Experimental and theoretical study of the temperature and concentration dependence of the short-range order in Pt-V alloys

Abstract

We present a detailed theoretical and experimental study of the short-range order in the ${\mathrm{Pt}}_{1\ensuremath{-}c}{\mathrm{V}}_{c}$ system at two concentrations ($c=$$\frac{1}{4}$ and $c=$$\frac{1}{9}$). In situ neutron-scattering experiments were performed in order to measure the short-range-order parameters in the disordered phase. We found a drastic effect of the concentration on the short-range order: in ${\mathrm{Pt}}_{3}\mathrm{V},$ the diffuse intensity is spread along the $(1k0)$ directions with maxima at the (100) positions, despite the stability at low temperature of a ${\mathrm{DO}}_{22}$ phase. In contrast, the diffuse intensity in ${\mathrm{Pt}}_{8}\mathrm{V}$ displays a splitting around the (100) positions with incommensurate maxima. Through inverse Monte Carlo simulations the two experiments yield, within the Ising model, two sets of effective-pair interactions. Despite quite different short-range-order patterns, the interactions seem nearly concentration independent with a dominant first-neighbors interaction ${V}_{1}.$ This concentration independence allows us to predict the ordered states and the ordering temperatures. In particular, at low temperatures, these interactions stabilize a new phase of composition ${A}_{5}B,$ which to our knowledge has not been observed until now. Finally, we analyze the origin and behavior of the incommensurate split peaks in ${\mathrm{Pt}}_{8}\mathrm{V}$ within a high-temperature expansion and show analytically that the splitting is due to a large decrease of the influence of ${V}_{1}$ on the short-range order as the concentration and/or the temperature decreases. This analysis shows also that the splitting distance should decrease with increasing temperature, in agreement with our Monte Carlo simulations, and in contrast with all the other alloys which have already been investigated, either experimentally or theoretically. More generally, we discuss the origin of the temperature behavior of a splitting distance in relation with the location in $q$ space of the incommensurate maxima. Using very simple arguments, we show, provided the restriction that the first-neighbor interactions are dominant, that the splitting distance increases or decreases with increasing temperature depending on whether these maxima lie along the $(1k0)$ axis or not.