Evaluating bounds and estimators for constants of random polycrystals composed of orthotropic elastic materials

While the well-known Voigt and Reuss (VR) bounds, and the Voigt-Reuss-Hill (VRH) elastic constant estimators for random polycrystals are all straightforwardly calculated once the elastic constants of anisotropic crystals are known, the Hashin-Shtrikman (HS) bounds and related self-consistent (SC) estimators for the same constants are, by comparison, more difficult to compute. Recent work has shown how to simplify (to some extent) these harder to compute HS bounds and SC estimators. An overview and analysis of a subsampling of these results is presented here with the main point being to show whether or not this extra work (i.e., in calculating both the HS bounds and the SC estimates) does provide added value since, in particular, the VRH estimators often do not fall within the HS bounds, while the SC estimators (for good reasons) have always been found to do so. The quantitative differences between the SC and the VRH estimators in the eight cases considered are often quite small however, being on the order of ±1%. These quantitative results hold true even though these polycrystal Voigt-Reuss-Hill estimators more typically (but not always) fall outside the Hashin-Shtrikman bounds, while the self-consistent estimators always fall inside (or on the boundaries of) these same bounds

Upper mantle anisotropy beneath the Geoscope stations

International audienceSeismic anisotropy has been widely studied this last decade, particularly by measuring splitting of vertically propagating core shear waves. The main interest in this technique is to characterize upper mantle flow beneath seismic stations. On the other hand, the major restriction in this method is that a single station gives a single anisotropy measurement. Alternative methods have been developed in order to avoid this restriction. An accurate determination of upper mantle seismic anisotropy beneath a seismic station may allow one, by doing anisotropy correction, to characterize remote or deeper anisotropy. The Geoscope network is ideal for this purpose because it is composed of a large set (about 26) of high-quality, broadband seismometers globally distributed and because some of these stations have run for more than 10 years and most of them for more than 5 years. We selected about 100 events at each site, generally of magnitude (m b) > 6.0, and we performed systematic measurements of the splitting parameters (fast polarization direction φ and delay time δt) on SKS, SKKS, and PKS phases. Splitting on oceanic islands has been difficult to observe owing to the low quality of the signal but also perhaps owing to complex upper mantle structures beneath the stations. Station KIP (Kipapa, Hawaii) in the Pacific is the only oceanic Geoscope station with a clear anisotropy. We determined well-constrained splitting parameters for 10 of the 17 continental stations that may be explained by a single anisotropic layer. The poor correlation between fast polarization directions and the absolute plate motion together with the apparent incoherence between the plate velocities and the observed delay times suggest that a simple drag-induced asthenospheric flow alone fails to explain most of the observations. For some stations located on or near major lithospheric structures (TAM, Tamanrasset, Algeria, for instance), we observe a good correlation between fast polarization directions and regional structures. At station SCZ (Santa Cruz, California), we found clear variations of the splitting parameters as a function of the event backazimuth, compatible with two layers of anisotropy. Three stations (CAN (Canberra), HYB (Hyderabad, India) and SSB (Saint Sauveur Badole, France)) seem to be devoid of detectable anisotropy

InBO3 and ScBO3 at high pressures: an ab initio study of elastic and thermodynamic properties

We have theoretically investigated the elastic properties of calcite-type orthoborates ABO(3) (A= Sc and In) at high pressure by means of ab initio total-energy calculations. From the elastic stiffness coefficients, we have obtained the elastic moduli (B, G and E), Poisson's ratio (nu), B/G ratio, universal elastic anisotropy index (A(U)), Vickers hardness, and sound wave velocities for both orthoborates. Our simulations show that both borates are more resistive to volume compression than to shear deformation (B > G). Both compounds are ductile and become more ductile, with an increasing elastic anisotropy, as pressure increases. We have also calculated some thermodynamic properties, like Debye temperature and minimum thermal conductivity. Finally, we have evaluated the theoretical mechanical stability of both borates at high hydrostatic pressures. It has been found that the calcite-type structure of InBO3 and ScBO3 becomes mechanically unstable at pressures beyond 56.2 and 57.7 GPa, respectively. (C) 2016 Elsevier Ltd. All rights reserved.This study is supported by the Spanish MICINN projects MAT2013-46649-C4-2-P/3-P and MAT2015-71070-REDC. H.M.O., A.M., and P.R-H. acknowledge computing time provided by Red Espanola de Supercomputacion (RES) and MALTA-Cluster. J.A.S. acknowledges Juan de la Cierva fellowship program for financial support.Gomis, O.; Ortiz, HM.; Sans Tresserras, JÁ.; Manjón Herrera, FJ.; Santamaría-Pérez, D.; Rodríguez-Hernández, P.; Muñoz, A. (2016). InBO3 and ScBO3 at high pressures: an ab initio study of elastic and thermodynamic properties. Journal of Physics and Chemistry of Solids. 98:198-208. https://doi.org/10.1016/j.jpcs.2016.07.002S1982089