Diagonal flipping of a Rhombus as elementary act of a polymorphic transformation. Calculation of energy threshold for the transformation in metals

TL;DR

This paper models the energy required for a fundamental atomic rearrangement in metals, specifically a rhombus diagonal flip, using Morse potentials and experimental data for Fe, Cr, and Mn.

Contribution

It introduces a method to estimate the energy threshold for atomic transformations in metals based on pair potentials and experimental elastic constants.

Findings

Energy thresholds at 1193 K: 195 kJ/mole for Cr, 150 for Fe, 94 for Mn.

Threshold varies with atom substitution and vertex angle type.

Energy threshold correlates with elastic bulk modulus values.

Abstract

Diagonal flipping of a rhombus consisting of two triangles sharing a common edge with atoms (ions) in vertices of the triangles is considered as an elementary act of the polymorphic transformation in metals. The estimation of the energy threshold for the diagonal flipping has been carried out for various combination of rhombus vertices occupation by Fe, Cr, and Mn atoms. The energy threshold has been calculated in the framework of Morse interatomic pair potential. Numerical coefficients for the approximation of the pair potential function have been scaled by experimental values of the sublimation energy and temperature dependencies of elastic constants for Fe, Cr, Mn. Values of the energy threshold at 1193 K were estimated equal to 195, 150 and 94 kJ/mole for pure Cr, Fe and Mn respectively, i.e. in the same sequence as values of elastic bulk modulus for these metals. The substitution of one Fe atom by Cr or Mn atom results in alteration of the energy threshold. This alteration is dependent on the angle type at this vertex (an acute or obtuse angle), as well as on the ratio of bulk modulus values of iron and alloying element.