Pseudopotential calculation of the bulk modulus and phonon dispersion of the bcc and hcp structures of titanium

Jafari, Mahmoud; Zarifi, Niloofar; Nobakhti, Maryam; Jahandoost, Atefeh; Lame, Maryam

doi:10.1088/0031-8949/83/06/065603

Cited by 16 publications

(6 citation statements)

References 20 publications

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“…As was mentioned above, the ratio of the elastic constants, C 11 /C 12 for the Ti bcc phase is less than 1 at T=0 [5,7,30,31]. Therefore, even excellent reproduction of the ab initio data on the bcc lattice parameter and relative (to hcp) formation energy at T=0 does not really provide any reliability of a semi-empirical potential at high temperature.…”

Section: Stability Of the Bcc Phasementioning

confidence: 95%

“…Fitting to these properties ensures that hcp is the most stable phase at T=0 and sets the correct energy scale. It should be noted that according to the ab initio calculations the Ti bcc phase is mechanically unstable at T=0 (C 11 < C 12 ) [5,7,30,31]. Therefore, reproducing the target values at T=0 for this phase does not ensure the correct description of this phase at high temperatures (including its mechanical stability).…”

Section: Potential Development Proceduresmentioning

confidence: 97%

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Development of an interatomic potential for the simulation of defects, plasticity, and phase transformations in titanium

Mendelev

Underwood

Ackland

2016

The Journal of Chemical Physics

142

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New interatomic potentials describing defects, plasticity, and high temperature phase transitions for Ti are presented. Fitting the martensitic hcp-bcc phase transformation temperature requires an efficient and accurate method to determine it. We apply a molecular dynamics method based on determination of the melting temperature of competing solid phases, and Gibbs-Helmholtz integration, and a lattice-switch Monte Carlo method: these agree on the hcp-bcc transformation temperatures to within 2 K. We were able to develop embedded atom potentials which give a good fit to either low or high temperature data, but not both. The first developed potential (Ti1) reproduces the hcp-bcc transformation and melting temperatures and is suitable for the simulation of phase transitions and bcc Ti. Two other potentials (Ti2 and Ti3) correctly describe defect properties and can be used to simulate plasticity or radiation damage in hcp Ti. The fact that a single embedded atom method potential cannot describe both low and high temperature phases may be attributed to neglect of electronic degrees of freedom, notably bcc has a much higher electronic entropy. A temperature-dependent potential obtained from the combination of potentials Ti1 and Ti2 may be used to simulate Ti properties at any temperature.

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Section: Stability Of the Bcc Phasementioning

confidence: 95%

Section: Potential Development Proceduresmentioning

confidence: 97%

Development of an interatomic potential for the simulation of defects, plasticity, and phase transformations in titanium

Mendelev

Underwood

Ackland

2016

The Journal of Chemical Physics

142

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“…In detail, we use variable-cell optimization calculations [43,44] and the finite difference formulas in Eq. 8 to calculate from DFT, first the volume, and then the SOECs of Si and Mg at a pressure p. To calculate B 0 (p) of fcc Si and hcp Mg, we use the formulas [39,60,61] B 0 (p) = C…”

Section: Potential Application Of Our Methodsmentioning

confidence: 99%

A first-principles method to calculate fourth-order elastic constants of solid materials

Pandit¹,

Bongiorno²

2023

Preprint

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A first-principles method is presented to calculate elastic constants up to the fourth order of crystals with the cubic and hexagonal symmetries. The method relies on the numerical differentiation of the second Piola-Kirchhoff stress tensor and a density functional theory approach to compute the Cauchy stress tensors for a minimal list of strained configurations of a reference state. The number of strained configurations required to calculate the independent elastic constants of the second, third, and fourth order is 24 and 37 for crystals with the cubic and hexagonal symmetries, respectively. Here, this method is applied to five crystalline materials with the cubic symmetry (diamond, silicon, aluminum, silver, and gold) and two metals with the hexagonal close packing structure (beryllium and magnesium). Our results are compared to available experimental data and previous computational studies. Calculated linear and nonlinear elastic constants are also used, within a nonlinear elasticity treatment of a material, to predict values of volume and bulk modulus at zero temperature over an interval of pressures. To further validate our method, these predictions are compared to results obtained from explicit density functional theory calculations.

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“…The elastic constants are saved every 0.1 ps. The bulk modulus and shear modulus are computed from elastic constants (in Voigt notation) [54,66,67] as K = 2 /9(C 11 + C 12 + 2C 13 + 1 /2C 33 ) and G = 1 /30(12C 44 + 7C 11 − 5C 12 + 2C 33 − 4C 13 ). The Poisson ratio is computed with σ = (3K − 2G)/(2G + 6K).…”

Section: Potential-driven MD Simulationsmentioning

confidence: 99%

Accurate machine learning force fields via experimental and simulation data fusion

Zavadlav,

Röcken

2023

Preprint

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Machine Learning (ML)-based force fields are attracting ever-increasing interest due to their capacity to span spatiotemporal scales of classical interatomic potentials at quantum-level accuracy. They can be trained based on high-fidelity simulations or experiments, the former being the common case. However, both approaches are impaired by scarce and erroneous data resulting in models that either do not agree with well-known experimental observations or are under-constrained and only reproduce some properties. Here we leverage both Density Functional Theory (DFT) calculations and experimentally measured mechanical properties and lattice parameters to train an ML potential of titanium. We demonstrate that the fused data learning strategy can concurrently satisfy all target objectives, thus resulting in a molecular model of higher accuracy compared to the models trained with a single data source. The inaccuracies of DFT functionals at target experimental properties were corrected, while the investigated off-target properties remained largely unperturbed. Our approach is applicable to any material and can serve as a general strategy to obtain highly accurate ML potentials.

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Pseudopotential calculation of the bulk modulus and phonon dispersion of the bcc and hcp structures of titanium

Cited by 16 publications

References 20 publications

Development of an interatomic potential for the simulation of defects, plasticity, and phase transformations in titanium

Development of an interatomic potential for the simulation of defects, plasticity, and phase transformations in titanium

A first-principles method to calculate fourth-order elastic constants of solid materials

Accurate machine learning force fields via experimental and simulation data fusion

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