EXPRESSION AND VALUES OF THE PARAMETERS OF MODIFIED EMBEDDED ATOM METHOD EQUATION

One major defect associated with embedded atom methods, (EAM) equations as proposed by Baskes and Daws was that the predictions of thermodynamics properties based this model were always smaller than the experimental values. On the basis of this,this studytends to restructure the bcc EAM equations to conform relatively with the other well know bcc equations, also determine the expressions for the embedded energy and pair potential parameters, and their values. This study is equally designed to obtained a self-consistent embedded energy function internally from the new set of equations EAM bccIn line with above intentions, EAM bcc equations of Baskes and Daws were compared with those of the separable potential, (SPM)bcc equations. The SPM and EAM were semi-empirical models whose equations have same structural background but quite different in parametric expressions. While they were similar in expressions for cubic parametric expressions, they differ considerable in the functional expressions, but all combined to represent ideal equations for bcc metals. The reasons for this comparison were that the summations of equations for the bcc metallic parameters were the same but differed in the functional summations. This comparisons were done through a set of generalized forms of EAM equations using adjustable parameters, , . The functional defect between the EAM and SPMbcc equations was obtained capitalizing on the missing link between the two models. Since the EAM equations were centered on the three functional representations of the embedded energy, pair potential and electron density functions as captioned in EAM bcc equations, a self-consistent embedded energy function was obtained from the generalized EAM bcc equations while the Morse potential represented the pair potential function. The values of the parameters of this embedded energy function and those of Morse potential were obtained by fitting into the experimental values of the pure bcc metals. The predicted values of the embedded energy function and those of the Morse potential from this study compared favorably with values obtainable from other studies.One important outcome is that the embedded energy function was readily obtained from the set of the generalized EAM equations for bcc metals.