Full-potential calculations using the generalized-gradient corrections: structural properties of Ti, Zr and Hf under compression

Jomard, Gérald; Magaud, Laurence; Pasturel, A.

doi:10.1080/13642819808206383

Cited by 55 publications

(32 citation statements)

References 27 publications

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“…Indeed, in our calculation, the crossing between the ω and α enthalpy curves lies at the pressure of −4.3 GPa. This result is consistent with the theoretical result of Ti [14,38], however, it is inconsistent with the transition sequence of Hf both experimentally and theoretically [9,[39][40][41]. To further investigate the phase stability, in Table II we list the transition pressures for HfTi alloy as well as for pure Hf and Ti metals from both experiments and theoretical calculations.…”

Section: B Pressure Induced Phase Transitionsupporting

confidence: 76%

“…This value coincides with the theoretical results of 30.7-66.2 GPa [39][40][41] for Hf metal, and is somewhat lower than the experimental data of 71 GPa [9]. Also, the temperature effect on phase transition pressure cannot be ignored.…”

Section: B Pressure Induced Phase Transitionsupporting

confidence: 72%

“…To further investigate the phase stability, in Table II we list the transition pressures for HfTi alloy as well as for pure Hf and Ti metals from both experiments and theoretical calculations. For metal Hf, at ambient pressure both the experimental [9] and theoretical studies [39][40][41] indicate that the most stable phase is the α phase. The measured transition pressure of α→ω is 38±8 GPa [9], and the theoretical results vary from 13.…”

Section: B Pressure Induced Phase Transitionmentioning

confidence: 99%

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Elasticity behavior, phonon spectra, and the pressure–temperature phase diagram of HfTi alloy: A density-functional theory study

Lu¹,

Zhang²

2014

Computational Materials Science

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The pressure-induced phase transition, elasticity behavior, thermodynamic properties, and P −T phase diagram of α, ω, and β equiatomic HfTi alloy are investigated using first-principles densityfunctional theory (DFT). The simulated pressure-induced phase transition of the alloy follows the sequence of α→ω→β, in agreement with the experimental results of Hf and Ti metals. Our calculated elastic constants show that the α and ω phases are mechanically stable at ambient pressure, while the β phase is unstable, where a critical pressure of 18.5 GPa is predicted for its mechanical stability. All the elastic constants, bulk modulus, and shear modulus increase upon compression for the three phases of HfTi. The ductility of the alloy is shown to be well improved with respect to pure Hf and Ti metals. The Mulliken charge population analysis illustrates that the increase of the d-band occupancy will stabilize the β phase under pressure. The phonon spectra and phonon density of states are studied using the supercell approach for the three phases, and the stable nature of α and ω phases at ambient pressure are observed, while the β phase is only stable along the [110] direction. With the Gibbs free energy calculated from DFT-parametrized Debye model as a function of temperature and pressure, the phase transformation boundaries of the α, ω, and β phases of HfTi are identified.

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Section: B Pressure Induced Phase Transitionsupporting

confidence: 76%

Section: B Pressure Induced Phase Transitionsupporting

confidence: 72%

Section: B Pressure Induced Phase Transitionmentioning

confidence: 99%

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Elasticity behavior, phonon spectra, and the pressure–temperature phase diagram of HfTi alloy: A density-functional theory study

Lu¹,

Zhang²

2014

Computational Materials Science

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“…The calculations were performed in the local density approximation (LDA) 1,2 and the parametrization used was the one of von Barth-Hedin 19 . Jomard et al 20 showed that generalized-gradient corrections have to be included in order to obtain a correct description of the stability of the different phases of pure Zr, but as we were interested only in the Al-rich part of the phase diagram we did not include these gradient corrections.…”

Section: Ground States Of Ordered Compoundsmentioning

confidence: 99%

First-principles study of the solubility of Zr in Al

Clouet¹,

Sanchez²,

Sigli³

2002

Phys. Rev. B

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The experimental solubility limit of Zr in Al is well-known. Al3Zr has a stable structure DO23 and a metastable one L12. Consequently there is a metastable solubility limit for which only few experimental data are available. The purpose of this study is to obtain by ab-initio calculations the solubility limit of Zr in Al for the stable as well as the metastable phase diagrams. The formation energies of several ordered compounds AlxZr (1−x) , all based on an fcc underlying lattice, were calculated using the FP-LMTO (Full Potential Linear Muffin Tin Orbital) method. Taking into account all the relaxations allowed by the symmetry, we found the DO23 structure to be the stable one for Al3Zr. This set of results was then used with the cluster expansion in order to fit a generalized Ising model through the inverse method of Connolly-Williams. Different ways to consider volume relaxations were examined. This allowed us to calculate in the Bragg-Williams approximation the configurational free energy at finite temperature. According to the previous FP-LMTO calculations the free energy due to electronic excitations can be neglected. For the vibrational free energy of ordered structures we compared results obtained from a calculation of the elastic constants used with the Debye model and results obtained from a calculation of the phonon spectrum. All these different steps lead to a calculation of the solubility limit of Zr in Al which is found to be lower than the experimental one. The solubility limit in the metastable phase diagram is calculated in the same way and can thus be compared to the stable one.

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“…It has been unveiled that the transition pressure of Ti (ranging from 2.9 to 11 GPa) [14] and Zr (∼2.2 GPa) [15] to the ω phase are very different from Hf. Several experimental and theoretical studies have shown that the α to ω phase transition of Hf occurs around 40 GPa [6,[16][17][18]. In fact, the E 2g optical phonon mode and the coupled elastic shear modulus C 44 were experimentally found to show an anomalous pressure-dependent behavior [19], but up to now this issue has not been clarified yet.…”

Section: Introductionmentioning

confidence: 99%

Anisotropic distortion and Lifshitz transition inα-Hf under pressure

et al. 2017

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In this work we report a theoretical investigation on behavior of the elastic constant C 44 and the transverse optical phonon mode E 2g of α-Hf under pressure within the density functional theory. In contrast to many other reported transition metals, the above two quantities do not show a synchronous relation as pressure increases. Below 13 GPa, an opposite shifting tendency has been observed. However, once the pressure is raised above 13 GPa, the trend is pulled back to be consistent. This anomalous behavior is figured out to be caused by the large lattice anisotropy of the c/a ratio along with the elastic anisotropy. The synchronous behavior is found to be in accordance with the behavior of c/a ratio with increased pressure. In our band-structure investigations the electronic topological transition has been discovered at 10 GPa, which relates to the change of c/a ratio suggested by recent literature. The presence of the Van Hove singularity shown in the densities of states has been identified and regarded as the origin of the variation of C 44 and E 2g .

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Full-potential calculations using the generalized-gradient corrections: structural properties of Ti, Zr and Hf under compression

Cited by 55 publications

References 27 publications

Elasticity behavior, phonon spectra, and the pressure–temperature phase diagram of HfTi alloy: A density-functional theory study

Elasticity behavior, phonon spectra, and the pressure–temperature phase diagram of HfTi alloy: A density-functional theory study

First-principles study of the solubility of Zr in Al

Anisotropic distortion and Lifshitz transition inα-Hf under pressure

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