Interatomic potentials and phonon spectra of dilute rare-gas mixtures

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Abstract
We have applied existing theoretical results for the impurity induced ir absorption in dilute alloys to study the following rare‐gas mixtures: Ar–Ne, Ar–Kr, Kr–Ar, and Kr–Xe. The theory takes into account both mass and force‐constant changes, within the harmonic approximation. In evaluating the latter, attempts were made to use realistic pair potentials. We have, surprisingly, identified a resonance mode for an argon crystal doped with neon, and a localized mode in krypton doped with xenon system. The predicted resonance mode agrees well with the observed spectrum of Keeler and Batchelder. Our model for krypton doped with xenon gives rise to a localized mode which happens to fall very close to the band edge. Any attempt to shift this mode far from the band edge would require an unreasonably large change in the force constant around the xenon site. Within the framework of our model and the assumption of randomly distributed impurity atoms, we find it difficult to support the observation of this mode claimed by Obriot et al. However, once allowance is made for the experimental resolution, their in‐band recorded spectra for both Kr–Ar and Kr–Xe agree fairly well with the theoretical predictions. On comparing our results for the in‐band absorption of the Ar–Kr system, with the experiments of Keeler and Bachelder, we found it necessary to allow for the finite lifetime of pure‐lattice phonons even at low temperatures. Such an effect appears to have a profound influence on the relative intensities in different regions of the absorption band. This effect does not appear to have been discussed previously in the literature.
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