Lattice dynamics of hcp Ti

Stassis, C.; Arch, D.K.; Harmon, B. N.; Wakabayashi, N.

doi:10.1103/physrevb.19.181

Cited by 73 publications

(32 citation statements)

References 15 publications

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“…Reduced 39,42 For the α phase the MEAM potential accurately reproduces the low energy acoustic branches reflecting the elastic constants. For optical and high-energy acoustic branches the potential reproduces the experimental phonon frequencies within 25%, generally underestimating the experimental values.…”

Section: Meam Potential Fitmentioning

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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Section: Meam Potential Fitmentioning

confidence: 99%

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

Lenosky²,

et al. 2008

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“…In the few cases tested to date, this approach seems to work well. Eriksson, Wills and Wallace [334] used neutron scattering phonon measurements at elevated temperatures by Stassis, Petry, Heiming, and co-workers [337,338,339,340] on bcc and hcp Ti, and bcc and hcp Zr to calculate the total phonon entropy at temperature (using Eq. 14).…”

Section: Anharmonicity and Heat Capacitymentioning

confidence: 99%

Vibrational thermodynamics of materials

Fultz¹

2010

Progress in Materials Science

558

428

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Abstract. The literature on vibrational thermodynamics of materials is reviewed. The emphasis is on metals and alloys, especially on the progress over the last decade in understanding differences in the vibrational entropy of different alloy phases and phase transformations. Some results on carbides, nitrides, oxides, hydrides and lithium-storage materials are also covered.Principles of harmonic phonons in alloys are organized into thermodynamic models for unmixing and ordering transformations on an Ising lattice, and extended for non-harmonic potentials. Owing to the high accuracy required for the phonon frequencies, quantitative predictions of vibrational entropy with analytical models prove elusive. Accurate tools for such calculations or measurements were challenging for many years, but are more accessible today. Ab-initio methods for calculating phonons in solids are summarized. The experimental techniques of calorimetry, inelastic neutron scattering, and inelastic x-ray scattering are explained with enough detail to show the issues of using these methods for investigations of vibrational thermodynamics. The explanations extend to methods of data analysis that affect the accuracy of thermodynamic information.It is sometimes possible to identify the structural and chemical origins of the differences in vibrational entropy of materials, and the number of these assessments is growing. There has been considerable progress in our understanding of the vibrational entropy of mixing in solid solutions, compound formation from pure elements, chemical unmixing of alloys, order-disorder transformations, and martensitic transformations. Systematic trends are available for some of these phase transformations, although more examples are needed, and many results are less reliable at high temperatures. Nanostructures in materials can alter sufficiently the vibrational dynamics to affect thermodynamic stability. Internal stresses in polycrystals of anisotropic materials also contribute to the heat capacity. Lanthanides and actinides show a complex interplay of vibrational, electronic, and magnetic entropy, even at low temperatures.A "quasiharmonic model" is often used to extend the systematics of harmonic phonons to high temperatures by accounting for the effects of thermal expansion against a bulk modulus. Non-harmonic effects beyond the quasiharmonic approximation originate from the interactions of thermally-excited phonons with other phonons, or with the interactions of phonons with electronic excitations. In the classical high temperature limit, the adiabatic electron-phonon coupling can have a surprisingly large effect in metals when temperature causes significant changes in the electron density near the Fermi level. There are useful similarities in how temperature, pressure, and composition alter the conduction electron screening and the interatomic force constants. Phononphonon "anharmonic" interactions arise from those non-harmonic parts of the interatomic potential that cannot be accounted for by the quasiharmonic ...

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“…5. Дисперсійні криві для спектру частот (  /2) власних коливань -Ti при температурі 295 К: а -хвильовий вектор k  (a/4)k x , напрямлений вздовж осі x, що лежить в базисній площині; б -хвильовий вектор k  (c/2)k z , напрямлений вздовж осі z, що перпендикулярна базисній пло-щині (суцільні лінії -розрахунок з врахуванням ефектів ангармонізму та нецентральних сил взаємодії, точки -експериментальні дані [135]). …”

Section: температурна залежність фононного спектру титануunclassified

“…Температурна залежність спектру частот -Ti, коли хвильовий век-тор k  (c/2)k z , напрямлений вздовж осі z, що перпендикулярна базисній площині (суцільні лінії -розрахунок з врахуванням ефектів ангармоніз-му та нецентральних сил взаємодії, точки -дані роботи [135]). …”

Section: температурна залежність фононного спектру титануunclassified

“…Отже, внесок до частоти поперечних коливань, пов'язаний з нецентральними силами міжатомової взаємодії пере-важає внесок, пов'язаний з ефектами ангармонізму. На рисунку 5 зображено дисперсійні криві частот власних коли-вань -Ti з врахуванням ефектів ангармонізму та нецентральних сил взаємодії між атомами кристалічної ґратниці у порівнянні з ек-спериментальними даними, одержаними за допомогою техніки не-пружнього невтронного розсіяння [135]. Наявність щілини між ві-дповідними акустичними і оптичними гілками коливань в симет-рійному напрямку вздовж осі x (рис.…”

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Influence of an Anharmonicity and Electron–Phonon Interaction on a Frequency Spectrum of Crystals with the Hexagonal Close-Packed Lattice

2011

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В огляді розглянуто основні методи опису енергетичного спектру електро-нів та спектру частот коливань атомів кристалічної ґратниці. Зроблено огляд основних метод дослідження впливу ефектів ангармонізму на фізич-ні властивості матеріялів та спектер частот коливань кристалічної ґратни-ці. Описано самоузгоджене гармонічне наближення, що базується на мето-ді двочасових Ґрінових функцій. В рамках цього наближення записано рі-внання руху для Ґрінових функцій «зміщення-зміщення», яке схоже на рівнання руху в гармонічному наближенні, але силові постійні будуть пе-ренормованими і визначаться термодинамічним усередненням других по-хідних потенціялу, а не їх рівноважним значенням. Досліджено вплив ефектів ангармонізму та електронної підсистеми на спектер частот криста-лічної ґратниці гексагонального щільнопакованого кристалу Ti 0,93 Al 0,07 .In a given review, the basic methods for description of the energy spectrum of electrons and the frequency spectrum of atomic vibrations of the crystal lattice are considered. The basic methods for investigation of influence of the anharmonicity effects on the physical properties of materials and a frequency spectrum of vibrations of the crystal lattice are reviewed. The self-consistent harmonic approximation, which is based on the method of double-time Green's functions, are described. Within the scope of this approximation, the equation of motion for the 'displacements-displacements' Green's functions, which is similar to the equation of motion in the harmonic approximation, is derived, but the force constants are renormalized and are determined by the thermodynamical averaging of second derivatives of potential rather than their equilibrium values. Appearances of the anharmonicity effects in the vibrational spectrum of the Ti 0.93 Al 0.07 hexagonal close-packed crystal lattice Успехи физ. мет. / Usp. Fiz. Met. 2011, т. 12, сс. 389-450 Îòòèñêè äîñòóïíû íåïîñðåäñòâåííî îò èçäàòåëÿ Ôîòîêîïèðîâàíèå ðàçðåøåíî òîëüêî â ñîîòâåòñòâèè ñ ëèöåíçèåé 2011 ÈÌÔ (Èíñòèòóò ìåòàëëîôèçèêè èì. Ã. Â. Êóðäþìîâà ÍÀÍ Óêðàèíû) Íàïå÷àòàíî â Óêðàèíå.

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Lattice dynamics of hcp Ti

Cited by 73 publications

References 15 publications

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

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

Vibrational thermodynamics of materials

Influence of an Anharmonicity and Electron–Phonon Interaction on a Frequency Spectrum of Crystals with the Hexagonal Close-Packed Lattice

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