Lattice Dynamics of Beryllium

Schmunk, R.E.; Brugger, R.M.; Randolph, P. D.; Strong, K. A.

doi:10.1103/physrev.128.562

Cited by 85 publications

(7 citation statements)

References 12 publications

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“…The phonon dispersion relationship predicted using this method, Fig. 3, demonstrates reasonable agreement with the phonons measured using neutron scattering [20,21]. At 300 K the impact of anharmonic forces in beryllium is expected to be small [22].…”

Section: Beryllium Phonon Dossupporting

confidence: 67%

Thermal neutron scattering law calculations using ab initio molecular dynamics

Wormald

Hawari

2017

EPJ Web Conf.

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Abstract. In recent years, methods for the calculation of the thermal scattering law (i.e. S(α, β), where α and β are dimensionless momentum and energy transfer variables, respectively) were developed based on ab initio lattice dynamics (AILD) and/or classical molecular dynamics (CMD). While these methods are now mature and efficient, further advancement in the application of such atomistic techniques is possible using ab initio molecular dynamics (AIMD) methods. In this case, temperature effects are inherently included in the calculation, e.g. phonon density of states (DOS), while using ab initio force fields that eliminate the need for parameterized semi-empirical force fields. In this work, AIMD simulations were performed to predict the phonon spectra as a function of temperature for beryllium and graphite, which are representative nuclear reactor moderator and reflector materials. Subsequently, the calculated phonon spectra were utilized to predict S(α, β) using the LEAPR module of the NJOY code. The AIMD models of beryllium and graphite were 5 × 5 × 5 crystal unit cells (250 atoms and 500 atoms respectively). Electronic structure calculations for the prediction of Hellman-Feynman forces were performed using density functional theory with a GGA exchange correlation functional and corresponding core electron pseudopotentials. AIMD simulations of 1000-10,000 time-steps were performed with the canonical ensemble (NVT thermostat) for several temperatures between 300 K and 900 K. The phonon DOS were calculated as the power spectrum of the AIMD predicted velocity autocorrelation functions. The resulting AIMD phonon DOS and corresponding inelastic thermal neutron scattering cross sections at 300 K, where anharmonic effects are expected to be small, were found to be in reasonable agreement with the results generated using traditional AILD. This illustrated the validity of the AIMD approach. However, since the impact of the temperature on the phonon DOS (e.g. broadening of spectral peaks) was observed in AIMD analysis, this technique may be envisioned as the approach for deriving the needed atomistic data for thermal scattering law calculations under realistic temperature and structural conditions for a given material.

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Section: Beryllium Phonon Dossupporting

confidence: 67%

Thermal neutron scattering law calculations using ab initio molecular dynamics

Wormald

Hawari

2017

EPJ Web Conf.

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“…For the three h.c.p. metals which are under examination, namely Be, Mg, and Zn, dispersion relations were measured a t 300 O K bySchmunk et al [12], Iyengar et al [13], Borgonovi et al [14], respectively. Starting from these experimental data and using the Raubenheimer-Gilat computer program the lattice dynamics can be completely specified at a temperature of 300 OK.…”

Section: Calculations and Resultsmentioning

confidence: 99%

Resistivity of Solid Be, Mg, and Zn

Borchi

Gennaro

Tasselli

1971

Physica Status Solidi (b)

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A theoretical study is made of the resistivities of the solid h.c.p. metals Be, Mg, and Zn. Information about the lattice dynamics is derived from inelastic neutron scattering using a slight modification of the Gilat-Raubenheimer computer program for calculating the frequency distribution functions. Empirical and Heine-Animalu pseudopotentials are used to calculate the electron-phonon coupling. Umklapp processes are explicitly evaluated. Good agreement is obtained with experimental data except in the low-temperature region.Es wird uber eine theoretische Studie des spezifischen Widerstandes der festen h.k.p.Metalle Be, Mg und Zn beriohtet. Informationen uber die Gitter-Dynamik wurden, mittels einer geringen Modifizierung des Gilat-Raubenheimer Computerprogrammes zur Berechnung der E'requenzverteilungsfunktionen, aus unelastischer Neutronenstreuung erhalten. Empirische Pseudopotentiale und die Pseudopotentiale von Heine und Animalu wurden zur Berechnung der Elektron-Phonon-Wechselwirkung benutzt. Umklappprozesse wurden ausfuhrlich berechnet. Mit experimentellen Daten wird gute ubereinstimmung gefunden, ausgenommen der Bereich geringer Temperaturen.

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“…To figure out the relative weights of the branches, the inelastic structure factor can be calculated in a number of ͑approxi-mate͒ ways, as in Ref. 27 for beryllium, another hcp solid. By virtue of the strongly geometrical nature of g 2 ͑Q ͉ j͒, it is sufficient to look at one of these approximate calculations performed for the hcp geometry to realize that, with few exceptions, the relative weights do generally suppress one mode and privilege the other.…”

Section: Longitudinal Modesmentioning

confidence: 99%

Zero-temperature dynamics of solidH4efrom quantum Monte Carlo simulations

2009

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The lattice dynamics of hcp crystalline 4 He is studied at zero temperature and for two different densities ͑near and far from melting͒, using a ground-state path-integral quantum Monte Carlo technique. The complete phonon dispersion is obtained, with particular attention to the separation of optic and acoustic branches and to the identification of transverse modes. Our study also sheds light on the residual coherence affecting quasiparticle excitations in the intermediate momentum region, in between the phonon and nearly free-particle regimes.The lattice dynamics of solid 4 He has long been considered a major challenge to ab initio calculations, due to the strong anharmonicity of this highly quantum solid. Many calculations have been performed within the self-consistent phonon ͑SCP͒ approximation, 1,2 which however may be rather unsatisfactory, due to the magnitude of anharmonic effects. A significant improvement has been made possible by the application of a variational quantum Monte Carlo ͑QMC͒ approach, based on the shadow wave function formalism, to bcc 3 He ͑Ref. 3͒ and to hcp 4 He. 4 The variational nature of this approach, however, makes it not fully suitable at high energy where optical or zone-boundary longitudinal excitations exhibit broad multiphonon features. In this spectral regime, the calculation of the full dynamic structure factor is therefore in order. QMC techniques based on path integrals allow quite naturally for the calculation of imaginarytime correlation functions from which various spectral functions, such as the dynamic structure factor, can be obtained upon analytical continuation. This technique has been successfully demonstrated for superfluid 4 He, 5,6 as well as for the bcc crystalline phases of 4 He ͑Refs. 7 and 8͒ and 3 He. 9 In the latter studies the spectrum of the transverse excitations has also been obtained, albeit in the one-phonon approximation only. 2 In this work we present an extensive study of the dynamical properties of hcp 4 He at zero temperature, performed by estimating the dynamic structure factor from ground-state path-integral simulations. 6,10,11 This technique allows us to parallel to some extent the procedure followed experimentally to map phonon dispersions from the measured neutron scattering. In the long-wavelength region-well approximated by a phonon picture of the collective density excitations-we thus obtain longitudinal as well as transverse modes for both acoustic and optical branches. For higher wave-vectors we analyze the dynamic structure factor in terms of corrections to the so-called impulse approximation, 12 finding a coherent response which is peculiar of both superfluid and solid helium.In Sec. I we give an introductory account of the phonon theory of long-wavelength excitations in solids. In Sec. II the reader is provided with an outline of the numerical methods adopted in this work. In Sec. III we report on the analysis of our QMC results both in the phonon regime and in the intermediate momentum region. Sec. IV is finally devoted to a few c...

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Lattice Dynamics of Beryllium

Cited by 85 publications

References 12 publications

Thermal neutron scattering law calculations using ab initio molecular dynamics

Thermal neutron scattering law calculations using ab initio molecular dynamics

Resistivity of Solid Be, Mg, and Zn

Zero-temperature dynamics of solidH4efrom quantum Monte Carlo simulations

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