Binding-Potential Modeling Of The Structural Instability In Prag1-Xcux

The strong negative quadrupolar coupling in the isoelectronic pseudobinary ${\mathrm{PrAg}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Cu}}_{\mathrm{x}}$ compounds has been ascribed to a lattice instability of the cubic (CsCl) phase, which grows with increasing x and culminates in a transformation to an orthorhombic (FeB) phase at x=0.5. To probe the basis of this instability, the chemical binding of these compounds is modeled with Lennard-Jones--like potentials for the A-B, A-A, and B-B pair interactions (A=Pr, B=Ag or Cu). The numerical coefficients of the potentials are determined by minimizing the total binding energy with respect to the seven structural parameters of the orthorhombic phase. The BB potential is found to be negligibly weak, and the calculated AB and AA potentials, when applied to the cubic phase, reveal that the strong short-range A---B and A---A bonds are stretched and compressed, respectively. This structural frustration grows as x exceeds 0.5 and the cubic lattice parameter is allowed to decrease as Ag is further replaced by smaller Cu atoms. The pair-binding potentials are then used in determining the dynamical matrix of the cubic phase. The calculated phonon dispersion curves show that as x exceeds 0.5 there is a rapid softening of the ${\mathrm{TA}}_{1}$ (${\mathrm{C}}_{44}$) mode, especially at the M ((1/2)(1/2)0) point. This zone-boundary phonon softening is shown to derive directly from the structural frustration and is consistent with the dominant internal static distortions involved in the cubic-to-orthorhombic transformation. It also supports the lattice-instability rationale for the strong antiferroquadrupolar coupling. However, it contrasts with the M-point softening of the ${\mathrm{TA}}_{2}$ (C') mode previously observed in the isomorphic (but not isoelectronic) ${\mathrm{LaAg}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{In}}_{\mathrm{x}}$ system, where the underlying mechanism is probably quite different.