Polycristals

3-D microstructure of polycrystalline aluminium microstructure has been reconstructed on the basis of microscopic analysis results of actual α-Al2O3 microstructure by using Laguerre tessellation. SEM images of sintered bodies were used to calculate values of equivalent grain diameters and shape coefficient which then the Laguerre tessellation utilised for the 3D-reconstruction. The condition of periodicity has been additionally introduced for the generated domains. 3D periodical models of sizes ranging from 5 μm × 5 μm × 5 μm (61 grains content) to 30 μm × 30 μm × 30 μm (13220 grains content) were obtained in this way. Values of equivalent grain diameters and shape coefficients were determined for the synthetic microstructures. A comparison between distributions of the latter parameters and the analogous distributions originated from the polycrystalline Al2O3 SEM image analysis showed good compatibility. Dihedral angles of the synthetic microstructures also showed good compatibility with the literature reported data. The presented models will constitute the basis of further works on analysis of thermomechanical properties of polycrystalline materials.

• We investigate the propagation properties of anisometric polycrystalline aggregates. • Attenuation and phase velocity are computed using a spectral function approach. • Attenuation and phase velocity vary with the grain shape/size and the frequency. • q-SV and q-SH attenuations differ in the Rayleigh-to-Stochastic transition regime. • q-SV and q-SH phase velocities differ from the Rayleigh to the Stochastic regime.
Abstract: Attenuation and phase velocity of seismic waves propagating in cubic polycrystalline aggregates with elongated grains are computed from the Rayleigh (low-frequency) to the geometrical optics (high-frequency) regime using a spectral function approach. In this study, we consider the case of perfectly aligned ellipsoidal grains with randomly oriented crystallographic axes. Such anisometric medium exhibits transverse isotropy. The frequency dependence of both phase velocity and scattering attenuation for quasi-compressional (q-P), quasi-shear vertical (q-SV) and quasi-shear horizontal (q-SH) waves are examined in detail. The attenuation depends on the effective volume of the grain in the Rayleigh regime, on the grain dimension in the direction of propagation in the stochastic regime, and is inversely proportional to the grain size in the direction of propagation in the geometrical optics regime. The phase velocity exhibits a much more complex pattern depending on the grain shape and frequency. In particular, the fast/slow direction of propagation is not systematically aligned with the direction of low/high attenuation. The anisotropy in velocity typically varies from 1% in the Rayleigh regime to a few percents at the transition from the stochastic to the geometrical optics regime. Even for a highly anisotropic cubic iron crystals, q-SV and q-SH attenuations differ by at most 12% in the Rayleigh-to-stochastic transition regime but are equal in other frequency ranges. The q-SV and q-SH phase velocities , from the Rayleigh to the stochastic regime, differ by at most 1%. Anisotropy induced by geometrical effects should therefore be detectable in laboratory or seismological data.