First-principles calculation of the elastic moduli of sheet silicates and their application to shale anisotropy

Ab initio calculations of elastic constants of plagioclase feldspars

“…Wave functions of valence electrons were expanded by a plane wave basis set with an energy cut off of 582 eV, and sampling points in the Brillouin zone were created with a Monkhorst-Pack grid of 4×2×2 (Monkhorst and Pack 1976). We used the finite strain approach (e.g., Karki et al 1997;Militzer et al 2011) and calculated elastic constants (C ijkl ) with Hooke's Law σ ij = ε kl C ijkl , where σ ij denotes directional stress, and ε kl , directional strain.…”

Mechanism of Strong Affinity of Clay Minerals to Radioactive Cesium: First-Principles Calculation Study for Adsorption of Cesium at Frayed Edge Sites in Muscovite

“…The distribution of substituted Al atoms in the bulk system follows that in ref. 26) (see the leftbottom panel in Fig. 1 and the left panel of Fig.…”

“…In particular, density functional theory (DFT) 19,20) and molecular dynamics have been frequently employed for clay minerals. [21][22][23][24][25][26][27] However, no direct work toward clarifying the mechanism of the strong affinity of Cs in FESs has been published yet. In this paper, we employ a first-principles calculation scheme based on DFT and microscopically examine the strong selective affinity of FES to Cs.…”

“…The employed calculation program is the Vienna Ab initio Simulation Package (VASP), 28,29) which supports the projected augmented wave method 30,31) and generalized gradient approximation, 32) which are also employed in this work similar to several previous works on clays. 25,26) The cutoff energy is 1600 eV, and 3×1×1 sampling points are used on kpoint grids. Structural relaxation is repeated until the gradient forces on atoms are less than 2.0 × 10 −2 eV/Å.…”

Theoretical Study of Kaolinite Structure; Energy Minimization and Crystal Properties

“…Differences in other elastic constants are either related to this or the difference of the density value, concentration and arrangement of defects ( [14] and [22]). The calculated elastic constant tensors indicate that the a direction is slightly more flexible than the b direction.…”