Anharmonic contributions to vibrational thermodynamic properties of solids

Maradudin, A. A.; Flinn, P. A.; Coldwell-Horsfall, Rosemary A.

doi:10.1016/0003-4916(61)90189-0

Cited by 146 publications

(44 citation statements)

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“…The main results include the correction to the Dulong-Petit result of solids, thermal expansion and modification of the phonon spectrum, phonon scattering and so on. Unfortunately, the quantitative evaluation of anharmonicity effects has remained a challenge, with the frequent result that the accuracy of leading-order anharmonic perturbation theory is unknown and the magnitude of anharmonic terms is challenging to justify [23][24][25][26][27]. Experimental data such as phonon lifetimes and frequency shifts can provide quantitative estimates for anharmonicity effects and expansion coefficients in particular, although this involves complications and limits the predictive power of the theory [23].…”

Section: First-principles Approach and Its Failurementioning

confidence: 99%

Collective modes and thermodynamics of the liquid state

2015

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Strongly interacting, dynamically disordered and with no small parameter, liquids took a theoretical status between gases and solids, with the historical tradition of hydrodynamic description as the starting point. We review different approaches to liquids as well as recent experimental and theoretical work, and propose that liquids do not need classifying in terms of their proximity to gases and solids or any categorizing for that matter. Instead, they are a unique system in their own class with a notably mixed dynamical state in contrast to pure dynamical states of solids and gases. We start with explaining how the first-principles approach to liquids is an intractable, exponentially complex problem of coupled non-linear oscillators with bifurcations. This is followed by a reduction of the problem based on liquid relaxation time τ representing non-perturbative treatment of strong interactions. On the basis of τ , solid-like high-frequency modes are predicted and we review related recent experiments. We demonstrate how the propagation of these modes can be derived by generalizing either hydrodynamic or elasticity equations. We comment on the historical trend to approach liquids using hydrodynamics and compare it to an alternative solid-like approach. We subsequently discuss how collective modes evolve with temperature and how this evolution affects liquid energy and heat capacity as well as other properties such as fast sound. Here, our emphasis is on understanding experimental data in real, rather than model, liquids. Highlighting the dominant role of solid-like high-frequency modes for liquid energy and heat capacity, we review a wide range of liquids: subcritical low-viscous liquids, supercritical state with two different dynamical and thermodynamic regimes separated by the Frenkel line, highly-viscous liquids in the glass transformation range and liquid-glass transition. We subsequently discuss the fairly recent area of liquid-liquid phase transitions, the area where the solid-like properties of liquids have become further apparent. We then discuss gas-like and solid-like approaches to quantum liquids and theoretical issues that are similar to the classical case. Finally, we summarize the emergent view of liquids as a unique system in a mixed dynamical state, and list several areas where interesting insights may appear and continue the extraordinary liquid story.

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Section: First-principles Approach and Its Failurementioning

confidence: 99%

Collective modes and thermodynamics of the liquid state

2015

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“…Even though this quantity has been investigated since long time 5 , complete information is not available for various rare gas solids and in particular for neon. The perturbative many-body approach can give frequency and lifetime of phonons only at low temperatures.…”

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confidence: 99%

Spectral shapes of solid neon

Pedrolli¹,

Cuccoli²,

Macchi³

et al. 1998

J. Phys.: Condens. Matter

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We present a Path Integral Monte Carlo calculation of the first three moments of the displacementdisplacement correlation functions of solid neon at different temperatures for longitudinal and transverse phonon modes. The Lennard-Jones potential is considered. The relevance of the quantum effects on the frequency position of the peak and principally on the line-width of the spectral shape is clearly pointed out. The spectrum is reconstructed via a continued fraction expansion; the approximations introduced using the effective potential quantum molecular dynamics are discussed.Rare gas solids (RGS) are the simplest real systems in which we can study lattice vibrations. Argon and the heavier RGS can be well approximated as a set of harmonic oscillators at lowest temperatures, while the classical behaviour is reached before the melting point. Quantum corrections on the thermodynamic quantities, like kinetic energy and specific heat, can be taken into account by means of the effective potential approach (EP) 1 only for small quantum coupling g, (g < 0.25) defined as the ratio between the characteristic frequency and the strength of the binding potential. For neon (g = 0.694) anharmonic effects are present even for determining the ground state 2,3 . Indeed, precise calculations of kinetic energy, to be compared with accurate experiments done by Deep Inelastic Neutron Scattering (DINS) 4 , needed a rather sophisticated Path Integral Monte Carlo (PIMC) computation, being the EP approach inadequate. These results show that quantum effects are very important also at rather high temperatures 2 . Information about phonon dynamics is given by spectral shape, namely the space and time Fourier transform of the (symmetrized) displacement-displacement correlation function:withx α i is α-th component of the displacement of the i-th atom from its equilibrium position. Even though this quantity has been investigated since long time 5 , complete information is not available for various rare gas solids and in particular for neon. The perturbative many-body approach can give frequency and lifetime of phonons only at low temperatures. Classical molecular dynamics (CMD) can describe the behaviour of argon and krypton at highest temperatures, but it is no more valid for lower temperatures or stronger coupling. As shown in the following, the spectra of neon present significant quantum effects up to the melting point and the high quantum coupling prevents us to use the EP method in the entire temperature range.We approach the calculation of the spectra of neon as given in equation (1), by PIMC, evaluating the first three even frequency moments, ω 2n αβ k

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“…ApPLICATION TO A FACE-CENTRED CUBIC CRYSTAL MODEL Maradudin, Flinn, and Coldwell-Horsfall (1961) have treated exactly a simple nearest neighbour model with central forces. They have, however, ignored all terms of order Ija (where a is the nearest neighbour distance) in the expansion of the potential given in equations (3.1) and (3.2).…”

Section: The Harmonic Free Energymentioning

confidence: 99%

“…Stern (1958) evaluated some of these complicated expressions exactly by analytical methods. However, this has been disputed by Maradudin, Flinn, and Coldwell-Horsfall (1961) and so the evaluation must be considered an approximation. Maradudin, Flinn, and Coldwell-Horsfall have evaluated the expressions for a simple model, using a computer to estimate the coefficients which appeared.…”

Section: Introductionmentioning

confidence: 99%

Anharmonic Contributions to the Vibratory Free Energy of a Lattice

Lloyd¹

1964

Aust. J. Phys.

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SummaryThe anharmonic contribution to the free energy of a lattice is evaluated by means of a Bethe approximation. The approximation is accurate to within 3% for the model evaluated by Maradudin, Flinn, and Coldwell· Horsfall. The anharmonic contribution to the specific heat at constant volume of a model of sodium is evaluated. The specific heat is found to increase as the temperature rises but the rate of increase is lower than the observed value.

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Anharmonic contributions to vibrational thermodynamic properties of solids

Cited by 146 publications

References 10 publications

Collective modes and thermodynamics of the liquid state

Collective modes and thermodynamics of the liquid state

Spectral shapes of solid neon

Anharmonic Contributions to the Vibratory Free Energy of a Lattice

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