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  • TITLE
  • CERTIFICATE
  • DECLARATION
  • DEDICATION
  • ACKNOWLEDGEMENT
  • CONTENTS
  • Preface
  • 1. Ultrasonic measurements of elastic constants of single crystals - An analysis
  • 1.1. Introduction
  • 1 1.1 Elastic properties of crystalline solids
  • 1.1.2 Equations of motion and their solution
  • 1.2 Ultrasonic wave propagation in single crystals
  • 1.2.1 Orthorhombic crystals
  • 1.2.2 Tetragonal Type I crystals
  • 1.2.3 Trigonal (Rhombohedral) Type II crystals
  • 1 2.4 Hexagonal crystals
  • 1.3 Measurements of elastic constants by ultrasonic methods
  • 1.3.1 Density measurements
  • 1.3.2 Elastic constants measurements in Orthorhombic crystal
  • 1 3.3 Elastic constants measurements in Tetragonal crystal
  • 1.3.4 Elastic constants measurements in Trigonal crystals
  • 1.3.5 Elastic constants measurements in Hexagonal crystal
  • 1.4 Other related elastic properties
  • 1.4.1 Youngs modulus
  • 1.4.2 Linear compressibility
  • 1.4.3 Volume compressibility
  • 1.4.4 Bulk Modulus
  • 1.4.5 Poissons ratio
  • 1.5 Acoustic wave fronts in crystalline solids
  • 1.5.1 Vibrational waves
  • 1.5.2 Anisotropy in phase velocity
  • 1.5.3 Anisotropy in slowness
  • 1.6 Structural phase transition
  • 1.6.1 Investigation of phase transition using ultrasonics
  • 1.6.2 Landau theory of second order phase transition
  • 1.7 Summary and conclusion
  • References
  • 2. Experimental techniques
  • 2. 1 Ultrasonic velocity measurement techniques
  • 2.1 1 Continuous wave methods
  • 2.1.2 Pulse methods
  • 2.1.3 Low frequency method
  • 2.1.4 The Pulse Echo Overlap method
  • Fig.2.1. Block diagram of the experimental set up.
  • Fig.2.2 Echo pair in the overlapped condition
  • 2.1.5 The experimental setup
  • Fig.2.3 Photograph of the Experimental setup
  • 2.1.6 McSkimins at criterion and Bond correction - Basic theory
  • 2.1.7 The Bond correction and identification technique
  • 2.1.8 Computer programme for bond correction
  • 2.2 Sample preparation technique
  • 2.2.1 Solution growth
  • 2.2.2 Constant temperature bath
  • Fig.2.6 The constant temperature bath for crystal growth.
  • Fig.2.7 Photograph of the Solution Growth apparatus
  • 2.2.3 Identification of the faces using stereographic net
  • 2.2.4 Differential scanning calorimetry (DSC) measurements
  • References
  • 3. Ultrasonic investigation on elastic properties and Phase Transition in Lithium Sodium Sulphate crystal
  • 3. 1 Introduction
  • 3.2 Experimental technique
  • 3.2.1 Sample preparation
  • 3.2.2 Density measurements
  • 3.2.3 Powder X-ray diffraction of LSS
  • Fig.3.1 Photograph of Lithium Sodium Sulphate Crystals grown at 35, 40, 42, 45, 47, &50c
  • Fig.3.2 morphology of Lithium Sodium Sulphate Crystals grown at 50c
  • Fig.3.3 (a) Stereographic projection of LSS about a-axis
  • Fig.3.3 (b) Stereographic projection of LSS about c-axis
  • Solubility curve
  • 3.3 Results and discussions
  • 3.3.1 Structure change of LSS with growth temperature
  • 3.3.2 Elastic stiffness constant measurements
  • 3.3.3 Surface plots of phase velocity, slowness, Youngs modulus and linear compressibility
  • 3.3.4 Temperature variations of elastic constants
  • 3.3.5 Investigation of phase transition using DSC
  • 3.4 Conclusions
  • References
  • 4. Elastic constants and Phase transition in Sulphamic Acid crystal
  • 4. 1 Introduction
  • 4.2 Experimental technique
  • 4.2.1 Sample preparation
  • Fig.4.1 Arrangement of molecules in the Unit cell of Sulphamic acid crystal about a axis
  • Fig.4.2.Photograph of the grown Sulphamic Acid Crystal
  • Fig.4.3 Morphology of the grown Sulphamic Acid Crystal
  • 4.2.2 Density measurements
  • 4.2.3 Ultrasonic velocity measurements
  • Fig.4.5 (a) Stereographic projection of Sulphamic acid about a-axis
  • Fig.4.5 (b) Stereographic projection Sulphamic acid about b-axis
  • Fig.4.5 (c) Stereographic projection of the Sulphamic acid crystal about c-axis
  • 4.3 Results and discussions
  • 4.3.1 Measurements of elastic constants
  • 4.3.2 Temperature variations of elastic constants
  • 4.3.3 Investigation of phase transition using DSC
  • 4.3.4 Surface plots of phase velocity, slowness, Youngs modulus and Linear compressibility
  • 4.4 Conclusions
  • References
  • 5. Ultrasonic Study of Elastic Properties and Phase Transition in Potassium Sulphamate crystal
  • 5. 1 Introduction
  • 5.2 Experimental technique
  • 5.2.1 Sample preparation
  • Fig.5.1 Photograph of grown Potassium Sulphamate Crystal
  • Fig.5.3 Arrangement of molecules in the Unit cell of Potassium Sulphamate crystal about a axis
  • Fig.54.Morphology of Potassium Sulphamate Crystal
  • Fig.5.5 (a) Stereographic projection of Potassium Sulphamate crystal about c-axis
  • Fig.5.5 (b) Stereographic projection of Potassium Sulphamate crystal about b-axis.
  • Fig.5.5 (c) Stereographic projection of Potassium Sulphamate crystal about a-axis
  • 5.3 Results and discussions
  • 5.3.1 Ultrasonic velocity measurements
  • 5.3.2 Temperature variations of elastic constants
  • 5.3.3 Investigation of phase transition using DSC
  • 5.3.4 Surface plots of phase velocity, slowness, Youngs modulus and linear compressibility
  • 5.4 Conclusions
  • References
  • 6. Ultrasonic investigation of Elastic Properties and Phase Transition in Li K0.9 Na 0.1 SO4 crystal
  • 6. 1 Introduction
  • 6.2 Experimental technique
  • 6.2.1 Sample preparation
  • 6.2.2 X-ray diffraction study
  • 6.2.3 Measurements of interfacial angles
  • 6.2.4 Density measurements
  • Fig.6.2 Photograph of Sodium doped Lithum Potassium Sulphate
  • Fig.6.3 Morphology of Sodium doped Lithum Potassium Sulphate
  • Fig.6.4 (a) Stereographic projections of doped LKS about a-axis
  • Fig.6.4 (b) Stereographic projection of sodium doped LKS about c-axis
  • 6.2.5 Ultrasonic velocity and elastic constant measurements
  • 6.3. Results and discussions
  • 6.3.1 Structure of the grown crystal
  • 6.3.2 Temperature variations of elastic constants
  • 6.3.3 Phase transition study using DSC
  • 6.3.4 Surface plots of phase velocity, slowness, Youngs modulus and linear compressibility
  • 6.4 Conclusions
  • References
  • 7. An ultrasonic study on Elastic Properties in Potassium Lithium Hydrogen Sulphate crystal
  • 7.1 Introduction
  • 7.2 Experimental technique
  • 7.2.1 Sample preparation
  • Fig.7.1 Photograph of Potassium Lithium Hydrogen Sulphate Crystal
  • Fig.7.2 Morphology of Potassium Lithium Hydrogen sulphate Crystal
  • Fig.7.4 (a) Stereographic projection of KLHS about a-axis
  • Fig.7.4 (b) Stereographic projection of KLHS about c-axis
  • 7.2.2 Ultrasonic velocity measurements
  • 7.3 Results and discussions
  • 7.3.1 Elastic constant measurements
  • 7.3.2 Temperature variations of elastic constants
  • 7..3.3 Elastic anisotropy of KLHS crystal
  • 7.4 Conclusions
  • References
  • 8. Summary and conclusions