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.

scholarly journals Higher Order Elastic Constants, Gruneisen Parameters and Lattice Thermal Expansion of Lithium Niobate

2006 ◽  
Vol 3 (3) ◽  
pp. 122-133 ◽  
Author(s):  
Thresiamma Philip ◽  
C. S. Menon ◽  
K. Indulekha
Keyword(s):  
Energy Density ◽  
Lithium Niobate ◽  
Elastic Constants ◽  
Elastic Stiffness ◽  
Higher Order ◽  
Second Order ◽  
Third Order ◽  
Third Order Elastic Constants ◽  
Gruneisen Parameters ◽  
Derivatives Of

The second and third-order elastic constants and pressure derivatives of second- order elastic constants of trigonal LiNbO3(lithium niobate) have been obtained using the deformation theory. The strain energy density estimated using finite strain elasticity is compared with the strain dependent lattice energy density obtained from the elastic continuum model approximation. The second-order elastic constants and the non-vanishing third-order elastic constants along with the pressure derivatives of trigonal LiNbO3are obtained in the present work. The second and third-order elastic constants are compared with available experimental values. The second-order elastic constant C11which corresponds to the elastic stiffness along the basal plane of the crystal is less than C33which corresponds to the elastic stiffness tensor component along thec-axis of the crystal. The pressure derivatives, dC'ij/dp obtained in the present work, indicate that trigonal LiNbO3is compressible. The higher order elastic constants are used to find the generalized Gruneisen parameters of the elastic waves propagating in different directions in LiNbO3. The Brugger gammas are evaluated and the low temperature limit of the Gruneisen gamma is obtained. The results are compared with available reported values.

Temperature Dependence of Second and Higher Order Elastic Constants of Orientationally Disordered (NH4I)x (KI)1-x Mixed Crystals

2014 ◽  
Vol 1047 ◽  
pp. 65-70 ◽  
Author(s):  
Alpana Tiwari
Keyword(s):  
Elastic Constants ◽  
Body Force ◽  
Coupling Effect ◽  
Second Order ◽  
Mixed Crystals ◽  
Elastic Behaviour ◽  
Coupling Term ◽  
Third Order ◽  
Third Order Elastic Constants ◽  
Three Body

We have incorporated the translational rotational (TR) coupling effects in the framework of three body force shell model (TSM) to develop an extended TSM (ETSM). This ETSM has been applied to reveal the second order elastic constants (C11, C12and C44) in the dilute regimes 0≤ x ≤ 0.50 as a function of temperature for 10K≤T≤300K. The anomalous elastic behaviour in C44below 100 K has been depicted well by ETSM results in the orientationally disordered (NH4I)x(KI)1-xmixed crystals. In order to present a visual comparison of the TR-coupling effect on second order elastic constants, we have evaluated the SOECs with and without TR coupling term in ETSM. Besides third order elastic constants have also been studied and discussed for concentration range 0≤x≤0.50 as a function of temperature for 10K≤T≤300K.

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