hcp-bcc structural phase transformation of titanium: Analytic model calculations

Masuda‐Jindo, K.; Nishitani, Shigeto R.; Hùng, Vũ Văn

doi:10.1103/physrevb.70.184122

Cited by 65 publications

(73 citation statements)

References 32 publications

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“…Information based on this approximation has ruled out that the bcc phase of pure Fe is stable in the inner core (10,11), on the assumption that the anharmonic contribution is not enough to make up for the free energy difference between the bcc and hcp phase. However, for many transition metals it is shown that the phonon-phonon coupling stabilizes the high-temperature bcc phase over the hcp phase, due to a large entropy relative to other lattice configurations (12)(13)(14).…”

mentioning

confidence: 99%

Dynamical stability of body center cubic iron at the Earth’s core conditions

Luo

Johansson

Eriksson

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

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Here, using self-consistent ab initio lattice dynamical calculations that go beyond the quasiharmonic approximation, we show that the high-pressure high-temperature bcc-Fe phase is dynamically stable. In this treatment the temperature-dependent phonon spectra are derived by exciting all the lattice vibrations, in which the phonon-phonon interactions are considered. The high-pressure and high-temperature bcc-Fe phase shows standard bcc-type phonon dispersion curves except for the transverse branch, which is overdamped along the high symmetry direction Γ-N, at temperatures below 4,500 K. When lowering the temperature down to a critical value T C , the lattice instability of the bcc structure is reached. The pressure dependence of this critical temperature is studied at conditions relevant for the Earth's core.ab initio | anharmonic lattice dynamics | high pressure and high temperature | inner core

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mentioning

confidence: 99%

Dynamical stability of body center cubic iron at the Earth’s core conditions

Luo

Johansson

Eriksson

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

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“…In Eqs. [2], [6], and [7], the site indices i for the parameters k, g 1 , and g 2 are omitted because each atomic site is equivalent when dealing with a monoatomic cubic crystal with primitive structure. The relationship between the isothermal and adiabatic compressibilities, x T and x s , is simply given by…”

Section: Theorymentioning

confidence: 99%

“…[1,2] However, they have been calculated so far extensively by using the molecular dynamics methods or the Monte Carlo simulations. [3,4] It is the purpose of the present article to study the thermodynamic quantities of metals and alloys using the moment method in the quantum statistical mechanics, hereafter referred to as the statistical moment method (SMM).…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic properties and phase diagram by the statistical moment and cluster variation methods: Application to pure metals and Ta-W alloys

Masuda‐Jindo

Hùng

Turchi

2006

Metall Mater Trans A

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The thermodynamic quantities of metals and alloys are studied using the moment method in the quantum statistical mechanics, going beyond the quasi-harmonic (QH) approximations. Including the power moments of the atomic displacements up to the fourth order, the free energies and the related thermodynamic quantities are derived explicitly in closed analytic forms. The configurational entropy term is taken into account by coupling the moment expansion scheme with the cluster variation method (CVM). The energetics of the binary (TaW) alloys are treated within the framework of the firstprinciples tight-binding linear muffin-tin orbital (TB-LMTO) method coupled to the coherent potential approximation (CPA) and generalized perturbation method (GPM). The equilibrium phase diagrams are calculated for the refractory Ta-W bcc alloys. I. INTRODUCTIONTHE explicit analytic calculations of the thermodynamic quantities of metals and alloys are of great importance for the fundamental understanding of phase stabilities and phase transitions and also for the purpose of materials (alloy) designs. [1,2] However, they have been calculated so far extensively by using the molecular dynamics methods or the Monte Carlo simulations. [3,4] It is the purpose of the present article to study the thermodynamic quantities of metals and alloys using the moment method in the quantum statistical mechanics, hereafter referred to as the statistical moment method (SMM). [5,6] We first derive the Helmholtz free energy formula, C 5 E À TS, of metals and alloys using the fourth-order moment approximation, and then calculate the thermodynamic quantities, i.e., thermal lattice expansions, root-mean-square atomic displacements, specific heats, Grüneisen constants, elastic moduli, and melting temperatures. The application calculations using the SMM are performed for ordinary cubic metals and for the bcc alloys. Recently, much attention has been paid to alloy systems made of refractory metals of columns VB and VIB of the Periodic Table [7,8] and, in particular, Nb, Mo, Ta, and W, which display high melting temperature space and nuclear applications. In view of this, we calculate the equilibrium phase diagram of Ta-W alloys including the effects of thermal lattice vibrations. II. THEORYWe derive the thermodynamic quantities of metals and alloys, taking into account the higher order (fourth-order) anharmonic contributions in the thermal lattice vibrations going beyond the quasi-harmonic (QH) approximation. The basic equations for obtaining thermodynamic quantities are derived in the following manner: The equilibrium thermal lattice expansions are calculated by the force balance criterion and then the thermodynamic quantities are determined for the equilibrium lattice spacings. The anharmonic contributions to the thermodynamic quantities are given explicitly in terms of the power moments of the thermal atomic displacements.We consider a quantum system, which is influenced by supplemental forces a i in the space of the generalized coordinates q i . [5,6] The Hami...

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“…Here, it is noted that the analytic expressions of the free energies [7][8][9][10][11][12][13][14] directly allow us to evaluate the hydrostatic pressure P. From the limiting condition of the absolute stability for the crystalline phase,…”

Section: Equation Of States and Melting Temperatures By Smmmentioning

confidence: 99%

“…High pressure behaviour of materials is also of great interest from the viewpoints of geophysics [5] as well as of solid state sciences and technologies, e.g., in relation to the residual stresses in solid-state devices [6]. It is the purpose of the present paper to study the pressure dependence of the melting temperatures of metals and semiconductors on the basis of the statistical moment method (SMM) [7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Equation of states and melting temperatures of diamond cubic and zincblende semiconductors: pressure dependence

Hùng¹,

Masuda‐Jindo

Hanh³

et al. 2008

J. Phys.: Conf. Ser.

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Abstract:The pressure dependence of the melting temperatures of tetrahedrally coordinated semiconductors are studied using the equation of states derived from the statistical moment method, in comparison with those of the normal metals. Using the general expressions of the limiting temperatures m T , we calculate the "melting" temperatures of the semiconductor crystals and normal metals as a function of the hydrostatic pressure. The physical origins for the inverse pressure dependence of m T observed for tetrahedrally coordinated semiconductors are also discussed.

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hcp-bcc structural phase transformation of titanium: Analytic model calculations

Cited by 65 publications

References 32 publications

Dynamical stability of body center cubic iron at the Earth’s core conditions

Dynamical stability of body center cubic iron at the Earth’s core conditions

Thermodynamic properties and phase diagram by the statistical moment and cluster variation methods: Application to pure metals and Ta-W alloys

Equation of states and melting temperatures of diamond cubic and zincblende semiconductors: pressure dependence

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