Impurity Green's function in the five frequency model of diffusion in the FCC host: General case and the limit of strong impurity-vacancy binding

TL;DR

This paper derives an exact Green's function for impurity diffusion in the five frequency model, validating phenomenological theories and applying results to experimental data in FeAl systems.

Contribution

It provides a rigorous analytical solution for the impurity Green's function in the 5FM, especially in the strong impurity-vacancy binding limit, and connects theory with experimental observations.

Findings

Analytical solution matches phenomenological diffusion theory.

Good agreement with experimental data on FeAl system.

Decay of impurity-vacancy pairs can be experimentally observed.

Abstract

The impurity Green's function exact to the first order in the vacancy concentration has been calculated in the framework of the five frequency model (5FM). The solution in terms of determinant ratios has been obtained with the use of the Cramer's rule. The determinant sizes varied from 54 for the most general case to three for the four frequency model. Both analytical and numerical techniques has been used to analyze the solution. Special attention has been devoted to the case of strong impurity-vacancy (I-v) binding in order to substantiate the picture of diffusion via bound I-v pairs developed earlier in a phenomenological approach. Complete agreement with the phenomenological theory has been established thus providing its rigorous justification. The solution has been also applied to the calculation of the diffusional broadening of the M\"ossbauer resonance in FeAl system and good agreement with available experimental data and calculations within the encounter model has been found. The decay of the density of the nearest neighborI-v pairs has been discussed in detail and suggested to be used as an additional constraint on the parameters of the 5FM. The possibility of experimental observation of the decay with the use of the positron annihilation technique has been pointed out.