxygen ions forming a hexagonal close- packed (hep) lattice. Only two thirds of the octahedral sites are occupied by Al-ions and the octahedron is severely distorted, the point group symmetry at the Al- site being C^. Although the Al^+ sites are physically equivalent, there are two types of magnetically distinct substitutional sites related to one another by rotation of their cubic axes about their [ill]direction. Similarly there are also two types of interstitial sites. The actual crystal field is usually treated as octahedral with a superimposed trigonal component. Figures 2 and 3 aid to further understand the way the lattice looks; Fig. 2 shows ideal octahedral coordina tion and Fig. 3 gives the arrangement of atoms in the rhombohedral unit cell of corundum. 4 5 TABLE 1 PROPERTIES OF a-Al203 Structure type General formula Coordination No. Space group Packing of oxygen Symmetry Cell dimensions No. of molecules per cell Volume of the rhombohedral cell Density Composition Molecular weight Melting point, deg. C Covalency of bond Dielectric Constant E J_c E| |c Bandgap Refractive index (400-700 mu) 3 Corundum M2X3 6:4 R T c hep Hexagonal a«4.76A C-12.98A 2 V-258.9 A d«3.98 gm/cc 52.9 w/o Al 47.1 w/o 0 101.92 2045 40* 8.6 10.55 9.0 eV 1.76 6 Fig. 1 Portion of Al^O^ lattice. The Al ions are between equally spaced planes of oxygens. They are in octahedral coordination which is severely distorted with the point symmetry at the Al sites being C^. The predom inant crystal field is still cubic, however with an added trigonal component. The angle a is 4.3°. O Al Fig. 2 (a) Pattern of octahedral sites and (b) Diagrammatic elevations of close packed structures. A, B, C refer to pattern sites of Figure (a). Q OXYGEN ALUMINUM Fig. 3 The arrangement of atoms in a rhombohedral unit cell of corundum (after Pauling and Hendricks (15)) III. THEORY Here the theoretical principles necessary to interpret the results of ESR, optical absorption and electrical measurements are outlined. A. Crystal Field Theory of Transition Metal Ion Spectra There are several excellent references (16-21) dealing with crystal field theory. Here we confine our- seves to a limited discussion of the splitting of the energy levels of dn-ions in crystal fields of different 3+ £ symmetry, with particular emphasis on Co (d ) and 2 + 7 Co (d ) in the corundum lattice. Absorption spectra of transition metal ions, corresponding to transitions between levels arising from crystal field splitting are characterized by low intensity and occurrence in the low energy spectral region -1 (50,000 cm ). The low intensity is due to their origin in parity forbidden d-*-d or f-*-f transitions and violation of the selection rule ±1, which applies for electric dipole transitions in the free atoms. To illustrate the crystal field splitting, consider the simplest example, a single 3d1 electron (Ti^+). in the free ion, the orbital degeneracy is five-fold and the electron may be in any one of the five d-orbitals with 8 equal energy. These orbitals are as shown in Fig. 4. The splitting of the 5-fold d-orbital levels in the three different kinds of cubic fields, namely cubic, tetrahedral and octahedral coordination can be understood qualitatively by placing the t2g or e^ orbital at the center of a cube as indicated in Fig. 5 (17). The anions assumed to act as point charge^ are present either at the 8 corners of the cube, or only at four alternate corners, or at the face centers, corresponding to cubic, tetrahedral and octahedral coordination respectively. The t2g orbital has relatively higher charge density distributed near the corners than the faces. This means that both with cubic or with the tetrahedral coordination, the electrons in the t2g-orbitals are repelled more than in the octahedral arrangement, while the opposite is true for electrons in the e -orbitals. Alternately, consider the wave functions g d _ and d which belong to the e and t2„ orbitals in x — y xy ® the octahedral coordination. One of these can be obtained from the other by a rotation of V4 around the z-axis. The function xy vanishes along the x or y axes where four of the six anions are located. The electrostatic repul sion between a d-electron and the anions will thus be smaller for the xy function than for the x^-y^ which has maxima along these axes, Energetically, this leads to a lowered triply degenerate t2g-orbital level and a raised doubly degenerate e^-orbital level in octahedral fields, 10 t,ORBITALS 2« v ORBITALS Fig. 4 Contours of constant amplitude of the d-functions. Above are the t2g orbitals and below are the two e orbitals. The d-functions are: g dxy ■ R3d dxz m R3d d y z m RSd dx2V - R3d dz2 m R3d 11 Fig. S (a) e orbital inscribed in a cube tetrahedron and octahedron. (b) t„ orbital in same z8 surroundings. 12 while the relative position is reversed in cubic and tetrahedral coordination. In the group theoretical sense, the labels t2g and e^ indicate the representation to which the orbitals belong in the groups of octahedron O^-Oxi and tetrahedron, T^, whose character tables are given in Table 2. (17) In the case of ions with more than a single electron, the details of splitting of energy levels are more easily de rived using group theory. Table 3 summarises the levels(22) arising in octahedral fields; their general splitting pattern is given in Fig. 6. At this point, it is expedient to briefly review some of the color properties of the d-ions in a-A^O^ as reported in the literature and relate them to the crystal field splitting parameter 10 Dq. This is done in Table 4; the unreferenced listings represent our own observations of the color. It is only necessary to remark here that the blue color of the natural sapphire is due to presence of Fe^+ and not due to cobalt in either x T + 2 4 Co or Co states; Co gives a green color, while Co gives a light pink color. In the case of CoiAljO^, the crystal field is octahedral, superimposed with a trigonal component at both substitutional Al-sites and interstitial centers. The nuclear surrounding in these two cases are different and there would be a third possibility in case associates form. However, the valence state (Co*^+ or Co^ + ) affects 13 / i / 6Dq d 1 , d6 (T i^ .F e ^ .C o 3*) 8H * 4Dq Dq 6Dq d4, d9 (Cr2+, Mn3+,Cu2+) 8H=4Dq / / 10 Dq / / / _ / ✓ _ 2D “ T« T 6Dq d2, d7 ( V3* Co2+) 6Dq < 8H < 8Dq ( V2*, Cr3* ,Ni2*) SH= 12 Dq Fig. 6 The effect of Octahedral field in lifting the orbital degeneracy of D and F state ions. 6H ■ crystal field stabilization energy. 14 TABLE 2 CHARACTER TABLE FOR THE GROUPS Td AND 0 T d E 8C3 3C2 6S4 6 d Representative of 0 E 8C3 3C2 6C4 6C; Some tensor Components A 1 1 1 1 1 1 XX+YY+ZZ \ 1 1 1 -1 -1 E 2 -1 2 0 0 XX+YY-2ZZ, XX-YY Ti 3 0 - 1 1 -1 X,Y,Z in 0; Rx’ Ry’ Rz T2 3 0 -1 1 X,Y,Z in T: xy, xz, yz Note: 0^*Qxi; E-identity: Cj-threefold axis; C^-fourfold axis; C2"C^; CJ- twofold (110) axes; R-rotation by 2*; S^-roto-reflection. TABLE 3 STATES ARISING IN OCTAHEDRAL FIELD FROM THE CONFIGURATION Free ion Strong Levels arising in Octahedral Configura- Octahedral Field tion Field Configuration ________ 1 ,9 1 2 TABLE 3 (Continued) Free ion Strong Levels arising in Octahedral Configura- Octahedral Field (87) tion Field ____________ Configuration__________________________________ TABLE 4 Gonfigu- Ions Free Ion ration Ground State COLOR PROPERTIES OF TRANSITION METAL IONS IN CORUNDUM X % - m * Trigonal Gcapanent rm'l an -1 Color Ref. 3d1 £♦ \ / 2 1905 500 154 154 Pink (1) 3d2 V1* \ 1750 760 104 Green (1) 3d5 y2+ *F 3/2 1850 1425 87 55 Pink (1) 3d4 Will Cr4+ Co* 50 0 1947 — 85 57 Pink Dirk Brown m 3d5 **2+ VkC 1440 1650 720 — Yellow (26) (1) 3d6 * 1: Co s». 1330 1830 720 -100 Blue Green (26) 3d7 „ 2+ COr* Ni 9/2 1230 750 1000 -180 Light Pink Yellow (6,8) (1) 3d8 Ni2+ % 1070 -1200 -335 Blue/Green (2) 3d9 Cu2+ 2n 5/2 -852 Blue/Green (25) 18 the magnitude of the crystal field relative to the coulomb repulsion or electron pairing and spin-orbit coupling. Three approximations have to be considered: (a) Weak field case: Fij>*'ij>^i (b) Medium field case: ^ij>'ri>^ij ant* (c) Strong field case: ^i>Fij>^Jij where F.. - e^/r.. * Coulomb repulsion of the electrons of the ij ' ij * reference ion. Ljj ■ “ Spin-orbit interaction of the reference ion. V » electrostatic field of the surrounding anions on the i reference ion. In (a) the ion behaves essentially similar to the free ion and the ground term will be determined by Hund's rule; this is the case for rare earth ions which give sharp line spectra. In iron group elements the approximations (b) and (c) apply. Since the spin-orbit interaction is negligibly small, one can distinguish between low and high spin complexes based on the relative magnitudes of coulomb repulsion and crystal field. If as in the intermediate field case, the electrons are accommodated in the t2g and e^ orbitals following Hund's rule and the spin value is maximized. On the other hand, if as *n the electrons are placed in the lower t2g orbitals more favorably and this results in lowered spin. Hund's rule 19 is no longer obeyed. The effect of inner orbital splitting on the thermodynamic properties of the transition metal complexes are reviewed by George and McClure (24). The spectra of Co and Co4 observed experimentally are 3+ 6 explained with CoJ (d ) in the strong field limit and 2+ 7 Co (d ) in the intermediate field approximation. 3+ 2 + B. Optical Absorption Spectra of Co * Ions in A ^ Og In this section we briefly review the interprets- tion of absorption spectra expected for Co* 5 and Co4 , referring to the energy level diagrams of Tanabe and Sugano f t 7 (23) for d and d ions given in Fig. 7 for octahedral coordination. In the corundum lattice, there is no center of symmetry at the cation sites. This causes the d-»d tran sitions, to be electric dipole allowed, though they are parity forbidden in the free ion. The odd power terms may mix the even d functions with odd functions, which may be either atomic p functions or odd molecular orbitals in the ligands. The spectra with the electric vector parallel and perpendicular to the trigonal axis (c-axis) differ in that the selection rules for E| |c allow transitions A-*A and E+E and for Ej_c allow transitions A-*-E and E+A. The selection rules for polarized spectra are listed in Table S for the point group symmetry and c3v* The bands observed in the E||c spec trum are expected to be 15,S60 cm"*: ^Aj-^Aj , 22,980 cm'*: 3 t r 60 *E (d ^ d y 3) 10 20 30 UJ 60- / 'T2 50- 5T2 (d€4dr2) 2_ - t ' Tl 'T, F' 30- /3t, (de5d^) 4p 6 ! 10- - l A,(d£6) < * A 2(d€3dr ‘ * ) V i % 4T (d64dy^ 4T.(d£5dj'2) ■b 20 30 (a) d6 , Co* C/B * 4.808 B - 1065 cm -1 (b ) d7t Co2+ C/B - 4.633 B » 971 ci -1 Fig.7. Energy plotted against lODq/B for, dn Iona as calculated by Tanabe and Sugano . The Ion for vhlch the calculation was made Is shown In each case. ho © 21 40 *1 30 20 K > O C o : d 4 40 3 V * v/2 % ^a Fig. 8 Splitting of the free ion levels of Co3+(d6) and Co^+(d7) by an octahedral crystal field (0) and a superimposed trigonal component (Cjy). The selection rules for electric dipole transitions for E||C (full arrows) and E_]_C (dotted arrows) are as indicated (v is taken positive). (Based on Ref. (2)). TABLE 5 22 SELECTION AND POLARIZATION RULES FOR ELECTRIC DIPOLE TRANSITIONS FOR IONS IN CORUNDUM 3/2 1/2 1/2 3/2 3v 1/2 1/2 1*11 3/2 3/2 23 1 while the corresponding bands in the EJ_C spectrum separated from those in the H||C would be The weaker bands arising from spin-forbidden transitions *A^+3Ti and 1Aj^T2 are not observable in our room temper ature spectra. 2 + 7 B.l Co (3d7) ra-A^Oj absorption spectrum The free ion ground state of the C0^+ ion (3d^) is *F. The sevenfold degeneracy is lifted by the octahedral crystal field into an orbital singlet and two lower triplets. These are labelled T^, T^f A^- The ground state in the crystal is *Tj and the other states are as shown in the Fig. 8 along with their trigonal field splitting (2) The stronger spin allowed transition is seen at 21400 cm'1 in the E| | C orientation. The other transitions are listed below with their polarization properties(2). 4a2-4t2 9100 cm’1 l 4a2-4a2 21400 cm'1 ii 4V 4t1 22800 cm-1 i * i V 2f. 7700 cm'1 i * i V S 16000 cm"1 i * i 4A2-2Tj 17200 cm'1 i » i 4a -*2*r 2 1 18300 cm'1 i * i Co3+(3d6): Al^Oj absorption spectrum The ground state is the nonmagnetic *Aj(t6) state. Our spectrum at room temperature consists of two well separated bands at 15,560 cm"1 and 22,980 cm 1. These correspond to the transitions and the and states being split by the trigonal field into 1T1:1E + XA2 and + XA . 2 + C. Paramagnetic Resonance Spectra of Co iA ^ Ot It was seen that the sevenfold orbital degeneracy of 4 2 + 7 the free ion ground state F of Co (3d ) is split into an orbital singlet and two triplets, the triplets lying lower. The trigonal field further splits the triplet into a sing let and a doublet. The question which of these is lower depends on the specific form of the crystal field. The spin multiplicity gives twelve levels, each orbital level being fourfold spin degenerate. The combined action of the trigonal field and spin-orbit coupling splits the low est orbital triplet into six Kramers doublets, the lowest of which corresponds to the doublet with m - +1/2. Zeeman s — interaction splits the two levels of the doublet ms-+.l/2 and transitions between them are caused by the microwave field in the ESR study. Since cobalt has a nuclear spin 1*7/2, the hyperfine sturcture consists of 21+1-8 compo nents. Figure 9 gives these details. 2 ^ The behavior of energy levels of Co* in different symmetries was investigated by Abragam and Pryce (27) . It was shown that the lowest isolated triplet can be assigned a fictitious orbital angular momentum of A'-l. The eneTgy levels in the trigonal field with the spin-orbit coupling bain Doublets - X An# ■ ±1, A*j ■ 0 Transitions 5.0. Octahedral Trigonal Field Field Coupling Hyperfine Splitting Splitting 4 2+ Fig.9 . Energy level splitting of F tern for Co In crystalline electric and strong magnetic fields. M tn •MCTJWftr J 26 mav be described bv the Hamiltonian: H c * - f) -oXl-SI-a'X(t;SX*1JSJ) fl) where: A :trigonal field splitting of the lower triplet, characterized by the orbital angular momentum t'-l X :spin-orbit coupling constant - -180 cm”* a,a' :factors depending on the admixture of higher states 4 4 belonging to the F and P terms in the wave func tions of the lower triplet, and equal 1 in the weak field and 1.5 in the strong field limit. Following the treatment of Abragam and Pryce (28), we realize the advantage of defining the fictitious orbital angular momentum and construct states |M>» I 1 + Sz which are diagonal in |M>. This gives us states with f * f l f Using vhe |m’, ms> as basis set, the secular determinant of the Hamiltonian eq* (1) leads to splitting of the six Kramers doublets; three belonging to M -+. j f two for Mz»+ - and one for Mz« + the lowest of these, found to be M — can be written as a linear combination of three z 2 Kramers doublets belonging to it in the form: |I> * a |-1, |> ♦ b |0, ~> ♦ c |l,-y> - \ > - a |1, -1> * b |0,- i>* c|-l i> (2) 2 2 c 2 a2 + b2 + c2 ** 1 27 the cobalt spectrum observed due to transitions between these levels is interpreted with the spin Hamiltonian H-*nHzsi ♦ «j_ < v i * w ♦ A v ; * + v p where S^, S^, are the three components of spin, Ix, 1^ Iz are the three components of nuclear spin and A and B are hyperfine parameters in the parallel and perpendicular orientations. The factors g| ^ and g^are g-factors in parallel and perpendicular orientations, given by the matrix elements (with L «-aJLl and L ■-a'A1) Z * XX «ir 2<?iLz ♦ 2S; '!> Bj. U x ♦ 2S*X hi, Based on the detailed treatment of Abragam and Pryce (28) , the values of the various parameters were estimated in references (7) and (8). The question of the accurate determination of the Co^+ concentration in samples annealed in atmospheres with different oxygen partial pressures is detailed in the next chapter on experimental techniques. D. Electrical Conductivity and Ionic Transport The electrical conductivity of a solid is due to the presence of mobile charge carriers, which can be electronic species (electrons and holes) or ionic species (intersti tials, vacancies). The total current density of a solid in an electric field is given by 28 J ■ oE (4.1) where (4.2) where concentration of the i**1 carrier per unit volume electrical charge on the i**1 carrier mobility of the i**1 carrier, i.e., drift velocity carrier per unit electric field * |U|/E, where U»velocity. The mobility is related to the diffusivity or diffusion constant through the Nernst-Einstein relation: v. l is mainly determined by scattering from longitudinal optical phonons (29). In aluminium oxide, we may assume a behavior of electrons similar to that in alkali halides. The validity of such an assumption is questionable in view of the estimated covalent character of the bonding of about 40t (see Table I). However, a recent experiment al determination of the electron mobility of 100 cm~*/V-sec. supports our view. An electron moving in the lattice interacts with the ions and creates a local deformation; the combination of the electron and its strain field forms a polaron. This tends to increase the effective i (4.3) where D^»diffusivity of the species i, cm^/sec. In ionic (polar) crystals the mobility of electrons 29 mass of the electron relative to the expected band mass. In other words, the moving electron sets the ions in motion and this is reflected as an increased mass of the electron. The lattice-electron interaction is measured by the dimensionless coupling constant a given by (30) deformation energy/hwf t where is the longitudinal optical phonon frequency near zero wavevector. For high a, the mobility is low when the temperature is high enough to excite optical phonons. The mobility of the ions, in hopping from one lattice site to the other has to overcome potential bar riers resulting from the presence of neighboring ions. The probability that the hopping takes place is given by exp (-AG^/kT), where AG^ is Gibbs free energy difference between the ion in one of the positions and the transition state. This leads to the temperature dependence of the ionic mobility as v- exp (-AGh/kT). This probability is dependent on the type of dis order prevalent in a crystal under the given conditions and a complete characterization of electronic and ionic conductivity is possible only through an analysis of the dependence of conductivity on the partial pressure of oxygen. The conductivity in any given range of oxygen partial pressure and temperature will have contributions by all species, each corresponding to its mobility- 30 concentration product. Separating the ionic and the elec tronic contributions, we can write <j*Oi +a . A convenient 1 e way of distinguishing between the ionic and electronic conductivities is by introducing transference numbers defined by tA - a ^/a and te - a e/a and tj + t * 1 A knowledge of the ionic transference number can help to identify the charge carriers mainly responsible for the conductivity. This can be obtained in the follow ing way: (1) Tracer self diffusion: Combining the electri cal conductivity and the Einstein relation between the mobility and the self diffusion constant D*D*/f we see that o “ Cq^D/kT for aluminum ions in Al^Oj, C*2N^d/M, where, D**tracer self diffusion coefficient, f“correlation factor, N - Avogadro's number, d * density of alumina and M - A molecular weight; factor 2 arises as there are 2 Al-ions per molecule, and oq can be estimated from the self diffusion constants, and using the measured conductivity, t., and tn can be found. A1 u (2) EMF measurements : Using a cell arrangement as shown here with Pt , p02(I)|Al203|p02(II), Pt. known oxygen partial pressures on either side, one can estimate the transference numbers. The potential across the cell is given by 1 f R T f1 1 E - / t dpO - dp / t. dlnp02, with t* - f(pO-). 4F I 1 2 I 1 This leads to T. pO (II) F - — RT In 2 4F po2 ( i ) where t\ is the average over the range of oxygen pressures used. The value of t^ at each pO^ is found by measuring E as a function of pC^CII) with pO^CI) kept constant; on differentiation with respect to pO^n), we see that «F/RT(.E/»Inp02(II) ^ ( n ^ V p C ^ ! ! ) (3) Mass transport: To verify if Al-ions are participating in conduction, a mass transport experiment can be done. In principle, choosing a cell Pt lAl 2°j!Pt , one finds no mass transport if oxygens are the charge carriers causing ionic current; oxygen gas will be absorbed and ionized at the cathode and evolved at the anode. On the other hand, if Al-ions are the conducting species, they will be produced at the anode by decomposition of the oxide and migrate under the influence of the field to the cathode for reoxidation. If I is the current flowing in time t, then the weight of the material transported is given by W«MIt/ZF, where F»Faraday constant, M-Molecular weight and Z«6, the number of electrons transported per molecule. The ratio of weight transported to that calculated gives t^. For a cell with one AI2O3 crystal, mass transport by A1 should result in a pit at the anode and a bulge at the cathode. With more 32 than one piece of crystal (say two) the crystal near the anode should lose weight, while there should be a corres ponding gain in the cathode side piece. The above treat ment is based on no polarization of the sample. Care must be taken to stop electronic surface and/or gas phase conduction, which would tend to reduce t . If polariza- i tion occurs, the mass transport will be reduced. (4) Polarization techniques: Upon application of a voltage to an unsymmetrical cell Pt^l ^*2*^ Pt the left side positive, keeping the voltage below the de composition of A1 0_, where it electrolyses, oxygen tends 2 ^ to move to the left and Al-ions to the right. If oxygen is totally absent at the right no reoxidation can occur and Al-ions accummulate, building up a positive space charge which tends to reduce the internal electric field. The Fermi level at the right is raised and some of the Al.-ions become atoms. The combined effect of the concen- l tration gradient and the modified electric field stops the flow of Al-ions to the right and O-ions to the left and the remaining current will be only due to electrons. In case of a symmetrical cell Pt | Al^O^I Pt polarization can be imposed only with ionic blocking electrodes. Again, initially under an applied field ions migrate to either 3 v ? - side, Al^* becomes partly AlJ and 0 partly 0. At the cathode surface oxygen tends to fill V*, thereby reoxidizing Al* to Al^*. Similar effects leading to 33 evolution of Oj, occur at the anode. If one of these electrode reactions is not fast enough, then the corres ponding electrode is a blocking electrode for ions and an accummulation of ions will occur, which sets up a space charge opposing further flow of ions, i.e., the cell is polarized and electronic current will result. E. Defect Equilibria The conditions of preparation of a crystal and the subsequent treatment influence the properties through disorder and the imperfections formed in the crystal. Real crystals differ from ideal ones in that there are almost always imperfections in the former. For our purposes, it is necessary to distinguish zero dimensional point defects, which are formed by disorder or nonstoi chiometry in any crystal in equilibrium with an outer phase at T >0 from one or two dimensional imperfections such as dislocations and grain boundaries. The equilibria of processes taking place at the crystal-vapor interface, or inside the crystal between the various point defects and components of the crystal are formulated with the assumption that the point defects can be treated thermodynamically as quasi-particles dissolved in the crystal, using the principle of law of mass action (31,32). These formulations should take into account proper balance of lattice sites, ions and charges. 34 All defect concentrations are interrelated due to the requirement of overall charge neutrality of the crystal, and vary over the various ranges of temperature and pres sure. Approximation of the charge neutrality by a pair of predominant defects compensating each othei*s charge leads to a simple pressure and temperature dependence of the concentrations (33). Different sets of defects may be dominant at different temperatures and/or pressures. With the help of graphical plots of isotherms and isobars as indicated by Krffger and Vink (13), one can identify the disorder model from the isotherms and estimate the forma tion enthalpies and entropies from the isobars. (1) Native atomic disorder: There are three main types of atomic disorder involving only two types of defects, namely Schottky, Frenkel, and Anti-strucure disorder. Anti - structure disorder of cations on anion sites and vice versa is probably energetically unfavorable in an ionic crystal and will not be considered further. The formation reactions for Schottky disorder (involving A1 and 0 vacancies) and Frenkel disorder of A1 (involving Al-vacancy and A1 interstitial) are indicated by (a) • (c) in Table 6. (2) Non-stoichiometry: Vacancies and interstitials arising from reaction with the gas phase resulting in non stoichiometry are given by (d) - (f) in Table 6. (3) Ionization reactions: In the formulation of the 35 TABLE 6 DEFECT FORM ATION REACTIONS FOR A1203 A N D THE CORRESPONDING M ASS ACTION RELATIONS Reaction Mass a ctio n re la tio n (a) 0 - 2V*, + 3Vq f t H s K s = [V *,]2 [Vg]3 (b) 0 ■ 2 V ''1 + 3V* * U *V A 1 5V0 * f t H s K s = [v ;;1]2 [Vj ] 3 (c) Al* + V* * Al* + A 1 1 1 * f t hfai kfai - [Al*] [» * ,] (d) | 02 (g) * 3 Oj + : !VA 1 f t hvai KVal P x _2 -3 /2 ^A1 ^ P02 (e) °0 * 7 °2<9> + V S f t H vo K vo ■ rv*i 0-* po2 (f) | o 2(g) ♦ V? = Of f t H 01 *01 [0?] P5l/2 (g) Al* - A l* + e* • f t Edl dl [A l;] [e'D / [Al*] (H) A1‘ - Al*’ + e ' • f t E«z S [A l* '] [ e '] / [A l; ] (D A l’ ' - A l j " + e ' * 1 S S [ A 1 J " ] [e') / [A l‘-] (J) V* + e ' - V Al 6 V A 1 • f t E*1 *■1 [ V ^ ] / [V*,] [ e '] (k> V + e ' ■ V ' Al Al • f t s K a2 [ V - ] / [»;,] [.•] ( i) V '* + e' * V " Al * Al • » S K »3 [ v ; ; ■ ] / [ v ; p [ e ’] (m) VS ’ r o + • ’ • f t E°1 s [ v ;] [*■] / [v£] (n) v0 * r o + e ' • » E°2 - [ v ; - ] [e1] / tV '] TABLE 6 (Continued) 36 R eaction Mass a c tio n r e la tio n (o) 0* + e ' - o; ; Efl K. * [O '] / [0*] [e'] ( p ) 0 * + e ' - 0 ; ' ; E. K. ■ [O j' ] / [0*] [ e 1] 2 2 (q) 0 » e ' + h » Ei K1 " [ h *l ( r ) Co' -Co* ♦ e ' i V K' - [ C o * ] [«■] / [Co' ] Al Al Co Co Al Al or c° ; * c<v h‘ : E C; kco - [ c ° a , ] [h -] 1 ccoa , ] ( s ) 3 C o ; ♦ A i r - + f ° 8(g). 3 Al^ P02 3Cox + Alx + 1 0* ; AG® K - -------------------------- Al Al 2 0 ox ox 3. [C°A1] W P ( t ) AlJ- + l o 2 (g) - A lJ, ♦ J 0 j + 3h‘ rh'l3 A -3/4 ag“ k, - [h] 2 [Alj’] (u) D' + CoJI, . D* + Co*, ; S . [°*J [C°A1 ] r P>] [Co' ] Al TABLE 6 (Continued) 37 Reaction Mass a c tio n r e l a ti o n (v) ZAl(g) + f 0 (g) - Al 0 (s); 1 r r < S >o > o ( i f p2 p 3/2 A l-0 , + Al 0 Z J 2 3 2 (1) Complete N e u tra lity C ondition: [e'D + [ V ^ ] + 2 [ V ^ ] + 3[V'j’] + [ C o ^ ] + [0J3 + 2 [ 0 ‘ *] [0*] + [Alj] + 2[A ir ] + 3 [ A i;’ *] +[h*] + [V*] + 2[Vq * ] (2) Cobalt Balance: tCO]tO t .l ■ [ C O il ] + [C0A ,] (3) Balance equ atio n f o r unknown fo re ig n donors (D) [D3t o t " [D‘ ] + [DX]* N otation: Square b ra c k e ts In d ic a te c o n c e n tra tio n o f th e sp e cie s 1n mole f r a c t io n s . N. B .: N e u tra lity c o n d itio n as w r itte n 1s good only fo r concen- 3 t r a t i o n s exp ressed In #/cm o r mole f r a c tio n s and does not apply f o r s i t e f r a c tio n s . 38 native atomic disorder in (a) - (f) in Table 6, interaction between the electronic and atomic disorder was not intro duced explicitly. This is done through ionization reac tions, which are to be treated as capture or release of electrons from or to the conduction band resulting in singly or multiply ionized acceptor and donor centers. Formation of ionized donor centers - donating electrons to the conduction band or capturing holes from the valence band is realized through reactions (g) - (i), (m) and (n) of Table 6. Formation of ionized acceptors - accepting electrons from the conduction band and donating holes to the valence band is given by (j) - (1), (o) and (p) of Table 6. (4) Native electronic disorder: Besides the electronic disorder from the ionization of atonic defects electrons and holes can be produced by intrinsic excitation across the band gap through reaction (q). (5) Incorporation of foreign atoms and its effect on atomic and electronic disorder: In principle, foreign atoms can be incorporated in a crystal substitutionally as well as interstitially. As we found no evidence of interstitial cobalt, we shall consider substitutional cobalt species only. Equation (r) gives interaction of electrons with cobalt. Equation (s) is the oxidation reaction converting CoAl t o CoAl * 39 (6) Associates of defects: The charged defects may form associates because of coulombic interaction. Association is not limited to charged species only. Even neutral defects may form associates (34). ^2°3 contain ing cobalt when reduced with hydrogen to convert cobalt to divalent form showed evidence in ESR experiments (35) of pairs between Col, and H:. Cobalt reduced with the CO-CO A1 i 2 gas mixture is expected to show pairs of Co^ with the aluminum interstitials. (7) Complete equilibrium between a crystal and a vapor at high temperature: The various equilibrium relations arrived in the foregoing, when combined with the charge neutrality of the crystal as a whole in the case of undoped Al^O^ and with the charge neutrality and mass balance of all the different centers of foreign atoms in the case of doped A1 0 , yield simple expressions of defect concentrations as product of simple powers of equilibrium constants, oxygen partial pressure, and cobalt concentra tion, namely £j]-n K [ CoF , po”. s s total r 2 (7a) Pure A^Oj: We limit the possible defects to those given in the following neutrality condition: [e’M V ^ l + ZCV^l^CV” '] - [h-MV->2rv;*MAi;i + 2rAip +3[Ai;*'] l A solution using Brouwer's approximation, gives the defect concentration as a function of oxygen partial pressure and Table 7 lists the results. The isotherms are as indicated ion band . . I h . F ^dl.*_ Al^ d2 ] ;d3 -L ai: i Al' Ja3 =a2 j. V" ' Al V” Al Al 7 7 / / / / / / / Valence band Fig. 10 Arbitrary energy levels in the forbidden gap. TABLE 7 O X Y G EN PARTIAL PRESSURE DEPENDENCE OF DEFECT CONCENTRATIONS (PURE A l ^ ) ! Frenkel Disorder o f Aluminum Schottky Disorder N eu trality Defect ..... , 2[A li*3-3[V ^’] 3[A1*’ *]=2[V“ ] [v*]=3[v;;*] 0 Al 2 [V * 1 = 3 [V :''] o Al [Vo W V Al1 [a i;*3 -3/20 I -1/4 -3/20 — — - [ v ; p ----- - ---- . ^ -3/20 | i 0 -3/20 -3/16 0 -3/16 [Al j " ] +3/20 0 +3/20 — — — r v i L¥A1j +3/20 1/4 +3/20 1/8 1/4 1/8 Ce'] -3/10 -1/4 -3/10 -5/16 -1/4 -5/16 [h*] +3/10 +1/4 +3/10 +5/16 1/4 5/16 i — t — — — -3/16 -1/4 -3/16 — — — 1/8 0 1/8 TABLE 8 O X Y G EN PARTIAL PRESSURE DEPENDENCE OF DEFECT CONCENTRATIONS (Co:A1203 Assuming [ C o j ^ M C o ] ^ ) i - i n n - < N eutrality r— i -5 o - < o 0 1 1 O < - > i _ _ i M w o LJ 1 1 n P “1 « j C LJ l — l » f n < _ ) N m n r 1 * 1 I I f — \ L _ _ J H H Defect a < — i > ° U0 j A < < V 1 - < . o - < > n - < > n Ul C M C J m u LJ u C M LJ -1/4 -1/6 -1/4 -3/16 0 -3/16 -1/4 -3/8 [Al • ■ • D 0 -1/4 0 -3/16 -3/4 -3/16 0 +3/8 [Al;-] -1/4 -5/12 -1/4 -3/8 -3/4 -3/8 -1/4 0 [Alj] -1/2 -7/12 -1/2 -9/16 -3/4 -9/16 -1/2 -3/8 CVM ,] 0 +1/4 0 +3/16 +3/4 +3/16 0 -3/8 [v;;] +1/4 +5/12 +1/4 +3/8 +3/4 +3/8 +1/4 0 +1/2 +7/12 +1/2 +9/16 +3/4 +9/16 +1/2 +3/8 [v6-] 0 -1/6 0 -1/8 -1/2 -1/8 0 +1/4 [»y -1/4 -1/3 -1/4 -5/16 -1/2 -5/16 -1/4 -1/8 [ e '] -1/4 -1/6 -1/4 -3/16 0 -3/16 -1/4 -3/8 [h-] +1/4 +1/6 +1/4 +3/16 0 +3/16 +1/4 +3/8 43 [^aiJ iNJ-Mi 1[h> >K] I . [ c# aJ* h I sl f s LOO •02 Fit. 11 A Mt of dtftet loothonM boood o f C01 AI2O3 m eenponootloa of Co|j by AlJ' 44 by Yee (12). (7b) Co-doped AljO^: Approximate solutions obtained by approximating the following neutrality condition and cobalt balance equations by their dominant member, and combining these with the mass action relations from Table 6 yields the oxygen partial pressure dependence of the concentration of the defects as in Table 8. (7c) Neutrality condition [e']*[V']+2[V'']+3[V''']+[Co'] - [h’] + [V].2[V].[Ai:]. Al Al Al Al o O l 2[A1j*]+3[Alj * *] (7d) Cobalt balance: [Co]t ” ^°A1^ + ^°A1^' Figure 11 shows the isotherms. IV EXPERIMENTAL RESULTS REPORTED IN THE LITERATURE This chapter reviews some of the previous work reported in the literature on optical absorption spectra, ESR and electrical conductivity. A. Optical Absorption Spectra The most extensive work on optical absorption spectra of trivalent iron group ions in A12Oj ls that of McClure (1). The spectrum of Co (d ) observed by him is explained in the strong field limit with the ground state being nonmagnetic *Aj (t6) state. The spectrum consists of two wel 1-separated bands *Aj-*-*Tj at 15,560 cm 1 and 1A1' > JT2 at 22,980 cm'1. These are split by the trigonal field of 720 cm"1 at 77°K. Besides these strong bands, two weak bands seen at 18,880 and 19,800 cm * are probably x A 2 due to the lowest T_ of t e and the accidentally degen- 3 3 A 7 erate pair T^ + T2 of t4e (see Figure 7, Ch. III). 34- Table 9 summarizes McClure's data on Co :A1 0^ spectrum. Study of optical absorption spectra of divalent transition ions is rather limited and the most interesting work is that of Muller and GUnthard (2). Their spectrum of Co^+ is explained in the intermediate field. The free- ion ground state of Co^+ (d^) is *F and is split by the 45 TABLE 9 46 DATA FROM OPTICAL ABSORPTION SPECTRUM OF Co3+:A1203 Cl) State Ground ^A, t^ lii : ii i 1st excited *Tj t^e 15,740 cm*1 f, i 0.27 x 10'4 15,380 cm*1 2nd excited 1Ty ,t3e 2 23,170 cm*1 1.05 x 10'4 22,800 cm"1 -4 fj^ 0.60 x 10 Dq 1850 cm-l 47 crystal field as in Fig. 8. The polarized spectrum of the ion in trigonal fields should be such that there is a transition 4A2-*^A2 which should occur in the E||C polari zation only. Such a transition is observed at 21,400 cm"*. This is the most intense band in the spectrum. Similarly the lowest optical transition ^ ^ ^ E should occur only in Ej_C orientation according to the selection rules already discussed in Chapter III and such a transition is assigned to a band at 9,100 cm The value of 10 Dq arrived at on this basis is 12,300 cm *. But the value of the trigonal field could not be determined solely from these measurements. The other transitions assigned by these authors are already given in Chapter III. B. Electron Spin Resonance Spectra ^ + The first ESR experiments on Co^ iA ^ O j at liquid helium temperatures were done by Zverev and Prokhorov (7). They found two inequivalent centers characterized by the spectra, Type I and II listed in Table 10. The method of crystal growth and thermal history of their samples are not reported. The measured ratio of integrated intensities for spectra 1 and II in the parallel orientation was 2.3:1. Since this ratio is nearly in the ratio of substitutional to interstitial Al-sites, their explanation was that this is due to the fact that two Cq2+ ions substitute for Al^+ ions, their TABLE 10 SPECTRA OF Co2+:A1203 Parameter i - l 3 _ i Spectra gj ^ A x 10^ cm B x 10 cm Type I 2.292*0.001 3.24+0.01 4.947+0.003 9.72+0.05 Type II 2.808+0.003 2.08+0.09 4.855+0.005 15.1+ 0.11 00 49 J + charge being compensated by a third Co£ ion in an interstitial position [Coj^] * 2[Co**]. Townsend (8) and Townsend and Hill (9) found the same two spectra in mea surements at 4.2°K in green colored CoiA^O^ (grown with PbO + ®2^3 ^ ux)* ^he intensity ratio was, however, different and was 10:1. Measurements (8) on a pink colored CoiA^Oj (grown from PbO + PbF^ flux) showed only spectrum I. In order to explain the ratio of 10:1 of spectra I to II in the green sample they proposed an alternative charge compensation mechanism in which one interstitial Al-ion 2 + charge compensates for three substitutional Co ions 3[ Al:**] - [Co^j] . If two Co^+ ions are not substituting for adjacent Al-ions,only one type of center is expected, namely Co'^j. Nevertheless, if associates or pairs of Co* and All* form the ratio 10:1 can be explained as due Al 1 to 271 of AK * * pairing up with the Coj^ centers (for if C A i r *] - x, [(Co^Al*’] ■ 1-x, and " 2+x, we have to have 2+x/l-x equal to 10:1, the observed ratio leading to x»8/ll or l-x»3/ll or 271). On the other hand, the lack of Type II spectrum in their pink crystal was ex plained on the basis that the fluorine (F ) ion substitu tion for 0~~ ions, charge compensates for substitutional cobalt, i-e. * [ Coj^j ] - [ Fq] and [Al'” ]is not appreciable. Townsend and Hill (9) report that dark brown Co+Mg : Al2°3 crystals grown by oxide flux (PbO + showed a weak resonance consisting of 8 hyperfine compo- 50 nents with gj^- 2.58 ±. 0.01 and g| i <1, A-0.01 ± 0.003 cm-1 and B - 0.0198 ± 0.0002 cm"* . This resonance along with the optical absorption edge causing the dark brown color of the Co+Mg crystals at energies above 20,000 cm * (500 mp) were lost on heating the crystal at 1200°C in oxygen or vacuum. The authors believed the ESR and the absorption spectra to be due to cobalt ion. Using the theory of Stevens (10) for d^ ion, they interpret this 4 + resonance as being due to the Co ion. Gachter et^ aj_. (35) performed ESR experiments on hydrogen reduced Co‘ : A1203 at liquid helium temperature and they attributed iheir spectrum to be arising from associates of (Co^jlL)x at three different sites. C. Electrical Conductivity A comprehensive survey of electrical conductivity and e.m.f. measurements highlighting the variations in experimental apparatus and the possible sources of error introduced in measurements performed without cylindrical volume guard was published by Brook at a_l. (11), Yee (12), and Yee and KrSger (36). Essentially, the conductivity of the gas phase around the sample and the surface conducti vity is comparable to or greater than the conductivity of the sample at temperatures of 1100°C - 1500°C (37 ,38). The surface and gas phase conduction can be prevented by using a cylindrical volume guard (39-41). The bulk con- 51 ductivity in was generally interpreted as ionic at low temperatures and electronic at high temperatures. Because of the variations in the experimental apparatus and purity of the samples used, there appears to be rather a wide spread in the experimental data on conductivity (II). Similarly, the ionic transport numbers measured by various authors (42-So) range from t^0.05 to t.«l. Kingery and Meiling (47) measured t^O.05 at 1550°C - 1750°C using mass transport experiments. Lackey (57) reports t^=0.6 at 1000°C and 0.01 to 0.02 at 1500°C. On poly-crystalline AljOj, Yee and Krbger (36) found t^=0.4 at 1500°C decreasing to 0.04 at 1000°C. On single crystal Mg-doped A^Oj, they found 1 up to 1450°C and t^-0.8 at 1650°C. Pappis and Kingery (51) from measurements on single crystal alumina with Fe as unintentional impurity of about 100 ppm, found n-type electronic conductivity at lower oxygen pressures (10*^ - 10" atm) and p-type hole con ductivity at higher oxygen pressures (10 ^ - 1 atm). This was interpreted as nonstoichiometric semiconduction with electrons compensating for ionic defects Al^*' or V^* on the low p(^ side and with holes compensating for * on the high pC^ side. They further found that the behavior of the poly-crystalline alumina was similar, except that the intrinsic conduction was masked by impurities and/or structure-sensitive defects. V EXPERIMENTAL TECHNIQUES AND RESULTS It is our goal to describe the dependence of physical properties of pure and doped crystals in terms of a defect model and its thermodynamic parameters. Such a model and its parameters can be arrived at on the basis of measurement of the physical properties as a function of the conditions of preparation or anneal. Three different properties shall be considered and measured: (1) Electron spin resonance, (2) Optical absorption, and C3) The elec trical conductivity and emf. A brief description of the sample preparation and the techniques and principles employed in performing the measurements is given, pointing out the precautions taken in each case to minimize errors. A. Sample Preparation For most of the work reported here Czochralski grown corundum* doped with cobalt was used. A spectro- graphic analysis of the sample is given in Table 11. In addition we performed measurements on a Czochralski grown (Ti, Co) doped alumina and on two flux grown crystals. The method of flux growth is similar to * Courtesy of Dr. G. A. Keig, Union Carbide, San Diego, California. 52 S3 TABLE 11 SPECTROGRAPHIC ANALYSIS OF CZOCHRALSKI GROWN Co:Al^Oj SAMPLE Element Ppm Co 31 Cr 4.6 Fe ND<8 Si 52 Mg 1.3 Ca 5.0 54 that of Nelson and Remeika (52). For optical and ESR experiments the Czochralski crystals were oriented by X-rays and cut to the required size; 3*5 x 2 x 4 mm. A disc shaped sample of 6 mm dia. x H mm was used in elec trical conductivity and emf measurement. The c-axis lies in the plane of the disc. For reasons explained later, the choice of a standard sample for use as a reference to compare the concentrations of divalent cobalt in ESR experiments, fell on a second untreated sample from the same Czochralski boule. This sample was of the same size as that mentioned above, but its orientation was different; its c-axis being perpendicular to the c-axis of the sample that underwent the oxidation-reduction anneals. All of the samples were polished with diamond grit in graded steps of 45/20/9/3/1 micron particle sizes. B. Annealing, Color Change and Blackening The Co-doped A120j sample used in ESR and optical experiments was annealed at a temperature of 1620°C in atmospheres with oxygen partial pressures, varying from 10'9 to 0.2 atm. A mixture of C0-C02 gases was employed to establish the required partial pressures of oxygen in the range 10~9 to 10"5 atm, a mixture of nitrogen and oxygen gases for the range 10"5 to 10 1 atm, and air to give 0.2 atm. The crystal was heated for 4 hours at these different oxygen activities at T»1620°C. This was enough 5S time to equilibrate the crystal with the surrounding gas phase, as seen from the resulting uniform coloration. At the end of the annealing period the crystals were quenched to room temperature. In a preliminary experiment, a sud den quenching cracked the sample and this set a limit on the quenching rate we could safely employ. To avoid cracking the crystal was gradually lowered from the hot zone of the furnace, letting it stand at intermediate temperatures for a few seconds before taking it to room temperature. The total time of quenching was roughly 1 to 2 minutes. This is considered to be fast enough to freeze the atomic disorder prevalent at the high tempera ture. In one case, at T«1620°C and pO “10"*^ atm, a 30 minute anneal converted the green colored Co-doped crystal to a pink one fthis crystal, incidentally, gave 2 + the highest Co signal in ESR); on prolonging the treat ment for 4 hours, the crystal turned dark brown to black, indicative of the formation of cobalt metal precipitates. The crystal was reoxidized by heating in air before the different anneals in measurement series were carried out. All of the anneals were done in Astro 1000A, a graphite element furnace supplied by Astro Industries, Inc., Santa Barbara, California. The element is protected from oxidation by a muffle tube of Coors AD 99S impervious alumina, effects of leakage being minimized by running nitrogen gas over the element. The furnace shell is water 56 cooled and to reach temperatures >1500°C it was found necessary to add water cooled jackets at either end. The maximum limit on the operating temperature is set by (1) the use of the muffle tube, and (2) heating of the electrical terminals supplying power to the graphite ele ment. At 1750°C, the softening of the muffle tube makes it necessary to operate the furnace in a vertical position to minimize bending of the muffle tube, which occurs to a great extent for operation in a horizontal position at these higher temperatures. C. Optical Absorption Measurements and Results Optical absorption measurements reported here are done on a double beam Cary 14 spectrometer. The polarized spectra are obtained with polaroid HN22 filters. Two special mounts that can be positioned properly in the Cary 14 cell compartment are used to mount the sample and polarizer, while a similar mount is used for the polar izer in the reference beam. That means that except for the sample, everything else is common to both the beams. The samples are attached to the mounts with rubber cement. For relative concentration determination, only room temperature spectra are used. Typical spectra are given in Fig. 12. It can be seen that the bands are superim posed on a background absorption possibly due to defect centers. Areas of the cobalt bands are taken to be the OPTICAL DENSITY (Arbitrary Unit*) Co: ALO» E iC OXIDIZED SAMPLE Co: A l,0, E II C OXIDIZED SAMPLE Co: A LO , E I C REDUCED SAMPLE A=0.1 Co: AljOj E II C REDUCED SAMPLE m < 4 0 0 450 500 550 600 700 650 WAVELENGTH , mM Ln FIG 1 2 Room Temperature Absorption Spectra ^ Log Relative Intensity 5 4 3 2 Co ( 4 3 3 0 A) 10 9 8 7 6 5 4 3 2 LOG p02 Fig. 13 Optical absorption band intensities Vs. p02 , OPTICAL DENSITY (Arbitrary Units) A=0.i < 500 400 450 600 650 700 550 WAVELENGTH , m F FIG 14 Room Temperature Absorption Spectra of Ti(Co:AI2 0 3 TABLE 12 RELATIVE CONCENTRATIONS OF Co2+, Co3+ AS A FUNCTION OF p02 n pO- TTT Sa*ple Standard 2+ I||(Co (Band at 4670A) , 2+ Xj^cxz ) (Double band: 5300-5500A) negligible but present 0.97 2.31 2.25 3.75 I^(Co3+) (4350A) T7JT 0.98 0.71 0.61 10 10 10 -5 -6 -7 -8 10 10 -9 1.91 2.23 2.45 2.65 1.72 0.38 0.35 0.43 0.61 negligible but present 4 Sample turned dark brown to black. Absorption - X indicative of Rayleigh scattering from precipitates, probably Co-metal. ‘Negligible on the sample used. Thicker samples may give measurable band intensity. 61 areas above the background as shown by the dotted lines drawn on all of the spectra in Fig. 12. It should be noted however, that this arbitrary choice of background might be in error, if the native defect centers formed absorb light in the wave length regions of interest. Moreover, the predominant defect centers are not the same in the oxidized and the reduced condition of the sample. Nevertheless, we do not feel that the choice of the back ground causes appreciable errors in the results. The band areas are measured with planimeter and the relative values of the areas are listed in Table 12 for the bands speci fied therein. The values are an average of six measure ments on each of the bands. These intensities are plotted in Fig. 13 as a func tion of oxygen partial pressure and the respective slopes obtained are given on the figure. Spectra of (Ti, Co): A^Oj are given in Fig. 14. These will be discussed later. Optical absorption spectra can be used to determine the concentration of the species (e.g., Co , Co ) if the oscillator strengths are known. However, in cases where the fact that the dopant can exist in more than one valence state is ignored, the estimates of reported oscillator strength, using the total concentrations from spectrochemical analysis, may be in error. Consequently, we determined the ratio of Co2+/Co3+ experimentally from 62 2 + T+ the observed relative variation of Co from ESR and CoJ from optical absorption, with oxygen pressure. We define e(X), the decadic molecular extinction coefficient from the absorbance A(A), measured directly from the absorption spectrum, where A(X) - log10 “ e(Mc* where c« concentration, in moles per liter length of the sample, cm The oscillator strength, f, of the transition is then defined by 1000 me2 . f - ---- — ^ 2*30* /e(v)dv N *eZ v - 4.32•10"9 /e(v)dv where e(v) * decadic coefficient as a function of wave- number v ■ wavenumber, cm"*. N ■ Avogadro's number. Assuming a gaussian line shape for the absorption band, for which 2 2 e(v) * eQ exp -a (v-vc) with being the maximum occurring at vQ and halfwidth being such that e(v)-eo/2 at V " V 0 ± 6 . Hence we have OS OB f V - V -I 2 / e(v)dv- 2e0 / exp ----*n2 d(v-v ) * Qo w o o - - e 5»2.1289eQ6 Therefore, we finally have f - 9.20.10”®e 6-9.20.10 o where AQ - maximum absorbence at vQ. If c is in atoms/ The following values of oscillator strengths are obtained from our measurements. D. ESR Experiments and Results The experiments to be reported here were performed with a homodyne reflection spectrometer operating at X constant of 1 second. Since absolute concentration determination is hard, a comparison method is followed. In general one looks for a standard that has the features of (53) (1) a resonance line width close to that of the unknown sample, (2) a spin concentration near that of the sample, (3) stability in time and temperature and (4) a short spin lattice relaxation time, t , to avoid rf power saturation and (5) the standard should have the same cm**, we get f - 9.20*10”® — cl 6.023.1023 Co2+: * ^1 |C transition, f - 5.15.10 * Co3+: ^ — * ■ * transition, f * 6.9S.10~^ 12 It band. The sensitivity of the instrument is 10 -10AJ spins per cm-3 for a line width of 1 gauss, for a time 64 dielectric losses so that the perturbations in the rf field will be the same for both spin systems. In a superheterodyne spectrometer one can operate at low rf power levels to avoid saturation, but in our case at liquid He temperatures (4.2°K) the system is highly saturated. This is due to the fact that the spin- lattice relaxation time at this temperature is large, 1 sec, following in the range 1.8-4.2°K, and falling rapidly ® t^-T'7 in the range 4.2-22°K; it is very short at liquid and room temperatures (7). This makes it difficult to observe C(^+ spectra at liquid or room temperature as well as at liquid He temperature. The spin-lattice relaxation measurements of Zverev and Petelina (54) showed that (a) in the range T«1.8-4.2°K, y-T_l results from a one phonon direct process, of the emission and absorption of single phonons between the two Zeeman split levels of the lowest Kramers doublet, and (b) in the range T«10-25°K, t^~exp (6/kT), where6 is the separation between the lowest Kramers doublet and the next excited doublet, resulting from the resonant absorption and emission of phonons involving a third level as first explained by Orbach (55). In the light of this information, our experiments were all performed at a temperature of 15-18°K sustained by means of a heater placed on top of the cavity which is situated in a vacuum enclosure immersed in liquid helium. 65 At this temperature the Orbach process shortens the relaxa tion time enough to avoid saturation and greatly improves the signal strength. The temperature is measured by a calibrated carbon resistor in the cavity. The sample is mounted on this resistor whose value changes from =*150n at room temperature to =4250fi at liquid helium temperature. These changes are measured by a bridge circuit. For rela tive concentration measurements, the reference or standard used is another sample from the same Czochralski grown boule, annealed at 1500°C in air to bring it to the oxi dized state. The sample and reference were cut and ground to the same size with their c-axes mutually perpendicular. This crossed c-axes mounting in the cavity facilitates recording of the parallel spectrum of one (H||C) and the perpendicular spectrum of the other (H_]_C) at the same time. The relative concentrations are estimated on the basis of the following analysis: The intensity 1(H) of ESR signal is proportional to where g^^ - g-factor along the rf field - gj^ $ * Bohr Magneton f(H) ■ Normalized line shape function /fdH * 1.0 Hrf ■ rf field, H ■ the modulating field. • i Tn In our experiments the sample is below the standard. Therefore, it is likely that the modulating field and the 66 rf field seen by the two differ; say H and H , by the in r t sample and (aHm) and (bHrf) by the standard. We now con sider the two cases that the c-axis of the sample is ||H andJ_H. In the following superscript S refers to sample and R to reference. Experimentally, the intensity of the ESR signals was monitored by the peak to peak value of the derivative spectra recorded, i.e., Then we have Case (1): H (|c-axis of the sample orJ_c-axis of the reference. Case (2): H|c-axis of the sample or f | c-axis of the reference (1) max (2) (3) From (1), (2), (3) and (4) above, we get (5) 67 I|S nS 1 , d£ . , df C6) d « R «k2 dH IR n ab max max II Multiplying (5) and (6) we find 'U lSj 2 _i_ 2 r , R, i\ Ur) .V* ("r) 61 C?) Assuming different coupling factors a' and b* when the positions of the sample and reference are reversed, we get» along similar lines, & k (») i|R iR R 2 In one condition of the sample (ng constant), two separate experiments were performed with the two positions of samples and reference to find the value of ^ 6^ * The ratio of (7) to (8) was found to be ( }* 3I )2 “ 1. 04 =6^ ^ • The volume of the cavity used in our experi ments was large compared to the size of the samples (1000 times). In view of this, although the permittivity of is 8-10, the "buckling" of the electric field in the cavity will not be severe and the values of can safely assumed to be equal. Thus /T7UT ■ 1.02 and the values of relative concentrations are to be cor rected accordingly. It is necessary to emphasize certain features contributing to the accuracy of these measurements. H1C I525g g„ * 2.292 ±aO O I A = 3.24 ± 0 ,01 xl0"*cm‘' g A* 4 .9 4 7 ± 0 .0 0 3 B = 9.72 ± 0.05 x I0 'scrn' FIG 15 ESR Spectra at x-band frequencies. \A 30l0g H II C O' OB Log Relative Intensity 10 9 8 7 6 5 4 3 2 -1/24 1 -10 8 6 4 2 0 Log p02 Fig. 16 ESR measurements of relative intensity 2 + of Co concentration. 70 The choice of a standard for comparison purposes having the same saturation characteristics, line width, dielectric behavior and similar concentrations has the great advantage of elimination of errors which result from differences in the above features between the sample 2 + and the reference. The anticipated variations in Co concentration with variation of oxygen activity are small and therefore a high accuracy in measurements is required. This we feel is met by the procedure outlined above. The HSR spectra obtained at T»18°K in H||c and Hjc orientations are given in Fig. 15. The relative intensity of ESR signals, which is a measure of the relative Co2 + concentration after the various anneals are listed in Table 12 and are plotted in Fig. 16. It is seen that the Co2 + varies as p02*/2* in the range 10"®-0.2 atm of oxygen partial pressures. E. Co2* and Co^* Concentrations as a Function of Oxygen Partial Pressure From the optical and ESR measurements described above it was seen how to measure the relative variation of Co2 + and Co3+ concentrations with oxygen partial pressure. In the following, we indicate the method of estimating 2 + 3^ the absolute concentrations of Co and Co ions. At two given oxygen partial pressures, say p02(l) and p02(2), let the intensities of ESR spectra of Co2+ and 3 + 1 1 2 2 optical spectra of Co be I ,1 and I , I , r sr op sr* op respectively. Therefore, we have, at pO^Cl) i1 - x £°2hK1 st *sr *op ' X op [Co3*] and at pC>2 (2) I2 - X [Co2+] sr sr 1 - X„„ [Co3*] Op °P 71 (1) ( 2) Also, at all oxygen partial pressures, we have [ Co2+] + [ Co3+] [Col 2 + or a+b-1, where a* [Co ]/ |Co] , tot Combining (3) with fl) and (2) leads to tot b«[Co3+] /[Co] tot sr °P x + X * sr op sr sr QP cop or sr _LC_ sr - I 1 (4) op °P Op Hence r can be evaluated from any two measurements. In fact r was determined from an average over all the pairs of measurements. Then the ratio of b/a can be found at any pressure from ! -x. Iop^Isr (5) Finally, a, b can be determined using in addition a + b * 1. 72 TABLE 13 CONCENTRATIONS OF Co2+ AND Co3+ AS A FUNCTION o. OF p02 at 1620 C [CoV ^ - 1.22 x 1018 cm"3 v Jtot [Co2*] [Co3*] pO-f atm a I b ” (1-a) - 2 [c°ltot E^tot 0.2 0.42 0.58 10"5 0.586 0.414 10-6 0.705 0.295 10"7 0.746 0.254 10'8 0.806 0.194 10~9 0.913 0.087 73 The results obtained on this basis from the measured intensities listed in Table 12 are given in Table 13. F. Electrical Measurements and Results A schematic arrangement of the cell used is given in Fig. 17, wherein all the parts used are illustrated. Essentially the crystal is held by two — inch x i inch x 4 8 18 inch long alumina tubes. One of them is covered with Pt over the whole length to form a cylindrical guard. This shield was applied by pasting several times with diluted flux free platinum paste. Platinum electrodes on either side of the sample are taken through alumina tubes of outside diameter of 0.05", wall thickness of 0.0125" and 20" long. The whole cell is surrounded by an outer alumina tube whose outside was platinum painted as des cribed above to form a screen and to avoid any electrical pick up; this screen was grounded. For the electrical conductivity measurements two Keithley electrometers, 602 and 610B, were used as shown in Fig. 18(a). The battery shown in the figure is used to compensate for surface and gas phase conduction as described below. The method of measuring conductivity, after equilibrating the crystal with the gas mixture around it, in principle, consists of 3 steps. (l)Measure the initial voltages VpG and V°pg and (2) Switch Keithley 1 into the gas out gas in ^WVYWY WWWvWWYA B Z II ^ 1 2 Fig. 17 Schematic arrangement of the electrical cell assembly. 1. Alumina tube painted with Pt paste on the outside. 2. Disc shaped sample. 3. Alumina tube. 3A. Alumina tube with Pt paste as guard on the outside. * 4. Alumina tube spacers. 5. Quartz joints. 6. Narrowed down pyrex joints. 7. Alumina spacers. 8. Alumina tubes carrying electrodes and gas. 9. Pyrex joints. 10. Rubber sleeves. 11. Shrinkable tubing. 12. Pt leads. 4* 75 Sample Pt p a i n t on AI 2O3 tube ^ 9uarc* c y l i n d e r £ I Cel th ley 610B Keithley ( • ) wWvw - a a Aa a a a t ■ V W W V V 0») Fig. 18 (a) Circuit Arrangement and (b) Equivalent circuit. 76 ohmic mode. In this operation a current as given by the inverse of the ohmic range is applied to the sample and the voltage developed is measured by the Keithley. In performing this step of the experiment the ohmic range selected should be such that a considerable change occurs in V . Now V«c and R, are recorded. (3) With the help PS PS 1 of the battery showi\ a voltage is applied between S and G to bring back Vpg to its initial value Vpg and then the resistance recorded by the other Keithley, R2 is noted. This method of measurement due to Brook et^ al. (11) and Yee (12) is a refinement of the method proposed originally by Mitoff (41). It is designed to eliminate the effects of surface and gas phase conduction. If the method func tions as intended, R2 should be greater than R . In the measurements reported here, this was found to be so only when the battery is connected between S and G. When the battery was between P and S, considerably smaller voltages were necessary to bring back the Vpg to Vpg and also R^ was less than Rj. In view of this the batteTy was always used between S and G rather than between P and S. Using the above method, conductivity was measured at T-1620° at various oxygen partial pressures ranging - f t from 10 to 1 atm., and as a function of temperature at -4 constant oxygen activities of 3.2 x 10 , 0.2, 1 atm. The latter activities of oxygen were established with nitrogen, air and oxygen respectively around the sample. 77 (1) pO? = 1 atm,AH*2.65 eV (2) p02 = 0.2 atm, aH=2.90 eV (3) p07 = 10'3*5atm,AH -3.48 eV *■ av (4) o . AH =3.97 eV ion av 5 .CD \ (4) 7 5.0 5.5 6.0 6.5 7.0 104/T Fig. 19 Conductivity as a function to ten|>erature 78 10 e x io5 el 2 4 0 8 6 Log p02 Fig. 20 Electrical conductivity as a function of pO 2 79 The results are plotted in Figures 19 and 20. The latter includes an analysis of our data, which is discussed in Chapter VI. For emf measurements a procedure similar to the one followed in the conductivity measurements is adopted. First we note the initial voltages with the same atmosphere on either side of the sample: Vpg, Vpfi. Then the gas on the probe side is changed. This develops a voltage across the sample which in turn affects Vpg. The two voltages Vpg and V£q are recorded. Lastly, the battery is applied between S and G to change V£g to V°g in sign and magnitude and V^, is noted. The voltage developed by the cell is taken to be f o _ rt P°2(it) E ■ VPC ■ VPG - *i S ln pof(I) As outlined in Section IVAf the slope at each pO^ of a plot of E Vs.pC^CII) gives t^ at that pC^ with pf^CI) kept constant; pC^CI) is chosen at 1.0 atm. The three step compensation method used here assumes that the imposed external conditions on the sample do not affect the surface and gas conduction mechanisms in different steps, e.g., in the emf measurements, when different gases are introduced on either side, the Vpg and V°G change to V£g and V£G- Now a potential is applied between S and G to bring back V ^ to the initial VPS to record VpG final. Connection of the battery as such 4FE/2.3RT 2.0 Nernst Value 1.0 Assumed, giving t.=l (See Fig. 22) / - + - - i -4 Log p02 -6 Fig. 21 Emf as a function of oxygen partial pressure at T*1620°C -8 00 o Ionic transference number 1.0 Assumed to suggest the model v as derived in Fig. 24 0.5 -8 -7 -6 -5 -4 -3 -2 -1 0 Log p02 Fig. 22 Ionic transference number as a f(p02) at 1620°C. should not affect the result; with and without battery connected, when Vp^ is the voltage between pTobe and shield, the emf between P and G shall remain the same to justify the above assumption. This has been veri fied to be the case in the measurements reported here. Our measurements are plotted in Fig. 21. From these results we derive t.(pO«) as shown in Fig. 22. X H VI DISCUSSION In this chapter, after a general survey of the nature of defect centers in Co-doped o-Al^O^, a discussion of our experimental results is presented. From an analysis of the results, using the qursichemical approach of Krdger and Vink (13), a plausible defect model is suggested and some of the equilibrium constants are estimated. The 7 + analysis also leads to the position of the Co* levels in the band gap. A. General Survey Cobalt is known to substitute for the Al-ions in A^Oj and exists as trivalent, divalent and quadrivalent species. In case of trivalent substitutional species (Co^i) no charge compensation is necessary but in quadri valent form (Co* ) and divalent form (Co* ), charge m Al compensation by effectively oppositely charged species is necessary to keep the crystal electrically neutral. Coj^j requires charge compensation by positively charged species. In principle, charge compensation may be provided by any one of the following: (1) Presence of foreign ions with a charge of (4+) or higher on Al-sites. (2) Presence of foreign electropositive (metal) ions on interstitial sites. (3) Presence of protons on interstitial sites; this 84 appears to be the case when Co-doped Al^O^ is reduced in a hydrogen atmosphere. (4) Presence of native donors,Al^*, V*’ and the like. (5) Electron holes, h‘. o In case (2), the foreign ion may be cobalt itself, giving compensation of cobalt ions on substitutional sites by those on the interstitial lattice according to[Co^j]* 2[Co**1 as proposed by Zverev and Prokhorov (7). In i mechanism (3), the protons may increase the conduction. Attempts to find this effect in Al^Oj heated in H^-HjO mixtures have so far been unsuccessful (58). Mechanism (4) would give rise to an increased concentration of native ionic defects, not to be expected for (1). This increased concentration leads to an increased ionic conductivity. If cobalt were present on interstitial sites and substitu tional sites, there would not be any effect on the native defects, but a cobalt doped sample might show conduction 2 + due to interstitial cobalt. However, the fact that Co 2 + and Mg have similar effects on the conductivity seems to rule out the possibility of appreciable charge compen sation of substitutional cobalt (Coj^) by interstitial cobalt (Coj*). This leaves open the possibility of either ionized oxygen vacancies or aluminum interstitial ions as the compensating native defects. Either of these could be participating in the ionic conduction to an extent deter mined by their mobility-concentration product under a given set of conditions. Both these species are expected to be 85 present in higher concentrations at lower oxygen partial pressures, where cobalt is predominantly divalent and the concentration of both of them decreases with increasing oxygen partial pressure around the crystal. On the basis of the defect models examined in Chapter n i with the assumption that most of the cobalt is the trivalent form, [Al3*] ~p023/16 and [Vq ] ~p02^ 6. These pressure dependences are so close, that it is practically impossible to decide which is the major species participating in conduction from conductivity data alone. Moreover, electronic species, which according to mechanism (5) could also compensate for the Coj^j charge have the same pressure dependence and can therefore also not be excluded. One has to be careful here to distinguish the electronic conductivity from major charge compensation by electronic species and partial electronic conductivity resulting from electrons or holes being present as minority species. The latter is possible because the mobility of the electronic species is probably far greater than that of ions. B. Optical Absorption Spectra The theory necessary to interpret the optical absorption spectra was outlined in IIIA. Typical spectra for cobalt doped alumina in the oxidized and reduced con ditions are given in Fig. 12. The relative changes in intensity of the bands chosen to represent the relative changes in concentration of the divalent and trivalent TABLE 14 ABSORPTION BAND INTENSITY AS A FUNCTION OF p02 Species Band Position Polarization Transition Band Intensity 0 Assigned x A P02 X=value listed -1/14 + 1/20 -3/17 Coj^ 4670 E||C 4A2*4A2 CoJj 4350 Ej_C 1a1^1t2 Unknown Double band E]_C Unknown . with peaks at (X* ) 5300/5500 A0 87 forms of cobalt are plotted in Fig. 13 , as a function of 2 + the oxygen partial pressure. The label X represents the species causing the double band at 5300 and 5500A, which we discuss presently. The intensity of these bands varies with pC>2 as given in the Table 14 . Within the framework of the theory, the double band with peaks at 5300A and 5500A does not appear to be arising from any of the allowed electric dipole transitions of the divalent or trivalent cobalt ion in the trigonal field of the AI2O3 lattice. The strength of the band and its occurrence in the two Ej_C spectra (a) with propagation vector along the optic axis (c-axis) (a-spectrum) and (b) with both propagation vector and the E vector perpendicular to the c-axis (o-spectrum) confirm that the transition is electric dipole type. The band appears only in Ej_C orien tation and does not show any related features in the E||C orientation. This band appears in other samples of cobalt-doped alumina obtained from the same source.* Spectra reported by Keig (6), reduced in hydrogen and nitrogen mixture, also show the double-band. However, Mtfller and Gffnthard's (2) spectrum does not show this double band. In a doubly doped system like Ti, Co: Al^O^, one expects titanium to be partially present as Ti4+, with c8+ to compensate its charge. A typical room temperature * Courtesy of Dr. G. A. Keig, Union Carbide, San Diego California. 88 spectrum of Ti, Co^l^O^ is shown in Fig. 14. This spec trum shows in the EXc orientation, a double band with maxima at 5000 and 5300A. Thus, though a double band is observed, its wavelengths are different. Also, now a related double band appears in the E||C orientation. The absorption spectrum of Ti, CorA^O^ resembles, in the essential features of the strong bands, that published by Townsend (8) f°r Co, F:A1 0 in the visible region. The £ j crystal used was grown from a PbO + PbF2 flux and one expects F~ incorporated on oxygen sites to compensate divalent cobalt on Al-sites. There is no specific assign ment of the strong double band to any transitions of the d -ion by Townsend(8). Therefore, at this stage, the origin of the double band, though it is the strongest feature observed in our reduced samples is unknown and 2 + though it may involve Co in one way or another, it is 2 + not assigned to Co in our analysis. An examination of dn-ion energy level diagrams of Tanabe and Sugano (23), shows that a perpendicularly polarized double band may occur with E_[C orientation only for a d^-ion in medium field. Since the band we observed appears in reduced crystals, the possibility of iron as an unintentional impurity has to be considered. In this case Fe^+(d**) with a dipole transition ^Tj^ E may give rise to a double band in the EJC polarization if the upper state is split by a Jahn-Teller distortion. This band is ex 89 pected to occur at *11,000 cm**. Since the double band in our samples occurs at 5300A - 5500A (18,200 - 18,800 cm"*) we do not think that it is due to Fe^+ ion. Both the chemical analysis and the spin resonance data support this conclusion. Hauffe and Hoeffgen (57) give optical absorption spectra of CoiA^O^ with 3 At* Co. Their unpolarized spectra show a double band around S600A - 5800A, these bands appear both in the reduced and oxidized samples. This suggests that this band is arising from pairs of Co* X A1 and Co^j, i.e., ^°ai CoA1^’' ®ur measurements indicate that nearly 2/3 [Co)tQt is divalent in the reduced crystal and is trivalent in the oxidized crystal. The concentra tion of (Co^j ^°Al^' Pa*rs *s proportional to the product X of the concentrations of Co^j and Co^ which is a constant 1 2 2 given by -(■y) (*y) ■ Therefore, the intensity of the band will be the same in both oxidized and reduced states as observed. An estimate of the oscillator strengths of the bands 2^ 1^, used to measure the concentrations of the Co and Co ions is given in Section V.C as f 2+ “5.15 x 10~* and The f- 2+ i? aboi mailer than that esti- Co mated by Townsend (8). The value of fCo3+ (2) is about a factor *10 larger than the value for the second excited state in E_[C orientation given by McClure (1). (band at 4670 A) Co%Cll) 10"’ (band at 43S0 A). 90 It was observed that when the sample was annealed at _ o pC^slO atm (T«1620°C) the crystal turned dark brown to black and the optical absorption shows a A* dependence. This could be explained as due to Rayleigh scattering from precipitates, which we expect to be cobalt metal. This finds support from ESR experiments in that the concentra- 2+ -9 tion of Co in the sample annealed at pO^lO atm is only about 6S% of that found when the sample was annealed _ o in an atmosphere of pO “10 atm, contrary to an increase 2 + in Co expected for stronger reduction. This indicates 2 + that the amount of Co in solid solution in the a-alumina is decreased by the formation of the precipitates. 2 + C. ESR Spectra of Co Ion in A^Oj The experimental results from literature and the nature of defect centers suggested for Co-doped A1 O, by 2 J previous authors (7,8,9) are discussed in IVB. Here we discuss our observations and compare with the earlier work. The samples of Zverev and Prokhorov (7) appear to be doped with 0.011 of cobalt and Townsend and Hill's (9) samples are also heavily doped as compared to the 0.0031 of cobalt present in the samples used in our work. It is certain that the cobalt ion is present in more than one valence state whatever thermal history the sample experi- 2 + enced. The Co concentration is correspondingly higher in their case and may be present in more than one kind of 91 defect centers. This is reflected in their observing two different spectra. The ratio of trivalent to divalent cobalt is not known and there is no evidence to support the view that all cobalt is converted to trivalent form by oxidation or to divalent form by reduction as assumed by Keig (6). Townsend (8) reported only one type of ESR spectra on pink colored CoiA^O^ crystals grown using PbO+PbF^ flux. This color being caused by octahedral divalent co balt, it can be assumed that most of the cobalt in those samples was in divalent form. However, their later work on samples grown using fluoride-free oxide flux (Pb0+B20^) is green in color and this is attributed to Co3+ in octahedral coordination. Although one assumes that in this latter sample the majority of cobalt in the trivalent form, the observation of spin resonance shows that divalent Co must be present. The formation of pairs or associates of CoJ^ T and Alf* in the green sample and their suggestion that the type II spectrum seen by them and Zverev and Prokhrov 2 + belong to the pairs indicates that the Co concentration cannot be very small. The type I spectrum appears to be definitely due to free Coj^. The observation that the intensity ratio is different in the two studies, references (7) and (9) suggest that the ratio of 2.3:1 seen in (7) is a coincidence and has nothing to do with the ratio of substitutional to interstitial sites. This suggests 92 that the type II spectrum could occur with different intensity depending on the thermal history of the sample and this behavior is unlikely if the spectrum II is due to an interstitial cobalt center. The measurements reported here show only type I spectrum; a type II spectrum is not seen. In one experiment efforts were made to adjust the conditions favorable for formation of associates of Co!, and Al?: Al i This was done by annealing the crystal first at 1620°C, at -8 10 atm, for 4 hours. Then the crystal was cooled over a o period of *20 hours to 1250 C, at which it was kept for ~30 hours. The sample was then slowly cooled to room temperature. This did not yield any spectrum other than the type I spectrum. This is probably due to the low doping level in our crystals. Experiments by us, on an oxide flux-grown, dark green sample*, at 18°K, with homodyne reflection type electron spin resonance spectro meter have not shown the type II spectrum. The temperature of 18°K was chosen, for the reasons explained in V.D, where the sensitivity is good and the saturation of the levels is avoided. We do not think that the absence of the type II spectrum in this sample is due to the lack of sensitivity as we could see a strong type I spectrum in this sample. Since there is not an appreciable difference * Courtesy of Dr. J. W. Orton, Mullard Research Labs, U.K. 93 in the spin-lattice behavior of the two centers (54) with temperature at 18°K the spectrum due to the second center should appear even if their concentration is only of the order of 1/50 of that of the free Co'A^ centers character ized by spectra I. A feature of our H||C and HjC spectra is that we see extra lines in the H||C orientation besides the main 8-hyperfine components and a clean 8-component spectrum in the H_[C orientation. The angular dependence or behavior of these extra lines can be described as follows: there are two extra lines growing when H is |) C-axis between hyperfine components* more strongly on the low field side, as shown in Figure 15. The two lines decay to one when the angle between H and C is a 2.5° and they completely disappear when the angle between H and C-axis is a 12°C, leaving an unperturbed spectrum at larger angles. At this stage no explanation for these forbidden transitions can be given. The relative change in Coj^j concentration repre sented by the signal strength of type I spectrum is arrived at on the basis of the comparison method outlined in V.D, taking as the intensity ratio the geometric mean of the relative strengths of the high field lines of the spectra of the sample and the reference in the two orientations. This leads to a variation of the concentra tion of[Coj^ as [Coj^] ~p02*1^24. 94 ESR experiments at room temperature indicated the 7^ T + presence of Cr and Fe ions as trace impurities. An attempt was made to measure the conversion of Fe^+ to Fe^+ by comparing the relative intensities of the Fe3+ ESR lines with those of Cr^+ lines, assuming that chromium is always present in trivalent form under oxidized as well as reduced condition of the other ions. However, comparison of a set of Fe^+ lines to Cr^+ lines showed that the ratio [Fe^+]/[Cr^4] is higher in reduced state of the crystal than in oxidized state. This indicates that Cr^+ is also reduced to Cr^+ and this reduction is stronger than that of Fe to Fe . This line of experimentation was there fore not pursued further. D. Electrical Conductivity and Ionic Transference Number determination The results of high temperature conductivity mea surements and the emf measurements are plotted in Figs. 19 - 21. From the emf VS pC^ data in Fig. 21, we find ti^P®2^ as shown in Fig. 22. The ionic trans- , 7 ference number is a maximum at pO^ =10 atm, where the total conductivity is a minimum. The t^ at this pressure is 0.73. By multiplying the conductivity data in Fig. 20 with ti and (1-t^) - tei» we *ot the contributions as shown in Fig. 20, from the ionic conductivity and the sum of the electron and the hole conductivities. The latter 95 can be separated into the individual electron and hole conductivities; the three partial conductivities are as shown in Fig. 20. There are two reasons why this result is unaccept able. In the first place, ck with a maximum as found here cannot be explained by any disorder model. For, if two species contribute to , this invariably leads to a with a minimum and, if only one ionic species were to contribute, must increase or decrease monotonically. Secondly, the above model giving ae and as shown in Fig. 20 leads to an unacceptable value for the bandgap of A^Oj, as shown below. Let us consider the following ionization reactions and the equilibrium constants Cl) [C° M ] ( 2) 0 - e' + h’ ; [e*] Ch] (3) Note that (4) 96 The constants K’ , K'' and K. are also given by Co Co 1 ®Co*, / 2nm0kT\ f C*x" ^ioA1) «Co A1 , *Al /2nmekTX ^ f _ - ■ 1 h2 ) eXPl‘ kT * 1 } K'' “ 2 ^ L . 2 e x p [. V EV ] (6) Co gCox \ 2 ) I kT * A1 and Ki ' 4 f 1^ ) 3 (memh)V 2 exP I' CkT V ] (7) where E^-Ey-E^, the bandgap, ®Co*^, ^ ° aj are statistical ^ + 2 + weight factors of CoJ and Co depending on the degeneracy of the ground states of these ions in the corundum lattice. The ground state of Co3+ is *A^ (a single state) and that of Co2 + is ^Tj (12 states). Therefore, ®Co^-l, ®Coj^-12. The other symbols have the usual meaning. Estimating the electron and hole mobilities, one can calculate the concentrations from the conduction data. An electron mobility as high as 100 cm^/V-sec has been measured at 1000°C in AI2O3. Therefore, at 1620°C, an electron mobility 7 2 ve“50 cm /V-sec and a hole mobility, vh“l cm /V-sec appears to be reasonable. From Fig. 20, at pC^lO'^atm, T-1620°C, ae*°h“2 .10‘ 5[j" 1cm" 1, [Co^1]-0.44[Co]tot, [Co^ ]-0 . 56 [Co\ot (see Table 13, we get [e' ]-2 . 5.10^cm~ 3, [h']-1. 25. lO^cm"3 K' -3.18.1012cm’3, K* '- 9.84.1013cm‘3, and Co Co Kj - 3.13.1026cm or 97 X* - 3.33.1019 exp (-2.56 eV/kT) cm-3 to K£o - 4.8.1021 exp (-2.91 eV/kT) cm-3 XA - 16.1040 exp (-5.56 eV/kT) cm'6 Therefore, the bandgap would be Eg * 5.56 eV and 2+ the occupied level of Co would be 2.65 eV below the conduction band and 2.91 eV above the valence band. It is known that the bandgap at room temperature E (300°C)« o 9 eV. If one assumes the bandgap to vary with the temper ature as Eg"EgQ-0l'r> with a«5.10 4 eV/°K, we find 9.15 eV and Egj^gg-8.25 eV much larger than the value of the bandgap of 5.56 eV arrived at above. This suggests that the emf measurements at either the low pC^ side or the high pC>2 side are in error. As we shall see, a good agreement between experimental and calculated on the basis of a disorder model is obtained, if we assume that the emf results on the low pC>2 side, indicating a low ionic transference number or large electronic conductivity, are in error. We shall therefore assume that t* varies with pC>2 as shown by the dotted line in Fig. 22. This leads to an electron hole conductivity, a^, increasing with Q increasing pOj and an ionic conductivity, °^, increasing with decreasing p02 as depicted in Fig. 23. The reason for the unreliability of the low p02 side emf measurements may be related to the fact that we experienced great difficulty in maintaining the appropriate oxygen partial pressures on either side of the sample at 98 \ ion < • 10 ion s 10 el ion Theoretical model 2 0 4 6 hog p02 Fig. 23 Modified version of Fig. 20 Log Concentration 99 10 19 10 17 10 16 ® Co2+ from optical absorption • Co2+ from ESR data X Co3+ from optical absorption 3+ y ■ 0.00 y ■ 0.10 * - 0.36 y - 0.10 y - 0.00 y - 0.00 y - 0.10 concentration obtd. from the exptl conducti vity — Revised calculation of Al?* taking into consideration the pC^ dependence of donor concentration. y - 0.62 y - Cd'3/GCo] >1 -2 Log PO Fig. 24 A set of defect isotherms based on the model suggested. 100 these high temperatures of measurement. This is indicated by fluctuating and inconsistent emf values. No such difficulty was experienced in conductivity measurements with the same gas mixture all around the sample to main tain the desired pO . Consequently, the low p0_ side z ^ conductivity measurements are trustworthy, but the emf measurements in Fig. 21, indicated by dotted lines are questionable. E. Disorder Model It is our goal to suggest a plausible disorder model and estimate the thermodynamic parameters therefor. In arriving at the proper disorder model to consistently explain the experimental data of high temperature conduc tivity and the optical absorption and ESR spectra obtained on cooled crystals, due consideration must be given to the equilibrium conditions at the high temperature of annealing and its relation to the state of the crystal after quench ing to room temperature. An ionic conductivity varying with p02 as shown in Fig. 23 arrived at by multiplying theo-measured by the modified t^ curve of Fig. 22 can be explained on the basis of a model in which the major 3 . charged defects are Coj^ and either or A l #', The concentration of holes is considerably smaller than that of Co1 . A1 If V** is the major charge compensating species, 101 the Ionic conduction would be mainly due to migration of 7- i # O ions by a vacancy mechanism. If Al^* is the major species, the ionic conductivity would be mainly due to the migration of interstitial aluminum ions, Al?*. A choice between the two can be made by comparing the observed conductivity with that predicted on the basis of self diffusion data of oxygen and aluminum. Using the Nernst-Einstein relation between mobility and diffusion coefficient, the conductivity can be expressed as ,2 2 nZ e d kT where 3 n»No. of charge carriers/cm Ze»Effective charge, in Coulombs 2 D«Diffusion coefficient in cm /sec k*Boltzmann constant. According to Oishi and Kingery (58), the tracer diffusion coefficient D* is 0 * 3 , 152000, Dq - 1.9.10 exp (- RT' ) and with the assumption of doubly charged oxygen vacancies, this leads to o0 (1620°C) - 3.6.lO'9.!!"1^ ’1 From Paladino and Kingery's (59) work on self diffusion of A1 into A12Oj performed in air, the tracer diffusion co- 102 efficient is This leads to D*t - 28 exp [ -(114000 ± 1S000)/RT] 0 Al3- (1620°C)«8.8.10'S fi ' W 1 The value of ck observed by us is o i (1602°C) - 1. lO^fl^cm'1 This is close to the value indicated for aluminum inter stitial conduction. Therefore, the charge neutrality ] ■ 3[A1?‘]+ 2[Vg-]t[h] can be approximated by [Co^] = 3[A1? * ] and o. by o. 3*. For a fixed cobalt content as present in i A1 j our crystal [Co],. . ■ [ Co' ] + [Co4 ] or 1 - a + b with t o t A1 A1 poig F°Ai] a » » and b » r (1) I C 0 \ ot [Co^ ot 2+ 3+ As seen in Fig. 13, (Chapter V) both Co and Co show similar relative variations with pO^- This indicates that the concentrations of [Co* ] and [Co* ] are of the same A1 A1 order. Therefore the cobalt balance equation cannot be approximated: We have to explain the variation of [Co' 1, A X [Co*^l , o jj“[hl and o^«[Al^’]with pO^ using the complete cobalt balance (]) in combination with (r), (s) of Table 6 and the equations VI D. 1,2 and 3 with the neutrality 103 approximated by 3[Al?*J[Co* ]. From the above conditions, 1 t\l. on rearranging, we get u - a ?5 . I K [Co] p o , s/4 m A 3 Kox tot H 2 » a* with Kqx as defined by equation (s). 2 + The variation of the concentrations of Co and 3+ Co with oxygen pressure obtained from the cooled cry stals is given in Table 13. We find good agreement for the 2+ 3 + concentration variation of Co and Co with pC>2 at the low p(>2 side, using this model, with K.QX*2.83,10®atm mol. fr’*, (see curves labelled (1) y*0, Co^+ and (2) y“0, CoJ in Fig. 24). However, the agreement on the high pt^ side between the model and the theory is not good. This discrepancy can be explained by the presence of a small, fixed concentration of unknown foreign donors. These donors may be S i ^ , Ti^ or interstitial sodium or potassium ions. Silicon is known to be present as seen from our chemical analysis (see Table 11). However, Yee (12) in conductivity measurements on a silicon doped crystal did not find a significant effect of silicon on the conductivity, which indicates that most of the Si was present as a second phase, probably Al^SiO^. Yet, some Si should enter the crystal and affect the properties. Inter stitial potassium was observed in Cr^ : A^Oj. Indepen dent of whatever the donors are, their effect will be to partially charge-compensate the Co* . Labelling the 104 * " ■ unknown donors as D , the neutrality has to be extended to [Co1 ]-3[Al3] * [D* ] (3) A1 l Then equation (2 ) becomes . “ I Kox £Co^totp02 (4) a (a-y) where y “ [D ] / [Co ] tot The optical and HSR data in Fig. 23 are explained on the basis of this model with y - 0.36 - 0.42 corresponding to an unknown donor concentration of 36 - 421 of total Q cobalt concentration. KQX in this case is 5.96 10 7.33.10®atm~mol. fr-1. The concentration of Al?* 3 . based on this model is indicated by curves labelled A1 ‘, l y * 0.36 and y ■ 0.42 in Fig. 24 . The ionic conductivity, 3 . assumed to be due to Al^*, shall vary similarly with pO^, since the ionic mobility at a given temperature is a constant. An attempt is made to explain the experimental data a . ■ t;* o indicated in Fig. 23 using this model, ion i tot If one matches the low pO side of a with the Air* and 2 tot 1 calculates values at higher p02 on the basis of the model, we arrive at the curve marked a-1 • This shows values ion of c^on on the high p02 side that are lower than the experimental ones. On the other hand, matching the high pO^ side experimental values with [Al?*] obtained from the 2 model, gives the curve o^ontwhich overshoots the measured 105 oexp values on the low pO^ side. Therefore, this model does not consistently explain the data across the whole range of oxygen partial pressures. It should be remembered, that the above model was based on experimental data obtained from optical and HSR measurements on the cooled crystal, while the conductivity measurements given in Fig. 23 refer to the high tempera ture equilibrium state of the crystal. During cooling of the crystal to room temperature, the atomic disorder is assumed to be frozen in, but the free electrons and holes tend to occupy lower and higher states. They recombine involving a band-band process, or fill local levels in the bandgap rearranging themselves over the various centers. This alters the concentration of the ionized atomic imperfections as the crystal is cooled from high to low temperature depending on the position of the localized levels in the bandgap. Let us suppose the cobalt level and the unknown donor level are as shown in Fig. 25. x As we cool the crystal, the electrons from the D x level fill the empty Coj^ levels and convert Co^ to Coj^. This tends to increase the concentration of ionized donors as well as Co' in the cooled crystal, at the same A J . time reducing the concentrations of Dx and CoJj* Inverse ly, heating the crystal from room temperature to high temperature reestablishes the high temperature state. With corresponding change in the concentrations of the 106 Conduction Band n n n x v Fe' Al ! 3. 61 eV \ I .Co I AH 3. 72 eV 2. 89 eV Valence Band Fig. 25 Level positions of Dx, Col- and Fe' Al Al in the bandgap. The level of Fej^ is determined from Pappis and Kingery*s conductivity data (51). 107 various defects. If the donor level was a deep level and excitation of electrons into the conduction band does not occur, the concentration of neutral donors will be higher (or that of ionized donors lower) at 1620°C than in the cooled crystal. The charge transfer process involved can be represented by the reaction Co' + D Co* + D* ; 4 E Al Al [Co*j] p*l ' [Co^HD ] (5) K is also given by r K - exp (AE/kT) 8 c° a i 8 d If the unknown donors are Si^j, as suggested earlier, we take 8dx«2, ®D«1, and * 12, ^Co^ ■ 1. Using equation (4 ) with Kqx ■ 3.29.10®atm ^*.mol fr * and y«0.10, corresponding to a concentration of the unknown donor in the ionized state at 1620°C of only [CotQt]/10, we obtain the Al?‘ concentration varying with pt^ as shown by the curve Al^’ , y-0.10 in Fig. 24. Using an ionic mobility of * 1.35.10~^cm^/V-sec at T«1620°C the Q model leads to a conductivity curve °ion as shown in Fig. 23, which closely corresponds to the experimental data. Similarly, choosing a hole mobility of ■ 1cm / V-sec, the model gives which is in agreement with ex perimental data for hole conductivity. Using the ojj curve, we reestimate the constant as follows: Taking the value of 0^-8, 2.10 ^ atm at pO^O.Z atm [h*] - 8.2.10— - 5.12.1014cm~3 1,6.10"9,1 At this pO, of 0.2 atm, [Co* J/[Co* ]- 0.17/0.83 * Al Al Therefore, K' ' - F°Al][h ] . l. 05.1014cm"3 Co ----------- CCoJi] From * 3/2 SCoI. / 2irinh kT . , b C o A -E K" - 2 Al /---- ^------ exp I---A1 . . Y--- Co 8Co* \ h2 / I kT Al With the values of the parameters as chosen earlier, we have .14 2.12. 1.05.10 (200.1018) exp ^ C°A1 ^ ^ leading to - E Al v ECo* - E - 2.89 eV and K1 ’ - 4.8.1021 exp (-2.89 eV/kT) cm"3 Co We can now calculate the equilibrium constant for the following reaction, 109 f o 2 0 0 ♦ A l ’ - . A l * , ♦ § 0* ♦ 3h 3 K . L i O _ p o , - v « X CA1i'l 3 [COAll p02 From the definition of K * -- £11---------- and o x 3 3 [Co;i] [Al,3'] [Co* ][ h*] K' ' - Al , we see that Co “ [ Co ] Al K„ - K (Kl'D3 x ox Co we find Kx - 9.18.1076atm"3/4 cm"6 From the values of y-0.10 required to explain the high temperature conductivity data and y«0.36 - 0.42 necessary to explain the properties of the cooled crystal we can find the equilibrium constant Kr of equation (5 )• In the low temperature state, all the donors are completely ionized; therefore, taking the mean value of y ■ 0.38, we have D -0.38 [Co] . At high temperature tot L tot K - CdX] Cc°aiJ tCD]tot EB-n [co;,] r " [D-] [ C o ;,] " [D‘] [ C o ;,] Since the presence of donors is required to explain the high p0£ experimental data, using ^°A 1^ _ 0•17 [CoJ^] 0.83 110 at pC>2 - 0.2 atm, and [D* ] - 0.1 [C°]tot» we find K (1620°C)« C0,38ff~i°'-1!- * - 13.7 r Sco* *DX & c and from ■ = . exp (+ — ), we find r 8Co‘ 8D kT Al A E - 2.3. log1() (6 x 13.7) . 0.164 - 2.3. 1.9.4 . 0.164 - 0.72 eV An examination of equation f 5 ) shows that the ratio of ionized donors to neutral donors is proportional to the ratio of [Co. „HCo* ] and is therefore dependent on AF Al oxygen partial pressure at any given temperature. To take this into account we modify equations (3 ) and ( 4) using ( S ) and on rearranging, we find ■J1-8?3_____ - 1 K [Cd nO.'3/4 , , 3 ox totr 2 (6) a [ a - (l-a)jq where x - [ D*yiCr [Co]tQt (6) Both a and x are functions of pt^- From optical and ESR spectra we have information of a vs. pC^. To a first approximation ( 6) can be solved keeping x as a parameter. With x - 0, C 4 ) and (6 ) reduce to (2 ) and give the same solution. With x * 0.02 and KQx ■ 2.84 atm"^* mol. fr \ we get the concentrations of aluminum interstitials and Co* as shown by the dashed curves in Fig. 24, Al corresponding closely with the experimental data. Taking the estimated values of Dx and K„ from the above we find r n 2f t x - - 0.02. This shows that our analysis and the 13.7 Ill being the native ionic charge carrier. This view finds support in the fact that the order of magnitude of con ductivity estimated from the self diffusion data of Al is close to what is measured. The situation in Pappis and Kingery’s crystal differs in three ways from that in our cobalt-doped alumina crystal. (1) The crystal is doped with Fe instead of Co. (2) The concentration of Fe in their samples is given . 18-3 as 100 ppm or [ Fe] ■ 1.83.10 mol. fr - 4.27.10 cm , i.e., higher than the Co concentration in our sample. CA (3) K will have a value K typical for Fe, where ox ox KFe . ox r 3 r ai3*i [Fer ] L i J Al 3 • This constant can be determined by estimating ^1^' from their conductivity data at 1627°C, using the value of mobility of aluminum interstitials arrived at in Section VI.E. Taking the value of their °i627°C at P®2 “ 10"® atm, from Figure 3 (ref. 51). o 1627°C a I*?*!® £1 cm , t 1.7.10"5 lfi t [Al3' ] - ---------=----------------- 2.62.10 /cm 1 1.35.10‘3. 3.1.6.10 Since (Fe’ ] - 3[Alf*] - 7.86.1016/cm3 - 3. 36 .10‘6mol. fr. A l 1 112 model proposed above based on ( 3 ) and ( 4 ) is not greatly influenced by the dependence of [DX]/[D*] ratio on F. An Alternative Interpretation on Pappis and Kingery*s Conductivity Data The value of K determined above can now be used x in understanding the behavior of Al Oj with other dopants £ as well. We now present an alternative interpretation of the experimental conductivity data of Pappis and Kingery (51). Their measurements on single crystal alumina containing 100 ppm of Fe,an unintentional impurity, shows a broad minimum in conductivity at pC>2 - 10*^ atm. At c -0.17*0.03 the higher oxygen pressures (10'3 -1 atm) o-pC^ and at lower oxygen pressures a-p02 + 0* — °*03. From thermoelectric power measurements they conclude that alumina is an amphoteric semiconductor, p-type on the high p©2 side and n-type on the low p(>2 side. These authors suggest that the conductivity may represent an intrinsic electronic conductivity corresponding to a bandgap of 11 eV. In view of the similarity in behavior of their crystals and our crystals, we believe, however, that their data also represents a mixed ionic and electron hole conductivity. The ionic conductivity dominant at low p02, can be explained on the basis of a charge compensation mechanism with tFe^j] - 3[A13^], the Al-interstitial 113 C Al]T ‘ P ^ t o t ‘ CFeAl^' 1-7964 10" mo1- fr- From this we obtain 4 KFe- - OX 3. (1.7964 10 ’) 10 (3.3610*6)4 1.37.10^ atm ^^mol.fr. We define an equilibrium constant Kp^ for the FeiA^O^ case, similar to K" , vi z, Co Kr Fe [Fe^] [ h' ] This constant can be obtained from K” Fe , Fe 1/3 ( V Kox) and is found to be K" *Fe Since Kpe is also given by 1.4.5.10** cm ^ KFe "2 8FeAl «Fex Al , 2*m*kT 3/2 f - i Fe* - E Al v kT The ground state of Fe2+ in A^O^ is T^ and Fe3+ is **A^ giving * 15» *FeAl " w*th the other parameters as chosen earlier, we find (EFe* Al Ev) - 3.72 ev. From the estimated values of KEe and K" 37.10*7atm^ Ox Fe Qx ionic transference number o(n cm 114 * Pappis and Kingery's data (51) — V — Predicted from our model 0.5 0 -10 -8 -6 -4 -2 0 Log p02 Fig. 26 Electrical Conductivity of A170j as a function of pC^ at 1620°C after Pappis and Kingery (51) vs. our model. 115 mol. fr-1, K'pe ■ 1.045. lO^cm 3) we can calculate the partial ionic and electronic contributions to the total conductivity as a function of at T«1620°C. This is outlined below: [Fe* f - -S/4 A1 J P°2 Fe K - j 4 (1) 3 £FeAl] on replacing [Al^*] by ~ [Fe' ]. l 3 A1 On substituting a « [FeAl1 /t Feltot and CFeM ] b ' C Feltot and a + b ■ 1, eq. Cl) becomes T KOx[Fe:>totP023/4 ■ d-»53/a4 (2) This biquadratic equation can be solved at different pO£ 5 * values giving "a" and therefore the Alj - concentration. The hole concentration can be obtained from [»•] - Kpe (S) _ 3 Knowing the concentrations and using v^“1.35.10 2 2 cm /Vsec and ■ 1 cm /Vsec, we determine the ionic conductivity a , and hole conductivity a. Their sum 1 h leads to o , which agrees well with the experimental V v I 116 values taken from (51). Figure 26 shows this correspon- o dence as well as a t^ as f(p02) at 1620 C. The estimated level positions of Dx, Co^i • an<* Fe^i are as shown in Figure 25. The charge transfer spectra of transition metal ions in A^O^ as published by Tippins (60) show Fe level positions at 4.78, 6.38 and 7.2 eV above the valence band. The 4.78 eV peak corres ponds to electron transfer to the unoccupied ground state level of The calculated thermal level is 3.72 eV. The difference between the optical and the thermal level is due to the Franck-Condon shift, possibly combined with a change with temperature. Following, (29,66) Tippins showed that the charge transfer process of transferring an electron from an oxygen ion to a nearest neighbor metal ion (MJ ) is represented by O2' (2p6) + M3+(3dn) O' (2p5) + M2* (3dn+1) («) The threshold energy for this porcess can be identified with the separation of the M ^ ^ 1^ ^eve^ from the edge of the valence band. It can be written as 2 hV_ - E + e - £_ ♦ X(02') - I(M2+) - » ♦ AEj (5) T + - rQ pol a where e+ and are the electrostatic lattice energies at the metal ion and 0” sites (the Madelung energy), VQ is the separation between the two ions, e is the electron- 2 ic charge, e /r is the electron hole binding energy of ihe 117 separated charge, x Is t^ie electron affinity of the oxygen, 2 + I (M ) is the third ionization energy of M, V i s the polarization energy of the dipole formed by the charge transfer and AE, is a term added to account for the differ- d ence of the d*electron stabilization energy of the two different configurations of divalent and trivalent ions. If the cation substituting for A1 ion has approximately the same ionic radius, neglecting the lattice distortion effects eq. (5) can be approximated by hVT - C - I(M2 + ) + AEd (6) since ■ 35.16 eV > I(Fe2+) * 30.64 eV, on this basis, we expect the level of Ni^ to be lower than that 2+ of as actually observed.The Coj^ level, with I(Co )* 2+ 2 + 34.0 eV should be between the Ni and Fe levels, i.e., below the Fe level. Since there are no data on charge transfer spectra of CorA^Oj, we estimate the position of the level by interpolation between the Fe and Ni levels, and find ECo' - E -3.58 eV. Our thermal value for this A1 v separation was 2.89 eV, again smaller as a result of the Franck-Condon principle. Since neutral level must lie below acceptor levels, the level Dx introduced in our analysis, if due to a transition element, should be due to one with a low third and fourth ionization energy. Possible candidates are La, Hf, Ta, W, Mo Ir. G. Determination of Thermodynamic parameters 118 G. 1. Activation Energies The conductivity at T«1620°C was seen to be a mixed conductivity with contributions from ions and electron holes. The curves of conductivity Vs.l/T at oxygen partial pressures of 1.0, 0.2 and 3.2*10'^ atm indicate an average activation energy of the total con ductivity due to both the species. The average activation energy changes with pC^ since the contributions from the two species vary with pC^. From the data given in Fig. 19, we see that the activation energy is increasing with decreasing pO^ and this combined with the fact that . 3 the conductivity at pressures lower than pO^ - 10 atm is mostly ionic, suggests that the activation energy for ions is greater than that of holes. The value of E' - E ■ CoAl v 2.89 eV determined from our model compares reasonably well with the activation energies of 2.65 eV in oxygen and 2.84 eV in air (see Fig. 19). The conductivity data of curve (3) of Fig. 19 represents a situation where the ionic and electric com ponents contribute to the total conductivity in 73/27 ratio. Since the total conductivity and the components contributing to it are dependent on pC^ and temperature, we may write ° t o t Cp02* T) “ ai (P°2 * T) + V p(V T) (1) The ionic (o.) and the hole (o ) conductivities can be 1 h 119 separated into a product of two terms , one dependent on pC>2 and the other on temperature. Therefore °tot (p02’ T) ' °io exp ( '“ki^ °iCp02) AHh. ho exp (p02) C2) Now, curve (3) of Fig. (19) gives atQt Vs.1/Tat p02 - 10~3*5atm. At 1620°C, we know that at this p02, t. * 0.73 and o. - 0.73 otQt. At lower temperatures, we can estimate o^ by a ± (10'3*5 atm, T) - a (10 3,5atm,T) (3) A H a, (10_3*5atm) -°ho exP < - kT ^(1 atm) From the data in Fig. (23) (10‘3*^atm/a^ (1 atm) is given by (3.7 10-5) / (1.3 10-4) - 0.28S. Using this in equation (3), we obtain the curve (4) shown in Fig. 19. The activation energy of ions given by the slope of this curve on the high temperature side is *3.97 eV. The ionic and electronic conductivities are found to be oi - 2.83.106 exp (-3.97 eV/kT) n^cm'1 (4) a, - 985 exp (-2.65 eV/kT) fl^cm-1 (5) n 120 The ionic conduction will vary only as a result of a variation in mobility; the electron hole conductivity will vary mainly as a result of a change in the concentra tion of free carriers resulting from increased trapping at lower temperatures. Therefore, the activation energy obtained for the ionic conductivity is mainly from the mobility term. Combining the temperature dependence of v , (1620°C) - 1.35 10'3 cm2/V-sec, We find v _ - A1.* Al. l l 3.6.107 exp (-3.97 eV/kT) cm2/V-sec. Activation energies of conduction of 4.0 eV are t i reported by Ozkan and Moulson (40) and about 3.8 eV by Alexandow et al. Alexandow et al. (62) did not distinguish between ionic and electronic conduction. Correspondence with our results for ionic conductivity ck are to be ex pected if their samples were undoped or contained foreign donors, so that the large hole conductivity resulting from acceptor doping in our case and in the samples of Pappis and Kingery (51) is absent. Indications of donor doping are found in observation of electron conduction at low pO and absence of hole conduction at high p©2 Fischer et al. (63). G.2. Estimation of Ionization Energies for Aluminum Interstitials and Equilibrium Constants The ionization energies of the donors Al*, Al^, AK; and their level positions in the bandgap may be found 121 , m 1^,5 i2 using where (thermal) - 13.6 C | e “ static dielectric constant Ce|| " 8.6, ■ 10.55) n* refractive index ■ 1.76 c -(K - - ) Taking e . e . 9.575 nz e we obtain 'i Ed - 0.407 eV Kd t 2 (IwmJcTj 3/2 exp (.0> 407 eV/kT) 1 h2 K, (1620) - 3.36.1020 cm-3, similarly dl E. - 1.045 eV 2 K, (1620°C) - 6.8.1017cm~3 2 Ed - 1.97 eV 3 Kd (1620°C) - 2.5.1013cm'3 H. Ternary Al-O-Co System When the sample with cobalt concentration of 18 x *9 I.22.10 /cm0 was annealed at 10 atm for 4 hours, the crystal turned dark brown to black. The divalent cobalt concentration as measured from ESR signals decreased by a factor of 1.72/2.65 (or 35t lower) from that in the same - 8 crystal annealed for four hours at 10 atm. Moreover, 122 4 the crystal shows absorption proportional to X indicative of Rayleigh scattering. Both these experimental facts point out that some of the divalent cobalt is not in solid solution and is probably present in the form of precipi tates. Assuming that the precipitate is cobalt metal, the activity of cobalt oxide (CoO) under these conditions can be estimated and used to evaluate the free energy of incorporation of CoO in and from this the solubility of Co in AI2O3 as ftP^^* Thus, at T-1620°C Co 02(g) - CoO(s) KCoO ‘ C-AG°/RT) (1 ) The standard free energy of this reacion (64) is given by AG° - AH0 + 2.303 a T log1Q T+b.lO'3T2 + C.10"ST_1 +IT ’ In the temperature range of 1763°K - 2000°K iHQ * -65680 cal/mole 2.303 a - -6.22 cal/°K mole b - c * 0, I - 43.43 cal/°K mole At T - 1620°C, we findAG0 - -22.08 K cal/mole and KCq0 ■ exp ( -AG°/RT) * 350 atm"** In the range of 10‘® < p02< 10 ® atm where blackening of the crystal was observed, assuming that -9 Co-metal was precipitated at 3.10 atm, we find, (with aCo” “ coO (C° ( l ) ’ A12 ° 3 ) ' 3S0- 1 C 3 .1 0 - 9 }** - 0 . 0192 123 where ag0Q is the value of the activity of cobalt oxide at the point where Co-metal just begins to form. It can be used to determine the value of the standard free energy of the reaction describing the incorporation of CoO in A1203 with the formation of defects presumed in our x 3 disorder model, viz. , ^°A1 * ant* ^he incorpora tion reaction can be written as 3 CoO + Alx + Vx - 3Co' + Al?’ + 30X ; 3AG° Al i Al l u Therefore, 3AG° - 3u°c0j^ + yAl?* + 3y°og " 3y CoO ’y AlJx ' M°V* aCo* aAl?• a0X Al 1 U RT*n I I (2) aCo0 aAlx V Al i where p ■ p° + RTfcna Where, with { ) » site fraction, [ ] ■ mole fraction a°g - tog> ■ i [Oj]-l; [0*] - J BA1M ’ {A1A l l ■ 7 [A1m ’ • [CoM ] - [C0A1]=I [A1M ]= 1; [ai: j aCo <c o I, > Al Al' ^ - Al and since there is only one octahedral interstitial site per molecule of A1203» we have M - tV^> - [V*] - 1- [Alj']« 1 124 “Al3- " i with the above eq. (2) reduces to o 3 [Co^]3tAl?-] 3AG - -Rttn (h) — — (3) 3 a CoO At a certain pC^ in the range 10'® - 10"® atm cobalt metal precipitates. We shall assume for the following analysis, that it occurs at 3.10‘® atm and later verify this assump tion. At pO2-3.10_9t T-1620°C, [Coj^]- 4 . 33.10' Smol. fr. [Al3’]- “ [Co' ]«1.443.10“5; a„ -al - 0.0192 i 3 L Al * CoO CoO we find, AG° - 41,333 cal/mol. CoO (4) This value of AG° (for incorporation of CoO in A1203 at 1620°C) can be used to calculate the solubility of Co in equilibrium with A12Oj as a function of pO^ at 1620°C. In Al-O-Co ternary system as shown in Fig. 27 one may anticipate precipitation of CoA120^, the spinel phase, at values of pO^ that are too high to allow forma tion of Co. The value of AG° found above, can be used to calculate the solubility of Co in A1203 in equilibrium with CoA1204- Consider the reaction, CoO(s) + A120j(s) ■ CoAl20^(s) Kspinel “ aCoA1 0 1 aCo0aAl203(s) 2 4 125 Co CoO Al Al-O Fig. 27 Schematic ternary Al-O-Co system. Arrow indicates the direction of increasing oxygen partial pressure. The standard free energy of formation of the spinel CoA^O^ was measured by Tretyakov and Schmalzried (65) , in the temperature range 1000 - 1500°K and was given as AG° - A + BT log T + CT where for 1000°K < T < 1500°K A « -10,700 cal/mole B ■ O, C * 2.67 cal/°K mole Extrapolating the value of AG° at 1620°C, we find t£s° (1620°C) - -5.64 Kcal/mole and K - 4.5 spinel For coexistence of and the spinel phase, assuming that the spinel phase remains essentially CoA^O^ (i.e. contains little Co^O^ in solid solution) with aA12°3* aCoAl204= we find K. _ spinel CoO K"1 - a*' - 0.222 where, is the activity of cobalt oxide when the spinel phase CoA^O^ is in equilibrium with A^O^. H.l. Solubility of Co in A120.j as a function of p02 at 1620°C On rearranging eq. (3), we get . 3 . 3 . t / 3AG° - RTtn 8 \ [CoAl] [Alt ] ' * l o 0 « p (------- ) 127 Using the neutrality [Co^j] - 3[A1^ ] , and T - 1620°C, flG° » 41,333 cal/mole of CoO, Kcoo “ 350 atm"*5 and (1) a^Q = 1 for equilibrium between Co(t) and Al203(s), and (2) a^QQ - 0.222 for equilibrium between CoAl^O^s) and AljO^fs), we get [Co’ ] - 4.73.10"2 P0 3/8 mol. fr. A1 Co(1), A1203Cs) 1 [Co' ] - 1.91.10'4 mol. fr. A1 CoA1204(s), A1203 In order to find Co* as a function of pO, in the two Al L cases, we invoke the definition of K from Table (6), ox equation (s) and obtain _ x 1/3 - 3/4 /124000 - RTJln 8 \ [Co 1 ■ K a_ pO- exp -(----------------- ) L AlJ ox CoO ^2 * \ 3RT With K * 3.29.108 atm~3^4 mol. f r ? and the other ox parameters as above, we find, at 1620°C, x 3/4 [Co* ] - 38.3 pO ' A1 Co(1), A1203(s) 2 x -2 1/4 [Co* ] - 2.43.10 * pO mol. fr. A1 CoA1204(s), A1203(s) 2 The isotherms of [Co* ], [Al?* ], [Co*J , are as shown in Fig. 25 (a). The solubility of cobalt is given by C C ° ]t o t * tCOM 3 * [C0A1 3 Here we are implicitly restricting ourselves to the species 128 2 10 Co tot Al 3 g 10 ■rt U* Co Al 10 Al. Co CoO i (b) pO *4.04.10 atm CoO 2 10 ■® "6 Log p02 '4 '2 Fig. 28 (a) Concentrations of Co^» ^ x i * aiw* ^°tot -10 in coexistence with Co(l) and Co (s) as function of pC^ at 1620°C. The [Co]tQt in our sample is also indicated, (b) a^ and a^jo as futction of oxygen partial pressure at 1620°C. 129 [Co^ ] and ]f though other kinds of centers were inferred from the work of Zverev and Prokhorov, (7) The transition pressure at which the two equilibria Co(£) + Al 0 (s) and CoA^O^Cs) + Al Oj(s) pass from one to 2 3 * the other is given by [Co* ] - fcox 1 A1 Co(l), Al203(s) Al CoA1204(s), A1203(s) The (pO-) is obtained as 4.04.10"^ atm. Fig. 28 (a) Tr shows the solubility of Cobalt in A^O^ at 1620 C as a function of pC>2 and Fig. 28 (b) shows the variation of a^Q and a^QQ with p02 in the two regions. The above analysis was based on the assumption that _ Q cobalt metal was precipitating at 3.10 atm. The iso therms given in Fig. 24 show that [Coj^ ] increases with decreasing p0_ and the values of -5 -5 -fl -9 0.85 Cor \Co'A l ] - 4.4.10 , 4.51.10 ) at 10 8 and 10 3 respectively. The corresponding ^°ax ^are indicated (a) and (b) in Fig 26 (a) and connected by the dotted line assuming a linear variation in this range of p02* From ESR, we found that [Co^j] at 10'^atm is 0.65 times that at 10-8 atm, i.e.,[Co^ ]« 0.65 0.85[Co]fcot - 2.86.10-5. This is given by point c- Now [c°3tot varies as pO^O.ZBe as shown. A line through point c, with this slope inter- 0.49 sects ab at d, at pO_ atm. This is the oxygen £i pressure of the phase boundary Al 0 /Co(l) for the cobalt £ J content of our samples; it is close to the value of 3 x 10"^ atm which we arbitrarily assumed and on which our calcula- P°A1 J ' £ Co \ o t bein8 130 tion of the solubilities were based. SUMMARY Room temperature optical absorption, electron spin resonance, and high temperature electrical conductivity and emf measurements are employed to determine the high temperature defect structure of Co-doped a'A^O^. Chapter I introduces the various suggestions of earlier workers about the prevailing disorder in Co-doped AI2O3 arrived at on the basis of independent measurements of optical absorption ESR and electrical conductivity. Chapter II collects together the structure and properties of AI2O3. Chapter III deals with an outline of essential theoretical principles involved in interpreting the opti cal and spin resonance spectra and electrical conductivity measurements. In this chapter a set of disorder models is examined in the framework of the quasi-chemical approach and isotherms are given for a model based on charge com- 3 pensation of divalent cobalt by native defects, Al^*, under the assumption that cobalt is mostly present in trivalent form under both the oxidizing and reducing conditions. Chapter IV reviews some of the experimental results reported in the literature on CotA^Oj qualitatively. 131 132 Chapter V treats the experimental techniques em ployed in determining the variation of concentrations as a function of oxygen partial pressure. For measuring the 2 +■ concentration of Co with pC^ a comparison method is adopted using two crystals with their c-axes mutually perpendicular. The concentrations are estimated from a geometric mean of the relative ratios of intensity of spectra in the two mutually perpendicular directions (|| and c-axes). The arguments leading to this measur ing principle are outlined. From the relative intensitites of ESR and optical absorption spectra measured at two different partial pressures of oxygen, the concentrations of Co2+ and Co3+ can be arrived at quantitatively. The procedure followed in this analysis was outlined. The electrical conductivity and emf measurements are performed using a cylindrical volume guard to compen sate the surface and gas conduction. The setup employed in our experiments was described. Oxygen partial pres- - 9 sures of 1 atm -10 atm were obtained using 0£, air, air and N2 gas, and Co- Co^ gas mixtures. Chapter VI presents a discussion correlating the results from the optical, magnetic and electrical measure ments, comparing whenever necessary with the earlier work. There are two results that remain unexplained. Firstly, ♦ we see a double band at 5300 - 5500 A in the reduced 133 samples of CoiA^O^ that varies as the origin of this band is unknown. Secondly, we observe forbidden transitions in H||C spectrum obtained in spin resonance and no explanation could be found that could account for these forbidden transitions. Omitting these and correlat ing the three measurements, a disorder model based on charge compensation of divalent cobalt by a combination of native Al?*and a small concentration of foreign donors, was proposed. A set of equilibrium constants was estimated and the level of cobalt in the bandgap was found to be at 2.89 eV above the valence band. An analysis similar to this was applied to an earlier work, where an unintentional impurity content of Fe was about 100 ppm and an equili- bruim constant for the process of oxidation of Fe^ + to Fe^ was estimated. The value of Fe level in the bandgap was estimated to be at 3.72 eV above the valence band. The conductivity and emf results are interpreted with the supporting evidence from optical and ESR spectra. Cobalt doped was found to be a mixed conduc tor at the high temperature (=f1600°C). The conductivity _ 3 is predominantly ionic at pO^lO atm and the migrating species are analysed to tealuminum interstitials. At p02>10"^ the conductivity gradually becomes electronic with holes as migrating species. An ionic mobility of 1.35 . 10~^ cm^/V-sec and a hole mobility of 1 cm^/V-sec were found based on our analysis. Within the range of a 134 temperature of 1600°C we may represent the ionic mobility by 7 7 vA13.“ 3.6.10 exp (-3.97 eV/kT)(cmz/V-s«c) i _ g Four hours of annealing at 10 atm turned the sample black. Assuming that cobalt metal was precipitating - 8 - 9 out in the range 10 - 10 atm, an analysis of the Co(l) + A^O^fs), CoA^O^Cs) + Al^OjCs) phase equilibria in the ternary Al-O-Co system was carried out to deter mine the solubility of Cobalt and its variation with oxygen partial pressure at 1620°C. The variation of activities of CoO and Co with pO£ in the two regions are also evaluated. REFERENCES 1. D. S. McClure, J. Chem. Phys., 36 (10), 2757, (1962). 2. R. Mtiller and Hs. H. Gunthard, ibid 44, (1) 365 (1966). 3. W. J. Borer, Hs. H. Gunthard and P. Ballmer, Helv. Phys. Acta 43, 74 (1970). 4. P. Ballmer, H. Blum, W. J. Borer, K. Eigenmann and Hs. H. Gunthard, ibid 43, 829 (1970). 5. K. Eigenmann, K. Kurtz and Hs. H. Gunthard, ibid 45, 452 (1972). 6. G. A. Keig, J. Cryst. Growth 2 (6), 356 (1968). 7. G. M. Zverev and A. M. Prokhorov, Sov. Phys. JETP 12, 41 (1961). 8. M. G. Townsend, J. Chem. Phys. 68, 1569 (1964). 9. M. G. Townsend and 0. F. Hill, Trans. Faraday Soc., 61, 2597 (1965). 10. K. W. H. Stevens, Proc. Roy. Soc. (A) 219, 542, 1953. 11. R. J. Brook, J. Yee and F. A. Krbger, J. Am. Ceram. Soc., 54, 444, 1971. 12. J. J. Yee, Ph.D. Dissertation, University of Southern California, 1973. 13. F. A. Krtiger and H. J. Vink, Solid State Phys. Vol. 3, 307, (1956). 14. S. Geschwind and J. P. Remeika, J. Appl. Phys. Supplement to Vol. 33, (1), 370 (1962). 135 REFERENCES (Continued) 136 15. Air Force Materials Laboratory Report AFML - TR - 66 - 396, 33 (1967). See also L. Pauling and S. B. Hendricks, J. Am. Chem. Soc. 47, 781 (1925). 16. H. A. Bethe, "Splitting of Terms in Crystals," (English translation of the original German paper from Ann. der Physik, 3, pp 133*206, 1929), Consultants Bureau, N. Y. 17. D. S. McClure, "Theory of Spectra of Ions in Crystals,” Solid State Phys, Vol. 9, (19S9). 18. C. J. Ballhausen, "Introduction to Ligand Field Theory," McGraw Hill, (1962). 19. B. N. Figgis, "Introduction to Ligand Field Theory," Interscience, 1966. 20. H. L. Schlafer and G. Glieman, "Basic Principles of Ligand Field Theory," Wiley - Interscience, 1969. 21. J. S. Griffith, "Theory of Transition Metal Ions," Cambridge Univ. Press, 1961. 22. T. M. Dunn, in Modern Coordination Chemistry, Ed. I. Lewis and R. G. Wilkins, Interscience, 1960. 23. Y. Tanabe and S. Sungano, J. Phys. Soc. (Japan) 9, 753, 766 (1954). 24. P. George and D. S. McClure, "The Effect of Inner Orbital Splitting on the Thermodynamic Properties of Transition Metal Compounds and Coordinate Complexes," Progress in Inorganic Chem., Ed. F. A. Cotton, Vol. 1, Academic Press, (1959). 25. E. A. D. White, Quart, Ref. 15, 1, (1961). 26. G. Lehmann and Harder, Am Minerologist, 55, 98 (1970). 27. A. Abragam and M. H. L. Pryce, Proc. Roy. Soc. A205, 135 (1951). 28. A. Abragam and M. H. L. Pryce, Proc. Roy. Soc. A206, 173 (1951). 29. N. F. Mott and R. W. Gurney, Electronic Processes in Ionic Crystals, Dover, 1964. 137 REFERENCES (Continued) 30. C. Kittel, Introduction to Solid State Phys., Ill Ed., John Wiley, 1966. 31. H. Reiss, C. S, Fuller, F. J. Morin, Bell Sys. Tech. Jour. 35, 535 (1956). 32. F. A. Kroger, The Chemistry of Imperfect Crystals, North Holland Publishing Co., (1964). 33. G. Brouwer, Philips Res. Repts. 9, 366 (1954). 34. F. A. Krbger, The Chemistry of Imperfect Crystals, North Holland Publishing Col, p. 282, (1964). 35. B. F. Gachter, H. Blum and Hs. H. Gunthard, Chem. Phys. Lett., 17 (2) 217 (1972). 36. J. Yee and F. A. Kroger, J, Am. Ceram. Soc. 56, (4) 189 (1973). 37. D. W. Peters, L. F. Feinstein and Christian Peltzer, J. Chem. Phys. 42 (7) 2345, (1964). 38. J. P. Loup and A. M. Anthony, Rev. Hautes, Temp. Refract., 1(1), (1964). 39. A. J. Moulson and P. Popper, Proc. Brit. Ceram. Soc., No. 10, 41 (1968). 40. 0. T. Ozkan and A. J. Moulson, Brit. J. Appl. Phys. 3(6) 983 (1970). 41. S. P. Mitoff, J. Chem. Phys., 41 (8), 2561, 1964. 42. H. Schmalzried, J. Phys. Chem. (Frankfurt am main), 38, 87, '’963). 43. J. J. Mills, Tech. Rept. ARL 68-D154, 1968, U. S. Clearinghouse Fed. Sci. Tech. Inform., AD (AD-680005), 51, 1968). 44. T. Matsumura, Can. J. Phys., 44 (8), 1685, 1966. 45. W. A. Fischer and Wilfried Ackermann, Arch. Eisenhiittenw. 39 (4), 273, 1968. REFERENCES (Continued) 138 46. P. Mitoff, G. E. Res. Lab, Rept. No. 65-RL-3964N Research Information Section, Schenectady, New York, 1965. 47. W. D. Kingery and G. E. Meiling, J. Appl. Phys. 32 (3) 556, (1961). 48. R. W. Cooper, Proc. Brit, Ceram. Soc. No. 1, 167, 1964. 49. P. Donneand, Rev. Hautes Temp. Refract, 3 (2), 157, 1966. 50. W. J. Lackey, Jr, "Electronic and Ionic Conductivity in Alumina," Ph.D. Thesis, North Carolina State Univ. Raleigh, N. C. (1970). 51. J. Pappis and W. D. Kingery, J. Am. Ceram. Soc. 44, 459, 1961. 52. D. F. Nelson and J. P. Remika, J. Appl. Phys., 35, 522, 1964. 53. R. s. Alger, Electronic Paramagnetic Resonance, Interscience, 1968. 54. G. M. Zverev and N. G. Petelina in "Spin-Lattice Relaxation in Ionic Solids*" Ed. A. A. Manenkov and R. Orbach, p. 404, Harper and Row (1966). 55. C. B. P. Finn, R. Orbach and W. P. Wolt, ibid, p. 166. 56. A. Y. Degani, Private Communication. 57. K. Hauffe and D. Hoeffgen, Ber. Bunsenges, Phys. Chem. 74 (7), 639 (1970). 58. Y. Oishi and W. D. Kingery, ibid, 33 (2) 335 (1963). 59. A. E. Paladino and W. D. Kingery, J. Chem. Phys. 37 (5), 957 (1962). 60. H. H. Tippins, Phys. Rev. (B) 1, 126, 1970. 61. Cohen, Bull. Am. Ceram. Soc. 38, 441 (1959). 62. V. I. Alexandow, V, V. Osiko and V. M. Tatorintsev, Inog. Mater., 8, (5), 835 (1972). 63. 64. 65. 66. 139 REFERENCES (Continued) W. A. Fischer and W. Ackerman, Archiv fur Eisenhiittenw 39, 273 (1968). Chem and Phys. Handbook, CRC (48th Ed. ), 1967 - 68). J. D. Tretyakov and H. Schmalzried, Ber Bunsenges, Phys. Chem. 69, 396 (1965). F. Seitz, Modern Theory of Solids, McGraw Hill, 1940.

Asset Metadata

Creator Dutt, Bulusu Venkateswara (author)

Core Title High-Temperature Defect Structure Of Cobalt Doped Alpha-Alumina

Contributor Digitized by ProQuest (provenance)

Degree Doctor of Philosophy

Degree Program Materials Science

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag engineering, materials science,OAI-PMH Harvest

Language English

Advisor Kroger, Ferdinand A. (committee chair), Hurrell, John P. (committee member), Porto, Sergio P.S. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-673711

Unique identifier UC11355802

Identifier 7414435.pdf (filename),usctheses-c18-673711 (legacy record id)

Legacy Identifier 7414435.pdf

Dmrecord 673711

Document Type Dissertation

Rights Dutt, Bulusu Venkateswara

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA