Crystal Dynamics of Sodium at 90°K

Woods, A. D. B.; Brockhouse, B. N.; March, R.; Stewart, Andrew; Bowers, R.

doi:10.1103/physrev.128.1112

Cited by 325 publications

(50 citation statements)

References 12 publications

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“…2. An overall satisfactory agreement between the theory and experiment [69] can be noticed from the dispersion curves. Here, the Taylor [65] dielectric function has reproduced the best results among all screening functions that we have considered.…”

Section: Sodium (Na)supporting

confidence: 70%

“…In order to achieve better accuracy at the smaller values of q, the real-space sum of D(q) was performed for 30 nearest neighbours. The radial (Rl) and tangential (Τl) force constants calculated for Li, Na, K, Rb, and Cs, and further used in the computation of phonon frequencies, are tabulated in Table II. In addition to experimental studies [11, [68][69][70][71] the phonon dispersion in the alkali metals have been the subject of several theoretical discussion also [3-10, 12-56] based on pseudopotential theory. The detailed account about the PDC of bcc alkali metals studied here is as below.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

On Phonon Dispersion in Alkali Metals

Gajjar¹,

Thakore²,

Patel³

et al. 1995

Acta Phys. Pol. A

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In the present paper, the calculatioii of the phonon dispersioii relations for alkali metals to second order in a local pseudopotential is discussed in terms of the real-space sum. Dicherent forms of dielectric functions are employed to judge the varying echects of exchange and correlation on the phonon frequencies. The quantitative agreement of phonon frequencies for the alkali metals reflects, satisfactorily, the experimental trend.

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Section: Sodium (Na)supporting

confidence: 70%

Section: Resultsmentioning

confidence: 99%

On Phonon Dispersion in Alkali Metals

Gajjar¹,

Thakore²,

Patel³

et al. 1995

Acta Phys. Pol. A

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“…2 (polycrystal, squares; liquid, circles) for two selected q values. The comparison is carried out within the quasi-harmonic approximation, i.e., assuming that frequencies simply scale with density, a scheme that works well for sodium (22,23). Discarding the elastic line, obviously different due to the presence of the structural relaxation in the liquid, the spectra look similar, though those of the liquid are clearly broader.…”

Section: Resultsmentioning

confidence: 99%

“…3 reports the dispersion curves for the longitudinal and transverse excitations for both the polycrystal (squares) and the liquid (circles). The phonon branches measured on a sodium single crystal at 90 K along the main symmetry directions (22) are shown as well. All the energy values are rescaled to the density of the polycrystal at room temperature and are reported in reduced zone units, q∕q 0 , where q 0 corresponds to the first diffraction peak for the liquid (2.02 Å −1 ) and for the crystal ([110] Bragg peak) (24).…”

Section: Resultsmentioning

confidence: 99%

Fingerprints of order and disorder on the high-frequency dynamics of liquids

Giordano

Monaco

2010

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

120

133

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It is largely accepted that liquids are characterized by a short-range order usually corresponding to that of the solid phase at the same density. It is less clear to what extent dynamic properties of liquids and crystals can be compared. In particular, high-frequency collective excitations reminiscent of phonons in solids exist as well in liquids. They are however traditionally discussed in terms of relaxation processes characteristic of the liquid phase. We report here on a quantitative comparison of the collective excitations in liquid and polycrystalline sodium. We show that liquid sodium exhibits acoustic excitations of both longitudinal and transverse polarization at frequencies strictly related to those of the corresponding crystal. The only relevant difference between the liquid and the polycrystal appears in the broadening of the excitations: An additional disorder-induced contribution comes into play in the case of the liquid, which we show to be related to the distribution of local structures around the average one. These results establish a direct connection between structural and dynamic properties of liquids, with shortrange order and overall structural disorder leaving very specific fingerprints.vibrational dynamics | X-ray scattering T he short-range order in liquids, characterized by parameters like, e.g., the first neighbors distance and number, is usually similar to that of the corresponding solids (1, 2). Ab initio calculations of liquid structures spanning a large density range do support this idea (3). For what concerns dynamic properties, the situation is more complex. Local vibrations appear in the liquid as in the corresponding solid, although they are usually much broader (1). This broadening is generally related to the distribution of local structures that is present in the liquid phase (4) and that is, e.g., characterized by the distribution of first neighbors distances. Collective excitations exist as well in liquids, and their broadening is usually attributed to relaxation processes (5-7). In fact, the response of a crystal to an external perturbation can be formally expressed in terms of phonons, the modes of lattice vibration that can be defined in presence of a long-range, periodic structure. In liquids this description is instead formally not appropriate, and the concept of relaxation is usually introduced with reference to a dynamic process that controls the reequilibration of the system after it has been perturbed (8). Several distinct relaxation processes can be introduced to describe the dynamics of liquids, each one characterized by a characteristic time, τ, that sets the timescale over which it is active and observable. Indeed, if the perturbation frequency, ω, is such that ωτ ≪ 1, the relaxation is active, whereas when ωτ ≫ 1 the relaxation process does not have the time to take place and is frozen. In the infinite frequency limit, where all relaxations are frozen, the liquid behaves like a solid: This limit corresponds to the elastic regime, where only the instantaneous ...

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“…The experimentalists such as Woods et al [7] have shown a necessity of including at least two neighbour ionic interactions. The use of ion-ion interaction effective between the first nearest neighbour is doubtworthy.…”

Section: Introductionmentioning

confidence: 99%

Lattice Dynamics of Noble Metals on Effective Three-Body Interaction

Coelho

Shukla

1996

Acta Phys. Pol. A

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Quite recently we modified the original model of Sarkar et al. for cubic metals in extending the ion-ion interaction, ion-electron interaction and the introduction of crystal equilibrium condition. We applied our scheme to alkali metals. We studied here the lattice dynamics of noble metals on our approach by calculating phonon dispersion relations along the three principal symmetry directions, [00J, [0] and [W] and the (θ-Τ) curves of three noble metals: copper, silver and gold. We obtained reasonable agreement with the experimental findings.

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Crystal Dynamics of Sodium at 90°K

Cited by 325 publications

References 12 publications

On Phonon Dispersion in Alkali Metals

On Phonon Dispersion in Alkali Metals

Fingerprints of order and disorder on the high-frequency dynamics of liquids

Lattice Dynamics of Noble Metals on Effective Three-Body Interaction

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