Real-space Atomic Dynamics in Liquid Gallium Studied by Inelastic Neutron Scattering

TL;DR

Using inelastic neutron scattering, the paper reconstructs the real-space Van Hove correlation function $G(r,t)$ for liquid gallium from the dynamic structure factor $S(Q,E)$. It reveals two coexisting dynamical medium-range orders with wavevectors $Q_{ ext{MRO1}}$ and $Q_{ ext{MRO2}}$ that share a common coherence length $\xi_s$ and decay time, distinct from the faster relaxation of short-range order. A density-wave interpretation attributes these MROs to two driving forces: an ionic-core repulsion and Friedel-like electronic modulations, corresponding to minima at $q_{min}$ in the pseudopotential. The findings provide a link between electronic structure and atomic dynamics in metallic liquids and suggest that the density-wave framework could generalize to other polyvalent melts and complex liquids.

Abstract

Gallium is a prototypical liquid metal and has gained renewed attention due to its unique properties. Characterizing and elucidating its atomic dynamics remains elusive despite numerous studies, primarily due to the challenges of quantifying atomic-scale dynamics in liquids. Recent developments in inelastic neutron scattering enable us to measure the Van Hove correlation function that describes the real-space motion of liquid atoms. In this work, we use this approach to reveal the dynamics in gallium liquids and find the co-existence of two dynamical medium-range orders (MROs), which have a dynamical behavior distinct from that of the short-range order (SRO). We propose that these MROs are driven by global forces in the form of two density waves, as a direct consequence of the underlying competition between ionic core repulsion and valence electron cohesion. We suggest that the density wave approach is not only applicable to other metallic liquids exhibiting similar structural anomalies, but also offers a promising direction for elucidating the dynamics of complex liquids and glasses by linking electronic-state fluctuations to atomic dynamics.

Figures (6)

• Figure 1: First row: resolution corrected Intermediate structure function, $F(Q,t)$ of liquid gallium at (a) 310 K, (b) 550 K, and (c) 950 K obtained by the Fourier transform of $S(Q,E)$ over the energy transfer, $E$; Second row: Van Hove function, $G(r,t)$, of liquid Gallium at (d) 310 K, (e) 550 K, and (f) 950 K obtained by the Fourier transform of $F(Q,t)$ over the momentum, $Q$.
• Figure 2: (a) The full set of the snapshot structure factor, $S(Q)$, from the INS measurements between 310 K (bottom) and 950 K (top). The values on the y-axis correspond to the curve at 310 K; the remaining solid curves are displaced upwards with a step of 0.5. The full set of temperatures is: 310 K, 350, 390, 430, 470, 510, 550, 650, 750, 850, and 950 K. (b) The measured $S(Q)$ at 430 K (circles) compared to the fits using a set of Lorentzian functions given by Eq. (\ref{['eq:SQ_FIT']}) (solid line) and a set of Gaussian functions (dashed line). (c) The position of the main peak (circles) and shoulder (squares) of $S(Q)$ found by the Lorentzian fit given by Eq. (\ref{['eq:SQ_FIT']}) as a function of temperature. (d) The corresponding amplitudes, $a_1$ and $a_2$ of the main peak (circles) and shoulder (squares) of $S(Q)$ as a function of temperature.
• Figure 3: (a) The measured pair distribution function, $r(g(r)-1)$ (solid lines) and the best fit (dashed lines) of the higher-order peaks ($r > 3.8 \mathrm{\AA}$) using Eq. (\ref{['eq:MRO']}) (dashed line) at 310 K, 550 K, and 950 K. The best-fit structural coherence length, $\xi_s$, is 5.88 $\mathrm{\AA}$ at 310 K, 4.17 $\mathrm{\AA}$ at 550 K, and 3.10 $\mathrm{\AA}$ at 950 K. (b) The best-fit $r(g_{MRO}(r)-1)$ (solid line) at 310 K consists of two decaying sinusoidal functions with wavevectors at $Q_{\mathrm{MRO1}} = 2.5\ \mathrm{\AA}^{-1}$ (dotted-dash line) and $Q_{\mathrm{MRO2}} = 3.2\ \mathrm{\AA}^{-1}$ (dashed line). (c) Fitted medium-range order wavevectors of the main peak ($Q_{\mathrm{MRO}1}$, circles) and shoulder ($Q_{\mathrm{MRO}2}$, squares) versus temperature from the snapshot PDF. (d) Fitted amplitudes of two MRO oscillations, $A_1$, (main MRO, circles) and, $A_2$, (shoulder MRO, squares) versus temperature.
• Figure 4: The time slices of VHF, $G(r,t)-1$, at (a) 310 K, (b) 550 K, and (c) 950 K. The decay behavior of the first peak describes the dynamics of the SRO while the decay behavior of the higher-order peaks gives the MRO dynamics. (d) The decay of the area under first peak of $G(r,t)-1$, $N(t)$, at 310 K (circles), 550 K (squares), and 950 K (diamonds) with their corresponding best-fit exponential decay curves. (e) The decay of $A_1(t)$ (open symbols) and $A_2(t)$ (filled symbols) at 310 K (circles) and 550 K (squares) with their corresponding best-fit exponential decay curves. (f) Relaxation times of the first peak ($\tau_{\mathrm{VH}}$, solid diamonds), the MRO corresponding to the main peak in $F(Q,t)$ ($\tau_{\mathrm{MRO}1}$, open circles), and the shoulder MRO ($\tau_{\mathrm{MRO}2}$, open squares), as a function of temperature.
• Figure 5: (a) The time slices of the intermediate scattering function, $F(Q,t)$, at 310 K. The dashed line is the x-ray diffraction measurement from Ref. narten_liquid_1972. (b) Best-fit relaxation times of the amplitude decay at $Q = Q_{\mathrm{main}}$ and $Q = Q_{\mathrm{shoulder}}$ as a function of inverse temperature. (c) The amplitude decay of F(Q,t) at $Q = Q_{\mathrm{main}}$ at 310 K (squares), 550 K (diamonds), and 950 K (circles) with their corresponding best-fit exponential decay curves. (d) The amplitude decay of F(Q,t) at $Q = Q_{\mathrm{shoulder}}$ at 310 K (squares), 550 K (diamonds), and 950 K (circles) with their corresponding best-fit exponential decay curves.