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 ${10}^9$ ${\mathrm{Nm}}^{-2\mathrm{}}$); $c_{11}=2.90\mathrm{}\pm 0.04$, $c_{12}=1.50\mathrm{}\pm 0.03$, $c_{13}=1.18\mathrm{}\pm 0.02$, $c_{33}=3.24\mathrm{}\pm 0.05$, and $c_{44}=0.656\mathrm{}\pm 0.011$. 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.