scholarly journals Nonlinear elastic response of strong solids: First-principles calculations of the third-order elastic constants of diamond

2016 ◽  
Vol 93 (17) ◽  
Author(s):  
A. Hmiel ◽  
J. M. Winey ◽  
Y. M. Gupta ◽  
M. P. Desjarlais
Keyword(s):  
Elastic Constants ◽  
First Principles ◽  
Elastic Response ◽  
First Principles Calculations ◽  
Third Order ◽  
The Third ◽  
Third Order Elastic Constants ◽  
Nonlinear Elastic

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 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.

The Nonlinear Elasticity of Hexagonal Ti2C Monolayer from First-Principles Calculations

2015 ◽  
Vol 833 ◽  
pp. 150-153
Author(s):  
Shun Wang ◽  
Jing Xiao Li ◽  
Yuan Yuan Ou ◽  
Yu Lei Du
Keyword(s):  
Nonlinear Elasticity ◽  
Elastic Constants ◽  
First Principles ◽  
Breaking Strength ◽  
First Principles Calculations ◽  
Third Order ◽  
Breaking Strain ◽  
Third Order Elastic Constants ◽  
Nonlinear Stress ◽  
Strain Relationship

In this work, the nonlinear elasticity of hexagonal Ti2C monolayer is studied by first-principles calculations. The second-and third-order elastic constants were calculated using nonlinear elasticity theory. The nonlinear stress-strain relationship depending on higher order elastic constants was also revealed. The intrinsic breaking strength and corresponding breaking strain were deduced as 11.9 N/m at the maximum strain 16.6% for Ti2C monolayer.

Elastic3rd: A tool for calculating third-order elastic constants from first-principles calculations

2021 ◽  
Vol 261 ◽  
pp. 107777
Author(s):  
Mingqing Liao ◽  
Yong Liu ◽  
Shun-Li Shang ◽  
Fei Zhou ◽  
Nan Qu ◽  
...  
Keyword(s):  
Elastic Constants ◽  
First Principles ◽  
First Principles Calculations ◽  
Third Order ◽  
Third Order Elastic Constants
Sign in / Sign up

Export Citation Format

Share Document