Homogeneous deformation theory with three-body interaction: Second- and third-order elastic constants of noncentrosymmetric crystals

1984 ◽  
Vol 30 (12) ◽  
pp. 7250-7254 ◽  
Author(s):  
Subinay Dasgupta
Keyword(s):  
Elastic Constants ◽  
Deformation Theory ◽  
Homogeneous Deformation ◽  
Third Order ◽  
Body Interaction ◽  
Third Order Elastic Constants ◽  
Three Body

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.

scholarly journals Third Order Pressure Derivative Elastic Properties of Alkali Cyanide

2020 ◽  
Vol 6 (10) ◽  
pp. 84-88
Author(s):  
Preeti Singh Bahadur
Keyword(s):  
Experimental Data ◽  
Elastic Constants ◽  
Body Force ◽  
Third Order ◽  
Pressure Derivative ◽  
Third Order Elastic Constants ◽  
Increasing Trend ◽  
Three Body ◽  
Increasing Temperature ◽  
Derivatives Of

In this paper we have evaluated the pressure derivatives of third order elastic constants in the CsCN material. An extended three body force shell model (ETSM), which incorporates the effects of translational– rotational (TR) coupling, three body interactions (TBI) and anharmonicity, has been applied. The pressure derivatives of TOECs, dc111/dp, dc112/dp, dc166/dp, dc111/dp dc123/dp and dc456/dp show increasing trend with increasing temperature. However their values could not be compared due to lack of experimental data.

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.

THERMOELASTIC BEHAVIOUR OF FLUORITE SOLIDS USING THREE-BODY FORCE SHELL MODEL

1992 ◽  
Vol 06 (19) ◽  
pp. 3179-3188 ◽  
Author(s):  
S. S. BEDI ◽  
MAJOR SINGH ◽  
JASPAL SINGH
Keyword(s):  
Shell Model ◽  
Elastic Constants ◽  
Body Force ◽  
Thermal Phonon ◽  
Third Order ◽  
Third Order Elastic Constants ◽  
Three Body ◽  
Body Potential ◽  
Derivatives Of ◽  
Theoretical Results

The expressions for the second and third order elastic constants of fluorite lattice are derived using Lundqvist three-body potential incorporating thermal phonon pressure and inter-sublattice displacement through the shell model. Theoretically calculated values of the third order elastic constants are compared with the theoretical results of other workers and experiments. First order pressure derivatives of the second order elastic constants calculated using Thurston and Brugger relations for Ca 1-x Sr x F 2 and Sr 1-x Ba x F 2 are found to be in agreement with the experiment.

Third Order Elastic Constants and Rayleigh Wave Dispersion of Shot Peened Aero-Engine Materials

2013 ◽  
Vol 768-769 ◽  
pp. 201-208 ◽  
Author(s):  
Marek Rjelka ◽  
Martin Barth ◽  
Sven Reinert ◽  
Bernd Koehler ◽  
Joachim Bamberg ◽  
...  
Keyword(s):  
Residual Stress ◽  
Rayleigh Wave ◽  
Elastic Constants ◽  
Cold Work ◽  
High Strength ◽  
Wave Dispersion ◽  
Third Order ◽  
Third Order Elastic Constants ◽  
Aero Engine ◽  
Rayleigh Wave Dispersion

Aero-engine components exposed to high mechanical stresses are made of high-strength alloys and additionally, they are surface treated by shot peening. This process introduces compressive residual stress into the material making it less sensitive to stress corrosion cracking and fatigue and therefore benefits the components performance and lifetime. Moreover cold work is induced in an amount depending on the peening parameters. To approximate the remaining lifetime, a quantitative, non-destructive method for stress assessment is required. It was shown that surface treatment of such alloys can be characterized by broadband Rayleigh wave dispersion measurements. However, the relative contributions of residual stress and cold work, respectively, remained an open point. This paper presents the determination of third order elastic constants (TOEC) for IN718 and Ti6246, providing, together with a model for the inversion of dispersion data, a quantitative access to the acoustoelastic effect. Finally, some measurements of differently treated samples are given.

Sign in / Sign up

Export Citation Format

Share Document