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ESR study of transition metal ions diffused into sodium -alumina Abello, Lawrence 1984

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ESR STUDY OF TRANSITION METAL IONS DIFFUSED INTO SODIUM 0"-ALUMINA By LAWRENCE ABELLO, S.J. M.Sc, St. Louis University, 1971 THESIS SUBMITTED IN PARTIAL FULFILLMENT THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF PHYSICS We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA July 1984 © Lawrence Abello, S.J., 1984 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Physics The University of B r i t i s h Columbia 1956 Main M a l l Vancouver, Canada V6T 1Y3 D a t e J u l y 31, 19 84 )E-6 (3/81) i i ABSTRACT ESR measurements are reported on the tr a n s i t i o n metal ions Mn2* and Cu 2 + diffused into s i t e s i n , and adjacent to, the conduction planes of sodium /3"-alumina single c r y s t a l s . The spin-Hamiltonian parameters obtained for Mn 2 + are g(( = 2.0000(2), g x = 2.0019(2), A,| = -8.39(3) mT, Aj. = -8.33 mT and D = -7.20(5) mT. The Mn2 + ions occupy the Al(3) s i t e s adjacent to the conduction planes. The symmetry of the Cu 2 + spectra place the Cu 2 + ions at the mid-oxygen s i t e s of the conduction planes. The complex spectra are a superposition of several d i f f e r e n t configurations of ions around t h i s s i t e which change as a function of the amount of Cu 2 + diffused. The angular variations of the spectra can be divided into two main types: an anisotropic s i t e symmetry with spin-Hamiltonian parameters g = 1 1- 2.355, g , 2.087, A „* 12.0 mT, A * 2.0 - 4.0 mT, and a 3 a|| 3 a i all ax more iso t r o p i c s i t e symmetry with g = 2.003, g =* 2.240, ill i x A... ^  9.9 mT, A. . =* 8.8 mT. These spectra are v i s i b l e at l i q u i d -ill i i . helium temperatures. In addition an anisotropic, random-type spectrum i s observed to replace the Cu 2 + spectra as the temperature of annealed c r y s t a l s i s increased. This i s attributed to the thermal motion of the Cu 2 + ions due to their weak binding to the s i t e . Suitable doping and annealing procedures to diff u s e Mn 2 + and Cu 2 + into sodium /3"-alumina are discussed and contrasted with the markedly d i f f e r e n t procedures in the case of the /3 structure. TABLE OF CONTENTS ABSTRACT i i TABLE OF CONTENTS . .. i i i LIST OF TABLES v LIST OF FIGURES v i ACKNOWLEDGEMENTS v i i i CHAPTER 1 - INTRODUCTION 1 1.1 GENERAL INTRODUCTION 1 1.2 THESIS OUTLINE 2 CHAPTER 2 - MATERIALS, DOPING PROCEDURE AND APPARATUS 4 2.1 SODIUM BETA-ALUMINA AND SODIUM BETA"-ALUMINA COMPARED 4 2.2 GENERAL DOPING PROCEDURE 7 2.3 GENERAL DESCRIPTION OF THE APPARATUS 8 2.4 RESONANT CAVITY USED FOR Mn2 + -DOPED SAMPLES 10 2.5 SPECIAL APPARATUS USED FOR THE Cu 2 + EXPERIMENTS 10 CHAPTER 3 - ESR STUDY OF Mn2 * IN SODIUM BETA"-ALUMINA 18 3.1 EXPERIMENTAL PROCEDURE FOR AN ESR STUDY OF Mn2 * IN SODIUM BETA"-ALUMINA 18 3.2 INTERPRETATION OF THE RESULTS 19 i v CHAPTER 4 - ESR STUDY OF Cu 2 + IN SODIUM BETA"-ALUMINA 32 4.1 EXPERIMENTAL PROCEDURE FOR AN ESR STUDY OF Cu 2 + IN SODIUM BETA"-ALUMINA 32 4.2 EXPERIMENTAL RESULTS AND LOCATION OF THE SITE OCCUPIED BY Cu 2 + 34 4.3 THE SPIN-HAMILTONIAN PARAMETERS FOR Cu 2 + IN SODIUM BETA"-ALUMINA BY A COMPUTER SIMULATION OF THE DATA 45 4.4 INTERPRETATION OF THE RESULTS 53 CHAPTER 5 - SUMMARY OF RESULTS AND SUGGESTIONS FOR FURTHER WORK 69 5.1 SUMMARY OF RESULTS 69 5.2 SUGGESTIONS FOR FURTHER STUDY 71 BIBLIOGRAPHY 74 APPENDIX A: DOPING AND ANNEALING PROCEDURES 76 V LIST OF TABLES Table 3.1 Spin-Hamiltonian parameters for Mn2* in the Al(3) s i t e of sodium 0"-alumina 29 Table 4.1 Spin-Hamiltonian parameters for Cu 2 + in the mid-oxygen s i t e s of sodium ^"-alumina 52 \ v i LIST OF FIGURES Figure 2.1 Unit c e l l of (a) sodium /J-alumina and (b) sodium ^"-alumina 6 Figure 2.2 Apparatus arrangement 9 Figure 2.3 Cavity used for Mn 2 + experiments 11 Figure 2.4 Cavity used for Cu 2 + experiments with provision for rotating the sample holder 12 Figure 2.5 Temperature-controlled cavity used for Cu 2 + experiments 16 Figure 3.1 Broadened ESR spectrum of Mn 2 + in sodium ^"-alumina 20 Figure 3.2 ESR spectrum of Mn 2 + in sodium /3"-alumina with (a) S II c and (b) with fi X c 21 Figure 3.3 Structure of (a) sodium 0-alumina and (b) sodium /3"-alumina adjacent to the Al(3) s i t e 26 Figure 4.1 Spectra from an unannealed c r y s t a l (a), and from an annealed c r y s t a l (b) 35 Figure 4.2 Plot displaying the complexity of the results obtained^by rotating an annealed c r y s t a l so that H sampled plane 1 37 Figure 4.3 Plot displaying the complexity of the results obtained^by rotating an annealed c r y s t a l so that H sampled the conduction plane 39 Figure 4.4 Conduction plane with i t s adjacent oxygen planes of a p a r t i a l unit c e l l of sodium /3"-alumina 41 Figure 4.5 Plot displaying the complexity of the results obtained by rotating an unannealed c r y s t a l so that H sampled plane. 1 44 Figure 4.6 (a) Display of the computer-generated three sets of l i n e s of the more anisotropic spectra around their minimum positions (b) Angular va r i a t i o n of the unshifted l i n e set of the more anisotropic spectra (c) Angular va r i a t i o n of the spectra of the more isotropic type 48 Figure 4.7 Comparison of computer-generated results and ESR spectra 50 v i i Figure 4.8 (a) Irregular dodecahedral s i t e (b) View along the c axis of the conduction plane 61 Figure 4.9 (a) Spectra from an annealed c r y s t a l with H J. c at the temperatures indicated (b) Spectra from an annealed c r y s t a l at 77.3 K as sampled the c r y s t a l at the orientations indicated 63 Figure 4.10 C u 2 + l i n e spectra from an unannealed c r y s t a l at < 1.6 K (a), and at 40 K (b) 66 Figure 4.11 Plot displaying the symmetric results obtained by rotating an annealed c r y s t a l so that H sampled plane 3 68 v i i i ACKNOWLEDGEMENTS I wish to express my deepest gratitude to Dr. C.F. Schwerdtfeger for his d i r e c t i o n and assistance in conducting the research work, in publishing our results and in preparation of th i s t h e s i s . I also wish to thank the other members of my committee (Dr. David A. Axen, Dr. Birger Bergersen and Dr. A.CD. Chaklader) for t h e i r helpful suggestions. A H.R. MacMillan Family Fellowship provided under the auspices of the University of B r i t i s h Columbia i s g r a t e f u l l y acknowledged as i s support, received through Dr. Schwerdtfeger, from a grant provided by the National Science and Engineering Research Council of Canada. F i n a l l y , I wish to thank my confreres belonging to the Calcutta Jesuit Missions (India) for t h e i r constant encouragement and trust during my extended stay abroad to complete t h i s work. 1 CHAPTER 1 - INTRODUCTION 1.1 GENERAL INTRODUCTION Over the past f i f t e e n years a strong interest in high-conductivity s o l i d e l e c t r o l y t e s has developed. This has resulted in a large research e f f o r t directed toward the use of these materials in high-energy-density batteries. One of the pioneering papers in t h i s f i e l d (Yao and Kummer, 1967) reported the discovery that the Na 1 +-ion conductivity in sodium /3-alumina at room temperature was comparable to that of aqueous solutions. Since the appearance of their work the two compounds, sodium /3-alumina and sodium ^"-alumina, have been the object of a large number of investigations. Of these two compounds, sodium 0 " -alumina has by far the higher conductivity. Although most investigations have centered on the conductivity of monovalent ions such as Na 1 +, L i 1 + , Ag 1 * and H 1 + , Farrington and Dunn (1982) have discovered that sodium /?"-alumina i s an excellent conductor of divalent cations. They investigated B a 2 +, S r 2 + , C a 2 + , C d 2 + , Mn2*, Cu 2 +, etc. While most of these ions gave complete cation exchange for the Na 1 * in the conduction plane, one of them, Cu 2 + , only "exchanged" up to 37%. The reasons for t h i s could not be determined by them since the extent of what was interpreted as an ion exchange, in the case of Cu 2* also, was measured by gravimetric and radiochemical techniques and an explanation would c l e a r l y be dependent on knowing where the ions resided i n , or close to, the conduction planes. Electron spin resonance (ESR) techniques are d i r e c t l y suited to study s i t e symmetries and divalent, t r a n s i t i o n metals such as Mn 2 + and Cu 2 + have been extensively studied in a variety of host materials. Hence these ions would be an ideal s t a r t i n g point for ESR studies on sodium ^"-alumina. Owing to the fact that complete ion exchange introduced too large a concentration of ions thus broadening the ESR signals through ion-ion i n t e r a c t i o n , a method had to be developed to suitably d i l u t e the t r a n s i t i o n metal ion concentration. This study represents the f i r s t ESR investigation of impurity ions in sodium ^"-alumina (cf Abello and Schwerdtfeger (1982) and Abello and Schwerdtfeger (1984)). Besides being a contribution in themselves, studies such as t h i s one could contribute to future studies of ionic conductivity which is so greatly affected by impurities in and adjacent to the conduction planes. The results presented here are also compared with the resul t s of ESR studies on sodium /3-alumina where several t r a n s i t i o n metal ions have already been investigated, e.g., C r 3 + ( S i x l and Hundhausen, 1980), Mn 2 t (Barklie and O'Donnell, 1977); C u 2 + (Gourier and a l . , 1977, Gourier and a l . , L978), etc. 1.2 THESIS OUTLINE Chapter 2 compares sodium /3- and /3"-alumina. Then the experimental apparatus and general doping procedure are described. 3 Chapter 3 contains an ESR study of Mn2 + diffused into sodium j3"-alumina. It includes the following: a discussion of the experimental procedure as i t applies to Mn 2 +, an interpretation of results and the location of the s i t e occupied. Chapter 4 contains an ESR study of C u 2 + ions in sodium 0 " -alumina. It includes the following: a discussion of the experimental procedure as i t applies to C u 2 +, a presentation of the data with a description of the s i t e occupied, a computer simulation of the data to evaluate the spin-Hamiltonian parameters, and an interpretation of the r e s u l t s . Chapter 5 summarizes the results and concludes by out l i n i n g suggestions for further ESR studies of ions in sodium 0 " -alumina. 4 CHAPTER 2 - MATERIALS, DOPING PROCEDURE AND APPARATUS 2.1 SODIUM BETA-ALUMINA AND SODIUM BETA"-ALUMINA COMPARED Stru c t u r a l l y the only difference between sodium /3-alumina (Na 20-11Al 20 3) and sodium /3"-alumina (Na 20«5A1 20 3) i s that every second spinel block i s inverted in the sodium ^''-alumina. The structures are compared in Figure 2.1. This figure i l l u s t r a t e s that /3- and j3"-alumina d i f f e r in the packing of the oxygen layers which brings about a d i f f e r e n t atomic arrangement in the sodium-oxygen layers as well. Consequently, the interactions of the Na1 * ions and the surrounding c r y s t a l f i e l d s are not the same in the two structures and this gives r i s e to s i g n i f i c a n t differences in the s t a b i l i t y and transport properties (Wynn-Jones and Miles, 1971). The more stable structure i s that of sodium /3-alumina. In order to s t a b i l i z e sodium /3"-alumina divalent atoms such as Mg2* are added. These ions substitute for the A l 3 * ions in the Al(2) and Al(3) s i t e s which are the tetragonally coordinated s i t e s . The Al(3) s i t e s are next to the conduction planes. This substitution s t a b i l i z e s the structure because the excess negative charge due to such a replacement compensates the excess posi t i v e charge due to sodium ions in the conduction planes (Wolf, 1979) and also because, in the Al(2) s i t e s , there i s a decrease in the inter-atomic distances in the A10„ coordination polyhedra located near the center of the spinel blocks (Wolf, 1979). 5 Figure 2.1 Unit c e l l of: (a) sodium B-alumina and (b) sodium 3"-alumina. A, B and C indicate compact oxygen layers i n the s p i n e l blocks. A 1, D' and C indicate non-compact oxygen layers which are the conduction planes. The A l ( l ) to Al(4) s i t e s are indicated i n the figure by the numbers 1 to 4. A l ( l ) and Al(4) are i n octahedral coordination i n the spinel block. Al(2) i s i n tetrahedral coordination i n the spinel block and Al(3) i s i n tetrahedral coordination i n the sp i n e l block but adjacent to the conduction plane. 6 7 2.2 GENERAL DOPING PROCEDURE A fused quartz tube 115 cms long and 6 cms in outside diameter was f i t t e d with a stopcock at one end and a stopper on the other. At the center of t h i s tube was placed a porcelain crucible containing the sample. A snugly f i t t i n g porcelain disk was inserted into the ceramic c r u c i b l e to separate the dopant s a l t ( s ) covering the c r y s t a l from the setter sand which f i l l e d the portion of the crucible above the porcelain disk. The purpose of the setter sand was to prevent excessive sodium loss from the sample c r y s t a l during the f i r i n g . (The setter sand was prepared by mixing 4.61 grams of lithium n i t r a t e , 15.4 grams of sodium carbonate and 90 grams of alpha alumina for every 100 grams of setter sand to be prepared and ca l c i n i n g ( i . e . , heating without fusing) t h i s mixture at 1250 °C for two hours. Note the weight decrease due to c a l c i n i n g which drove off v o l a t i l e materials.) Prior to f i r i n g , the stoppered tube was evacuated and flushed with argon gas and then i t was evacuated a second time before being f i l l e d with argon at s l i g h t l y above atmospheric pressure. The furnace used for a l l f i r i n g s was a "Lindberg Hevi-Duty" tube furnace, 54000 series, with s o l i d state d i g i t a l c o n t r o l l e r that regulated temperatures to better than ± 1 °C. To prevent a i r from entering the tube the stopcock remained closed u n t i l the tube had been placed in the furnace which had already been brought to the doping temperature. Only then was the stopcock opened intermittently to prevent a build-up of pressure 8 while the tube and i t s contents were being heated. As soon as the temperature of the furnace had s t a b i l i z e d after the insertion of the tube, the stopcock was closed and remained closed u n t i l the tube had cooled after the doping procedure. As soon as the f i r i n g was completed the tube was removed from the furnace, quickly t i l t e d , rotated 180° and agitated in order to drive the c r u c i b l e towards the stoppered end and to empty i t . This was done to disperse the molten s a l t ( s ) before i t could congeal on the sample at the bottom of the ceramic c r u c i b l e . The sample was then scraped with a blade under a microscope to remove as completely as possible the sa l t that had congealed on i t s surfaces. (To avoid deterioration of the c r y s t a l there was no etching with acid.) 2.3 GENERAL DESCRIPTION OF THE APPARATUS For most of the experiments an X-band spectrometer was used (cf Figure 2.2). For a few experiments, which led to a conclusion that w i l l be discussed l a t e r , a 35 GHz (Q-band) spectrometer was employed. The cavity frequency was measured with a Hewlett Packard 5255A counter and the f i e l d , with an NMR probe outside the dewar system. Unless otherwise indicated, the experiments were conducted while the cavity containing the sample was maintained at * 1,5 K. These temperatures were reached by precooling the cavity-dewar assembly to 77.3 K with l i q u i d nitrogen maintained in the outer dewar. After about one hour of precooling, l i q u i d helium was transferred to the inner 9 F i g u r e 2.2 A p p a r a t u s a r r a n g e m e n t . 10 dewar. By means of a vacuum pump connected to the helium dewar the pressure on the l i q u i d helium was lowered to about 5 Torr thus cooling the helium from 4 K to below the X point (< 1.6 K). The temperature of the helium was maintained below the X point throughout the experiment to eliminate the production of helium bubbles which cause large fluctuations in the cavity coupling and thus in the s e n s i t i v i t y . 2.4 RESONANT CAVITY USED FOR Mn2+-DOPED SAMPLES For the low-temperature experiments on sodium /3"-alumina single c r y s t a l s , doped with Mn2 + , a T E 1 0 2 brass cavity was used. The sample was placed on the floor of the cavity for the experiments in which the magnetic f i e l d , H, was perpendicular to the c axis of the c r y s t a l the c axis is perpendicular to the conduction planes. The sample was placed against the wall of the cavity for the experiments in which H was p a r a l l e l to the c axis (cf Figure 2.3). 2.5 SPECIAL APPARATUS USED FOR THE C u 2 + EXPERIMENTS For most of the Cu 2 + experiments, a l l of which were at low temperatures, a T E 1 0 2 brass cavity, equipped with a rotatable holder, was used (cf Figure 2.4). Since the solder in the cavity and impurities in the o r i g i n a l nylon and l u c i t e sample holders were y i e l d i n g spurious ESR signals at l i q u i d helium temperatures SAMPLE FLAT SAMPLE UPRIGHT 0 N U F . L 0 0 R AGAINST WALL H l c Hllc 2 + Figure 2.3 Cavity used for Mn experiments. 12 BOLTED TO GUIDE K5EAR TRAIN HOLDER SOLDERED TO CAVITY , .BRASS WAVE GUIDE iJ SECTION SOLDERED BRASS PLATE 4-40 SCREW-COLLAR i-OCK NUT IsPRING-^ NYLON WASHERS UPRIGHT-PLANE 2 SAMPLER FLAT-PLANES I OR 3 2 + Figure 2.4 Cavity used for Cu experiments with provision for rotating the sample holder. 13 that interfered with the Cu 2 + signals, the cavity was gold plated and a signal-free sample holder was designed. This holder consists of a fused quartz rod 3 mm in diameter and 2.4 cm long. M i l l e d about halfway along the length of t h i s rod i s a flattened section 5 mm long and 1.5 mm deep on which to mount the sample. The sample-holder drive gear, which i s 1 mm wide and 1.5 cm in diameter, was cut from brass stock which was lathed down to 8 mm in diameter next to the gear to provide a 1.4 mm-wide hub. This hub f i t s snugly into the 8 mm hole d r i l l e d into the rectangular cavity's narrow side which i s also 1.4 mm thick. A well-centered, 3 mm hole was d r i l l e d 2 mm deep along the p r i n c i p a l axis of thi s hub and gear to receive the fused quartz rod. To mount the other end of the fused quartz rod a 4-40 screw was cut from brass stock with a head lathed to 1.4 mm in thickness and 4.5 mm in diameter to f i t the 5-mm hole d r i l l e d into the other narrow side of the rectangular cavity a tolerance of 0.5 mm was provided because even the s l i g h t e s t side thrust or binding on the fused quartz rod would break i t at l i q u i d helium temperatures. D r i l l e d into the lathed head of the 4-40 screw was a 3-mm hole, 1 mm deep to form a c o l l a r that received the end of the fused quartz rod. Severe l i m i t a t i o n s in space rendered impossible a c o l l a r deeper than 1 mm with the result that, although i t was easy to attach the rod to the gear because i t could be inserted 2 mm into the hub, the c o l l a r had to be notched to provide enough surface for the RTV s i l i c o n e adhesive to attach i t s e l f . (Even when applied only to one side of the notched c o l l a r , stronger and harder bonding materials with the 14 same contraction c o e f f i c i e n t as brass such as Empress & Cuming's "Stycast, L.N. 78058" hardened by "24LV" ca t a l y s t , invariably shattered the fused quartz to which they adhered when cooled to l i q u i d helium temperatures). The ends of the fused quartz rod were roughened on a diamond saw to reduce the diameter s l i g h t l y and to provide a roughened surface for the adhesive. It was essential to reduce s l i g h t l y the diameter of the 3-mm fused quartz rod at the ends to allow for the greater contraction of the brass, but too loose a f i t had to be avoided because i t greatly reduced the strength of the RTV bond. Even the s l i g h t e s t vibrations of the sample on the holder or of the holder i t s e l f caused large fluctuations in the cavity coupling and thus in the s e n s i t i v i t y . To prevent the sample from vib r a t i n g on the holder, the sample was secured to the holder with t e f l o n tape which, because of i t s e l a s t i c i t y , kept the sample from vibrating even at l i q u i d helium temperatures. The amount of t e f l o n introduced into the cavity in the form of t h i s tape was so miniscule that i t did not y i e l d any detectable spurious signals. To prevent the holder from vibrating a s p i r a l -shaped c o i l e d spring, which retained r e s i l i e n c e at l i q u i d helium temperatures, was inserted over the screw. The wide end of thi s spring bore against a nylon washer which provided a lo w - f r i c t i o n bearing between the spring and the outside surface of the cavity wall. Due to the very limited space between the cavity and the inner surface of the helium dewar, the shank of the 4-40 screw could be only 4 .5 mm in ov e r a l l length, including the threaded 15 portion. Within these 4.5 mm a nylon washer on each end of the spring and two very thin nuts had to be f i t t e d . (The outer nut acted as a lock nut. A single nut tended to tighten on rotation of the holder and resulted in excess f r i c t i o n between the nylon washer and the cavity wall thereby causing the fused quartz rod to break.) To determine the temperature ef f e c t on the C u 2 + spectrum, the sample was mounted in a temperature-controlled cavity (cf Figure 2.5). The voltage-controlled heating element was mounted in a separate copper block below the cavity. A low-temperature thermocouple junction was inserted into a nylon plug placed in the cavity wall. The thermocouple consists of a d i l u t e a l l o y of iron in gold (Au - 0.07% Fe). The Seebeck thermoelectric voltages of t h i s a l l o y were determined with respect to KP (90% Ni + 10% Cr) from 4 K to 280 K. The power series representation of t h i s data along with the calculated Seebeck c o e f f i c i e n t s and the derivatives of the Seebeck c o e f f i c i e n t s were extrapolated to 0 K (Sparks and Powell, 1972). The reference end of the thermocouple was immersed in l i q u i d nitrogen (77.3 K). A Hewlett Packard 6215A power supply was used to supply the heating element, and the thermocouple voltages were measured with a Keithley 177 d i g i t a l display, microvolt meter. The cavity and the wave guide were enclosed in a stainless steel tube (4.2 cm in inside diameter and 0.254 mm in wall thickness) which was closed off at the bottom end by a soft-soldered, brass disk. The top end was equipped with a so f t -soldered flange which made a vacuum-tight seal with the wave 16 BRASS FLANGE CUT-AWAY TUBE NYLON SPACERS HEATER LEADS CAVITY SPRING-LOADED //SCREWS "0" RING \ \ \ IN GROOVE-THERMO-COUPLE Figure 2.5 Temperature-controlled cavity used for Cu experiments. 2 + 17 guide mounting plate by means of an "0" ring compressed by the three spring-loaded nylon screws that secured the flange to the mounting plate. (The spring-loading was a safety device to release excess pressure should i t ever b u i l d up in the stainl e s s steel tube.) After mounting the sample and connecting the heater and thermocouple leads, the st a i n l e s s steel tube assembly, which had been purged with nitrogen gas, was slipped over the cavity-wave guide assembly. Two nylon spacers secured to the sides of the wave guide prevented the st a i n l e s s steel housing from touching the cavity in order to thermally insulate the cavity from the tube. After assembly was completed, the precooling and the f i n a l cooling to < 1.6 K were achieved in the manner described in 2.3. As the i n t e r i o r of the st a i n l e s s s t e e l tube cooled to l i q u i d helium temperatures, the nitrogen s o l i d i f i e d on the walls of the tube thereby acting as a getter which provided a very good, thermally insulating vacuum. Temperatures could be maintained constant within a fr a c t i o n of one degree Kelvin for extended periods by c o n t r o l l i n g the voltage applied to the thermocouple. Spectra were obtained from about 1.5 K to 77.3 K. 18 CHAPTER 3 - ESR STUDY OF Mn2 * IN SODIUM BETA"-ALUMINA 3. 1 EXPERIMENTAL PROCEDURE FOR AN ESR STUDY OF Mn2 * I_N SODIUM  BETA"-ALUMINA I n i t i a l l y attempts were made to dope the single c r y s t a l s using procedures reported in the l i t e r a t u r e (Barklie, O'Donnell and Murtagh, 1977) for d i f f u s i n g Mn 2 + into sodium /3-alumina by submerging i t by a platinum wire in molten manganese chloride at 650 °C for varying lengths of time from 10 to 20 minutes. Crystals doped in thi s manner yielded only a very broad signal i n d i c a t i v e of excessive doping which emphasized the fact that the ionic conductivity of sodium 5"-alumina i s much greater than that of sodium /3-alumina. To reduce the dopant concentration a mixture of a-alumina ( A l 2 0 3 ) and manganese chloride in the weight r a t i o 95% : 5% was prepared. (The a-alumina used is known commercially as Alcoa Alumina A-17.) The sodium /3"-alumina single c r y s t a l was covered by t h i s mixture which was placed in a ceramic c r u c i b l e . A porcelain disk was inserted above th i s mixture so that the top portion of the cru c i b l e could be f i l l e d with setter sand to prevent excessive sodium loss from the sample during the f i r i n g as described in 2.2. The f i r i n g consisted in maintaining the cruc i b l e and i t s contents at a temperature of » 700 °C for two hours in an argon atmosphere at about atmospheric pressure. During the doping procedure a sample, which t y p i c a l l y measured about 4 x 4 mm along the edges and 1 mm in thickness, 19 usually cleaved into two or three layers. Upon examining these thinner samples under a microscope, i t was noted that a-alumina had penetrated along the edges and into any fissures in the top and bottom surfaces. Probably t h i s penetration by the a-alumina i s what caused the cleaving. As i s to be expected, the cleaving of the c r y s t a l , and the consequent penetration by the a-alumina, occurred mostly along the ab or conduction planes which are perpendicular to the c axis. The ESR signal of the samples that were doped as described above displayed a very broadened but recognizable hyperfine spectrum from the Mn 2 + ions (cf. Figure 3.1). A middle section was selected i f the o r i g i n a l sample had cleaved into three or more layers. Then the edges of the selected section, which contained a-alumina, and an excess of manganese, were trimmed o f f . This c r y s t a l was then annealed in setter sand under an argon atmosphere for a period of ten minutes and then for three successive periods of two hours each at 700 °C. 3.2 INTERPRETATION OF THE RESULTS The ESR spectrum was not changed by ten minutes of annealing but the signals became progressively sharpened by each successive annealing. After a t o t a l of six hours and ten minutes of annealing the ESR spectrum displayed in Figure 3.2 was observed. The hyperfine structure has a t o t a l width of about 42.7 mT. It should be noted here that, due to the lower ionic mobility in the /^-structure, the sodium /J-alumina samples had to F i g u r e 3.1 B r o a d e n e d ESR s p e c t r u m o f Mn i n s o d i u m 3 " - a l u m i n a . The s m a l l p e a k n e a r t h e c e n t e r o f t h e s p e c t r u m (g = 2.035) i s a s i g n a l t h a t m a n i f e s t s no a n g u l a r d e p e n d e n c e and a p p e a r s a g a i n a t t h o s e a n g l e s i n t h e C u 2 + s p e c t r a where i t i s n o t masked. 21 J : J, ; L_ 300 320 340 Figure 3.2 ESR spectrum of I l n 2 + i n sodium 6 "-alumina with (a) 5 II c and (b) l i e . The small peak (+) near the center of the spectrum i s due to L i F : L i which was used as a probe. Due to a lower-frequency cavity, the tra n s i t i o n s occur at lower f i e l d here than did the corresponding transitions i n Figure 3.1. 22 be annealed for 116 hours at 700 °C (Barklie, O'Donnell and Murtagh, 1977). When a c r y s t a l was doped in pure MnCl 2 at 650 °C for about 10 minutes, i t became almost black and yielded a very broad ESR 1 ine (about 60 to 70 mT) indic a t i v e of very heavy overdoping. Moreover, even when doped in the A l 2 0 3 - MnCl 2 mixture at 700 °C, the unannealed c r y s t a l s displayed a very broadened, but recognizable Mn 2 + hyperfine spectrum (Figure 3.1). However, as the spectrum sharpens with annealing, the g and A values do not change. This suggests that the broadened, hyperfine l i n e s from the unannealed samples are already due to Mn 2 + ions residing in a well defined s i t e while the broadening of the lin e s i s due to dipolar interaction a r i s i n g from the high concentration of Mn 2 + ions. The overdoping and subsequent sharpening of the hyperfine l i n e s by annealing can be explained by taking into account the results reported in a recent paper by Farrington and Dunn (1982). Their paper shows that complete ion exchange of Na 1 * with Mn 2 + can be achieved in 15 hours. Moreover, the exchange proceeds exponentially and already between 80 to 90 percent of the exchange occurs in the f i r s t hour. The paper reports that t h i s exchange can be reversed by exposing the divalent /?"-alumina to sodium under conditions comparable to the o r i g i n a l exchange. The paper also points out that the Na 1 + - divalent ion exchange occurs much more readily and completely in 0"-alumina than in the 0 structure. By taking into account the resu l t s reported in thi s paper, 23 i t becomes clear that the broad ESR signal that was obtained when the cr y s t a l s were doped in pure MnCl 2 for ten minutes was predominantly due to Mn 2 + ions which to a large extent replaced the Na 1 * ions in the conduction planes. When the cr y s t a l s were doped in the A1 20 3 - MnCl 2 mixture, the lower dopant concentration produced a lower Na 1 + - Mn2* exchange and hence a lowered dipolar interaction thus allowing the observation of a broadened hyperfine spectrum. As the c r y s t a l s were annealed in setter sand, the sodium vapour pressure caused a reversal of the o r i g i n a l exchange with Na 1 + again replacing Mn2* ions, some of which diffused out of the c r y s t a l while others entered the well defined s i t e as evidenced by a strengthening of the hyperfine l i n e s . As the Mn 2 + - Na 1 * ionic exchange proceeded due to annealing, the diminishing Mn2* concentration in the conduction planes meant a gradually lowered dipolar i n t e r a c t i o n . This resulted in a hyperfine spectrum that retained the same g and A values but which became progressively sharper as the annealing continued. When the c r y s t a l s were doped in the a-alumina - MnCl 2 mixture, the outer edges also assumed a strong, brown coloration which faded towards the c r y s t a l ' s center. This coloration has been noted in the l i t e r a t u r e in regard to the doping of sodium /3-alumina with Mn2* (Barklie, O'Donnell and Murtagh, 1977). However, unlike the reported case of sodium 0-alumina, due to the greater ionic mobility in the case of the 0" structure, there was no portion of the c r y s t a l which remained e n t i r e l y c l e a r . The actual cause of the coloration was not ascertained 24 and could be due either to vacancies or to the Mn 2 + ions in the sodium s i t e s . As a f i r s t step in locating the occupied s i t e which gives r i s e to the hyperfine l i n e s , i t must be pointed out that the Mn 2 + ions cannot cross a close-packed layer of oxygen atoms such as the A, B or C layers in the spinel block. Therefore, the only s i t e s to be considered are si t e s in or adjacent to the conduction planes. The only s i t e in the spinel block but adjacent to the conduction plane i s an Al(3) s i t e . The s i t e s in the conduction planes are the mid-oxygen s i t e s , and the a n t i -Beevers-Ross and Beevers-Ross s i t e s . Cf Figure 3.3 which displays only that portion of the sodium /3"-alumina structure which is relevant to the results presented here. In thi s structure the anti-Beevers-Ross and the Beevers-Ross s i t e s are id e n t i c a l in everything except position (cf, e.g., p.1829 in Peters et a l . , 1971). Another preliminary step in locating the s i t e occupied by the Mn2* ion i s to take into account that the /?" structure i s s t a b i l i z e d by replacing A l 3 * (ionic radius = 0.050 nm) with the larger and less positive Mg 2 + (ionic radius = 0.065 nm). S i m i l a r i l y , Mn 2 + (ionic radius = 0.080 nm) i s likewise larger and less p o s i t i v e than A l 3 * . Most l i k e l y , therefore, either by substituting for the Mg2* ions or by f i l l i n g vacancies, the Mn2* ions w i l l occupy the only tetrahedrally coordinated Al s i t e s that can be reached by d i f f u s i o n , the Al(3) s i t e s adjacent to the conduction planes. As in the case of Mn 2 + occupying the same Al(3) s i t e in 0-alumina (cf Antoine et a l . , 1975), the hyperfine 25 F i g u r e 3.3 S t r u c t u r e o f (a) s o d i u m 3 - a l u m i n a and (b) s o d i u m 0 " - a l u m i n a a d j a c e n t t o t h e A l ( 3 ) s i t e . "BR" and "aBR" d e n o t e t h e B e e v e r s - R o s s and a n t i - B e e v e r s - R o s s s i t e s r e s p e c t i v e l y . The o x y g e n atom i n t h e c o n d u c t i o n p l a n e ( p l a n e C ) i s t h e c o l u m n - o x y g e n (cO) atom. The t h r e e t r i a n g l e s i n d i c a t e t h e p o s i t i o n s o f t h e t h r e e m i d - o x y g e n (mO) s i t e s w h i c h a r e midway b e t w e e n a d j a c e n t c o l u m n - o x y g e n atoms and a l s o midway b e t w e e n a d j a c e n t BR a n d aBR s i t e s . "W" i n d i c a t e s a d i r e c t i o n i n t h e c o n d u c t i o n p l a n e p a r a l l e l t o a cO-mO-cO b o n d d i r e c t i o n a n d " c " i n d i c a t e s t h e d i r e c t i o n o f t h e c a x i s . 26 27 structure does not manifest any angular dependence as H samples the plane perpendicular to the c axis. In fact, the values obtained for An and A x (cf Table 3.1) display an anisotropy of only 0.7% which i s well within the one or two percent anisotropy usually measured for Mn 2 + in nearly symmetric s i t e s such as si t e s that are almost tetrahedral (cf p. 439 in Abragam and Bleaney, (1970)). This high degree of a x i a l symmetry i s also a further indication that the occupied s i t e i s not in the conduction plane, i . e . , d i s t o r t i o n s due to vacancies in the Beevers-Ross and anti-Beevers-Ross s i t e s and due to the column oxygens should cause the three s i t e s in the conduction plane to display more a x i a l anisotropy. Furthermore, as discussed in more d e t a i l below, within experimental error, the g and A values are the same as for the Al(3) s i t e in sodium /3-alumina. It i s concluded, therefore, that the Mn 2 + ions that diffuse into the Al(3) s i t e s give r i s e to the observed hyperfine spectrum but, before annealing, the l i n e s are broadened by dipolar interaction between the Mn 2 + ions in the Al(3) s i t e s and the Mn 2 + ions that displace the Na 1 * ions in the aBR and BR sit e s in the conduction planes. During annealing the reverse exchange occurs by which Na 1 + ions replace Mn 2 + ions in the aBR and BR s i t e s but the Mn 2 + ions in the Al(3) s i t e remain in place. The ESR spectrum was analyzed with the spin Hamiltonian > = /3 S • g • H + D[S 2 - 1/3S(S + 1)] + S-I«I where the z axis i s the axis of symmetry assumed to be coincident with the c axis of the sodium /3"-alumina c r y s t a l . Both the spectra and the c r y s t a l f i e l d parameter, D, d i f f e r 28 s i g n i f i c a n t l y from those of Mn 2 + diffused into sodium /3-alumina. These differences arise from the differences in the nearest-neighbour positions of the Al(3) s i t e s as can be seen in Figure 2.1. In sodium /3-alumina the oxygen ions possess r e f l e c t i o n symmetry about the conduction plane whereas t h i s i s not the case for sodium /3"-alumina. The mirror symmetry in the sodium /3-alumina gives a well defined, equivalent positioning of the oxygen ions with respect to the c axis and hence the ESR spectrum, with H along the c axis, becomes sharp (AH ^  1.0 mT). This is not the case in sodium /3"-alumina where the ESR spectrum taken with H p a r a l l e l to the c axis has broader l i n e s which are s l i g h t l y asymmetric. This spectrum i s most probably due to a superposition of the spectra from various tetrahedrally coordinated Al(3) si t e s with ESR axes that are not exactly aligned with the c r y s t a l ' s c axis. This explanation i s strengthened by the fact that, even in the case of the more stable sodium /3-alumina structure, S i x l and Hundhausen (1980) report a m u l t i p l i c i t y of ESR li n e s from C r 3 + occupying the aBR s i t e because of the nonsymmetric arrangement of the ESR axes with respect to the main c r y s t a l axes. One would expect similar and even stronger e f f e c t s in the /3" structure. Compared to the /3-alumina with i t s more stable structure, the ESR axes of the Al(3) s i t e s in the /3"-alumina can deviate more from the c r y s t a l axes because of the Na ion d e f i c i e n c i e s in the conduction plane. In addition the hyperfine spectrum did not become sharper during the la s t two hours of annealing. Thus i t is not l i k e l y that residual Mn 2 + ions in the sodium si t e s caused 29 t h i s residual broadening of the spectrum from the annealed c r y s t a l . The spin-Hamiltonian parameters are given in Table 2.1. The g value anisotropy and hyperfine coupling constant, A, are close to the values for the Al(3) s i t e s in sodium /3-alumina (Barklie, O'Donnell and Murtagh, 1977). Antoine et a l . (1975) and also Barklie, O'Donnell and Murtagh (1977) assume the sign of A to be negative. As in their case which concerned Mn 2 +-doped, sodium /3-alumina, so also in the present case i t was not possible even at 1.6 K to determine the sign of A by measuring, beyond experimental error, differences in i n t e n s i t i e s between upper and lower l i n e s . Table 3.1 Spin-Hamiltonian parameters for Mn 2 + in the Al(3) s i t e of sodium /3"-alumina (The corresponding parameters for the /3 structure are those reported by Barklie, O'Donnell and Murtagh (1977).) /3" /3 g„ = 2.0000(2) g„ = 2.0006(2) g_L = 2.0019(2) g x = 2.0019(2) A|| = -8.39(3) mT A|| = -8.20(3) mT Aj. = -8.33(3) mT Aj. = -8.24(4) mT D = -7.20(5) mT D = -27.11(6) mT 30 The f a i l u r e to observe the l i n e s corresponding to M = ± 5/2 «--»• ± 3/2, ± 3/2 •*•-»• ± 1/2 t r a n s i t i o n s is attributed to broadening of these l i n e s to the extent that they are not v i s i b l e . In the case of Mn 2 +-doped sodium /3-alumina, Barklie and O'Donnell (1977) att r i b u t e d the broadening of the l i n e s from these t r a n s i t i o n s to small fluctuations in D caused by random l a t t i c e s t r a i n s . By broadening these l i n e s within each set, these l a t t i c e strains consequently reduce the peaks. Since sodium /3"-alumina i s even less stable than the /3 structure, i t is very l i k e l y that similar strains cause these tra n s i t i o n s to be unobservable in /3"-alumina also. The lower value of D implies that the d i s t o r t i o n of the Al(3) s i t e s i s less in sodium ^"-alumina, which is supported by the fact that the "column" oxygens are on centers in /3"-alumina but not in /3-alumina (Bettman and Peters, 1969). In addition, in tetrahedral symmetry increased bond strength causes increased d i s t o r t i o n of the s i t e . The average e l e c t r o s t a t i c bond strength in /3-alumina i s s l i g h t l y greater than in /3"-alumina (Roth, Reidinger and LaPlaca, 1976). This greater d i s t o r t i o n of the Al(3) s i t e in /3-alumina, evidenced by the s h i f t in 0(5), the "column" oxygen, may account for i t s greater D value. By ESR measurements on Mn 2 +, etc., substituting for A l 3 * in a-alumina (Krebbs (1967)), or in the host, MgO (Feher, 1964), i t has been demonstrated that application of uniaxial stress or uniaxial e l e c t r i c f i e l d s leads to a linear s h i f t in the fine structure parameters while leaving g and A unchanged. It i s reasonable to infer from t h i s that g and A are far less sensitive to the l o c a l 31 environment, of the Mn2 + ion than i s D. If a method could be found to place the Mn2* ions into the Al(3) s i t e s with less d i s t o r t i o n of the structure and hence obtain an improved spectrum, then one could envisage the use of the Mn 2 + ESR spectrum to monitor the eff e c t s of impurities on ionic conductivity and/or to measure exchange in the conduction planes. This would be a useful tool to study the properties of sodium ^"-alumina as a s o l i d e l e c t r o l y t e . 32 CHAPTER 4 - ESR STUDY OF C u 2 + IN SODIUM BETA"-ALUMINA 4.1 EXPERIMENTAL PROCEDURE FOR AN ESR STUDY OF Cu 2 * IN SODIUM  BETA"-ALUMINA For most of the experiments with C u 2 + the doping apparatus and procedure described in 2.2 were used. C u 2 + was introduced into sodium j3"-alumina single c r y s t a l s , which t y p i c a l l y measured about 4 x 4 mm along the edges and 0.5 mm in thickness, by submerging them in a molten mixture of 98% CuCl - 2% CuCl 2 by weight, and held at 627 °C for about two minutes. The c r y s t a l s were kept submerged by a platinum wire. As described in 2.2 the cruc i b l e was partitioned by a t i g h t l y f i t t i n g disk so that the portion of the cru c i b l e above the disk could be f i l l e d with setter sand to prevent excessive sodium loss from the c r y s t a l . The composition of the setter sand was given in 2.2. The cruc i b l e and i t s contents were maintained in an argon atmosphere. The procedure for extracting and scraping the cr y s t a l s (to remove congealed sa l t s ) was the same as the one described in 2.2. Attempts to anneal the c r y s t a l s only in setter sand destroyed the Cu 2 + signals. It i s postulated that t h i s loss of signal was due to reduction of the Cu 2 + to the diamagnetic ion, C u 1 + . This postulate i s supported by the fact that immersing the c r y s t a l s in Nal for fi v e minutes at 651 °C,,the melting point of Nal, also resulted in the disappearance of the si g n a l . As the Nal enters the conduction planes, the Na 1 * probably occupies 33 vacancies leaving the I 1 " to reduce the Cu 2 + to the diamagnetic molecule Cul. Subsequently the c r y s t a l s were annealed by using the same arrangement as for the doping process but, in t h i s case, the c r y s t a l s were submerged in CuCl only and were maintained at 627 °C for two hours. By Le Chatelier's p r i n c i p l e , the CuCl prevented the Cu 2 + from reducing to C u 1 + . For most of the experiments the X-band spectrometer described in 2.3 and sketched in Figure 2.2 was used. However, ESR measurements at Q-band detected the individual Cu 2 + l i n e s from an annealed c r y s t a l but detected only broad l i n e s from an unannealed one, although the individual Cu 2* l i n e s were obtained from both these c r y s t a l s at X-band. Subsequent experiments at high power le v e l s 50 mW) at X-band indicated that saturation occurred much more readily in the case of the unannealed c r y s t a l than in the case of the annealed one. This leads to the conclusion that the s p i n - l a t t i c e , relaxation-time constant i s decreased by annealing. In turn, t h i s i s an indication that the prolonged high temperature to which the c r y s t a l was subjected caused more impurities to enter the conduction planes (cf Nash, 1965). The greater concentration of impurities in the annealed c r y s t a l i s also indicated by i t s darker color. Laue X-rays were used to orient the c r y s t a l s . ESR spectra were recorded as a function of angle in 2.5° or 5° steps as the sample was rotated so that H sampled, f i r s t of a l l , a plane c a l l e d plane 1, containing both the c axis (the 1,1,1 axis perpendicular to the conduction planes) and one of the three main axes of s i t e symmetry determined by the X-ray patterns. 34 4.2 EXPERIMENTAL RESULTS AND LOCATION OF THE SITE OCCUPIED BY THE Cu 2 * ION Figure 4.1 compares two spectra taken (a) after two minutes of d i f f u s i o n of Cu 2 + ions into the sample and (b) after two hours of annealing at 627 °C. Except at the extremum positions of the g values, the spectra are very complex, as i s immediately evident and a part of the spectrum which "grows" in intensity with annealing i s indicated. In the case of both these spectra, H was sampling plane 1, which contains the c axis, and had reached the angle at which both the maximum and minimum for d i f f e r e n t sets of l i n e s had been attained and hence the l i n e s are most separated. Also, annealing causes a s h i f t in the spin parameters which i s attributed to additional d i f f u s i o n of copper ions into the conduction planes and/or d i f f u s i o n of the sodium ions out of the conduction planes thus respectively stretching or contracting the bonds between the spinel blocks. Due to overlapping of several four-line sets of Cu 2 + hyperfine l i n e s at intermediate f i e l d s , the positions of the individual l i n e s can be determined only at extremum positions of the g values. The plot given in Figure 4.2 displays the complexity of the results obtained by rotating an annealed c r y s t a l so that H sampled, in 5° steps, plane 1 over a range of 180°. The positions of the points, indicating the t r a n s i t i o n s , are only approximate, esp e c i a l l y in the intermediate f i e l d positions where many tr a n s i t i o n s overlap, and t h i s overlapping makes i t impossible to determine the l i n e s in some places. The plot given 35 260 300 H(mT) 340 Figure 4.1 Spectra from an unannealed c r y s t a l (a), and from an annealed c r y s t a l (b). Both spectra were taken at 0° (it II g z) where the spectra are most separated. The shorter scale at the r i g h t i n (b) indicates the more i s o t r o p i c set of l i n e s which "grows i n " during annealing. The gain i n (a) i s higher than that i n (b) thereby o f f s e t t i n g the greater i n t e n s i t y of the l i n e s i n (b). Also, the strong l i n e at ^ 292.5 mT i n (a) i s due to a superposition of l i n e s which, due to the change of g and A values through annealing, are more spread out i n (b). Figure 4.2 Plot displaying the complexity of the results obtained by rotating an annealed c r y s t a l so that S sampled plane 1. The x*s represent a l i n e that manifests no angular dependence. 38 in Figure 4.3 likewise displays the complexity of the results obtained by rotating an annealed c r y s t a l about the c axis (the 1,1,1 axis perpendicular to the conduction planes cf Figure 2.1). As in the case of plane 1 of the annealed c r y s t a l , the conduction plane, hereafter also c a l l e d plane 2, was sampled by the f i e l d in 5° steps over a range of 180°. As in the previous data, the positions of the individual l i n e s cannot be determined in some places. The recurrent patterns in the data from plane 2, the conduction plane, indicate that the Cu 2 + ions occupy three equivalent s i t e s with 120° symmetry. Furthermore, in the data from both plane 1 and plane 2, sets of l i n e s with the same symmetry reach opposite extrema at the same angle. When one examines the s i t e s in or near the conduction plane the only three equivalent s i t e s with 120° symmetry are the "mid-oxygen" s i t e s . Figure 4.4 displays a conduction plane with i t s adjacent oxygen planes of a p a r t i a l unit c e l l of sodium )3"-alumina. Also shown i s a column oxygen atom (denoted by cO) in the conduction plane of each of two adjacent unit c e l l s . The s i t e s situated halfway between adjacent column oxygen atoms, the mid-oxygen s i t e s , are denoted by mO. Thus there are three equivalent s i t e s rotated 120° with respect to one another about the c axis of the c r y s t a l . In or adjacent to the conduction planes there are no equivalent s i t e s which are rotated by 90° with respect to the occupied s i t e s with their 120° symmetry. Therefore, one cannot account for the sets of l i n e s with the same symmetry, but which 340 320-£300 280 260t=i • * O(Hlly) 30 60 9 90(HIIW) 120 150 F i g u r e 4.3 P l o t d i s p l a y i n g t h e complexity o f t h e r e s u l t s o b t a i n e d b y r o t a t i n g an a n n e a l e d c r y s t a l so t h a t H s a m p l e d t h e c o n d u c t i o n p l a n e . The x's r e p r e s e n t a l i n e t h a t m a n i f e s t s no a n g u l a r d e p e n d e n c e . o F i g u r e 4.4 C o n d u c t i o n p l a n e w i t h i t s a d j a c e n t o x y g e n p l a n e s o f a p a r t i a l u n i t c e l l o f s o d i u m 3 " - a l u m i n a . A l s o shown a r e c o l u m n - o x y g e n atoms ( d e n o t e d b y cO) i n t h e same c o n d u c t i o n p l a n e b u t f o r e a c h o f two a d j a c e n t u n i t c e l l s . The s i t e s s i t u a t e d h a l f w a y b e t w e e n a d j a c e n t c o l u m n - o x y g e n a t o m s , t h e m i d - o x y g e n s i t e s , a r e d e n o t e d by mO. The bonds b e t w e e n t h e Cu2+ i o n and t h e t h r e e n e a r e s t - n e i g h b o u r o x y g e n atoms i n t h e B o r C p l a n e a r e n o t i n d i c a t e d . 41 42 reach opposite extrema at the same angle, by postulating that they originate from equivalent, orthogonally oriented s i t e s . Hence the only postulate that accounts for sets of l i n e s with the same symmetry but reaching opposite extrema at the same angle i s that there are two types of mO s i t e , one with regular g values (gj| > gj_) and one with "reversed" g values (gjj < gj_). In the results displayed in Figure 4.2 the positions of the sets of l i n e s at the extrema, where individual l i n e s can be determined, indicate that the A values of the set of l i n e s at the maximum are more isotropic than the A values of the sets of l i n e s at minimum f i e l d . (A i s the hyperfine constant.) In Figure 4.4 the sodium atoms that are the nearest neighbours to the mO s i t e s are indicated by the l e t t e r s aBR and BR (anti-Beevers-Ross and Beevers-Ross s i t e s c f , e.g., Peters et a l . , 1971, p. 1829). Unlike the case of sodium 0-alumina, in sodium /3"-alumina the aBR and BR s i t e s are i d e n t i c a l in everything except p o s i t i o n . Figure 4.5 displays the r e s u l t s obtained from rotating an unannealed c r y s t a l so that S sampled, in 2.5° steps, plane 1 over a range of 180°. The number of points, indicating the best estimates of the positions of the t r a n s i t i o n s , and the complexity of the plot are i n d i c a t i v e of the great number of signals, most of which are overlapping. In the case of the unannealed c r y s t a l i t i s even more d i f f i c u l t than in the case of the annealed one to determine exactly where the t r a n s i t i o n s occur, i . e . , annealing increases the intensity of the main l i n e s , thereby simplifying the spectrum. to F i g u r e 4.5 P l o t d i s p l a y i n g t h e c o m p l e x i t y o f t h e r e s u l t s o b t a i n e d b y r o t a t i n g an u n a n n e a l e d c r y s t a l s o t h a t 3 s a m p l e d p l a n e 1. The x ' s r e p r e s e n t a l i n e t h a t m a n i f e s t s no a n g u l a r d e p e n d e n c e . 45 Comparing Figures 4.2 and 4.5, one notices that the plo t , in Figure 4.2, of the more i s o t r o p i c , single set of l i n e s which reach the maximum f i e l d i s much better defined because of the increased strength of the l i n e s compared to the corresponding l i n e s from the unannealed c r y s t a l which are only s l i g h t l y v i s i b l e within a narrow range of angles near the maximum, and which appear in the plot displayed by Figure 4.5. Hence the set of l i n e s with "reversed" g values which "grows" with annealing is due to the more isotropic type of mO s i t e which becomes more numerous with annealing. Cf Figure 4.1b which displays a part of the more isotropic spectrum that "grows" in intensity with annealing and which is hardly v i s i b l e in Figure 4.1a. 4.3 THE SPIN-HAMILTONIAN PARAMETERS FOR CU 2 + IN SODIUM BETA"-ALUMINA BY A COMPUTER SIMULATION OF THE DATA As already discussed and demonstrated in the figures, the ESR results are a complex superposition of several c h a r a c t e r i s t i c f o u r - l i n e , Cu 2* spectra. It i s d i f f i c u l t , i f not impossible, to i d e n t i f y a l l four l i n e s of any given set except possibly at extremum positions of the g values. In order to obtain the best possible g and A parameters the spectra were f i t by computer simulation in an i t e r a t i v e way. (In hindsight, the computer simulation also was a reminder of the need to include modifications of s i t e s due to t i l t in angle caused by aBR or BR vacancies in order to explain why two of the more anisotropic sets of l i n e s are shifted with respect to the t h i r d set and with 46 respect to the more isotropic set of l i n e s , as w i l l be discussed l a t e r . ) A Lorentzian l i n e shape and i d e n t i c a l l i n e width 1.5 mT) were chosen for each l i n e . From the data, values were estimated for g(| , g^, A|| and Aj_ for both the more anisotropic and the more isotropic types of s i t e s . These values were then inserted into the computer program. The computer program contained the following equations which y i e l d the g and A values at any angle, 6, between 0° and 90°: g(0) = (g,jcos 20 + g£sin 20) 1 / 2 and A(0) = {(A, 2g | 2/g(0) 2)cos 2 e + (A2gl/g(0) 2)sin 20} i * . The estimated values of g(, , gj_, Aj| and Aj^ were varied in an i t e r a t i v e procedure for the d i f f e r e n t types of s i t e s to obtain the best f i t over the whole range of angles. Owing to the underlying, residual, random-type spectrum and most l i k e l y some other contributions, which were not taken into account, the f i t i s not perfect. However, the general features are reasonably well reproduced. Due to overlap, the positions of the i n d i v i d u a l l i n e s on the o r i g i n a l spectra can only be approximated. The f i t of the simulated spectra gives a much better determination of the individual l i n e positions. This i s seen in Figure 4.6a which displays the three sets of l i n e s of the more anisotropic spectra around their minimum positions. In the case of the p a r t i c u l a r c r y s t a l which yielded the data displayed in Figure 4.2, which i s simulated in Figure 4.6a, one of the more anisotropic sets of l i n e s i s s h i f t e d -2.5° and the other i s s h i f t e d +7° where 0° i s taken as the angle at which the unshifted l i n e set of the more anisotropic spectra reaches i t s 47 Figure 4.6 (a) Display of the computer-generated three sets of l i n e s of the more anisotropic spectra around th e i r minimum positions and ori g i n a t i n g from the described s i t e s i n plane 1. Note how the set of li n e s s h i f t e d by +7° ( ) crosses the set shi f t e d by -2.5° (— - • — -) and then crosses the unshifted set of li n e s ( ). The dots represent the best eye-estimate of the l i n e positions i n the o r i g i n a l data around the maximum positions of the g values; overlapping at intermediate f i e l d s makes i t impossible to distinguish i n d i v i d u a l l i n e s . The g and A values used i n Figure 4.6a, 4.6b and 4.6c were obtained from the computer f i t . (b) Angular v a r i a t i o n of the unshifted l i n e set of the more anisotropic spectra from the described s i t e i n plane 1 (yielding the lines at minimum f i e l d ) , and from the two equivalent s i t e s which are rotated ± 120° with respect to the described s i t e . (c) Angular v a r i a t i o n of the spectra from the described and equivalent s i t e s of the more i s o t r o p i c type with "reversed" g values. 48 49 minimum and the more isotropic spectrum reaches i t s maximum. Figure 4.6b shows the angular v a r i a t i o n in plane 1 of the hyperfine spectra for the more anisotropic s i t e and Figure 4.6c shows the angular v a r i a t i o n for the more isotropic s i t e . Shown for comparison in Figures 4.7a, 4.7b and 4.7c are the simulation and experimental data for three d i f f e r e n t angles in plane 1. These are for an annealed sample. The g and A values vary as a function of annealing time and hence these values should be taken as t y p i c a l values allowing for at least a 10% v a r i a t i o n . The approach taken was to use as few parameters as possible to obtain a meaningful and reasonable f i t of the computer-generated spectra. The rather close correspondence between the data and the simulation in Figures 4.7a and 4.7b i s t y p i c a l of the close correspondence achieved over the whole range of angles, except for the.somewhat poorer correspondence when H i s within a few degrees from being p a r a l l e l to the xy plane (cf Figure 4.4), the worst f i t being given in Figure 4.7c. This more noticeable discrepancy seems to be due to an extra set of l i n e s at minimum f i e l d . An unexplained d i s t o r t i o n a f f e c t i n g only some of the more isotropic-type of s i t e s would cause a doubling of the more isotropic l i n e s which, at t h i s orientation, are at their minimum f i e l d but there i s no apparent reason why such a doubling would not appear at other orientations. Since there i s no firm explanation for what appear to be extra l i n e s within t h i s narrow range of angles, the addition of more parameters to the computer programme to simulate t h i s l o c a l i z e d discrepancy was not j u s t i f i e d . 260 300 340 260 300 340 260 300 340 H (mT) H (mT) H (mT) (a) (b) (c) F i g u r e 4.7 C o m p a r i s o n o f c o m p u t e r - g e n e r a t e d r e s u l t s ( t o p ) a n d ESR s p e c t r a w i t h (a) H i n p l a n e 1 and m a k i n g an a n g l e o f 24° w i t h g z and an a n g l e o f 9.5° w i t h t h e c o n d u c t i o n p l a n e ; (b) w i t h 3 a l o n g t h e c a x i s ; (c) w i t h H i n p l a n e 1 and p e r p e n d i c u l a r t o t h e g z a x i s ( i . e . , i n t h e g ^ p l a n e ) . o 51 One extra l i n e i s independent of angle but appears in most of the spectra at g = 2.035. This signal i s also v i s i b l e in Figure 3.1 which displays the spectrum from a c r y s t a l overdoped with Mn 2 + and i t appears even in undoped c r y s t a l s as received from the supplier. Since t h i s l i n e manifests no angular dependence and has a g value which i s considerably d i f f e r e n t from that of the free electron, there i s not much data on which to base speculation regarding either the source of t h i s signal or the location of t h i s source within the c r y s t a l . This l i n e was included in the simulation for esthetic purposes. The computer-generated spectra are thus a superposition of the l i n e s from: (a) the three anisotropic s i t e s in the plane of rotation and their respective two equivalent s i t e s at ± 120° (Figure 4.6b); (b) the isotropic s i t e as well as i t s two equivalent s i t e s (Figure 4.6c); (c) the signal which i s independent of angle. Thus each computer-generated spectrum i s the sum of 49 Lorentzian l i n e s . 52 The spin-Hamiltonian parameters used in the computer simulation are given in the table below in which the parameters for the more anisotropic s i t e symmetry are denoted by a subscript "a" and those for the more isotropic s i t e symmetry are denoted by a subscript " i " . Table 4.1 Spin-Hamiltonian parameters for Cu 2 + in the mid-oxygen s i t e s of sodium /3"-alumina 9a|| = 2.355 Aa|| =* 12.0 mT ' i l l = 2.003 A i | | ~ 9 , 9 m T g a X - 2.087 AaJ_ =* 2.0 - 4.0 mT 9iX = 2.240 A i J . ~ 8 , 8 m T 53 4.4 INTERPRETATION OF THE RESULTS The complex spectra reveal a great deal about the occupied s i t e s . F i r s t of a l l , the more anisotropic type of spectra can be explained by postulating that these spectra ari s e from mO s i t e s which have either a BR or aBR nearest neighbour vacant. Probably during the two minutes of doping, the only type of s i t e that i s present in any great numbers to receive the Cu 2* ions are the mO s i t e s which have either a BR or aBR nearest neighbour vacant. The distance (between centers) of the mO s i t e to the aBR and BR s i t e s i s only 0.08 nm. Hence a Cu 2 + ion (ionic radius = 0.072 nm) could hardly occupy an mO s i t e i f the neighbouring aBR and BR s i t e s were both occupied by a sodium ion (ionic radius = 0.095 nm). This i s p a r t i c u l a r l y true because both the C u 2 + and Na 1 + are e l e c t r o p o s i t i v e ions. Furthermore, when only one neighbouring Na 1 + i s missing the mO s i t e would undergo a d i s t o r t i o n that e a s i l y could cause the Cu 2 + spectra to have more anisotropic A values. Moreover, the mO s i t e would become t i l t e d in one d i r e c t i o n or the other depending upon which neighbouring Na i s missing. Hence one would expect that, at any p a r t i c u l a r angle as the c r y s t a l i s being rotated in plane 1, two mO s i t e s t i l t e d in opposite directions would y i e l d spectra which are s h i f t e d with respect to each other. It i s t h i s t i l t , due to vacancies in the neighbouring sodium s i t e s , which caused the minima of the two more anisotropic sets of l i n e s to be s h i f t e d by -2.5° and +7° where 0° i s taken as the angle at which a t h i r d , unshifted, more anisotropic set of l i n e s reaches i t s 54 minimum and the more isotropic set reaches i t s maximum. The most l i k e l y reason why the more isotropic type of spectrum i s hardly v i s i b l e a f t e r two minutes of doping i s that, within such a short time, i t i s only near the edges of the c r y s t a l , from where sodium most readily escapes, that a few mO s i t e s can be created which have neighbouring aBR and BR s i t e s that are both vacant. As annealing proceeds, more and more sodium i s diffused out of the c r y s t a l from s i t e s that are further from the edges and hence more mO s i t e s with both neighbouring sodium s i t e s vacant become available for occupation by Cu 2 + ions. This explains why the more isotropic spectrum gradually grows with annealing. Such an mO s i t e probably would be less distorted and would not be t i l t e d . Hence the Cu 2 + spectra from such a s i t e should have more isotropic A values and there should be no s h i f t of li n e s due to t i l t as, indeed, i s the case for the more is o t r o p i c , single set of li n e s that reaches the maximum f i e l d in the data from the annealed c r y s t a l . Therefore, the set of l i n e s at maximum f i e l d in Figures 4.4 and 4.7 i s attributed to mO si t e s which have both neighbouring sodium s i t e s vacant. As mentioned in 4.2, the more isotropic type of spectrum has "reversed" g values (g^ < g_j_). Such a "reversal" of g values for C u 2 + i s usually attributed to a compression of charges along the z axis in an octahedral-type s i t e with tetragonal d i s t o r t i o n (cf, e.g., McGarvey, 1966, p. 182). D i f f r a c t i o n studies by Takagi, Joesten and Lenhert (1975) have shown that the CuN6 configuration changes from an elongated tetragonal configuration 55 in K 2BaCu(N0 2) 6 and K 2CaCu(N0 2) 6 to a compressed tetragonal configuration in Rb 2PbCu(N0 2) 6. Hence the mere replacement of K 1 + by Rb1* changes the configuration from elongated to compressed. Harrowfield and Pilbrow (1973) reported that K 2PbCu(N0 2) 6 undergoes a reversible phase t r a n s i t i o n at 280 K from a configuration with i s o t r o p i c g values to one with "reversed" g values. At 295 K, g = 2.120(5) (iso t r o p i c ) and, below 245 K, g„ = 2.062(1) and q ± = 2.150(1). Harrowfield, Dempster, Freeman and Pilbrow (1973) report that Tl 2PbCu(N0 2) 6 has a temperature-dependent behaviour and g values that are very similar to those of K 2PbCu(N0 2) 6. These are but a few examples of analogous situations occurring in other structures which compare with the change reported here from a more anisotropic type of s i t e with "normal" g values to a more iso t r o p i c type of s i t e with "reversed" g values by the creation of an extra vacancy in a nearest-neighbour sodium s i t e . Annealing the c r y s t a l decreases the A values of both the more anisotropic and the more is o t r o p i c spectra by about 10%. This decrease in A values by annealing i s attributed to additional d i f f u s i o n of copper ions and possibly other impurities into the conduction planes and/or d i f f u s i o n of sodium ions out of the conduction planes. As has been explained, t h i s respectively stretches or contracts the bonds between the spinel blocks which, in turn, causes the values of A to decrease. The ease of d i f f u s i o n of the C u 2 + ions would seem to suggest that the ions are not bound very t i g h t l y to the mO s i t e s . This i s supported by the temperature dependence of the spectra which 56 w i l l be discussed l a t e r . However, to determine how annealing a f f e c t s the spin-Hamiltonian parameters qu a n t i t a t i v e l y would require an evaluation of these parameters from the much more complex spectra of the unannealed c r y s t a l (displayed in Figure 4.5). This would represent, i f not an impossible task, at least a rather more d i f f i c u l t one than obtaining these parameters by simulating the considerably simpler spectra from the annealed c r y s t a l s . I f , with annealing, there were a linear d i f f u s i o n both of sodium atoms out of the c r y s t a l and of other ions into the c r y s t a l and i f there were a known way (by ESR) to relate the more isotropic type of spectra to the C u 2 + - 0 bond length along the z axis of the mO s i t e , i t might be possible to v e r i f y experimentally the compression of charges along the z axis as the more isotropic type of s i t e i s created. However, there i s no guarantee of l i n e a r i t y in d i f f u s i o n nor in the resulting changes in bond lengths. It should be mentioned here that, according to the study of Farrington and Dunn (1982), what they interpreted as Na 1 * - Cu 2 + "exchange" occurred only up to 37% even after maintaining the temperature at 600 °C for 24 hours while other divalent ions exchanged almost 100% within about one hour. Since Farrington and Dunn (1982) made their estimates from the results of gravimetric and radiochemical measurements, they could not be sure whether even the C u 2 + ions that did enter the c r y s t a l a c t u a l l y exchanged for the Na 1 + ions at the aBR and BR 57 s i t e s or whether i n f a c t they went i n t o t h e mO s i t e s as det e r m i n e d here and the Na 1 * i o n s d i f f u s e d out of the c r y s t a l l e a v i n g the aBR and BR s i t e s v a c a n t . The v e r y slow and l i m i t e d i n c o r p o r a t i o n of C u 2 * i o n s i n t o the c r y s t a l , even t o the e x t e n t t h a t i t d i d o c c u r , might now be e x p l a i n e d by C u 2 + i o n s e i t h e r f o l l o w i n g the Na 1 * m i g r a t i n g i n the c o n d u c t i o n p l a n e s or p a s s i n g t h r o u g h Na 1 * v a c a n c i e s t o d i f f u s e i n t o the p l a n e s . I t i s w e l l known ( c f Ba t e s ) t h a t h e a t i n g the 0" s t r u c t u r e w i t h o u t an e x t e r n a l sodium vapour p r e s s u r e causes Na 1* i o n s t o d i f f u s e out of the c o n d u c t i o n p l a n e s l e a v i n g many v a c a n c i e s i n the aBR and BR s i t e s . I t i s thus v e r y p l a u s i b l e t o f i n d C u 2 * i n the mO s i t e s w i t h one or the o t h e r or both n e i g h b o u r i n g Na 1 * i o n ( s ) m i s s i n g . S i n c e t h e r e a r e o n l y h a l f as many mO s i t e s as t h e r e a re sodium (aBR and BR) s i t e s , i t i s not s u r p r i s i n g t h a t i f the Cu 2* i o n s occupy o n l y the mO s i t e s whereas many o t h e r i o n s l i k e Mn 2* exchange w i t h the sodium, the i n f e r r e d Na 1 * - Cu 2* exchange proceeded t o o n l y 37%. F i g u r e 4.8a d i s p l a y s an o c c u p i e d s i t e and i t s n e a r e s t n e i g h b o u r s c o m p r i s i n g t h r e e oxygen atoms above and t h r e e below the mO s i t e and two column oxygen atoms i n t h e c o n d u c t i o n p l a n e p e r p e n d i c u l a r t o the c a x i s . The shaded a r e a r e p r e s e n t s t h e xy p l a n e . The bonds which the Cu 2* i o n forms w i t h the t h r e e oxygen n e a r e s t n e i g h b o u r s above and below the c o n d u c t i o n p l a n e form an i r r e g u l a r o c t a h e d r o n because the d i s t a n c e between n e a r e s t -n e i g h b o u r oxygen atoms (0.28 nm) i s l e s s than the O-Cu 2* d i s t a n c e (0.294 nm). Moreover, t h e r e a r e two column oxygen atoms t h a t a r e 0.28 nm from the Cu 2* i o n . Thus the t h r e e mO s i t e s a r e 58 i r r e g u l a r , ,dodecahedral s i t e s . The spectra obtained from planes 1 and 2 of the annealed c r y s t a l , from which respectively the plots given in Figures 4.2 and 4.5 were obtained, were compared in order to i d e n t i f y at which angles in the two planes the spectra correspond. In this way one can determine at which angle, in sampling plane 1, ^ was p a r a l l e l to plane 2, the conduction plane. "W" in Figure 4.4 indicates the d i r e c t i o n of H in plane 1 when H i s also p a r a l l e l to plane 2. Relating the data obtained by rotating the c r y s t a l in plane 1 (cf Figure 4.2 or 4.5) to the s i t e displayed in Figure 4.4, one can determine that when the c r y s t a l has been rotated, in plane 1, about 35° from W, the unshifted, more anisotropic set of l i n e s and the more isotropic set reach the absolute minimum and maximum respectively. From the c r y s t a l ' s dimensions (Bettman and Peters, 1971) one can calculate that at 33.5° the f i e l d is perpendicular to the bond in plane 1. Therefore, t h i s d i r e c t i o n at which the spectra reach the extrema i s i d e n t i f i e d as the z axis (0° in Figures 4.2 and 4.5) and establishes the value of g 2, or gjj. As the f i e l d i s rotated a further 56.5°, i t i s p a r a l l e l to the c axis and therefore i t forms an equal angle with a l l the bonds. Hence the spectra at t h i s angle reach their maximum coalescence. When the c r y s t a l i s rotated a further 33.5° ( i . e . , at 90° in Figures 4.2 and 4.5), H i s p a r a l l e l to the bond in plane 1 and hence perpendicular to z. This d i r e c t i o n i s i d e n t i f i e d as x and y i e l d s the value of g x or gj_. By comparing the data obtained from planes 1 and 2, and 59 having i d e n t i f i e d the spectrum in plane 2 corresponding to H sampling the d i r e c t i o n indicated by W, one can compare the spectrum obtained from the x d i r e c t i o n in plane 1 with the spectrum obtained in plane 2 when H i s p a r a l l e l to y. Since these two spectra are i d e n t i c a l , i t follows that g has a x i a l symmetry in the xy plane, the plane represented by the shaded area in Figure 4.8a. Owing to the fact that within experimental accuracy g x - g y, the results are described by the a x i a l l y symmetric spin Hamiltonian * = 09,|HZSZ + /3gj.(HxSx + H yS y) + A„I ZS Z + A j . ( l x S x + I y S y ) . Relating the data obtained by rotating the c r y s t a l about the c axis (Figure 4.3) to the three s i t e s displayed in Figure 4.6 and supposing that i n i t i a l l y H" i s perpendicular to any cO-cO bond, one would expect a set of l i n e s due to the mO s i t e included in that cO-cO bond to be at minimum f i e l d . (However, thi s minimum i s not as low as the absolute minimum obtained at 0° (H || z) in Figure 4.2 where H i s perpendicular both to the cO-cO bond and to the bond contained in plane 1 (cf Figure 4.8a)). Simultaneously S makes an angle of 30° to the other two cO-cO bonds and hence the spectra from these s i t e s coalesce at an intermediate f i e l d . When the c r y s t a l i s rotated 30° about the c axis in either d i r e c t i o n , H i s p a r a l l e l to the cO-cO bond which causes the set of l i n e s due to the mO s i t e included in t h i s cO-cO bond to undergo a maximum which occurs at a lower f i e l d than, and halfway between, successive maxima due to the set of l i n e s with "reversed" g values. Simultaneously 8 forms an angle of 60° to o F i g u r e 4.8 (a) I r r e g u l a r d o d e c a h e d r a l s i t e c o m p r i s i n g t h r e e o x y g e n atoms above and b e l o w t h e mO s i t e and two c o l u m n - o x y g e n atoms i n t h e c o n d u c t i o n p l a n e p e r p e n d i c u l a r t o t h e c a x i s . The s h a d e d a r e a r e p r e s e n t s t h e g ^ p l a n e . (b) V i e w a l o n g t h e c a x i s o f t h e c o n d u c t i o n p l a n e d i s p l a y e d i n F i g u r e 4.4. 62 the other two cO-cO bonds and thus the spectral l i n e s o r i g i n a t i n g from the mO s i t e s included in these bonds w i l l coalesce at intermediate f i e l d . When the c r y s t a l i s rotated a further 30° about the c axis, H w i l l be perpendicular again to a cO-cO bond and hence the spectra obtained i n i t i a l l y w i l l be repeated. As there i s a 60° p e r i o d i c i t y , the above spectra w i l l be repeated as the c r y s t a l i s rotated about the c axis beyond 60°. Therefore, although only the l i n e s at minimum f i e l d can be distinguished, the general pattern obtained from sampling plane 2 i s consistent with the postulate that the C u 2 + ions occupy the three equivalent mO s i t e s which are rotated 120° with respect to each other. The resultant spectrum i s thus a superposition, not only of the more anisotropic and isotropic spectra already mentioned, but also of the corresponding spectra from the two equivalent s i t e s which are rotated by ± 120° with respect to the s i t e described (Cf Figures 4.4 and 4.8a). As the temperature of the annealed c r y s t a l i s increased, the Cu 2* l i n e spectra f i r s t broaden. Upon further increase in temperature the spectra broaden to the extent that individual l i n e s are no longer d i s c e r n i b l e but are replaced by an anisotropic, random-type spectrum (cf Figure 4.9a). A somewhat similar e f f e c t i s observed in many compounds containing Cu 2* ions (cf, for example, Bleaney, Bowers and Trenam, 1955) and i s attributed to a dynamic Jahn-Teller e f f e c t . These random-type spectra, however, are not usually as anisotropic as the present spectra shown in Figure 4.9b. The anisotropic, random character 63 F i g u r e 4.9 (a) S p e c t r a f r o m an a n n e a l e d c r y s t a l w i t h H X c a t t h e t e m p e r a t u r e s i n d i c a t e d . (b) S p e c t r a f r o m an a n n e a l e d c r y s t a l a t 77.3 K a s H s a m p l e d t h e c r y s t a l a t t h e o r i e n t a t i o n s i n d i c a t e d . 64 of the spectrum is most l i k e l y due to thermal motional averaging caused by the fact that the C u 2 + ions are not t i g h t l y bound to the mO s i t e s and thermally vibrate, moving more ea s i l y in the conduction planes than perpendicular to them. As the temperature of the unannealed c r y s t a l i s increased, the C u 2 + l i n e spectra decrease much more slowly than in the case of the annealed c r y s t a l . Moreover, no anisotropic, random-type spectrum i s detected at any temperature in the case of the unannealed c r y s t a l . This could be due to the much lower concentration of impurities in i t s conduction planes. Figure 4.10 displays the Cu 2 + l i n e spectra from an unannealed c r y s t a l at < 1.6 K (a), and at 40 K (b). Though the gain i s greatly increased in (b), the signal is s t i l l c l e a r l y v i s i b l e over the background noise and has not broadened s i g n i f i c a n t l y . In sharp contrast, the Cu 2 + l i n e spectra in the case of the annealed c r y s t a l have already broadened to the extent that they are almost i n v i s i b l e at 5 K (cf Figure 4.9a). Another plane that was sampled by the f i e l d in 5° steps i s the plane (called plane 3) which contains the c axis and an axis along the d i r e c t i o n of two column oxygens, i . e . , along a cO-mO-cO bond d i r e c t i o n that i s also p a r a l l e l to one of the c r y s t a l symmetry axes. From the previous analyses, one would expect that rotating the c r y s t a l such that the f i e l d samples plane 3 would y i e l d very symmetric r e s u l t s . The data displayed in Figure 4.11 confirm t h i s analysis. gure 4.10 Cu l i n e spectra from an unannealed c r y s t a l at < 1.6 K (a), and at 40 K (b). Though the gain i s greatly increased i n (b), the signal i s s t i l l c l e a r l y v i s i b l e over the background noise and has not broadene s i g n i f i c a n t l y . 66 cn F i g u r e 4.11 P l o t d i s p l a y i n g t h e s y m m e t r i c r e s u l t s o b t a i n e d b y r o t a t i n g an a n n e a l e d c r y s t a l s o t h a t H s a m p l e d p l a n e 3. The x ' s r e p r e s e n t a l i n e t h a t m a n i f e s t s no a n g u l a r d e p e n d e n c e . 68 i 1 1 r (±w)H 69 CHAPTER 5 - SUMMARY OF RESULTS AND SUGGESTIONS FOR FURTHER  WORK 5.1 SUMMARY OF RESULTS In summary suitable d i f f u s i o n and annealing procedures were developed which permitted analyzable ESR spectra to be obtained and spin-Hamiltonian parameters to be determined for Mn 2 + and Cu 2* ions diffused into sodium ^"-alumina. The results were compared to similar studies on sodium /3-alumina and emphasized the differences between the two structures. In p a r t i c u l a r , differences such as higher ionic conductivity, a larger Na 1 + ion concentration in the conduction planes and a di f f e r e n t oxygen layer configuration adjacent to the conduction plane of the /3" structure were manifest. The Mn2* ion was found to exchange readily with the Na 1 + ions in the conduction plane as confirmed by a recent study by Farrington and Dunn (1982) but i t was also found to occupy the tetrahedrally coordinated Al(3) s i t e adjacent to the conduction plane. Reversal of the Na 1 * exchange during the annealing l e f t a s u f f i c i e n t l y sharpened Mn 2 + spectrum from the Al(3) s i t e to obtain the spin-Hamiltonian parameters. The g and A values compared favourably with those reported for the Mn2* in the Al(3) s i t e in sodium /3-alumina. The D value d i f f e r e d by a factor of four which is not surprising in that i t i s the parameter most affected by the environment of the Mn2*. That t h i s environment d i f f e r s in the two structures i s clear from the fact that the 70 e l e c t r o s t a t i c f i e l d s in the v i c i n i t y of the Al(3) s i t e adjacent to the conduction plane are lower in the 0" structure than in the (S structure. This i s evidenced by the s h i f t of the column oxygen from the 0(5) s i t e only in the 0 structure which indicates a greater d i s t o r t i o n of the Al(3) s i t e and hence a higher D value. This s e n s i t i v i t y of the value of D to the environment suggests, as a p o s i t i v e application, using the Mn 2 + ESR spectrum as a monitor to study the e f f e c t s of ionic migration in the /3" structure. The Cu 2 + ion was found to d i f f u s e into the mid-oxygen s i t e rather than exchange d i r e c t l y with the Na 1 + ion. These results explain the anomalous behaviour observed for the Cu 2 + ion exchange inferred by Farrington and Dunn (1982). Four d i f f e r e n t configurations were i d e n t i f i e d depending on Na 1 + ion vacancies. The most interesting feature of these was that one configuration exhibited "reversed" g values. The s i t e symmetry i s d i f f e r e n t from that of the sodium /3-alumina structure so that no di r e c t comparison of spin-Hamiltonian parameters was f e a s i b l e . The only point of d i r e c t comparison i s that the Cu 2 + occupy the mid-oxygen s i t e s in both structures. However, the symmetry of the mid-oxygen s i t e in the two structures i s not the same so that most of the other results point to the differences between the two structures. The fact that the anti-Beevers-Ross s i t e can be occupied by sodium atoms only in the 0" structure gives r i s e to a l l the uniquely interesting ESR c h a r a c t e r i s t i c s of the Cu 2 + ion in sodium /3"-alumina as the host. The four d i f f e r e n t configurations reported here and the "reversal" of the g values 71 are a l l dependent upon the fact that the mO s i t e in the 0" structure has, not only one, but two neighbouring sodium s i t e s , either of which can be occupied or both of which can be empty. The marked difference in the temperature dependence of the spectra from the unannealed and annealed c r y s t a l s (compare Figure 4.9a and 4.10) indicates a strong r e l a t i o n s h i p between impurity concentration and the ra p i d i t y with which the Cu 2 + l i n e s disappear as the temperature i s raised. In the case of the annealed c r y s t a l with i t s heavier doping the C u 2 + l i n e s broaden readily and disappear due to increased ion-ion interaction with even a s l i g h t increase in temperature above the X point of helium. The more pronounced temperature dependence of the Cu 2 + l i n e s in the case of the annealed c r y s t a l along with the decreased s p i n - l a t t i c e , relaxation-time constant as evidenced by the data at Q band could form the basis for further study of impurity-impurity interactions e s p e c i a l l y insofar as they may aff e c t ionic mobility. To interpret the present temperature-dependent spectra and saturation phenomena in terms of impurity-impurity interactions and ionic mobility would require equipment to measure relaxation times and ionic conductivity (cf respectively, e.g., chapter 4 of Bersohn and Baired (1966) and Wolf (1979) reqarding measurements of these parameters). 5.2 SUGGESTIONS FOR FURTHER STUDY Spectra were detected from ions inadvertently incorporated into the spinel blocks during the growth of the sodium 0 " -72 alumina used in t h i s study. However, even from a large c r y s t a l (<* 10 x 4 mm along the edges and 0.5 mm in thickness) only very weak signals were obtained. These signals, which manifested an angular dependence, were v i s i b l e only at low f i e l d s . When the c r y s t a l ' s orientation caused these signals to go above «* 160 mT, they were too broadened to be distinguished from the background noise. Therefore i t was not possible to evaluate the spin-Hamiltonian parameters even by conducting experiments with the largest c r y s t a l on hand. According to a personal communication from the producer of the c r y s t a l s , mass spectral analysis shows trace amounts of chromium and iron either of which could account for the low-field signals. However, i t was not possible to obtain sodium ^"-alumina single c r y s t a l s purposely doped during growth with the proper chromium or iron concentration. Other work that may be undertaken in the ESR study of t r a n s i t i o n metal ions in sodium 0"-alumina might be to attempt to dope the single c r y s t a l s with Co 2 + by modifying the doping procedure so that the CoCl 2 i s maintained in HC1 gas (cf The Chemical Rubber Company Handbook of Chemistry and Physics, 50th ed., p. B104). The HC1 gas would prevent d i s s o c i a t i o n of the CoCl 2 before i t reaches the molten state at 724 °C. A suitable substrate may be required, along with the appropriate doping-time i n t e r v a l , to prevent overdoping. Further studies on c r y s t a l s doped with t r a n s i t i o n metal ions might determine whether, for each of these dopants, a spectral change could be observed as a function of the amount of L i 1 + diffused into the conduction planes. One might thus be able 73 to use these ions as a monitor to study the c r y s t a l ' s ionic and electronic conductivity. It has been mentioned already that Mn 2 + placed in the A l ( 3 ) s i t e adjacent to the conduction plane might be used as an ESR probe to study the e f f e c t s of ionic conduction and/or ion exchange in the conduction planes i f the Mn2* ion could be placed in the s i t e without undue d i s t o r t i o n of the si g n a l . Perhaps Mn 2 + could be introduced into t h i s s i t e during growth of the c r y s t a l . 74 BIBLIOGRAPHY Abello, L., S.J., and Schwerdtfeger, C.F., S o l i d State Commun. 44, 497 (1982). Abello, L., S.J., and Schwerdtfeger, C.F., Accepted for publication in Physica Status S o l i d i (1984). Abragam, A., and Bleaney, B., Electron Paramagnetic Resonance of Transition Ions, Oxford University Press (1970). Antoine, J . , Vivien, D., Livage, J . , Thery, J . , and Collongues, R., Mat. Res. B u l l . J_0, 865 ( 1975). Barklie, R.C., and O'Donnell, K. , J. Phys. C J_0, 4127 (1977). Barklie, R.C., O'Donnell, K., and Murtagh, A., J . Phys. C j_0, 4815 (1977). Bates, J.B., private communication. Bersohn, M., and Baird, J.C., An Introduction to Electron Paramagnetic Resonance, W.C. Benjamin, Inc. 1966. Bettman, M., and Peters, C.R., J. Phys. Chem. 73, 1774 (1969). Bleaney, B., F.R.S., Bowers, K.D., and Trenam, R.S., Proc. Roy. Soc. A228, 157 (1955). Farrington, G.C., and Dunn, B., So l i d State Ionics, 7, 267 (1982). Feher, E.R., Phys. Rev. Al36, 145 (1964). Gourier, D., Antoine, J., Vivien, D., Thery, J . , Livage, J . , and Collongues, R., Phys. Stat. Sol. (a), 4J., 423 (1977). Gourier, D., Vivien, D., Thery, J . , Livage, J . , and Collongues, R., Phys. Stat. Sol. (a), 45, 599 (1978). Harrowfield, B.V., Dempster, A.J., Freeman, T.E., and Pilbrow, J.R., J. Phys. C: S o l i d State Phys. 6, 2058 (1973). Harrowfield, B.V., and Pilbrow, J.R., J . Phys. C: S o l i d State Phys. 6, 755 (1973). Krebbs, J.J., Phys. Rev. JJ55, 246 ( 1966). McGarvey, B.R., Transition Metal Chem. 3, 89 (1966). Nash, F.R., Phys. Rev. J_38, A1500 ( 1965). 75 Peters, C.R., Bettman, M., Moore, J.W., and Glick, M.D., Acta Cryst. B 27, 1826 (1971). Roth, W.L., Reidinger, F., and La Placa, S., Superionic Conductors (Proceed. Conf. Edited by Mahan, G.D., and Roth, W.L.), 237 (1976). S i x l , H., and Hundhausen, R., Z. Physik B, 3_8, 299 (1980). Sparks, L.A., and Powell, R.L., Journal of Research, National Bureau of Standards, 76A, 263, 1972. Takagi, S., Joesten, M.D., and Lenhert, P.G., J. Am. Chem. S o c , 97, 444 (1975). Wolf, D., Fast Ion Transport in Solids (Proceed. Intern'l Conf. Edited by Vai s h i s t a , P., Mundy, J.N., and Shenoy, G.K.), 341 (1979). Wynn-Jones, I., and Miles, L.J., Proc. Br. Ceram. Soc. _1_9, 161 (1971). Yao, Y.F.Y., and Kummer, J.T., J . Inorg. Nucl. Chem., 29, 2463 (1967). 76 APPENDIX A: DOPING AND ANNEALING PROCEDURES It has to be stressed at the very outset that finding a workable procedure to dope by d i f f u s i o n single c r y s t a l s of sodium 0"-alumina can be a very lengthy process which, to a large extent, has to be conducted by t r i a l and error. Temperature, length of doping time and concentration of the dopant in the "dopant ion - substrate" mixture or in the mixture of molten s a l t s are quite c r i t i c a l i f one i s to avoid either overdoping or underdoping. Furthermore, i t must be emphasized again that in the case of some ions, l i k e C u 2 +, provision must be made to prevent reduction to a diamagnetic ion, such as C u 1 +, during the doping and/or annealing processes. Moreover, i f a sodium ion - dopant ion exchange takes place, one must reverse th i s exchange i f one i s interested in studying ESR signals from any s i t e other than the aBR and BR octahedrally coordinated s i t e s . A further stringent condition that has to be met i s that the dopant, the substrate, etc., must be of very high purity to prevent spurious signals from other paramagnetic ions. Although in hindsight the recent work of Farrington and Dunn (1982) has helped to explain many of the observed e f f e c t s of the procedures used for Mn 2 + and could have reduced the e f f o r t involved, the end results could not have been predicted. The d i f f u s i o n of four d i f f e r e n t ions was attempted: Mn 2 +, Cu 2 +, Co 2* and C r 3 + . The Mn 2 + and Cu 2 + doping and annealing procedures and the resu l t s have already been discussed in d e t a i l and w i l l not be repeated here. It should be mentioned that very pure 77 materials had to be obtained since off-the-shelf cuprous and cupric chloride and chromic chloride gave a large Mn 2 + spectrum. In the case of Co 2 + the s a l t used as the dopant was CoCl 2. It i s suspected that the constant f a i l u r e to detect a Co 2 + l i n e spectrum was due either to d i s s o c i a t i o n of the CoCl 2 before i t reached i t s melting point (724 °C), the temperature at which the doping and annealing were usually attempted or to a high degree of exchange re s u l t i n g in an extremely broad s i g n a l . Protracted and repeated attempts to dope single c r y s t a l s with C r 3 + from C r C l 3 at temperatures above and below 800 °C, the temperature at which S i x l and Hundhausen (1980) doped sodium 0-alumina from C r C l 3 , ended in f a i l u r e . Indeed, a C r 3 + signal was obtained but i t displayed v i r t u a l l y no angular dependence. Hence th i s microcrystalline-type signal probably originated from the surfaces and/or conduction planes, but not from a s i t e . In the case of Cr 3 +-doped, sodium 0-alumina, S i x l and Hundhausen (1980) id e n t i f y the anti-Beevers-Ross s i t e as the one occupied. However, the anti-Beevers-Ross s i t e s in the sodium 0- and alumina structures are quite d i f f e r e n t . This i s evident from the fact that in the case of the j3" structure the anti-Beevers-Ross and Beevers-Ross s i t e s are equivalent in everything except position and both can be occupied by Na 1 + whereas in the |3 structure these two s i t e s are quite d i f f e r e n t and the a n t i -Beevers-Ross s i t e i s never occupied by Na 1 +. This difference in the two structures may explain why, though the 0 structure can be doped with C r 3 + , a l l attempts to dope the 0" structure with C r 3 + f a i l e d . 

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