Correlation Functions of Disordered Binary Alloys. II

Abstract

It has been previously established on the basis of an Ising model of alloy ordering (part I of this series) that the observed maxima of short-range-order diffuse scattering in disordered alloys mark the positions of the minima of $V\left(\mathrm{k}\right)$, the Fourier transform of the pairwise interatomic potential $V\left(r\right)\mathrm{}$. It was suggested in I that the superlattice spots of the ordered state should occur at these same positions. This would establish a consistency requirement connecting the ordered and disordered configurations. We prove here that this is a sufficient but not a necessary condition, and we derive the full set of necessary conditions. We also show that for most of the diffuse maxima locations observed in bcc and fcc alloys, it is possible to establish the ordered configuration required by the disordered phase, or conversely to use a knowledge of the ordered configuration to restrict the possible choices of $V\left(r\right)\mathrm{}$ in fitting the disordered-phase scattering data. The linear approximation for correlation functions in binary alloys presented by the authors in I is compared quantitatively with the more exact but less general formula of Fisher and Burford. Except at temperatures very close to $T_c$, it is found that the theoretical shape of the short-range order diffuse scattering is in agreement but the temperature dependencies differ. We note also that all the currently known approximate calculations of $\alpha \left(\mathrm{k}\right)$ for arbitrary $V\left(r\right)\mathrm{}$ can be represented in the same functional form, $\alpha \left(\mathrm{k}\right)=\frac{G_2\mathrm{}\left(T\right)\mathrm{}}{[1+G_1\mathrm{}(T\left)V\right(\mathrm{k}\left)\right]}$, where the temperature-dependent factors $G_1$ and $G_2$ vary according to the method of calculation used, but that $V\left(\mathrm{k}\right)$, the Fourier transform of $V\left(r\right)\mathrm{}$, is the same for all. This leads to the conclusion that the ratios $\frac{V\left(r_{n+1\mathrm{}}\right)}{V\left(r_n\right)}$ determined by fitting the theoretical form to experimental data are insensitive to the particular choice of $G_1$ and $G_2$, but that the magnitudes of the $V\left(r_n\right)$ so determined vary according to this choice. As a consequence, the values obtained for $\frac{V\left(r_{n+1\mathrm{}}\right)}{V\left(r_n\right)}$ are to be regarded as more accurate than those for $V\left(r_n\right)$.