In this study, using the density functional theory, the mechanical properties of methylammonium lead halide perovskites (CH 3 NH 3 PbX 3 , X = I, Br, Cl) were investigated. Young's modulus, bulk modulus, and shear modulus, Poisson's ratio, and many other parameters were calculated using the PBEsol and vdW approximations. Also, in this work, utilizing a new accuracy in calculating the elastic constants, the intense conflict between the previous theoretical results and the experimental data were fixed. Moreover, for the first time, through combination of the PBEsol and vdW methods, the effect of the interaction between methylammonium and PbX 3 scaffold on the mechanical properties of lead halide perovskites was well cleared. In continuation, using the PBEsol+vdW method, a phase transition appeared for the MAPbBr 3 and MAPbCl 3 structures, which proved more stability of MAPbBr 3 and MAPbCl 3 in comparison with MAPbI 3 . In what follows, by studying these materials under an applied strain beyond the harmonic region, the transition zone to the plastic area in the strain region of 5.5% and smaller was identified, and the small values of the aforementioned applied strains were found to be the reason for the instability of these materials at room temperature and above.

Using high-resolution x-ray scattering, we have demonstrated the existence of quenched disordered charge stripes in a single crystal of La (5/3)Sr (1/3)NiO (4) at low temperatures. Above the second-order transition critical scattering was observed due to fluctuations into the charge stripe phase. The charge stripes are shown to be two dimensional in nature both by measurements of their correlation lengths (xi(a) approximately 185 A, xi(b) = 400 A, and xi(c) approximately 25 A) and by the critical exponents of the charge strip transition. The charge stripe ordering did not develop long-range order even at low temperatures, indicating that the charge stripes are disordered and that the length scale of the disorder is quenched.