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

Abstract

Cubic solids such as NaCl, crystalline argon, or H 2 O-ice VII exhibit significant elastic anisotropy strongly increasing upon compression. As earlier recognized for solid argon and H 2 O-ice (both exhibiting Zener ratio A>1), longitudinal sound velocities of their polycrystals, V Lav , measured using Brillouin light scattering (BLS) or pulse-echo ultrasonics are much closer to V L111 than to V L100 , the V L -extremes in any cubic single crystal. Here, we experimentally confirm, using the technique of time-domain Brillouin scattering, the same tendency for NaCl exhibiting the opposite anisotropy type, A<1. To understand this tendency, we modelled orientational distribution and the frequency of occurrence of V L values in texture-free polycrystalline samples of NaCl and solid argon. We found a remarkable and predictable asymmetry of the V L distributions with maxima at V L110 which is always much closer to V L111 . This asymmetry persists in BLS peaks but can be obscured in experiments. In the case of solid argon at 49 GPa, the asymmetry can lead to a moderate deviation of experimental V Lav from V LH (obtained from elastic-stiffness constants C ij applying the Hill approximation) by ~7%. The latter can cause, however, a significant overestimation of the aggregate shear modulus by δG/G~50% or of the bulk modulus by δB/B~20% if just one BLS peak of longitudinal modes is detectable. A similar analysis, performed for transverse sound velocities, V T and V Tav , has shown that, by use of a BLS spectrum showing peaks of both longitudinal and transverse modes, overestimation of B is similarly high but that of G is much less dramatic.

Elastic moduli and refractive index of γ-Ge 3 N 4

“…As a result, V L and V T derived from such BLS peaks are overestimated if the Zener anisotropy ratio A exceeds unity, as is the case for γ-Ge 3 N 4 (table 2). In order to evaluate the influence of elastic anisotropy on the RW-peak shape in our BLS measurements, we applied a procedure analogous to that developed for the LWs and TWs [57]. We modelled the BLS peak shape in the relevant frequency/velocity range (figure 3c,d) in two steps: (1) we derived the appearance-frequency histogram for frequencies of the sound waves propagating along all directions of the surface delimiting the semi-infinite singlecrystalline medium of γ-Ge 3 N 4 with a particular crystallographic orientation.…”

Sound Velocity Anisotropy and Single‐Crystal Elastic Moduli of MgO to 43 GPa

“…This loading method minimized local/non‐uniform deformation of the sample upon further compression. NaCl was selected as the PTM because: (a) it possesses comparable yield strength as the typical gas‐PTMs (such as solid helium, neon or argon) in the whole pressure range of our experiments (Mi et al., 2018); (b) a moderate compressibility of NaCl ensured a considerable thickness of the sample chamber and, accordingly, moderate pressure gradients when compared with such noble‐gas PTM such as helium (Xu et al., 2022); (c) loading of a fluid PTM can easily cause lifting of the sample from the anvil culet, and thus change the sample orientation (Kuriakose, Chigarev, et al., 2017). Suitability of NaCl as a quasi‐hydrostatic PTM is also supported by its application in the classical BLS measurements to pressures exceeding 100 GPa (Fei et al., 2007; Murakami et al., 2009).…”

“…In the present work, we used the TDBS to measure sound velocities in MgO but via a rather traditional way: In particular, we measured pressure dependences of velocities of longitudinal acoustic waves (LAW) in MgO single crystals, V L[100] and V L[111] , along the specific crystallographic directions, [100] and [111]. Our choice was based on the well‐known fact, also applied in the previous studies, that velocities of LAWs along these directions reach the extreme values in any cubic crystal including MgO (Karki et al., 1999; Kuriakose, Raetz, et al., 2017; Raetz et al., 2019; Xu et al., 2021; Zha et al., 2000). Then, applying the previously measured equation of state (EOS), the complete set of C ij ( P ) of MgO was determined up to 43 GPa.…”

“…Then, applying the previously measured equation of state (EOS), the complete set of C ij ( P ) of MgO was determined up to 43 GPa. Here, measurement of the LAW velocities along the third special direction in a cubic crystal, namely [110], was dispensable because it is not an independent parameter and can be derived from the V L[100] and V L[111] (Xu et al., 2021).…”

“…The further advantage of the TDBS technique is a high axial resolution of the velocity measurements, better than 1 μm (Nikitin et al., 2015; Sandeep et al., 2021; Xu et al., 2021), not accessible for the conventional pulse‐echo ultrasonics and for the BLS method. Power of the TDBS in high‐pressure studies was already proved in earlier publications reporting extraction of complete sets of C ij ( P ) of cubic solids from polycrystalline sample (Kuriakose, Raetz, et al., 2017; Raetz et al., 2019; Xu et al., 2021, 2022).…”