Elastic anisotropy and single-crystal moduli of solid argon up to 64 GPa from time-domain Brillouin scattering

Abstract

Single-crystal elastic moduli C i j , shear modulus G, and Zener anisotropic ratio A of solid argon having the face-centered cubic (fcc) structure were determined at high pressures between 12 and 64 GPa using a combination of experimental and theoretical approaches. The experimental data, namely, the maximal and minimal values of the product of the longitudinal sound velocity and refractive index n·V L , were obtained from the 3D scanning of elastic inhomogeneities in compressed samples of argon using the technique of time-domain Brillouin scattering. These inhomogeneities, caused by elastic anisotropy of solid argon, were revealed to be about twice as strong as those reported in the earlier experiments using classical Brillouin light scattering (BLS). To derive the V L values, we used the refractive index obtained here from ab initio calculations which also permitted us to rule out any contribution to the amplitude of the observed elastic inhomogeneities of the hexagonal close-packed phase of argon, proposed to coexist with the fcc phase at high pressures. From the measured C i j (P), we derived pressure dependence of shear modulus of the fcc argon G H (P) using the Voigt-Reuss-Hill approximation and found a very good agreement with the earlier G(P) obtained from shear sound velocities in the classical BLS measurements. Our results agree very well with the earlier predictions based on a relatively simple many-body model employing the Buckingham pair potential. Finally, our measurements show a much weaker change of the Cauchy discrepancy (C 12 − C 44 − 2P) of the fcc argon with pressure than reported in all earlier experimental and theoretical works.

Influence of elastic anisotropy on measured sound velocities and elastic moduli of polycrystalline cubic solids

“…In this work, we performed the first TDBS measurements on a polycrystalline sample of NaCl (having A<1) compressed to 24 GPa in a DAC using the approach developed earlier. 8,9,[13][14][15] Our V L111 and V L100 data confirmed, within experimental uncertainties, the previous unique BLS data-point for a NaCl single crystal compressed to a similar pressure of P=26 GPa, 10 as well as the experimental C ij (P) derived from XRD examination of polycrystalline NaCl samples non-hydrostatically compressed in a DAC. 16 Comparison of the existing and of our V L111 and V L100 values with earlier experimental dependences V Lav (P) for NaCl polycrystals revealed a significant shift of the latter towards V L111 (P).…”

“…These approximations are used in various technical application such as engineering or building construction but are of exceptional importance for understanding of propagation of seismic waves in the deep Earth and, as a consequence, of its composition e.g.. 5 According to earlier reports, a significant part of rock-forming minerals exhibits a moderate or decreasing with pressure elastic anisotropy. 6,7 However, there are also cubic solids showing a strong increase of elastic anisotropy on compression, as recognized earlier 8,9 and in the present work. For the latter type of cubic solids, a reliable recovery of elastic properties from experimental signals remains a subject of continuous efforts, e.g.…”

“…The fact that V Lav obtained in classical BLS measurements and, in particular cases considered below, in PEUS measurements are much closer to V L111 than to V L100 was first recognized in high-pressure experiments on H 2 O ice 8 and argon 9 crystallizing on compression in cubic structures. The important difference of these two solids from NaCl is the inverse ratio of the velocity extremes: In H 2 O ice and cubic argon, V L111 is not the slowest but the fastest direction of sound propagation in a single crystal.…”

“…16 Comparison of the existing and of our V L111 and V L100 values with earlier experimental dependences V Lav (P) for NaCl polycrystals revealed a significant shift of the latter towards V L111 (P). In order to understand nature of this shift, recognized earlier for anisotropic cubic solids with A>1 where V Lav (P) was also found to approach V L111 (P), 8,9 we performed a detailed analysis of possible origins. For this aim, we modelled shapes of BLS peaks of strongly anisotropic polycrystalline cubic solids with A<1 (NaCl) and A>1 (solid argon).…”

“…Combined with independently measured bulk modulus and density, knowledge of V L111 and V L100 provides access to the complete set of C ij of any cubic solid. 8,9 The V Lav -and V Tav values can then be derived using one of the approximations mentioned above. In this work, we performed the first TDBS measurements on a polycrystalline sample of NaCl (having A<1) compressed to 24 GPa in a DAC using the approach developed earlier.…”