Determination of active sites on Na2SiO3 and Li2SiO3 catalysts for methanol dissociation and methoxide stabilization concerning biodiesel production

Electronic, mechanical, optical and piezoelectric properties of glass-like sodium silicate (Na2SiO3) under compressive pressure

“…1 . Table 1 shows the agreement between our results and the previously calculated results from Cuautli et al 46 using PBE as the exchange-correlation functional. Our calculated volume is 2.04% and 3.95% higher than the volume calculated using the Becke, 3-parameter, Lee–Yang–Parr (B3LYP) functional by Belmonte et al 47 and the one experimentally obtained by McDonald et al , 48 respectively.…”

Electronic, mechanical and piezoelectric properties of glass-like complex Na2Si1−xGexO3 (x = 0.0, 0.25, 0.50, 0.75, 1.0)

“…From Table 1, it can be seen that our calculated volume is 3.06%, 0.93%, 8.02% and 4.95% larger than those reported by Belmonte et al, 28 Cuautli et al, 29 Liu et al 30 et al 27 respectively. The dissimilarities of volumes are due to the well-known effect of the PBE exchange-correlation in the GGA.…”

“…The optimized result of Na 2 SiO 3 with 12 atoms in the unit cell is in the orthorhombic Cmc2 1 space group and in good agreement with the previously reported results. [27][28][29]51 The optimised lattice parameters are a ¼ 10.683 Å, b ¼ 6.172 Å and c ¼ 4.892 Å, with an optimised volume of V ¼ 322.559 Å3 . The calculated lattice parameters 'a', 'b' and 'c' are comparable to those of the previously reported theoretical results from PBE as the exchange correlation functional, 29,53 the Becke 3-parameter, 28 the Lee-Yang-Parr (B3LYP) functional, 30 and the experimental data obtained by McDonald et al 27 For further conrmation of the structural stability we have calculated the formation energies (E form ) 62 by using eqn (2) given below…”

“…[23][24][25][26] The structural prole and the atomic arrangement of silicate glasses are well investigated by both experimental and computational methods. [27][28][29][30] The most common superlative experimental set-ups employed for determination of many ngerprints of the structures were: Raman spectroscopy, extended X-ray absorption ne structure (EXAFS) spectroscopy, nuclear magnetic resonance (NMR), neutron diffraction and so on. [31][32][33][34][35][36][37][38][39][40] The experimental studies mainly highlighted the structure of silicate glasses and were mostly dened by the medium range or short range order (MRO or SRO), i.e., the order over distances comparable to inter-atomic distances, and lacked long-range order (LRO) leading to more complications and challenges when examining the structural properties.…”

“…Calculated optimised lattice parameters of the Na 2 SiO 3 unit cell (12-atoms) compared to B3LYP (Belmonte et al28 ), PBE (Cuautli et al29 ), LDA (Liu et al)30 and experimental values (McDonald et al27 ). Here, the relative errors are calculated with respect to the experimental data…”