Temperature dependence of TiN elastic constants from<i>ab initio</i>molecular dynamics simulations

Steneteg, Peter; Hellman, Olle; Vekilova, Olga Yu.; Shulumba, Nina; Tasnádi, Ferenc; Abrikosov, Igor A.

doi:10.1103/physrevb.87.094114

Cited by 84 publications

(59 citation statements)

References 57 publications

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“…These results are in line with previous studies for TiN, 38 with a significant softening of all elastic constants. For TiN, our results agree well with the values obtained by full AIMD simulations by Steneteg et al 38 We view this as a strong justification for the reliability and accuracy of the scheme based on the use of Eqs. (2) and (3).…”

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confidence: 93%

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Temperature-dependent elastic properties of Ti1−xAlxN alloys

Shulumba

Hellman

Rogström

et al. 2015

Applied Physics Letters

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Ti1−xAlxN is a technologically important alloy that undergoes a process of high temperature age-hardening that is strongly influenced by its elastic properties. We have performed first principles calculations of the elastic constants and anisotropy using the newly developed symmetry imposed force constant temperature dependent effective potential method, that include lattice vibrations and therefore the effects of temperature, including thermal expansion and intrinsic anharmonicity. These are compared with in situ high temperature x-ray diffraction measurements of the lattice parameter. We show that anharmonic effects are crucial to the recovery of finite temperature elasticity. The effects of thermal expansion and intrinsic anharmonicity on the elastic constants are of the same order, and cannot be considered separately. Furthermore, the effect of thermal expansion on elastic constants is such that the volume change induced by zero point motion has a significant effect. For TiAlN, the elastic constants soften non-uniformly with temperature: C11 decreases substantially when the temperature increases for all compositions, resulting in an increased anisotropy. These findings suggest that an increased Al content and annealing at higher temperatures will result in a harder alloy.

Funding agencies: Swedish Research Council (VR) [621-2011-4426, 621-2012-4401, 637-2013-7296]; Swedish Foundation for Strategic Research (SSF) [RMA08-0069, SRL10-0026]; VINNOVA [2013-02355(MC2)]; Erasmus Mundus Joint European Doctoral Program DocMASE; Ministry of Education

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confidence: 93%

“…This can be explained with the fact that in Ref. 38, the simulations were based on classical equations of motions for atoms, whereas this work includes quantum effects on the vibrational free energy.…”

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confidence: 99%

Temperature-dependent elastic properties of Ti1−xAlxN alloys

Shulumba

Hellman

Rogström

et al. 2015

Applied Physics Letters

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“…More specifically, we prepared ensembles of ten supercells with atoms displaced with a Monte Carlo algorithm 46 for phonons calculated with experimental force constants 29,47,48 . For each configuration of displaced atoms, the electronic DOS (N MC ) was calculated, and an ∆S ad el,ep was calculated as…”

Section: Entropymentioning

confidence: 99%

Phonon anharmonicity and components of the entropy in palladium and platinum

Shen

Tang

et al. 2016

Phys. Rev. B

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Inelastic neutron scattering was used to measure the phonon density of states in fcc palladium and platinum metal at temperatures from 7 K to 1576 K. Both phonon-phonon interactions and electronphonon interactions were calculated by methods based on density functional theory (DFT), and were consistent with the measured shifts and broadenings of phonons with temperature. Unlike the longitudinal modes, the characteristic transverse modes had a nonlinear dependence on temperature owing to the requirement for a population of thermal phonons for upscattering. Kohn anomalies were observed in the measurements at low temperature, and were reproduced by calculations based on DFT. Contributions to the entropy from phonons and electrons were assessed and summed to obtain excellent agreement with prior calorimetric data. The entropy from thermal expansion is positive for both phonons and electrons, but larger for phonons. The anharmonic phonon entropy is negative in Pt, but in Pd it changes from positive to negative with increasing temperature. Owing to the position of the Fermi level on the electronic DOS, the electronic entropy was sensitive to the adiabatic electron-phonon interaction in both Pd and Pt. The adiabatic EPI depended strongly on thermal atom displacements.

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“…TiN, for example, has elastic constants that are strongly temperature dependent, and the isotropy of the elastic constants increases with temperature. 6 Using my newly developed SIFC-TDEP methodology for alloys, I also show that the elastic constants for Ti 1-x Al x N are strongly temperature dependent, and that the anisotropy increases with temperature. This is particularly interesting, because at low anisotropies, nanocrystals will grow in a notionally spherical way, whereas high anisotropies result in elongated and irregular nanocrystalline domains through which it is harder to propagate internal stresses.…”

Section: Temperature Dependent Electronic Structure Of Aluminium Nitridementioning

confidence: 88%

“…5,4 I use finite-temperature first principles calculations to recover the temperature dependence of the elastic constants, and demonstrate that elastic anisotropy decreases as the temperature increases, which may explain the high temperature reduction in hardness. 6 CrN is a hard ceramic generally used in protective coating applications. 7,8,9,10,11 Crucially, it has been observed in two phases with distinct magnetic states: at ambient pressure, it adopts a paramagnetic rocksalt structure, and when cooled it changes to an antiferromagnetic orthorhombic structure, which can also be stabilised at room temperature by the application of pressure.…”

Section: Introductionmentioning

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Vibrations in solids : From first principles lattice dynamics to high temperature phase stability

Shulumba¹

2015

Linköping Studies in Science and Technology. Dissertations

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In this thesis I introduce a new method for calculating the temperature dependent vibrational contribution to the free energy of a substitutionally disordered alloy that accounts for anharmonicity at high temperatures. This method exploits the underlying crystal symmetries in an alloy to make the calculations tractable. The validity of this approach is demonstrated by constructing the phase diagram via direct minimization of the Gibbs free energy of a notoriously awkward and technologically important system, Ti 1-x Al x N. The vibrational entropy including anharmonic effects is shown to be large and comparable to the configurational entropy at high temperatures, and with its inclusion, the theoretical miscibility gap of Ti 1-x Al x N is reduced from 6560 K to 2860 K, in line with atom probe experiments. A similar treatment of Zr 1-x Al x N and Hf 1-x Al x N alloys suggests that mass disorder has a minimal effect on phase stability compared with chemical ordering. My method is also capable of demonstrating that Hf 1-x Al x N, which is dynamically unstable at room temperature, is stabilised at high temperatures. Moreover I develop a new method of computing temperature dependent elastic constants for alloys from their phonon spectra, and show that for Ti 1-x Al x N, the elastic anisotropy is found to increase with temperature, helping to explain the spinodal decomposition.The effects of lattice dynamics on phase stability, mechanical, magnetic and transport properties on other materials are also examined. Four specific systems are discussed in detail. Firstly, in the case of CrN, lattice vibrations are shown to decrease the antiferromagnetic to paramagnetic phase transition temperature from 500 K to 380 K, in line with experimental evidence. Secondly, a temperature/pressure induced phase transition in AlN becomes much more facile than in the quasiharmonic approximation, and the thermal conductivity of the rocksalt phase is shown to be much lower than that of the wurtzite phase, as a result of the increased anharmonicity in the rocksalt structure. Thirdly, the temperature dependence of elastic constants of TiN becomes more isotropic as the temperature increases. Finally, iron carbides are evaluated as potentially important phases at the Earth's core; specifically, calculating the Gibbs free energy of a recently discovered orthorhombic phase of Fe 7 C 3 demonstrates that it is not stable relative to the known hexagonal phase at extreme pressure and temperatures.V Popular science summary Solid materials can be described using a simple mathematical model from the theory of lattice dynamics. In a solid, atoms are arranged in a regular and repeating structure (a lattice), and the forces between them can essentially be modelled as springs. Despite the simplicity of this model, it is possible to derive a surprising amount of information on materials from it. One can determine which arrangements of atoms, or phases, form the stable microscopic structures that we encounter in the real world, their mechanical properti...

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Temperature dependence of TiN elastic constants fromab initiomolecular dynamics simulations

Cited by 84 publications

References 57 publications

Temperature-dependent elastic properties of Ti1−xAlxN alloys

Temperature-dependent elastic properties of Ti1−xAlxN alloys

Phonon anharmonicity and components of the entropy in palladium and platinum

Vibrations in solids : From first principles lattice dynamics to high temperature phase stability

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