Determination of the elastic constants of single crystals of fcc and hcp argon alloys by Brillouin scattering

Abstract

The elastic constants of single crystals of Ar(${\mathrm{O}}_{2}$) and Ar(${\mathrm{N}}_{2}$) alloys, both for the fcc and hcp structures near their melting points, have been accurately determined using high-resolution Brillouin spectroscopy. The elastic constants were found to be relatively insensitive to changes in the concentration of ${\mathrm{O}}_{2}$ (and ${\mathrm{N}}_{2}$) up to about 4% in the fcc phase. Mode softening was, however, reflected in the dependence of ${c}_{44}$ on solute concentration, as phase instability increased. The hcp elastic constants of Ar(${\mathrm{O}}_{2}$) at 6% concentration at 81.3 K were determined to be (in units of ${10}^{9}$ ${\mathrm{Nm}}^{\ensuremath{-}2}$); ${c}_{11}=2.90\ifmmode\pm\else\textpm\fi{}0.04$, ${c}_{12}=1.50\ifmmode\pm\else\textpm\fi{}0.03$, ${c}_{13}=1.18\ifmmode\pm\else\textpm\fi{}0.02$, ${c}_{33}=3.24\ifmmode\pm\else\textpm\fi{}0.05$, and ${c}_{44}=0.656\ifmmode\pm\else\textpm\fi{}0.011$. Even at this high concentration the elastic constants are relatively consistent with pure Ar values, except for ${c}_{13}$ and $\frac{{c}_{13}}{{c}_{44}}$. From model calculations it was shown that the observed differences cannot be explained either in the presence or absence of spherical ${\mathrm{O}}_{2}$ impurity molecules. The use of nonspherical impurity interactions indicated that the anisotropy of the ${\mathrm{O}}_{2}$ (and ${\mathrm{N}}_{2}$) molecule plays a strong role in the intermolecular forces, the anomalous change in ${c}_{13}$ was, however, not reproduced. It is concluded, also on the basis of further experimental and theoretical evidence, that rotation-translation coupling is an important mechanism in van der Waals solids, especially for phase transitions, and that $\frac{{c}_{13}}{{c}_{44}}$ (for hexagonal systems, at least) is a sensitive measure of this effect. This almost certainly defines the role of diatomic impurities in stabilizing the hcp Ar structure.