First-principles theory of the evolution of vibrational properties with long-range order inGaInP2

We predict the phonon spectra of zinc-blende GaP and InP, of CuPt-type ordered ${\mathrm{GaInP}}_2,$ and of the random ${\mathrm{Ga}}_{0.5}{\mathrm{In}}_{0.5}\mathrm{P}$ alloy using first-principles density-functional linear-reponse theory. We find that (i) ordered ${\mathrm{GaInP}}_2$ exhibits two GaP-like and two InP-like phonon modes (a “two-mode” behavior), (ii) ordering reverses the order of frequencies of the TO-phonon modes of zinc-blende GaP and InP due to a frustrated bond geometry in the ordered phase, and (iii) each of the LO-phonon modes of the ternary ${\mathrm{GaInP}}_2$ phase represents a mixture of Γ and $L$ phonons of the corresponding binary compound (${\mathrm{LO}}_1$ is GaP-like, ${\mathrm{LO}}_2$ is InP-like), yet the TO (LO) modes of the random alloy represent an amalgamation of the TO (LO) modes of $\mathrm{G}\mathrm{a}\mathrm{P}+\mathrm{I}\mathrm{n}\mathrm{P}.$ Consequently, the ordered phase is predicted to exhibit a two-mode behavior, while the random alloy is a pseudo-one-mode system.