Phonon instabilities in bcc Sc, Ti, La, and Hf

Persson, Kristin A.; Ekman, Mathias; Ozoliņš, Vidvuds

doi:10.1103/physrevb.61.11221

Cited by 60 publications

(43 citation statements)

References 35 publications

(28 reference statements)

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“…5. For Ti metal, the instability is relatively strong because C' is greatly negative in agreement with the result of a previous theoretical study [19]. However, small amounts of vanadium strongly increase C' and reduce the strength of the instability, in accordance with the behavior of the bcc phase line in the Ti-V alloy.…”

Section: Discussionsupporting

confidence: 79%

First-principles phase stability in the Ti-V alloy system

Söderlind

Landa

Yang

et al. 2013

Journal of Alloys and Compounds

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Phase stability in the transition metals are mostly dictated by the bonding of the d electrons and is believed to be fairly well understood from either a canonical-band picture or a tight-binding model. These models are related and capture the fact that as one proceeds through the nonmagnetic d-transition series one encounters the hexagonal closepacked (hcp), body-centered cubic (bcc), hcp, and face-centered cubic (fcc) phases. This structural sequence depends on the gradual filling of the d band (roughly one electron per atomic number increase) that is altered when magnetism is present simply due to the spin polarization of the d band. However, recent more careful experimental and theoretical studies have shown that the aforementioned appealing models do not entirely explain the bonding and phase stability in the transition metals. First, there is a destabilization of the bcc phase due to pressure in the Group Vb metals (V, Nb, and Ta) and second, a temperature-induced stabilization of the bcc phase in the Group IVb (Ti, Zr, and Hf) metals even though at low temperatures it is strongly unstable. Here we address the latter phenomenon and study the influence of alloying titanium with its next neighbor vanadium by applying the recently developed self-consistent ab initio lattice dynamics (SCAILD) approach that has heretofore never been utilized for an alloy system.

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Section: Discussionsupporting

confidence: 79%

First-principles phase stability in the Ti-V alloy system

Söderlind

Landa

Yang

et al. 2013

Journal of Alloys and Compounds

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“…The β to ω transformation occurs via plane collapse along the [111] direction corresponding to the longitudinal 2 3 [111] phonon. 12,13,14 More recently Trinkle et al determined the homogeneous pathway of the α to ω transformation. 15,16 A systematic approach generated all possible pathways that were then successively pruned by energy estimates using elastic theory, tight-binding (TB) methods and density-functional theory (DFT).…”

Section: Introductionmentioning

confidence: 99%

Classical potential describes martensitic phase transformations between theα,β, andωtitanium phases

Lenosky²,

et al. 2008

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A description of the martensitic transformations between the α, β and ω phases of titanium that includes nucleation and growth requires an accurate classical potential. Optimization of the parameters of a modified embedded atom potential to a database of density-functional calculations yields an accurate and transferable potential as verified by comparison to experimental and density functional data for phonons, surface and stacking fault energies and energy barriers for homogeneous martensitic transformations. Molecular dynamics simulations map out the pressure-temperature phase diagram of titanium. For this potential the martensitic phase transformation between α and β appears at ambient pressure and 1200 K, between α and ω at ambient conditions, between β and ω at 1200 K and pressures above 8 GPa, and the triple point occurs at 8GPa and 1200 K. Molecular dynamics explorations of the dynamics of the martensitic α − ω transformation show a fast-moving interface with a low interfacial energy of 30 meV/ Å2 . The potential is applicable to the study of defects and phase transformations of Ti.

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“…The body centered cubic (bcc) structure prevails as the simplest and best known example. Although a stable structure at low temperatures for several elements in the Periodic Table, bcc becomes unstable in the harmonic approximation [1,2,3] for the group IVB elements, for the rare-earth elements, for the actinides, and for several alkaline-earth elements. Nevertheless, at elevated temperatures the bcc structure emerges as the stable crystal structure for all these elements.…”

mentioning

confidence: 99%

Entropy Driven Stabilization of Energetically Unstable Crystal Structures Explained from First Principles Theory

et al. 2008

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Conventional methods to calculate the thermodynamics of crystals evaluate the harmonic phonon spectra and therefore do not work in frequent and important situations where the crystal structure is unstable in the harmonic approximation, such as the body-centered cubic (bcc) crystal structure when it appears as a high-temperature phase of many metals. A method for calculating temperature dependent phonon spectra self consistently from first principles has been developed to address this issue. The method combines concepts from Born's inter-atomic self-consistent phonon approach with first principles calculations of accurate inter-atomic forces in a super-cell. The method has been tested on the high temperature bcc phase of Ti, Zr and Hf, as representative examples, and is found to reproduce the observed high temperature phonon frequencies with good accuracy.Many elements, alloys, and compounds appear in crystal structures which should not be energetically stable. The inter-atomic interactions places these systems at energy saddle points on the potential surface for atomic positions corresponding to the lattice sites of these structures rather than minima for statically stable structures. The body centered cubic (bcc) structure prevails as the simplest and best known example. Although a stable structure at low temperatures for several elements in the Periodic Table, bcc becomes unstable in the harmonic approximation [1,2,3] for the group IVB elements, for the rare-earth elements, for the actinides, and for several alkaline-earth elements. Nevertheless, at elevated temperatures the bcc structure emerges as the stable crystal structure for all these elements. Zener considered this enigma long ago and proposed a possible explanation: the large vibrational entropy of the bcc crystal structure makes it thermodynamically favourable at finite temperatures [5]. Also, Grimvall et al [4] pointed out the importance of electronic entropy in the stabilization of the bcc crystal structure of the group IVB elements Ti and Zr.So far no satisfactory, quantitative explanation has been presented for this situation. Density functional theory (DFT) [6] forms the basis of contemporary microscopic solid state theory and allows, in principle, to calculate different properties of crystals completely ab initio, without any fitting parameters. In particular, phonon spectra in the harmonic approximation can be efficiently evaluated in this way [7]. However, for the bcc phases mentioned above the phonon spectra in the harmonic approximation reveal imaginary phonon frequencies of e.g. Zr [8,9] for some wave-vectors, which shows that the bcc phase is from a lattice dynamics point of view unstable (hence these elements are energetically unstable, and are referred to as dynamically unstable in the bcc phase). A straightforward calculation using DFT molecular dynamics (MD) [10] should in principle be able to reproduce the stability of the bcc phase for the above discussed elements, since MD implicitly include temperature effects. However, MD suffers...

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Phonon instabilities in bcc Sc, Ti, La, and Hf

Cited by 60 publications

References 35 publications

First-principles phase stability in the Ti-V alloy system

First-principles phase stability in the Ti-V alloy system

Classical potential describes martensitic phase transformations between theα,β, andωtitanium phases

Entropy Driven Stabilization of Energetically Unstable Crystal Structures Explained from First Principles Theory

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