Density of states from mode expansion of the self-dynamic structure factor of a liquid metal

Abstract

We show that by exploiting multi-Lorentzian fits of the self-dynamic structure factor at various wave vectors it is possible to carefully perform the Q→0 extrapolation required to determine the spectrum Z(ω) of the velocity autocorrelation function of a liquid. The smooth Q dependence of the fit parameters makes their extrapolation to Q=0 a simple procedure from which Z(ω) becomes computable, with the great advantage of solving the problems related to resolution broadening of either experimental or simulated self-spectra. Determination of a single-particle property like the spectrum of the velocity autocorrelation function turns out to be crucial to understanding the whole dynamics of the liquid. In fact, we demonstrate a clear link between the collective mode frequencies and the shape of the frequency distribution Z(ω). In the specific case considered in this work, i.e., liquid Au, analysis of Z(ω) revealed the presence, along with propagating sound waves, of lower frequency modes that were not observed before by means of dynamic structure factor measurements. By exploiting ab initio simulations for this liquid metal we could also calculate the transverse current-current correlation spectra and clearly identify the transverse nature of the above mentioned less energetic modes. Evidence of propagating transverse excitations has actually been reported in various works in the recent literature. However, in some cases, like the present one, these modes are difficult to detect in density fluctuation spectra. We show here that the analysis of the single-particle dynamics is able to unveil their presence in a very effective way. The properties here shown to characterize Z(ω), and the information in it contained therefore allow us to identify it with the density of states (DoS) of the liquid. We demonstrate that only nonhydrodynamic modes contribute to the DoS, thus establishing its purely microscopic origin. Finally, as a by-product of this work, we provide our estimate of the self-diffusion coefficient of liquid gold just above melting.

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“…Analysis of the VAF spectrum Z ( ω ) can further support the preceding deductions, keeping in mind that such a function has peaks or shoulders where vibrational state frequencies occur more often with varying Q , i.e., as already stated, it represents the DoS of the liquid 17 , 34 . The DoS behaviour can help not only in confirming the presence of propagating modes of both longitudinal and transverse nature, but also in establishing which excitations give rise to flat branches in the dispersion curve.…”

“…To reach a clear picture about the propagating modes, it is very important to calculate various functions from the time evolution of the particle configurations. Indeed, as shown in the case of liquid gold 17 , the analysis of S ( Q , ω ) alone can sometimes be insufficient to characterise the dynamics completely, thus other quantities need also to be scrutinised for a correct interpretation. Among these, there are certainly the VAF and its spectrum, as well as the longitudinal, C L ( Q , ω ), and transverse, C T ( Q , ω ), current-current correlation spectra.…”

“…As a final, useful note about the DoS behaviour, we recall that its ω = 0 value is proportional to the self diffusion coefficient D s , and, in particular, D s = πZ ( ω = 0)/3 17 , 25 . Figure 4(a) thus shows that HB hinders diffusion to a large extent, providing D s = 2.5 · 10 −4 nm 2 ps −1 , which is nearly an order of magnitude lower than the HB-off value D s = 2.1 · 10 −3 nm 2 ps −1 .…”

“…typically featuring propagation of transverse waves, large positive dispersion of the longitudinal ones, existence of intra-associate excitations) in terms of hydrogen bond effects. Nevertheless, some doubt that HB may be the responsible for shear waves descends from the literature of the last decade, as commented on in a very recent paper 17 . In fact, that work and several papers therein quoted 18 – 23 have shown that propagating shear modes are not a peculiarity of HB liquids.…”

“…In fact, that work and several papers therein quoted 18 – 23 have shown that propagating shear modes are not a peculiarity of HB liquids. However, while in some liquid metals 18 – 23 transverse modes have been detected directly in the dynamic structure factor S ( Q , ω ), this was not the case of liquid gold 24 , where their presence has been assessed 17 only through the analysis of the density of states (DoS) of the liquid, i.e. the spectrum Z ( ω ) of the velocity autocorrelation function (VAF) 25 , and of the transverse current-current correlation spectrum C T ( Q , ω ) 25 .…”