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TITLE
DEDICATION
DECLARATION
CERTIFICATE
ACKNOWLEDGEMENT
CONTENTS
PREFACE
I. ELASTIC COEFFICIENTS AND THERMAL EXPANSION SUPERCONDUCTING SINGLE CRYSTALS
1.1. Introduction.
1.2. Theory of elasticity.
1.3. Experimental methods in the study of elastic wave propagation in crystals.
1.4. Velocity measurements leading to determination of elastic constants.
Fig. 1.2. BLOCK DIAGRAM OF PULSE ECRO SET UP ANDTHE FORM OF THE PATTERN ON CRO SCREEN.
1.5. Quasiharmonic theory of thermal expansion of orthorhombic crystals.
1.6. High temperature super conducting systems.
Fig. 1.3. PEROVSKITE STRUCTURE AB03
Fig. 1.4. ARRANGEMENT OF THE DIFFERENT ATOMSIN TEE UNIT CELL OF THE HIGH TEMPERATURESUPERCONDUCTING CRYSTAL YB~CYO,.
References.
II. INTERLATTICE DISPLACEMENTS OF THE HIGH TC SUPERCONDUCTORS
2.1. Introduction.
Fig. 2.1. ARRANGEMENT OF THE DIFFERENT RARE EARTH IBARIUM, COPPER AND OXYGEN ATOMS I N THE UNIT CELL OFTHE HIGH TEMPERATURE SUPERCONDUCTING CRYSTALRB%C%07.
2.2. Interlattice displacements.
2.3. Interlattice displacements of RBa2Cu3O7
Table 2.1: Unit cell dimensions of RBa2Cu3O7 where R = Y, Sm, Gd, Dy, Ho, Er, Tm and a, h, c are0 lattice parameters in A 0
Table 2.2 Position co-ordinates o: the neighbour of13 atoms in the unit cell
References.
III. SECOND ORDER ELASTIC CONSTANTS OF YBa2Cu3O7 AND GdBa2Cu307
3.1. Introduction.
3.2. Theory of second order elastic constants.
3.3. Second order elastic constants of YBa2Cu3O7.
3.4. Second order elastic constants of GdBa2Cu307.
3.5. Results and discussion.
Table (3.1) Second order elastic constants of the hightemperature superconducting compound YBa Cu 02 3 7
Table (3.2) Second order elastic constants of GdBa Cu 02 3 7
References.
IV. THIRD ORDER ELASTIC CONSTANTS OF YBa2Cu3O7 AN GdBa2Cu3O7
4.1. Introduction.
4.2. General theory of third order elastic constants.
4.3. Third order elastic constants of YBa2Cu3O7.
4.4. Third order elastic constants of GdBa2Cu3O7.
4.5. Results and discussion.
Table 4. 1: Third order elastic constants of the hightemperature superconducting compound YBa Cu 0 2 3 7
Tahle 4.2: Third order elastic constants of the hightemperature superconducting compound GdBa 2 Cu3 07
References.
V. PRESSURE DERIVATIVES OF THE SECOND ORDER ELASTIC CONSTANTS OF HIGH TEMPERATURE SUPERCONDUCTOR YBa2Cu3O7 AND Gdna2Cu3O7.
5.1. Introduction.
5.2. Pressure derivatives of the second order elastic constants from third order elastic constants data.
5.3. Pressure derivatives of the second order elastic constants of YBa2Cu3O7 and GdBa2Cu3O7.
5.4. Results and discussion.
Table 5.1 Pressure derivatives of second order elastic constantsof high temperature superconducting compound YBa Cu 0. 2 3 7
Table 5.2 Pressure derivatives of second order elastic constnnt~of h ~ g h temperature superconducting compound GdRa Cu 0. 2 3 7
Reference
VI. LOW TEMPERATURE THERMAL EXPANSION OF YBa2Cu3O7 AND GdBa2Cu3O7.
6.1. Introduction.
6.2. Introduction to finite strain elasticity theory and calculation of the generalized gruneisen parameters for acoustic waves in orthorhombic crystals from third order elastic constants.
6.3. Low temperature thermal expansion of YBa2Cu3O7
Fig. 6.1 GPs FOR THE THREE ACOUSTIC BRANCHESAS A FUNCTION OP ANGLE FOR YBa2Cu3O7.
Fig. 6.2 GPs FOR THE THREE ACOUSTIC BRANCHESAS A FUNCTION OF ANGLE FOR YBa2Cu307.
Fig. 6.3. POLAR DIAGRAM SHOWING THE PLOT OF THE GPS AND rsFOR THE ACOUSTIC BRANCHES AS A FUNCTION OF THE ANGLE WHICHTHE DIRECTION OF PROPAGATION MAKES W I T 6 THE ORTHORHOMBIC AXISFOR YBa2Cu307-
Fig. 6.4. POLAR DIAGRAM SHOWING THE PLOT OF THE GPs FOR THE ACOUSTIC BRANCH AS A FUNCTION OF THE ANGLE WHICH THE DIRECTION OF PROPAGATION MAKES WITH THE ORTHORBOMBIC AXIS FOR YBa2Cu3o7
Fig. 6.5. POLAR DIAGRAM SHOWING THE PLOT OF THE GPS r, FOR THE ACOUSTIC BRANCH AS A FUNCTION OF THE ANGLE WHICH THEDIRECTION OF PROPAGATION MAKES WITH THE ORTHORAOMBIC AXISFOR YBa2C?0,.
Fig. 6.6. POLAR DIAGRAM SHOWING THE PLOT OF THE GPs r, AND r2 FOR THE ACOUSTIC BRANCHES AS A FUNCTION OF THE ANGLE WHICH THE DIRECTION OF THE PROPAGATION MAKES WITH THE ORTHOBOMBIC AXIS FOR YBa2Cu3O7
6.4. Low temperature thermal expansion of GdBa2Cu307
Fig. 6.7. GPO r FOR TRE TRREK ACOUgRC BRANCRWAS A FUNCTION OF ANGLE FOR C d ~ C u 3 0
Fig. 6.8 GPs r FOR THE THREE ACOUSTIC BRANCHESAS A FUNCTION OP ANGLE FOR GdBa2Cu3O7
Fig. 6.9. POLAR DUCRAIl SROWMG TEE PLOT OF TALI GPs f4 AND 7; OR THE Acommc BRANCRW AS A r m c n o N or r n A~NG LE WRICATHE DIRECTION Or PROPAGATION MAKES WITH TRI! ORTAORflOIlBIC AXISroll Gd~ClL, O7-
Fig. 6.10. POLAR DIAGRAH SAOWMG THE PLOT OF THE GPs yrFOR THE ACOUSTIC BRANCH AS A FUNCTION OF THE ANGLE WAICA TIDIRECTION OF PROPAGATION MAKES WITH TEE ORTAORAOMBIC AXISFOR GdBa2Cu307.
Fig. 6.11. POLAR DIAGRAM SHOWING THE PLOT OF THE G P s NFOR THE ACOUSTIC BRANcHx AS A FUNCTION OF THE ANGLE WHICH %HEDIRECTION OF PROPAGATION UAKES WITH THE ORTHORAOMBIC AXISFOR GdBa2Cu30,.
Fig. 6.U. POLAR DIAGRAM SHOWING TIIE PC., OF F I E GPO rs AND FOR THE AcOaSnC BRANCHES AS A FUNCTION OF TEE ANGLE *HXCnTHE DIRECTION OF PROPAGATION MAKW WITH TFIE ORTROREOMBIC AX=FOR GdBa2CU, 0,.
6.5. Results and discussions.
References.