Third-order elastic constants and the low-temperature limit of the Gr�neisen parameter of Mg2Pb on axe's shell model

1982 ◽  
Vol 47 (3-4) ◽  
pp. 351-353 ◽  
Author(s):  
V. Ramachandran ◽  
M. Md. Ibrahim
Keyword(s):  
Low Temperature ◽  
Shell Model ◽  
Elastic Constants ◽  
Temperature Limit ◽  
Third Order ◽  
Third Order Elastic Constants

Some aspects of thermal and elastic properties of yttrium

1979 ◽  
Vol 57 (2) ◽  
pp. 120-127 ◽  
Author(s):  
R. Ramji Rao ◽  
A. Rajput
Keyword(s):  
Thermal Expansion ◽  
Temperature Variation ◽  
Elastic Constants ◽  
Temperature Limit ◽  
Third Order ◽  
Thermal Expansion Data ◽  
Systematic Calculation ◽  
Limit Formula ◽  
Third Order Elastic Constants ◽  
Good Agreement

A systematic calculation of the lattice heat capacity, third-order elastic constants and the temperature variation of the effective Grüneisen functions of the hexagonal close-packed metal yttrium is carried out using the approach of Keating. The normalized frequency distribution function employed for specific heat calculations is obtained using 50 880 frequencies. Good agreement is found between the calculated and experimental Cv1 values. The l0 third-order elastic constants are evaluated using two anharmonic parameters and these, in turn, are utilized to calculate the low-temperature limit [Formula: see text] of thermal expansion, the Anderson–Güneisen (A–G) parameter δ, and the second Grüneisen constant q of yttrium. The temperature dependence of the volume Grüneisen function and its high-temperature limit [Formula: see text] are determined. The theoretical values of [Formula: see text] and [Formula: see text] are in excellent agreement with those estimated from the experimental thermal expansion data of Meyerhoff and Smith obtained for this metal. The calculated value of the A–G parameter δ is used in Anderson's equation to determine the temperature variation of the bulk modulus of yttrium and it is found that the change in Bs from 4 to 400 K calculated in this manner shows good agreement with that estimated from the experimental results of Smith and Gjevre. The variation of the lattice parameters of yttrium with hydrostatic pressure is also investigated using its third-order elastic constants and Thurston's extrapolation formulae.

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.

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