Statistical model of matter

Kirzhnit︠s︡, D. A.; Lozovik, Yurii E.; Shpatakovskaya, G. V.

doi:10.1070/pu1975v018n09abeh005199

Cited by 141 publications

(96 citation statements)

References 3 publications

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“…Thus, only the second derivative of Helmholtz potential with respect to temperature is sensible enough to reflect a change in the electronic structure. A striking manifestation of shell effects may be observed on the dependency of atomic volume vs. atomic number [10,11,55,56]. Experimental values of atomic volumes at different pressures can be estimated from shock-wave data [55].…”

Section: Resultsmentioning

confidence: 99%

“…To describe shell effects one should take into account discrete energy levels. Analytically shell corrections to the TF model have been studied in [12,13] using the Poisson formula in the transition from summation to integration (see also the review [14]). Average atom models [15][16][17][18][19] are based on a radial solution of the single-particle Schrödinger (Dirac) equation so that the discrete spectrum and shell effects are taken into account implicitly.…”

Section: Introductionmentioning

confidence: 99%

“…For example, in low-density plasma step-wise dependencies of thermodynamic functions on isochors or isobars are quite typical [9]. The other well-known effect is connected with the non-regular behavior of density of elements vs. atomic mass [10,11]. To describe shell effects one should take into account discrete energy levels.…”

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confidence: 99%

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Influence of shell effects on thermodynamic properties of matter at high pressures

Levashov

Minakov

2018

J. Phys.: Conf. Ser.

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Abstract. We analyze the influence of shell effects on thermodynamic properties of matter at high pressures. Spherically symmetric average atom models show significant contribution of electronic transitions to cold pressure which is not confirmed by more accurate density functional theory models. In particular, the s-d transition in aluminum and potassium does not reveal itself on the shock Hugoniots. Oscillations on shock Hugoniots at very high pressures predicted earlier by many authors should be confirmed by precise first-principle calculations. IntroductionThermodynamic properties of matter at high pressure are of importance in many problems of high energy density physics, in particular, in astrophysics [1], in wide-range equations of state [2,3], in the problems of interaction of intense energy fluxes with matter [4-6], in perspective power generation facilities [7] and in some others. The finite-temperature Thomas-Fermi (TF) model [8] based upon semiclassical approximation is widely used to describe thermodynamic properties of matter, but there are many phenomena beyond this approach. In particular, shell effects reflect non-regularities of physical parameters because of the discrete energy spectrum. For example, in low-density plasma step-wise dependencies of thermodynamic functions on isochors or isobars are quite typical [9]. The other well-known effect is connected with the non-regular behavior of density of elements vs. atomic mass [10,11]. To describe shell effects one should take into account discrete energy levels. Analytically shell corrections to the TF model have been studied in [12,13] using the Poisson formula in the transition from summation to integration (see also the review [14]). Average atom models [15][16][17][18][19] are based on a radial solution of the single-particle Schrödinger (Dirac) equation so that the discrete spectrum and shell effects are taken into account implicitly. During the last 30 years it became possible to obtain approximate three-dimensional (3D) solutions of a quantum many-particle problem using density functional theory (DFT) [20,21]. In this case one gets a 3D band structure of a system of particles that provides for the appearance of shell effects through non-regularities of the electronic density and some thermodynamic functions. There were several attempts to register shell effects at high pressures and temperatures experimentally [22][23][24] using underground nuclear explosions. It is claimed [24] that the influence of the discrete energy spectrum is

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Influence of shell effects on thermodynamic properties of matter at high pressures

Levashov

Minakov

2018

J. Phys.: Conf. Ser.

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“…A relation of this form has been given by Kirzhnitz [13]. We present a detailed derivation, based on Liouville's equation, below.…”

Section: Equivalence With Perturbation Theorymentioning

confidence: 99%

Absorption of low-frequency radiation by small metal particles: a semiclassical random-phase-approximation

Wilkinson¹,

Mehlig²

2000

J. Phys.: Condens. Matter

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We introduce a theory for the absorption of electromagnetic radiation by small metal particles, which generalises the random phase approximation by incorporating both electric and magnetic dipole absorption within a unified self-consistent scheme. We demonstrate the equivalence of the new approach to a superficially dissimilar perturbative approach. We show how to obtain solutions to the self-consistent equations using a classical approximation, taking into account the non-locality of the polarisability and the conductivity tensor. We discuss the nature of the self-consistent solutions for diffusive and ballistic electron dynamics.

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“…The ETF model well describes the average characteristics of a system, while the shell effects of interest will be studied using the following expression for the correction to the free energy (in atomic units) [13,15]:…”

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Orbits in large aluminum clusters: Five-pointed stars

Shpatakovskaya

2000

Jetp Lett.

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1.The oscillations in the mass spectra of metal clusters may be caused by both the shell structure of electronic spectra and the positioning of ions in lattice sites [1]. Experiments show that the oscillations in the mass spectra of large aluminum Al N [2][3][4] and sodium Na N [5] clusters ( N is the number of atoms in a cluster) differ significantly in shape. Whereas the oscillations for sodium proceed with beats, the aluminum clusters with N > 250 exhibit sinusoidal behavior with a frequency approximately twice that for sodium. The spectra of the Al N clusters of smaller sizes represent an intricate pattern without any distinct period. In the literature, the cause of this distinction is discussed in terms of classical trajectories of electron motion in a self-consistent potential (the number of electrons in a cluster is N e = wN , where w is the valence of a metal).In [3], an attempt was undertaken to explain the experiment by invoking a spherical jellium model and the quasiclassical theory [6][7][8][9]. It was conjectured that, contrary to a hard potential of Na N clusters, in which a triangular trajectory and a square trajectory of a close frequency dominate (the oscillations with beats result from the interference of the relevant contributions), in a soft potential of Al N clusters with 250 < N < 900, the main contribution comes from a single trajectory shaped like a five-pointed star. According to this theory, the clusters of larger size should have triangular and, later, square trajectories (this is confirmed by the selfconsistent computation [2] of the density of states for N e = 4940), leading to a change in the oscillation frequency.An alternative explanation was suggested in [4], where the mass spectra of "cold" ( T = 100 K) Al N clusters were experimentally measured and analyzed over a very wide range of N values (250 < N < 10000). An analysis of the spectra showed that the oscillation maxima, numbered sequentially by the index k ( k > 25), appeared with a constant frequency over the entire range studied and fitted the law N Ӎ 0.0104 k 3 , which is readily explained by the atomic positioning in an octahedral lattice. Accordingly, the cluster shape is not a sphere but an octahedron, so that the shell filling corresponds to the assembling of one of its faces. Evidently, the spherical jellium model with uniformly distributed ions inside the sphere is not adequate in this case.In [10], the assumption about the dominant contribution from a five-point-star orbit in the aluminum clusters was ruled out by the quantum-mechanical calculation of the density of states for N e = 1000 electrons in the Saxon-Woods potential.Nevertheless, the positions of the maxima observed in [2] for 250 < N < 430 at T = 295 K agree well with the results of self-consistent calculations carried out in the same work with the jellium model, while the comparison of the mass spectra of Al N observed at T = 110 K and T = 295 K for N < 250 reveals that the temperature has an appreciable effect on the shapes of the corresponding curves, ...

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Statistical model of matter

Cited by 141 publications

References 3 publications

Influence of shell effects on thermodynamic properties of matter at high pressures

Influence of shell effects on thermodynamic properties of matter at high pressures

Absorption of low-frequency radiation by small metal particles: a semiclassical random-phase-approximation

Orbits in large aluminum clusters: Five-pointed stars

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