^ ^ ^^^ STUDIES OF DEUTERATED POTASSIUM CHROME ALUM by RONALD EUGENE MILLER, B. S., M. S. A DISSERTATION IN PHYSICS Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Aec-1 q^.3 T5 197/ ACKNOWLEDGMENTS I would like to express my appreciation to Dr. Edward Teller, who suggested that this research be undertaken, for the contributions he made to the interpretation of the results. I would also like to express my sincere appreciation to Dr. B. J. Marshall for his direction of this dissertation and to the Robert A. Welch Foundation of Texas for the financial support given to this project. 11 TABLE OF CONTENTS Page ACKNOWLEDGMENTS ii LIST OF TABLES v LIST OF FIGURES vi I. PRELIMINARY CONSIDERATIONS . .' 1 Introduction 1 Previous Related Research on Alums 3 II. GROWTH OF SINGLE CRYSTALS 9 Supersaturated Solution 9 Seed Crystal Growth 10 Crystal Growth 11 III. EXPERIMENTAL PROCEDURES AND EQUIPMENT 14 Electronics for Ultrasonic Measurements 14 Crystal Preparation for Ultrasonics Measurements. 16 Ultrasonic Cryostat and Dewars 16 Temperature Measurement for Ultrasonics 19 Ultrasonic Transducers 19 Ultrasonic Binders 20 Collection of Attenuation Data 22 Cryostat for Measurement of the Dielectric Coefficients 23 Electronics for the Dielectric Constants 25 Temperature Measurement for the Dielectric Constants 25 Dielectric Sample Preparation 25 lii IV Page Collection of Dielectric Data 26 Continuous Cooling Method for Measuring the Specific Heat 27 Electronics for Specific Heat 29 IV. RESULTS AND CONCLUSIONS 31 Ultrasonic Attenuation Results 31 Coraplex Dielectric Coefficient Results 33 Specific Heat Results 62 Conclusion 62 Future Work 70 LIST OF REFERENCES 72 APPENDIX I 74 LIST OF TABLES Table Page 1. Values of a in the [100] Direction at 10 MHz 51 2. Values of a in the [100] Direction at 30 MHz 52 3. Values of a in the [110] Direction at 10 MHz 53 4. Values of a in the [110] Direction at 30 MHz 54 5. Values of a in the [110] Direction at 50 MHz 55 6. Values of a in the [111] Direction at 10 MHz 56 7. Values of a in the [111] Direction at 30 MHz 57 8. Values of K' and K" in the [100] Direction as a Function of Temperature 58 9- Values of K' and K" in the [110] Direction as a Function of Temperature 59 10. Values of K' and K" in the [111] Direction as a Function of Temperature 60 11. Specific Heat Values as a Function of Temperature . 61 vi LIST OF FIGURES Figure Page 1. a Crystal Structure for the Alums 4 2. Directions of the Crystallographic Axes 13 3. Block Diagram of the Apparatus for Ultrasonic Measurements 15 4. Cryostat and Dewars for Ultrasonic Measurements ... 17 5. Cryostat and Dewars for Dielectric Coefficient Measurements 24 6. Block Diagram of the Apparatus for Specific Heat Measurements 30 7. Echo Patterns Showing Increasing Attenuation with Decreasing Temperature 32 8. Ultrasonic Attenuation versus Temperature in the [100] Direction at 10 MHz 34 9- Ultrasonic Attenuation versus Temperature in the [100] Direction at 30 MHz 35 10. Ultrasonic Attenuation versus Temperature in the . [110] Direction at 10 MHz 36 11. Ultrasonic Attenuation versus Temperature in the [110] Direction at 30 MHz 37 12. Ultrasonic Attenuation versus Temperature in the [110] Direction at 50 MHz 38 13. Ultrasonic Attenuation versus Temperature in the [111] Direction at 10 MHz 39 14. Ultrasonic Attenuation versus Temperature in the [111] Direction at 30 MHz 40 15. K' and K" versus Temperature in the [100] Direction at 10 MHz 41 16. K' and K" versus Temperature in the [100] Direction at 30 MHz 42 17. K' and K" versus Temperature in the [100] Direction at 50 MHz 43 vii Page 18. K' and K" versus Temperature in the [110] Direction at 10 MHz 44 19. K' and K" versus Temperature in the [110] Direction at 30 MHz 45 20. K' and K" versus Temperature in the [110] Direction at 50 MHz 46 21. K' and K" versus Temperature in the [111] Direction at 10 MHz 47 22. K' and K" versus Temperature in the [111] Direction at 30 MHz 48 23. K' and K" versus Temperature in the [111] Direction at 50 MHz 49 24. Specific Heat versus Temperature 50 25. Curve Shapes Expected for K' and K" and C for a Ferroelectric Phase Transition ^ 65 26. Curve Shapes Expected for a Debye-type of Relaxation 66 27. Representation of r 75 CHAPTER I PRELIMINARY CONSIDERATIONS Introduction Potassium chrome alura (KCr(SO ) '12H 0), due to : ts paramagnetic behavior, has long been used for both the production of and thermom- -4 etry in extreraely low temperatures (T - 10 K). As a result, this and other paramagnetic alums have been studied extensiveLy. Howcver, many of their properties are still not well understood. Many alums 12 3 have shown anomalous behavior in some, * ' if not all, of the fol- lowing properties in the temperature region of 300 to 4.2 K. (1) Ultrasonic Attenuation (2) Dielectric Coefficients (3) Optical Absorption and Transmission (4) Crystal Structure (5) Paramagnetic Resonance (6) Thermal Conductivity A specific discussion of related research will follow this introduc- tion. Of particular interest in this dissertation is a study of the ultrasonic attenuation and dielectric coefficients of the alums. The attenuation of ultrasound in alums generally shows a very large 2 3 peak in the temperature range of 60 to 160 K. * The dielectric coefficients, both real and imaginary, have also shown peaks in this same general temperature range in some of the clear aluras. The two explanations for this behavior have suggested that since raany of the alums becorae ferroelectric, (1) the absorption is due to a ferroelec- 3 4 tric phase transition, * (2) the absorption of ultrasound raight be caused by a hindered rotation of the water molecules due to the inter- action of the perraanent dipole raoments of the water molecules and the dipole moraents produced by the forced motion of the ions in the 2 lattice. This is known as a Debye type of relaxation. The present work was designed to investigate what effects would be seen in the ultrasonic attenuation and dielectric coefficients if the water molecules were deuterated. If the mass of the water molecules were changed by deuteration then any resonant phenomena involving the rotation or vibration of the water molecules would change its temperature dependence. Furthermore, if the increase in the absorption of ultrasound were due to ferroelectric behavior, an anomaly in the dielectric coefficients would be expected in both the deuterated and undeuterated case. Also this work was designed to check for the possibility of a phase transition that would show up in the measurement of the specific heat. Measureraents of the ultrasonic attenuation and the dielectric coefficients were conducted in the temperature range of 300 to 4.2 K. The specific heat was measured over the teraperature range of 80 to 100 K. The results indicate that the effects of deuteration are not of prirae importance. Furthermore, the previously held ideas concern- ing the possible ferroelectric transition and hindered molecular rota- tion do not seem to be entirely proper for KCr(SO,^^'12D-0 in the light of the absence of anomalies in either the specific heat or the dielectric coefficients. A complete discussion of the results and conclusions can be found in Chapter IV. Previous Related Research on Aluras In the following paragraphs a suramary will be raade of the re- lated work conducted on the class of double salts known as alums. These salts have the general formula AB(SO ) 'l^H^O, where A and B are monovalent and trivalent ions respectively. An excellent summary of the work done on the chrome alums prior to 1951 may be found in the review article by J. Eisenstein. The crystal structures of aluras are known frora x-ray raeasurements by Lipson and Beevers. * Figure 1 shov^/s a diagram of 1/8 of a unit cell for the alum a structure. The A ions and the B ions form two interpcnctrating face-centered cubic lattices. Each B ion is sur- rounded by six water molecules which forra an octahedron with axes slightly rotated frora the cubic axis. The octahedron is slightly distorted along a trigonal axis, producing an electric field at the B ion site. The SO, groups are arranged such that the S atom and one 0 atom lie on a trigonal axis. The other three 0 atoms lie at the other points of a tetrahedron with the S atom in the center. The re- maining six water molecules are spaced at odd points in the lattice and may be considered to be loosely associated with one A ion. Only two of these molecules are shown. The other water molecules may be located by knowing that each one touches two 0 atoms, a water raolecule associated with a B atom, and an A atom. It is known that among the chromiura alums there are three slightly Water molecule associated o with "B" ion Other water molecule Figure 1. a Crystal Structure for the Alums. different structures. They are the a, 3, and y structures. These structures are differentiated by the positions of the sulfate ions along the trigonai axis of the unit cell. This positioning is de- pendent on the size of the raonovalent ion. The positions of the water molecules are also slightly shifted frora a to 3 structure. Potassium chrome alum is a member of the a-type structure. This structure is known to undergo transitions in the 60 to 160 K range. The water-containing complexes are thought to be involved in this transition.