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Computational Nondestructive Evaluation (CNDE)
Published in Sourav Banerjee, Cara A.C. Leckey, Computational Nondestructive Evaluation Handbook, 2020
Sourav Banerjee, Cara A.C. Leckey
Improved understanding of sensor signals, and more precisely, the nature of wave propagation in different types of materials (such as isotropic and anisotropic materials), has been a topic of interest in NDE research for the past few decades. Due to the widespread application of engineered anisotropic materials, most prevalently composites, in many different fields of engineering and technology (e.g., mechanical and aerospace industries), tools to aid the understanding of wave propagation in these complex materials are of great importance across numerous industries relying on NDE. Wave propagation behavior is studied by investigating wave interaction with the material in the form of scattering, reflection, and transmission of the wave, giving rise to geometric dispersion. These interactions of waves depend on many factors such as the part geometry, mechanical properties, number and nature of the interfacial conditions, loading conditions, and environmental conditions the part is subjected to [20]. The mechanical properties (number of independent material constants) vary from the simple case of isotropic materials to the most general anisotropic case for triclinic materials.
Birefringent Optical Waveguides
Published in María L. Calvo, Vasudevan Lakshminarayanan, Optical Waveguides, 2018
María L. Calvo, Ramόn F. Alvarez-Estrada
The propagation of electromagnetic waves (and, in particular, of light) in crystals depends, typically but not necessarily, on the direction. That is, crystals may display, but not necessarily, optical anisotropy. In fact, there are crystals in which the relative dielectric permittivity tensor reduces to a scalar (that is, ϵ˜ becomes proportional, but not equal, to the 3 × 3 unit matrix I3). Such crystals are those belonging to the so-called cubic system (in which three mutually orthogonal and crystallographically equivalent directions may be chosen). Crystals belonging not to the cubic system, but to either the trigonal or the tetragonal or the hexagonal systems (in all of which, two or more crystallographically equivalent directions may be chosen in one plane) are uniaxial and, so, optically anisotropic. Crystals belonging not to any of the above four systems but to either the orthorhombic or the monoclinic or the triclinic systems (in all of which, no two crystallographically equivalent directions may be chosen) are biaxial and, so, optically anisotropic as well. Quartz and calcite are examples of uniaxial crystals. Aragonite and Brazil topaz provide examples of biaxial crystals.
On the impact of zero-point vibrations in calcium carbonate
Published in Phase Transitions, 2021
R. Belkofsi, G. Chahi, O. Adjaoud, I. Belabbas
Three high pressure polymorphs of calcium carbonate were considered, which are calcite-III, calcite-IIIb and calcite-VI (Figure 1). All these polymorphs have triclinic crystal structures. These crystal structures were determined in 2012 by Merlini et al. [17], who carried out synchrotron X-ray diffraction experiments. The determined lattice parameters of calcite-III at 2.8 GPa are a=6.281 Å, b=7.507 Å, c=12.516 Å, α=93.76°, β=98.95° and γ=106.49° [17]. Those of calcite-IIIb, at 3.1 GPa, are: a=6.144 Å, b=6.372 Å, c=6.376 Å, α=93.84°, β=107.34° and γ=107.16° [17]. Calcite-VI was observed at 30.4 GPa with the following lattice parameters: a=3.319 Å, b=4.883 Å, c=5.590 Å, α=103.30°, β=94.73° and γ=89.21° [17].