Lattice dynamics of molybdenum and tungsten

Summary The lattice dynamics of molybdenum and tungsten has been re-examined within the framework of the transition metal model potential by incorporating the local-field correction to the dynamical matrix for phonon dispersion relation. It is observed that the local-field correction can be represented by an attractive short-range potential which tends to cancel or ?screen? the Born-Mayer repulsion. The numerical calculations for molybdenum and tungsten show that the local-field correction plays a significant role and leads to a better agreement between the theoretically computed phonon dispersion curves and the experimental data.     

On the lattice dynamics of AgGaS2

Summary The vibrational spectrum and one-phonon density of states of a chalcopyrite crystal AgGaS₂ are calculated in an extended Keating’s model with two-bond-stretching and one-bond-bending force constants. Three charges of ions and three force constants are determined by a least-square fitting to experimental frequencies of long-wave phonons taken from Raman-scattering experiments. The calculated constant-volume specific heat, Debye temperature and elastic constants, of AgGaS₂ are in agreement with the experimental data of other authors.     

A quantum field theory of lattice dynamics and melting in compounds

Summary A unified theory on the lattice dynamics and the melting in compounds is presented by taking into account the Coulomb interaction. The melting temperature is determined by the mean value of the eigenfrequencies of the atoms. The theory is applied to zincblende and rock salt structure crystals.

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Riassunto Si presenta una teoria unificata sulla dinamica dei reticoli e sulla fusione nei composti considerando l’interazione di Coulomb. La temperatura di fusione è determinata dal valore medio delle autofrequenze degli atomi. Si applica la teoria alla zinco-blenda e a cristalli con struttura del tipo di sali di rocca.

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Резюме Предлагается теория динамики решетки и плавления в химических соединениях, которя учитывает кулоновское взаимодействие. Температупа плавления определяется, как средияя величина собстенных чатстот атомов. Предложенная теория применяется к кристаллам со структурой цинковой обманки и кчменной соли.

     

Attractive short-range interatomic potential in the lattice dynamics of niobium and tantalum

Summary It is shown in the framework of the pseudopotential approach that there is a sizable attractive short-range component of the interatomic potential due to thes-d interaction which has the same functional form in real space as the Born-Mayer repulsion due to the overlap of core electron wave functions centred on neighbouring ions. The magnitude of this attractive component is such as to completely cancel the conventional Born-Mayer repulsion, making the resultant short-range interatomic potential attractive rather than repulsive. Numerical calculations show that the attractive interatomic potential, which represents the local-field correction, leads to a better understanding of the occurrence of the soft modes in the phonon dispersion curves of niobium and tantalum.

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Riassunto Si mostra, nell'ambito dell'approccio allo pseudopotenziale, che vi è una componente di considerevoli dimensioni attrattiva a corto raggio del potenziale interatomico, dovuta alla interaziones-d, che ha la stessa forma funzionale nello spazio reale della repulsione di Born-Mayer dovuta al sovrapporsi delle funzioni d'onda degli elettroni del nucleo centrate su ioni confinanti. L'ampiezza di questa componente attrattiva è tale da cancellare completamente la repulsione convenzionale di Born-Mayer, rendendo attrattivo, piuttosto che repulsivo, il risultante potenziale interatomico a corto raggio. I calcoli numerici mostrano che il potenziale attrattivo interatomico, che rappresenta la correzione del campo locale, porta ad una migliore comprensione della presenza dei modi molli nelle curve di dispersione dei fononi del niobio e del tantalio.

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Резюме В рамках псевдопотенциального подхода показывается, что заметный короткодействующий вклад в межатомный потенциал притяжения, обусловленныйs-d взаимодействием, имеет такую же функциональную форму в реальном пространстве, как отталкивание Борна-Майера, обусловленное перекрытием электронных волновых функций, центрированных на соседних ионах. Величина этой компоненты притяжения полностью компенсирует обычное отталкивание Борна-Майера, что приводит к результирующему короткодействующему межатомному потенциалу притяжения, а не отталкивания. Численные вычисления показывают, что межатомный потенциал притяжения, который представляет поправку локального поля, приводит к лучшему пониманию существования мягких мод в фононных дисперсионных кривых ниобия и тантала.

     

Temperature dependence of the phonon dynamics of CD4 in plastic phase

Summary We have investigated the phonon dynamics of CD₄ in its plastic phase at 22.0, 32.5 and 89.2 K using three-body rigid molecular model whose interaction system consists of van der Waals, three-body and overlap repulsive interactions. The anharmonic elastic constants, Grüneisen parameters and Debye temperatures have also been evaluated and found to follow a reasonable and systematic trend. The results on phonon dispersion curves from the models with and without three-body interaction (TBI) effects have been compared with their available experimental results. The overall agreements achieved from the model with TBI effects are better than those obtained from the model without TBI effects. These investigations have revealed that the three-body interactions play an important role in describing the phonon dispersion, anharmonic and thermal properties of CD₄ crystals.

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Riassunto Si è ricercata la dinamica dei fononi di CD₄ nella sua fase plastica a 22.0, 32.5 e 89.2 K usando un modello molecolare rigido a tre corpi il cui sistema d'interazione è costituito da interazioni di van der Waals, a tre corpi e repulsivi di sovrapposizione. Sono anche state calcolate le costanti elastiche anarmoniche, i parametri di Grüneisen e le temperature di Debye e si è trovato che essi seguono una tendenza ragionevole e sistematica. Sono stati paragonati i risultati sulle curve di dispersione dei fononi dai modelli con e senza gli effetti delle interazioni a tre corpi (TBI) con loro risultati sperimentali disponibili. Gli accordi complessivi ottenuti dal modello con gli effetti TBI sono migliori di quelli ottenuti dal modello senza tali effetti. Le ricerche hanno rivelato che le interazioni a tre corpi giocano un ruolo importante nel descrivere la dispersione dei fononi e le proprietà termiche e anarmoniche dei cristalli di CD₄.

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Резюме Мы исследуем динамику фононов для CD₄ в пластической фазе при 22.0, 32.5 и 89.2 K, используя трех-частичную модель жестких молекул, в которой система взаимодействий состоит из взаимодействия ван дер Ваальса, трех-частичного взаимодействия и перекрывающегося взаимодействия отталкивания. Вычисляются ангармонические упругие постоянные, параметры Грюнайзена и температуры Дебая. Результаты для фононных дисперсионных кривых из моделейси без эффектов трех-частичных взаимодействий сравниваются с имеющимися экопериментальными данными. Согласие модельных результатов с эффектами трех-частичных оказываются лучше, чем согласие результатов без учета эффектов трех-частичных взаимодействий. Проведенные исследования показывают, что трех-частичные взаимодействия играют важную роль в описании дисперсии фононов, ангармонических и тепловых свойств кристаллов CD₄.

     

Role of nonpair forces in the lattice dynamics of h.c.p. metals

Summary An analysis of the role of the nonpair forces in the lattice dynamics of s.p. bonded h.c.p. metalsviz. Mg and Zn has been presented. The total energy has been extended up to third order in the electron-ion pseudopotential. The dynamical matrix contains the terms arising from central pairwise interactions between the ions as well as contributions due to sums of nonpair three-body forces. Such forces, arising from the inclusion of third-order terms, are of short-range nature and possess the character of tensor forces. It is concluded that the nonpair three-body interaction is necessary for explaining the lattice dynamics of h.c.p. metals. The theoretical dispersion curves are compared with the experimental data. Good agreement is found between the computed and experimental results along the symmetry directions.

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Riassunto Si è presentata un’analisi del ruolo delle forze non appaiate nella dinamica reticolare di metalli h.c.p. limitati da s.p. rispetto a Mg e Zn. L’energia totale è stata estesa fino al terz’ordine nel potenziale elettrone-ione. La matrice dinamica contiene termini che originano da interazioni del tipo a coppie tra ioni cosiccome contributi dovuti a somme di forze a tre corpi non accoppiati. Tali forze, che derivano dall’inclusione di termini di terz’ordine, sono del tipo a corto raggio e possiedono le caratteristiche di forze tensoriali. Si conclude che l’interazione a tre corpi non appaiata è necessaria per spiegare la dinamica reticolare di metalli h.c.p. Le curve teoriche di dispersione sono confrontate coi dati sperimentali. Si è trovato un buon accordo tra i risultati teorici e sperimentali lungo le direzioni di simmetria.

     

Mössbauer spectroscopy,intracluster atomic mobility and thermodynamics of ultrafine oxide clusters

Summary Dynamic properties of ultrafine clusters of γ-Fe₂O₃ (ferric oxide, FO) were studied by M?ssbauer spectroscopy and by thermodynamic analysis. The data obtained for FO clusters allowed the conclusion that dynamic properties of clusters as well as the decrease of melting point and the appearance of a gap between freezing and melting points depend on intracluster atomic mobility. Intracluster atomic mobility in FO clusters was shown to increase by the action of surfactants which decrease intercluster interactions. The increase in intracluster atomic mobility was suggested to proceed via formation of a solid-liquid state. Paper presented at ICAME-95, Rimini, 10–16 September 1995.     

Phonon anomalies in Co−Ni alloys

Summary A detailed experimental analysis of the inelastic crosssection along the [111]-direction in Co−Ni alloys is presented. Using a simple model and studying the cross-section as a function of both composition and temperature, it is shown that interesting information about the h.c.p.-f.c.c. transition can be gained in these alloys.

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Riassunto Nel presente lavoro si describe un’analisi sperimentale dettagliata della sezione d’urto anelastica dei neutroni lungo la direzione [111] in leghe Co−Ni. Impiegando un modello relativamente semplice e studiando la sezione d’urto in funzione di temperatura e concentrazione, si mostra che si possono ottenere utili informazioni riguardanti la transizione h.c.p.-f.c.c.

     

Nuclear-resonance beamline at ESRF

Summary The Nuclear-Resonance Beamline at ESRF is dedicated to the excitation of nuclear levels by synchrotron radiation. The source of radiation and optical elements are optimized to provide an intense, highly monochromatic, collimated and stable X-ray beam of small cross-section at the M?ssbauer transition energies between 6 keV and 30 keV. The set-up of the beamline allows to perform studies in diffraction, small-angle scattering, forward scattering and incoherent scattering. Equipment is available to maintain the sample at variable temperature and magnetic field. Fast detectors and timing electronics serve to separate the delayed nuclear scattering from the ?prompt? electronic scattering and to measure the time spectra of nuclear radiation with sub-nanosecond resolution. The general layout and the parameters of the beamline are reported. Typical domains of applications are discussed and illustrated by first experimental results. Paper presented at ICAME-95, Rimini, 10–16 September 1995.     

Correlated squeezed-state approach for the ground state of strongly correlated electrons coupled to local Holstein phonons

Summary In the present work we have applied the correlated squeezed-state approach to investigate the ground state of the extended Hubbard model which is coupled to local Holstein phonons. Our study begins with decoupling the electron and phonon subsystems approximately by introducing a variational correlated squeezed-state ansatz for the phonons. Then assuming the renormalized intersite electron correlation of the effective electronic Hamiltonian to be attractive and the renormalized on-site correlation repulsive, we have applied the generalized Hartree-Fock approximation to obtain the ground state of the system, which is a superconducting state with intersite pairing. With optimal values of the variational parameters the correlated squeezed-state approach will by construction yield a ground-state energy lower than those obtained in previous studies. This means that our variational ansatz is more stable as the ground state of the system. Furthermore, our variational study shows that in the correlated squeezed state the polaronic reduction effect of phonons is much more alleviated, and thus the mass enhancement inherent to the polaron effect is noticeably weakened. This weakening of the reduction effect should, in turn, significantly affect other physical properties of the system.     

Study of the Yu-Anderson model for the electron-local phonon interaction in terms of instantons

Summary The Yu and Anderson model in which a single harmonic oscillator interacts strongly with an electron gas is discussed in terms of instantonlike classical paths of the oscillator in the double-well effective potential provided by the electrons. Fluctuations around the instanton are carefully analysed and, using the Faddeev-Popov technique, the partition function of the system is expressed in terms of that of a classical gas of instantons, which is of the same form as suggested by Yu and Anderson.

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Riassunto Il modello di Yu e Anderson, in cui si considera un singolo oscillatore armonico interagente in modo intenso con un gas di elettroni, si discute in termini di cammini classici di tipo istantonico dell'oscillatore nel potenziale a doppia buca fornito dagli elettroni. Si analizzano in dettaglio le fluttuazioni attorno all'istantone e, usando la tecnica di Faddeev-Popov, la funzione di ripartizione del sistema si esprime in termini di quella di un gas classico d'istantoni, che è della stessa forma suggerita da Yu e Anderson.

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Резюме Модель Ю и Андерсона, в которой отдельный гармонический осциллятор сильно взаимодействует с электронным газом, обсуждается в рамках классического инстантонного подхода для осциллятрова в эффективном потенциале в виде двойной ямы, образованном электронами. Подробно аналиэируются флуктуации около инстантона. Используя технику Фаддеева-Попова, функция распределения системы выражается через функций распределения для классического газа инстантонов, которая имеет тот же вид, как предлагалось Ю и Андерсоном.

     

Ab initio lattice dynamics and elastic constants of ZrC

Ab initio calculations and a direct method are applied to derive the phonon dispersion relations and phonon density of states for the ZrC crystal. The results are in good agreement with neutron scattering data. The force constants are determined from the Hellmann-Feynman forces induced by atomic displacements in a 222 supercell. The elastic constants are found using the deformation method and successfully compare with experimental data. Received 2 July 1999 and Received in final form 26 November 1999     

TiC lattice dynamics from ab initio calculations

Ab initio calculations and a direct method have been applied to derive the phonon dispersion curves and phonon density of states for the TiC crystal. The results are compared and found to be in a good agreement with the experimental neutron scattering data. The force constants have been determined from the Hellmann-Feynman forces induced by atomic displacements in a supercell. The calculated phonon density of states suggests that vibrations of Ti atoms form acoustic branches, whereas the motion of C atoms is confined to optic branches. The elastic constants have been found using the deformation method and compared with the results obtained from acoustic phonon slopes. Received 23 February 1998     

A first principles lattice dynamics and Raman spectra of the ferroelastic rutile to CaCl2 phase transition in SnO2 at high pressure

A first principles calculation of the lattice dynamical properties of rutile SnO₂ has been performed using density functional perturbation theory at ambient and high‐pressure conditions to understand the pressure‐induced phase transition. The calculated zone centre phonon modes at ambient and high pressures have been compared with Raman scattering and infrared measurements. Full phonon dispersion curves and phonon densities of states and Raman intensities at high pressures are calculated and given for the first time in literature. The ferroelastic transition from the rutile to the CaCl₂‐type structure was confirmed. It is clearly illustrated that the first transition is associated with macroscopic shear instability which arises from the strong coupling between elastic constants and softening of Raman active B_1g mode. The observed pressure of phase transition in experimental measurements was reproduced more accurately than in previous calculations, and the difference between observed and calculated transition pressure is only of the order of 2%. The mode Grüneisen parameter is quantitatively as well as qualitatively different from the earlier reported values. Copyright © 2013 John Wiley & Sons, Ltd.     

Lattice dynamics of ferromagnetic superconductor UGe2

This paper reports the lattice dynamical study of the UGe₂ using a lattice dynamical model theory based on pairwise interactions under the framework of the shell model. The calculated phonon dispersion curves and phonon density of states are in good agreement with the measured data.      

IrTi合金晶格动力学的第一性原理研究

利用密度泛函理论的平面波赝势方法研究了IrTi合金的晶格动力学行为. 声子谱计算表明四方(L1₀)结构动力学不稳定,通过冷冻不稳定声子模式, 发现IrTi会发生从四方(L1₀)到正交的结构相变.进一步分析软模对应的原子振动, 得到了具有正交对称性,空间群为Cmmm,相对于四方(L1₀)相能量更低、更稳定的结构. 这种正交新相(Cmmm)弹性稳定和动力学稳定,而且其结构参数与实验上观察到的低温结构有限的晶格参数相符合,表明IrTi合金的低温相是正交结构(Cmmm). 从理论上肯定了IrTi合金立方到四方再到正交的相变机制, 解决了实验上关于相变机制和低温相结构形式的争议.     

Acoustic wavefront imaging

We introduce a new class of experiments which provide graphic insights into the propagation of acoustic waves in anisotropic media. Simply stated, we have devised a means of observing the expanding acoustic wavefront from a point disturbance in a solid. The data may be viewed as a movie or a series of snapshots. The observed wavefronts represent the group-velocity surfaces of acoustic waves, which reflect the basic elastic anisotropy of the solid. The technique has been applied to coherent acoustic waves with frequencies in the megahertz range (at ambient temperatures) and to incoherent heat pulses in the hundred-gigahertz range (at liquid-helium temperatures). In this article, we first provide a pedagogical introduction to wave propagation in elastically anisotropic media, reviewing some early methods for visualizing acoustic waves. Next, we describe the “acoustic wavefront imaging” method and give representative results in crystals and composite materials. Finally, we show how this method relates to recent advances in phonon imaging and internal diffraction of ultrasound.