Single-crystal elastic moduli Cij(P)and shear modulus G(P)of solid argon up to 64 GPa from time-domain Brillouin scattering

Abstract : Solid argon, crystallizing above 1.3 GPa in the face-centered cubic (fcc) structure, is considered as the archetype of a simple classical solid [1] due to a highly symmetric distribution of electron density in the atoms having completely filled electron shells. For this reason, its behavior at high pressures was intensively investigated, also by theory, aiming understanding of evolution of solids upon a strong density increase. Symmetric electron shells and cubic structure of solid argon imply elastic isotropy of its crystals which, however, was not confirmed experimentally. Accordingly, a significant and growing-with-compression contribution of non-central interaction between the Ar-atoms was hypothesized as an explanation. Also, solid argon (as well as other solidified noble gases such as neon or helium) is extremely compressible and produces a quasi-hydrostatic environment, as has been concluded on the basis of sharpness of its X-ray diffraction peaks measured up to ~8 GPa [2]. However, the degree of its hydrostaticity at higher pressures was a subject of recent controversial discussions [3,4]. Due to a strong change of its lattice parameter with pressure, solid argon was also suggested and used as an internal pressure standard [5-7]. In the present work, we have measured the maximal and minimal values of the product of the refractive index n(P) with the longitudinal sound velocity V L (P), n(P)·V L (P), in single crystals of solid argon up to 64 GPa (Figure 1). For solid argon having cubic structure, the maximal sound velocity corresponds to that along the 111 direction in a single crystal, V L111 , and the minimal sound velocity to that along the 100 direction, V L100. The observed in this work strong deviation of V L111 (P) from V L100 (P) with pressure increase (Figure 1) indicated a strong elastic anisotropy of this solid, which deserves a special attention because, at the maximal pressure, the density of solid argon is more than twice higher than that just after its solidification at P=1.2 GPa [6]. It should be mentioned here that the detected strong elastic anisotropy of solid argon could not be falsified by the presence of the hcp phase, potentially coexisting with the main fcc phase at high pressures [8]. This is because our theoretical calculations showed that the hcp phase could not contribute to the measured-by-us strong deviation of the maximal and minimal n(P)·V L (P) values (Figure 1). In the present work we used the technique of time-domain Brillouin scattering (TDBS) [9] permiting 3D-scanning of the n·V L distribution in transparent samples with sub-μm resolution along the DAC axis, in addition to the micrometric lateral resolution [10-12]. Important is to mention that the spatial resolution of the TDBS technique did not degrade with pressure. These capabilities of the TDBS technique permitted us to pitch on the extremes of the n·V L values in the polycrystalline samples of fcc argon compressed in a DAC and to closely approach the n·V L111 and n·V L100 values up to the highest pressure of our work of 64 GPa (Figure 1). Calculation of the refractive index of the fcc argon as a function of pressure n(P) was another part of the work which allowed to derive V L (P) values from the the products n(P)·V L (P) obtained directly from the oscilating TDBS signals S(t). To obtain the reliable axially resolved data, we applied the same demanding time-frequency analysis of the raw TDBS signals S(t) as described in detail earlier [11]. Figure 1. Our experimental and theoretical data on longitudinal sound velocities of solid argon at high pressures. The experimental datapoints in terms of the product n·V L , obtained using the TDBS technique, are represented by triangles pointing up and down corresponding to n(P)·V L111 (P) and n(P)·V L100 (P), respectively. They are compared with the same theoretically-calculated values for the fcc phase (solid red lines) and hcp phase (dashed violet lines) Using the envelope method and our theoretical n(P) for the fcc phase we determined, with a high degree of confidence, pressure dependences of the fastest and
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Andreas Zerr, Samuel Raetz, Maju Kuriakose, Philippe Djemia, Sergey M. Nikitin, et al.. Single-crystal elastic moduli Cij(P)and shear modulus G(P)of solid argon up to 64 GPa from time-domain Brillouin scattering. 57th European High Pressure Research Group (EHPRG) Meeting on High Pressure Science and Technology, Sep 2019, Prague, Czech Republic. ⟨hal-02352691⟩

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