Interplay between the ionic and electronic density profiles in liquid metal surfaces

Abstract

First principles molecular dynamics simulations have been performed for the liquid-vapor interfaces of liquid Li, Mg, Al and Si. We analize the oscillatory ionic and valence electronic density profiles obtained, their wavelengths and the mechanisms behind their relative phase-shift.PACS numbers: 61.25. Mv, 64.70.Fx, 71.15.Pd X-ray reflectivity measurements on the surface of liquid metals and alloys, along with other techniques like diffuse scattering or grazing incidence diffraction, have shown the existence of layering in the ionic density profile. 1,2,3,4,5,6,7,8 Its origin is yet not clear and several reasons have been mooted. Rice and coworkers 9,10,11 have pointed that the reason for surface layering in metals is the interconnection between the ionic and electronic densities and that the abrupt decay of the electron density at the surface induces an effective wall against which the ions, behaving like hard-spheres, stack. Recently, it has been suggested that surface layering is a rather universal phenomenon, although in most cases it is frustrated by solidification; 12,13 therefore it only appears in systems whose melting temperature is very low compared with the critical temperature.The reflectivity experiments probe the total electronic density profile. Therefrom, the ionic density profile is derived by a superposition approximation where the the total electron density is taken as the sum of atomic-like electron densities around each of the nuclei in the system. Whereas this approach may be vindicated for the tightly bound core electrons, the case of valence electrons is more subtle. Early calculations of Lang and Kohn for semiinfinite step surfaces 14 showed that the valence electron density does not decay so abruptly, but displays some spill-out outside the surface; moreover inside the bulk its exhibits the so called Friedel oscillations.Computer simulations of liquid surfaces can evaluate directly the ionic density profile. But only a fully ab initio method can deliver an electronic density selfconsistent with the discrete nature of the ions. Orbital based ab initio simulations are scarce (just for Si 15 and Na 16 ) due to the huge computational demands they pose. Orbital free ab initio simulations are less demanding, although still expensive, and recent orbital free ab initio molecular dynamics (OFAIMD) calculations with 2000 and 3000 particles have studied the surface properties of liquid Li, Na, Na 0.3 K 0.7 and Li 0.4 Na 0.6 . 17,18 These studies showed that the superposition approximation produces a valence electronic density profile very similar to the fully selfconsistent one, except for the width of the interface due to the spill-out.This communication reports results for the liquidvapor interface of liquid Li, Mg, Al and Si near their respective melting points. The calculations were per- formed by the OFAIMD method where the forces acting on the nuclei are computed from electronic structure calculations, based on the density functional theory (DFT), which are performed as the ionic trajecto...

Anab initiostudy of the structure and dynamics of bulk liquid Cd and its liquid–vapor interface

“…In previous studies concerning the ionic DP in a wide range of simple liquid metals, we found a linear relationship between the wavelength of the ionic oscillations and the radii of the associated Wigner-Seitz spheres [46]. We have verified that this relationship is also fulfilled by the previous calculated value of 2.82 Å.…”

Effect of Concentration on the Interfacial and Bulk Structure of Ionic Liquids in Aqueous Solution

“…At larger distances from the interface, details of the specific interactions between the ions and the solid play a minor role. As for most other isotropic liquids, from the third layer on, interfacial profiles are quantitatively described by generic mean-field models. − In this regime, for most liquids, the structure at buried solid/liquid interfaces and the free surface is determined by bulk parameters, namely, the dominating length scale d b and the decay length ξ b of the bulk’s correlation function. − Indeed, X-ray reflectivity experiments indicate that for a wide range of commonly used anions and cations in this respect ILs do not behave differently compared to the mere of other standard liquids . ,− In neat bulk IL, Triolo et al showed that imidazolium-based ILs with cations featuring long aliphatic side chain exhibit long range density fluctuations in X-ray scattering that correlate with the length of the hydrocarbon chain. Similarly, Nishi et al , studied the gas/IL interface and showed that an ordered interfacial structure evolves because of interfacial pinning of bulk density fluctuations, without extended lateral ordering within the layering .…”

Structure and dynamics of bulk liquid Ga and the liquid-vapor interface: Anab initiostudy

“…However, this explanation has recently been questioned and, based on ab initio results for several liquid metals, a different cause has been proposed. 41 Specifically it hinges on the interplay between the width ͑͒ of the pseudoatomic valence density and the separation of layers ͑͒ in the ionic DP. Indeed, three broad groups were identified: ͑i͒ those with a ratio of 0.62Յ / Յ0.64, where the ionic and electronic DPs oscillated in the opposite phase ͑i.e., the alkalis͒, ͑ii͒ those with 0.44Յ / Յ0.47 had ionic and electronic DPs nearly in phase ͑i.e., Tl and Si͒, and ͑iii͒ those with 0.55Յ / Յ0.59 which showed an intermediate behavior ͑i.e., Mg, Ba, and Al͒.…”

“…Parenthetically, this explanation has also accounted for the variety of relative phases between the ionic and valence electronic density profiles obtained for the LV interface in a wide range of simple liquid metals. 41 From the previous density profiles, we have evaluated the total electronic density profile ͑which is the physical magnitude probed in the x-ray reflectivity measurements͒ and therefrom the associated reflected intensity R͑q z ͒. This latter step involves accounting for the surface roughness c , which appears in the form of a Debye-Waller-type factor ͓see Eq.…”