Nonlinear theoretical formulation of elastic stability criterion of crystal solids

Wang, Hao; Li, Mo

doi:10.1103/physrevb.85.104103

Cited by 14 publications

(4 citation statements)

References 30 publications

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“…The linear model (L) uses the same energy-strain equation as DNS, equation (3), to obtain SOECs at zero pressures. Then equations (4)-( 7) [42] were applied for the predictions of SOECs under pressure. The deformed strain , e is defined as the uniformed deformation in x, y, z directions due to hydrostatic pressure P:…”

Section: ! ( )mentioning

confidence: 99%

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DFT-continuum characterization of third-order elasticity of sI methane hydrates under pressure

Zhu

Guerra²,

Servio³

et al. 2023

Mater. Res. Express

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Methane gas hydrates (GHs) are polyhedral crystalline guest-host materials found under high pressure and low-temperature conditions which can serve as an energy source. Previous work on methane GH material physics was limited to simple linear models, which only involves second-order elasticity. However, this is not fully suited to high-stress load conditions in technological applications and fundamental material physics. For other material systems it has been demonstrated that third-order elasticity and pressure derivatives of second-order elasticity have a strong and hence significant correlation. To narrow a critical theory-simulation gap in gas hydrates materials research, in this work we expand prior work from second-order elastic constants (SOECs) to third-order elastic constants (TOECs). By using the open-source Python tool Elastic3rd and the DFT calculation software Vienna Ab initio Simulation Package (VASP), we found that the non-linear fitting involving TOECs gave a better overall prediction and a smaller root-mean-square deviation on pressure-strain evaluation when compared with linear fitting. In addition, the non-linear fitting provides robust results on the piezo-effect on the shear constant C44 and the ductile-to-brittle transition (P=-0.5 GPa). These results are not achievable from previous work based on a linear model and these findings prove that non-linear models, including TOECs, are needed under high pressures. In addition, this research includes a detailed analysis of the calculation of TOECs and mechanical properties to study pressure stability limits and ductile-brittle transitions. Together the results, findings, and analyses from this work are a novel and significant contribution to the material physics knowledge of gas hydrates and hydrogen-bonded crystalline materials.

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Section: ! ( )mentioning

confidence: 99%

“…Once the SOECs and TOECs under zero pressures are obtained, the predictions of values under pressure are found using equations ( 9)-( 12) [42]. The definition of deformed strain e is the same as in the equations shown above.…”

Section: = + Ementioning

confidence: 99%

DFT-continuum characterization of third-order elasticity of sI methane hydrates under pressure

Zhu

Guerra²,

Servio³

et al. 2023

Mater. Res. Express

View full text Add to dashboard Cite

show abstract

“…Note that since the films are under a nonzero state of in-plane strain, the elastic stiffness tensor is no longer symmetric, i.e. C 13 = C 31 , and requires both second derivatives of energy with respect to strain as well as first derivatives (stress) to calculate [28][29][30].…”

Section: A the Thermal Expansion And Grüneisen Tensorsmentioning

confidence: 99%

Understanding mechanisms of thermal expansion in PbTiO$_3$ thin-films from first principles: role of high-order phonon-strain anharmonicity

Ritz,

Benedek

2021

Preprint

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The thermal properties of materials are critically important to various technologies and are increasingly the target of materials design efforts. However, it is only relatively recent advances in first-principles computational techniques that have enabled researchers to explore the microscopic mechanisms of thermal properties, such as thermal expansion. We use the Grüneisen theory of thermal expansion in combination with density functional calculations and the quasiharmonic approximation to uncover mechanisms of thermal expansion in PbTiO3 thin-films in terms of elastic and vibrational contributions to the free energy. Surprisingly, we find that although the structural parameters of PbTiO3 thin-films evolve with temperature as if they are dominated by linear elasticity, PbTiO3 thin-films are strongly anharmonic, with large changes in the elastic constants and Grüneisen parameters with both misfit strain and temperature. We show that a fortuitous near-cancellation between different types of anharmonicity gives rise to this behavior. Our results illustrate the importance of high-order phonon-strain anharmonicity in determining the temperaturedependent structural parameters of PbTiO3 thin-films, and highlight the complex manner in which thermal expansion, misfit strain and elastic and vibrational properties are intertwined.

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“…1) as a function of strain via higher-order elastic constants. A similar approach has been used in the past to study a small set of cubic materials and metallic glasses 4,24 . The deformed elastic constants C ′ ijkl and the stress σ are calculated as described in subsequent sections, from a knowledge of the SOEC's, TOEC's and applied strain only.…”

Section: Methodology a Wallace Formalism And Elastic Instabilitiesmentioning

confidence: 99%

Ideal strength and ductility in metals from second- and third-order elastic constants

et al. 2017

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Under tensile loading the ideal strength of a solid is governed by mechanical instabilities corresponding to failure in tension or shear, indicative of intrinsically brittle or ductile behavior, respectively. Ideal-strength first-principles calculations are performed in this work on several hexagonalclose-packed (hcp) and body-centered-cubic (bcc) metals. It is shown that some metals fail in tension under uniaxial loading, whereas others fail in shear. The observed behavior is rationalized with a simple analytical model based on second-order and third-order elastic constants. This formalism correctly predicts the failure mode of all but one of the metals studied in this work and leads to fundamental new insights into why some classes of metals are intrinsically brittle or ductile. Further, for the transition metals, filling of the d-bands is shown to correlate with the type of mechanical instability encountered, thus providing new insights into the effect of alloying on the intrinsic mechanical behavior of hcp and bcc metals.

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Nonlinear theoretical formulation of elastic stability criterion of crystal solids

Cited by 14 publications

References 30 publications

DFT-continuum characterization of third-order elasticity of sI methane hydrates under pressure

DFT-continuum characterization of third-order elasticity of sI methane hydrates under pressure

Understanding mechanisms of thermal expansion in PbTiO$_3$ thin-films from first principles: role of high-order phonon-strain anharmonicity

Ideal strength and ductility in metals from second- and third-order elastic constants

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