Dislocation solution in slowly varying approximation

Advances in Materials Science and Engineering

Gao

et al. 2021

The second-order elastic constants, third-order elastic constants, and the generalized-stacking-fault energy for semiconductor GaAs are investigated using the first-principles calculations. The predictions of elastic constants are obtained from the coefficients of the fitted polynomials of the energy-strain functions. It is found that the nonlinear elastic effects must be considered when the applied deformations are larger than approximately 1.5%. With the Lagrangian strains up to 6.4%, the terms included up to third order in energy expansion functions are sufficient. The elastic constants given in this work agree well with the previous results and experimental data except for C144. C144 given by the present paper is a positive value, and the estimated 3 GPa agrees well with the experimental result of 2 GPa. The research results can provide a reference for understanding the elasticity of GaAs. The generalized-stacking-fault energy has been calculated without and with structural relaxation, respectively. The unstable stacking fault energy with structural relaxation is about two-thirds of that without relaxation. The dislocation width and Peierls stress for 30° partial in GaAs have been investigated based on the improved P-N theory. The dislocation width is very narrow (only about one-fifth of Burgers vector b), which is reasonable for covalent materials. The Peierls stress is about 4 GPa, in good agreement with the experimental result of 2∼3 GPa.

Section: Strain Typementioning

confidence: 99%

First‐Principles Study on the Elastic Constants and Structural and Mechanical Properties of 30° Partial Dislocation in GaAs

Advances in Materials Science and Engineering

Gao

et al. 2021

“…In this section, the mechanical properties of 30 • partial dislocation in germanium have been investigated theoretically based on the improved Peierls-Nabarro model. The equation satisfied by the displacement field u of dislocation can be expressed as [39] − β 2…”

Section: Mechanical Properties Of 30 • Partial Dislocation In Germaniummentioning

confidence: 99%

“…The calculation methods of dislocation width and Peierls stress have been given in detail in ref. [22,39,42], and will not be repeated in this paper. The calculated half-width ξ and Peierls stress σ p of 30 • partial in germanium are listed in Table 3.…”

Section: Mechanical Properties Of 30 • Partial Dislocation In Germaniummentioning

confidence: 99%

The Third-Order Elastic Constants and Mechanical Properties of 30° Partial Dislocation in Germanium: A Study from the First-Principles Calculations and the Improved Peierls–Nabarro Model

Sun

et al. 2021

Crystals

The elastic constants, core width and Peierls stress of partial dislocation in germanium has been investigated based on the first-principles calculations and the improved Peierls−Nabarro model. Our results suggest that the predictions of lattice constant and elastic constants given by LDA are in better agreement with experiment results. While the lattice constant is overestimated at about 2.4% and most elastic constants are underestimated at about 20% by the GGA method. Furthermore, when the applied deformation is larger than 2%, the nonlinear elastic effects should be considered. And with the Lagrangian strains up to 8%, taking into account the third-order terms in the energy expansion is sufficient. Except the original γ—surface generally used before (given by the first-principles calculations directly), the effective γ—surface proposed by Kamimura et al. derived from the original one is also used to study the Peierls stress. The research results show that when the intrinsic−stacking−fault energy (ISFE) is very low relative to the unstable−stacking−fault energy (USFE), the difference between the original γ—surface and the effective γ—surface is inapparent and there is nearly no difference between the results of Peierls stresses calculated from these two kinds of γ—surfaces. As a result, the original γ—surface can be directly used to study the core width and Peierls stress when the ratio of ISFE to the USFE is small. Since the negligence of the discrete effect and the contribution of strain energy to the dislocation energy, the Peierls stress given by the classical Peierls−Nabarro model is about one order of magnitude larger than that given by the improved Peierls−Nabarro model. The result of Peierls stress estimated by the improved Peierls−Nabarro model agrees well with the 2~3 GPa reported in the book of Solid State Physics edited by F. Seitz and D. Turnbull.

“…( 9), a similar result can be obtained for the right-hand side by a series expansion in c 1 and c 2 as small corrections. Taking into account that u r y is small and can be ignored, we obtain the values of the parameters c 1 , c 2 , and g by truncating the series rationally using orthogonal polynomials, [21,22] as shown in Fig. 3(a).…”

Section: Applicationmentioning

confidence: 99%

Modification of the Peierls–Nabarro model for misfit dislocation*

Wang

2020

Chinese Phys. B

Self Cite

For a misfit dislocation, the balance equations satisfied by the displacement fields are modified, and an extra term proportional to the second-order derivative appears in the resulting misfit equation compared with the equation derived by Yao et al. This second-order derivative describes the lattice discreteness effect that arises from the surface effect. The core structure of a misfit dislocation and the change in interfacial spacing that it induces are investigated theoretically in the framework of an improved Peierls–Nabarro equation in which the effect of discreteness is fully taken into account. As an application, the structure of the misfit dislocation for a honeycomb structure in a two-dimensional heterostructure is presented.