Calculation of the Generalized Grüneisen Parameters for Acoustic Waves in Uniaxial Crystals from the Third Order Elastic Constants

1968 ◽  
Vol 29 (2) ◽  
pp. 865-871 ◽  
Author(s):  
R. Ramji Rao ◽  
R. Srinivasan
Keyword(s):  
Elastic Constants ◽  
Acoustic Waves ◽  
Third Order ◽  
The Third ◽  
Third Order Elastic Constants ◽  
Grüneisen Parameters ◽  
Gruneisen Parameters

scholarly journals Higher Order Elastic Constants, Gruneisen Parameters and Lattice Thermal Expansion of Trigonal Calcite

2005 ◽  
Vol 2 (4) ◽  
pp. 207-217
Author(s):  
Thresiamma Phlip ◽  
C. S. Menon ◽  
K. Indulekha
Keyword(s):  
Elastic Constants ◽  
Deformation Theory ◽  
Elastic Stiffness ◽  
Higher Order ◽  
Second Order ◽  
Model Approximation ◽  
Third Order ◽  
Third Order Elastic Constants ◽  
Grüneisen Parameters ◽  
Gruneisen Parameters

The second- and third-order elastic constants of trigonal calcite have been obtained using the deformation theory. The strain energy density derived using the deformation theory is compared with the strain dependent lattice energy obtained from the elastic continuum model approximation to get the expressions for the second- and third-order elastic constants. Higher order elastic constants are a measure of the anharmonicity of a crystal lattice. The seven second-order elastic constants and the fourteen non-vanishing third-order elastic constants of trigonal calcite are obtained. The second-order elastic constants C11, which corresponds to the elastic stiffness along the basal plane of the crystal is greater than C33, which corresponds to the elastic stiffness tensor component along the c-axis of the crystal. First order pressure derivatives of the second-order elastic constants of calcite are evaluated. The higher order elastic constants are used to find the generalized Gruneisen parameters of the elastic waves propagating in different directions in calcite. The Brugger gammas are evaluated and the low temperature limit of the Gruneisen gamma is obtained. The results are compared with available reported values.

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