scholarly journals 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

Crystals ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 4
Author(s):  
Huili Zhang ◽  
Defang Lu ◽  
Yu Sun ◽  
Yunchang Fu ◽  
Lumei Tong
Keyword(s):  
Lattice Constant ◽  
Elastic Constants ◽  
First Principles ◽  
Partial Dislocation ◽  
Stacking Fault ◽  
Peierls Stress ◽  
First Principles Calculations ◽  
Third Order ◽  
The Third ◽  
Core Width

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.

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

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Huili Zhang ◽  
Qiannan Gao ◽  
Defang Lu ◽  
Yunchang Fu ◽  
Lumei Tong
Keyword(s):  
Elastic Constants ◽  
Structural Relaxation ◽  
First Principles ◽  
Stacking Fault ◽  
Stacking Fault Energy ◽  
Peierls Stress ◽  
Experimental Result ◽  
Third Order ◽  
Generalized Stacking Fault ◽  
Generalized Stacking Fault Energy

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.

scholarly journals Temperature Effects on the Elastic Constants, Stacking Fault Energy and Twinnability of Ni3Si and Ni3Ge: A First-Principles Study

Crystals ◽  
2018 ◽  
Vol 8 (9) ◽  
pp. 364 ◽  
Author(s):  
Lili Liu ◽  
Liwan Chen ◽  
Youchang Jiang ◽  
Chenglin He ◽  
Gang Xu ◽  
...  
Keyword(s):  
Elastic Constants ◽  
First Principles ◽  
Antiphase Boundary ◽  
Stacking Fault ◽  
First Principles Calculations ◽  
Planar Fault ◽  
Different Temperatures ◽  
Generalized Stacking Fault ◽  
Increasing Temperature ◽  
Stacking Fault Energies

The volume versus temperature relations for Ni 3 Si and Ni 3 Ge are obtained by using the first principles calculations combined with the quasiharmonic approach. Based on the equilibrium volumes at temperature T, the temperature dependence of the elastic constants, generalized stacking fault energies and generalized planar fault energies of Ni 3 Si and Ni 3 Ge are investigated by first principles calculations. The elastic constants, antiphase boundary energies, complex stacking fault energies, superlattice intrinsic stacking fault energies and twinning energy decrease with increasing temperature. The twinnability of Ni 3 Si and Ni 3 Ge are examined using the twinnability criteria. It is found that their twinnability decrease with increasing temperature. Furthermore, Ni 3 Si has better twinnability than Ni 3 Ge at different temperatures.

First-Principles Calculations of Elastic Properties of HoBi and ErBi

2013 ◽  
Vol 664 ◽  
pp. 672-676
Author(s):  
De Ming Han ◽  
Gang Zhang ◽  
Li Hui Zhao
Keyword(s):  
Shear Modulus ◽  
Physical Properties ◽  
Bulk Modulus ◽  
Elastic Properties ◽  
Lattice Constant ◽  
Elastic Constants ◽  
First Principles ◽  
Energy Band ◽  
First Principles Calculations ◽  
Future Work

We present first-principles investigations on the elastic properties of XBi (X=Ho, Er) compounds. Basic physical properties, such as lattice constant, elastic constants (Cij), isotropic shear modulus (G), bulk modulus (B), Young’s modulus (Y), Poisson’s ratio (υ), and Anisotropy factor (A) are calculated. The calculated energy band structures show that the two compounds possess semi-metallic character. We hope that these results would be useful for future work on two compounds.

scholarly journals Nonlinear Elasticity of Borocarbide Superconductor YNi2B2C: A First-Principles Study

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Lili Liu ◽  
Cai Chen ◽  
Dingxing Liu ◽  
Zhengquan Hu ◽  
Gang Xu ◽  
...  
Keyword(s):  
High Pressure ◽  
Elastic Constants ◽  
Vickers Hardness ◽  
First Principles ◽  
Second Order ◽  
First Principles Calculations ◽  
Modulus Ratio ◽  
Third Order ◽  
Lattice Constants ◽  
Third Order Elastic Constants

First-principles calculations combined with homogeneous deformation methods are used to investigate the second- and third-order elastic constants of YNi2B2C with tetragonal structure. The predicted lattice constants and second-order elastic constants of YNi2B2C agree well with the available data. The effective second-order elastic constants are obtained from the second- and third-order elastic constants for YNi2B2C. Based on the effective second-order elastic constants, Pugh’s modulus ratio, Poisson’s ratio, and Vickers hardness of YNi2B2C under high pressure are further investigated. It is shown that the ductility of YNi2B2C increases with increasing pressure.

scholarly journals First-Principles Calculations to Investigate the Third-Order Elastic Constants and Mechanical Properties of Mg, Be, Ti, Zn, Zr, and Cd

2021 ◽  
Vol 2021 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaoqing Yang ◽  
Zhenya Meng ◽  
Hailin Cao
Keyword(s):  
High Pressure ◽  
Elastic Constants ◽  
First Principles ◽  
Deformation Gradient ◽  
Elastic Strain Energy ◽  
Pressure Effects ◽  
First Principles Calculation ◽  
Third Order ◽  
The Third ◽  
Third Order Elastic Constants

We present theoretical studies for the third-order elastic constants of Mg, Be, Ti, Zn, Zr, and Cd with a hexagonal-close-packed (HCP) structure. The method of homogeneous deformation combined with first-principles total-energy calculations is employed. The deformation gradient F i j is applied to the crystal lattice vectors r i , and the elastic strain energy can be obtained from the first-principles calculation. The second- and third-order elastic constants are extracted by a polynomial fit to the calculated energy-strain results. In order to assure the accuracy of our method, we calculated the complete set of the equilibrium lattice parameters and second-order elastic constants for Mg, Be, Ti, Zn, Zr, and Cd, and our results provide better agreement with the previous calculated and experimental values. Besides, we have calculated the pressure derivatives of SOECs related to third-order elastic constants, and high-pressure effects on elastic anisotropy, ductile-to-brittle criterion, and Vickers hardness are also investigated. The results show that the hardness model H v = 1.877 k 2 G 0.585 is more appropriate than H v = 2 k 2 G 0.585 − 3 for HCP metals under high pressure.

Sign in / Sign up

Export Citation Format

Share Document