New Insight into Elastic Mechanical Properties and Anisotropies of Crystal Defect α-Quartz from DFT Calculation

To reveal the cleavage mechanism of α-quartz in the grinding process of nonferrous metal ores, mechanical and charge properties of α-quartz crystals are investigated using the density functional theory. Based on the elastic constant matrix, the bulk and shear moduli were calculated before and after the α-quartz with oxygen atom defects. The results show that the ratios of bulk and shear moduli (B/G) were 0.87 and 0.95, respectively, which indicated that at the same stress level, it was easier to fracture without O-vacancy defects than with O-vacancy defects. The mapping surfaces indicated that the O-vacancy defect increased the bulk-, shear-, and Young's moduli, and Poisson ratio while decreasing the hardness. The anisotropy index (A_L and A^U) was calculated which illustrated that the O-vacancy can result in an increased anisotropy; meanwhile, the bulk anisotropy index (A_B) increased strongly about two times. The anisotropy analysis shows the dominance crystal cleavage of the (011) plane in the shear stress and the dominance crystal cleavage of the (111) plane in the normal stress. The electron localization function α-quartz show that the O-vacancy defect can decrease the Si-Si length from 3.703 to 2.442 Å, which indicated that the O-vacancy formed the new covalent bonds between silicon atoms. Our work provided a systematic approach containing the mechanical, anisotropic, and electronic properties of mineral crystals to explain the cleavage behavior of crystals.