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.

Lattice Thermal Expansion of the Shape Memory Alloys Cu-Al-Ni, Cu-Al-Zn, Cu-Al-Be and Cu-Al-Pd

2008 ◽  
Vol 52 ◽  
pp. 135-142
Author(s):  
Santhosh Potharay Kuruvilla ◽  
C.S. Menon
Keyword(s):  
Thermal Expansion ◽  
Shape Memory ◽  
Wave Velocity ◽  
Elastic Constants ◽  
Damping Capacity ◽  
Shear Mode ◽  
Potential Candidate ◽  
Lattice Thermal Expansion ◽  
Third Order ◽  
Third Order Elastic Constants

Theoretical and experimental investigations are being carried out on Cu based alloys due to their technologically important shape memory properties and pseudo-elasticity, which are intimately associated with the martensitic transformation. The transition between the two phases, martensite to austenite, is of continued interest in academics and in industry. The shape memory effect, superelastic properties and biocompatibility are being applied in a variety of fields. Cu based SMA system has large vibrational entropy, high damping capacity and good economic viability. All these make it a potential candidate in the field of sensors and actuators. The concurrent knowledge of the second order elastic constants (SOEC) and third order elastic constants (TOEC) enables a better understanding of the nonlinear elasticity exhibited by these alloys. We have used a model based on deformation theory and Keating’s potential scheme to obtain the expressions for TOEC of the above alloys. In this paper we have calculated the complete sets of six non-vanishing TOEC of Cu-Al-Ni, Cu-Al-Zn, Cu-Al-Be and Cu-Al-Pd and are presented along with the available experimental data. It is remarkable that all the third order elastic constants are negative, indicating an increase in the vibrational frequencies under stress, giving rise to an increase in the strain-free energy. The absolute values of the TOEC are large. This means that the bcc phase observed is considerably anharmonic. The TOEC C144 representing the shear mode has a smaller value than C111. Hence, the effect of pressure is much greater on longitudinal wave velocity than on the shear wave velocity in the above Cu based SMA. The mode Grüneisen parameters of the acoustic waves are determined based on the quasi-harmonic approximation method. The low temperature limit of the lattice thermal expansion and the Anderson– Grüneisen parameter of these alloys are also obtained.

Sign in / Sign up

Export Citation Format

Share Document