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TITLE
DEDICATION
CERTIFICATE
DECLARATION
ACKNOWLEDGEMENT
CONTENTS
PREFACE
1 BRIEF REVIEW OF THE FINITE STRAIN ELASTICITY THEORY AND ANISOTROPIC THERMAL EXPANSION IN CRYSTALS
1.1 Introduction
1.2 Finite Strain Elasticity Theory
1.3 Quasi Harmonic Theory of Thermal Expansion
References
2 SECOND, THIRD AND FOURTH ORDER ELASTIC CONSTANTS AND THE FIRST AND SECOND ORDER PRESSURE DERIVATIVES OF SECOND ORDER ELASTIC CONSTANTS IN HEXAGONAL CRYSTALS
2.1 Introduction
2.2 Expressions for the Second, Third and Fourth Order Elastic Constants of a Hexagonal Close Packed (hcp) Crystal
Table 2.2.1 Position co-ordinates of the nearest neighbours of the same typein the basal plane. These neighbours are denoted by I.
2.3 Expressions for the First Order Pressure Derivatives of the Second Order Elastic Constants of Hexagonal Crystals
2.4 Expressions for the Second Order Pressure Derivatives of the Second Order Elastic Constants of Hexagonal Crystals
References
3 HIGHER ORDER ELASTIC CONSTANTS AND PRESSURE DERIVATIVES OF THE TRANSITION METALS CADMIUM, ZIRCONIUM AND TITANIUM
3.1 Introduction
3.2 Cadmium
Table 3.2.1 The second, third and fourth order parameters K2, K3, & in 10
Table 3.2.2 Second order elastic constants of cadmium in 10ON/m2
Table 3.2.3 Third order elastic constants of cadmium in 10 N/m2
Table 3.2.4 Fourth order elastic constants of cadmium in 1 0 ~ ~ l m
Table 3.2.5 First order pressure derivatives and second order pressurederivatives of cadmium
3.3 Zirconium
Table 3.3.5 First order pressure derivatives and second order pressurederivatives of zirconium
3.4 Titanium
Table 3.4.5 First order pressure derivatives and second order pressurederivatives of titanium
3.5 Discussion of the results
References
4 HIGHER ORDER ELASTIC CONSTANTS AND PRESSURE DERIVATIVES OF THE RARE EARTH METALS GADOLINIUM, DYSPROSIUM AND ERBIUM
4.1 Introduction
4.2 Gadolinium
4.3 Dysprosium
4.4 Erbium
4.5 Discussion of the Results
References
5 LOW TEMPERATURE THERMAL EXPANSION OF THE HEXAGONAL METALS CADMIUM, ZIRCONIUM, TITANIUM, GADOLINIUM, DYSPROSIUM AND ERBIUM
5.1 Introduction
5.2 Procedure to obtain the Low Temperature Limit of Gruneisen Function
5.3 Cadmium
Fig. 5.3.1 Variation of the generalised Griineisen parameters γas a function of 8 for the azimuthal angle Ф = 15
Fig. 5.3.2 Variation of the generalised Griineisen parameters γ as a function of 8 for the azimuthal angle Ф = 35 in cadmium
5.4 Zirconium
Fig. 5.4.1 Variation of the generalised Griineisen parameters yas a function of 0 for the azimuthal angle I$ = 15
Fig. 5.4.2 Variation of the generalised Griineisenp arametersfas a function of 0 for the azimuthal angle I$ = 35 in zirconium
5.5 Titanium
Fig. 5.5.1 Variation of the generalised Griineisen parameters 7as a function of 0 for the azimuthal angle $ = 15 in titanium
Fig. 5.5.2 Variation of the generalised Griineisen parameters */as a function of 0 for the azimuthal angle $ = 35
5.6 Gadolinium
Fig. 5.6.1 Variation of the generalised Griineisen parameters yas a function of 0 for the azimuthal angle $ = 15
Fig. 5.6.2 Variation of the generalised Griineisen parameters yas a function of 9 for the azimuthal angle 4 = 35
5.7 Dysprosium
Fig. 5.7.1 Variation of the generalised Griineisen parameters yas a function of 0 for the azimuthal angle 4 = 15
Fig. 5.7.2 Variation of the generalised Gliineisen parameters yas a function of 0 for the azimuthal angle (I = 35 in dysprosium
5.8 Erbium
Fig. 5.8.1 Variation of the generalised GrUneisen parameters 7as a function of 0 for the azimuthal angle @ = 15 in erhiurn
Fig. 5.8.2 Variation of the generalised Griineisen parameters 7as a function of 0 for the azimuthal angle $ = 35 in erbium
5.9 Discussion of the results
References
SUMMARY AND CONCLUSION
APPENDIX
THIRD ORDER ELASTIC CONSTANTS AND LOW TEMPERATURE LATTICE THERMAL EXPANSION OF THE HIGH TEMPERATURE STRUCTURE MATERIAL TIAI
Third Order Elastic Constants of TlAl
Low temperature limit of the lattice thermal expansion of TiAl
DISCUSSION
References