Analytic pair potential functions for the calculation of thermal expansion coefficient of body centercubic metals

Abajingin David Dele

Volume : V, Issue : VII, July - 2015

Analytic pair potential functions for the calculation of thermal expansion coefficient of body centercubic metals

Abajingin David Dele

Abstract :

In this study, atoms are considered to be related to one another by inter atomic forces which are considered as a networks of anharmonic oscillators. The corresponding oscillations are here described by a first order polynomial modulated by a simple exponential anharmonic potential function. Using this function, an expression for the coefficient of thermal expansion which depends on the parameters of this function was developed and used to calculate the of some selected body centered cubic, (bcc) at room temperatures. The sensitivity of the calculated values on the cutoff radius of the interatomic radius was equally investigated. A temperature dependentpair potential function was developed, and validated with some selected bcc metals to generate the functional fit for the variation of ( ) with increase in temperature.The parameters in this pair potential function were fitted to the experimental values of lattice constant, the internal energy and the bulk modulus of the selected cubes. The values of the coefficient of thermal expansion ( ) of cubic metals at room temperature with cutoff interatomic radius showed a good agreement with both experimental values and some theoretical values.The functional fit for the variation of ( ) with increase in temperature equally showed a good agreement with the experimental curve fit.