Unequal wave vectors in short- versus long-range ordering in intermetallic compounds

Abstract

The sign of the formation energy Δ${\mathit{H}}_{\mathit{F}}$ of a compound indicates if the low-temperature long-range order (LRO) corresponds to compound formation (when Δ${\mathit{H}}_{\mathit{F}}$${\mathit{H}}_{\mathit{F}}$>0). However, Δ${\mathit{H}}_{\mathit{F}}$ by itself does not tell us what type (ordering or clustering) of high-temperature short-range order (SRO) can be expected. The reason is that Δ${\mathit{H}}_{\mathit{F}}$ contains two types of contributions: an ‘‘elastic,’’ volume-deformation energy G(x) that reflects the energy invested in deforming the constituents A and B to the volume V(x) of the ${\mathit{A}}_{1\mathrm{-}\mathit{x}}$ ${\mathit{B}}_{\mathit{x}}$ alloy, and a ‘‘chemical’’ energy ɛ that reflects A-B interactions (charge transfer and atomic relaxations) at a fixed V(x). We show that the LRO and the SRO have the same behavior only when the signs of Δ${\mathit{H}}_{\mathit{F}}$ and ɛ are the same: ordering tendencies (‘‘type I’’) when both Δ${\mathit{H}}_{\mathit{F}}$${\mathit{H}}_{\mathit{F}}$>0 and ɛ>0. However, ‘‘type II’’ systems (Δ${\mathit{H}}_{\mathit{F}}$>0; ɛ