The third-order elastic moduli and pressure derivatives for AlRE (RE=Y, Pr, Nd, Tb, Dy, Ce) intermetallics with B2-structure: A first-principles study

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.

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A first principles study of the mechanical properties of Li–Sn alloys

RSC Advances ◽

10.1039/c5ra04685h ◽

2015 ◽

Vol 5 (45) ◽

pp. 36022-36029 ◽

Cited By ~ 27

Author(s):

Panpan Zhang ◽

Zengsheng Ma ◽

Yan Wang ◽

Youlan Zou ◽

Weixin Lei ◽

...

Keyword(s):

Mechanical Properties ◽

Density Functional Theory ◽

Failure Mechanism ◽

First Principles ◽

Density Functional ◽

Elastic Moduli ◽

Poisson's Ratio ◽

Active Materials ◽

Functional Theory ◽

First Principles Study

Focusing on the failure mechanism of active materials during charging–discharging, the mechanical properties of Li–Sn alloys are studied by density functional theory, including elastic moduli, Poisson's ratio, anisotropy, and brittleness-ductility.

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

Advances in Materials Science and Engineering ◽

10.1155/2021/8726250 ◽

2021 ◽

Vol 2021 ◽

pp. 1-12 ◽

Cited By ~ 1

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.

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