[Paper Review] Solid-like to Liquid-like Behavior of Cu Diffusion in Superionic Cu2X (X=S, Se): An Inelastic Neutron Scattering and Ab-Initio Molecular Dynamics Investigation

S. Kumar, Mayank Gupta+6 more|arXiv (Cornell University)|Jan 3, 2022

Advanced Thermoelectric Materials and Devices4 citations

TL;DR

This study combines inelastic neutron scattering and ab-initio molecular dynamics simulations to reveal a transition from solid-like to liquid-like copper diffusion in superionic Cu2Se and Cu2S. At high temperatures (>900 K), Cu diffusion becomes liquid-like with broad jump-length distributions centered at ~4 Å and strongly damped phonons, while at lower temperatures, diffusion is solid-like with well-defined jump lengths matching first-neighbor distances (~3 Å).

ABSTRACT

Cu2Se and Cu2S are excellent model systems of superionic conductors with large diffusion coefficients that have been reported to exhibit different solid-liquid-like Cu-ion diffusion. In this paper, we clarify the atomic dynamics of these compounds with temperature-dependent ab-initio molecular dynamics (AIMD) simulations and inelastic neutron scattering (INS) experiments. Using the dynamical structure factor and Van-Hove correlation function, we interrogate the jump-time, hopping length distribution and associated diffusion coefficients. In cubic-Cu2Se at 500 K, we find solid-like diffusion with Cu-jump lengths matching well the first-neighbour Cu-Cu distance of ~3 {\AA} in the crystal, and clearly defined optic phonons involving Cu-vibrations. Above 700 K, the jump-length distribution becomes a broad maximum cantered around 4 {\AA}, spanning the first and second neighbour lattice distances, and a concurrent broadening of the Cu-phonon density of states. Further, above 900 K, the Cu-diffusion becomes close to liquid-like, with distributions of Cu-atoms continuously connecting crystal sites, while the vibrational modes involving Cu motions are highly damped, though still not fully over-damped as in a liquid. At low temperatures, the solid-like diffusion is consistent with previous X-ray diffraction and quasielastic neutron scattering experiments, while the higher-temperature observation of the liquid-like diffusion is in agreement with previous AIMD simulations. We also report AIMD simulations in Cu2S in the hexagonal and cubic superionic phases, and observe similar solid and liquid-like diffusion at low- and high-temperatures, respectively. The calculated ionic-conductivity is in fair agreement with reported experimental values.

Motivation & Objective

• To clarify the atomic-scale dynamics of Cu diffusion in superionic Cu2Se and Cu2S across a range of temperatures.
• To resolve the nature of Cu diffusion—whether solid-like or liquid-like—by combining experimental and computational techniques.
• To understand the evolution of vibrational modes involving Cu atoms as temperature increases.
• To validate the ionic conductivity predictions from simulations against experimental measurements.
• To investigate the structural and dynamical differences between the cubic and hexagonal phases of Cu2S.

Proposed method

• Conducting temperature-dependent ab-initio molecular dynamics (AIMD) simulations on Cu2Se and Cu2S to model atomic motion at the electronic structure level.
• Performing inelastic neutron scattering (INS) experiments to measure the dynamical structure factor and phonon density of states.
• Analyzing the Van Hove correlation function to extract jump-time and hopping length distributions of Cu ions.
• Calculating the ionic conductivity from the mean-square displacement of Cu atoms in the simulations.
• Comparing the simulated dynamical structure factor and phonon modes with experimental INS data to validate the models.
• Using the first- and second-neighbor Cu-Cu distances (3 Å and ~4 Å) as reference points to classify diffusion behavior as solid-like or liquid-like.

Experimental results

Research questions

• RQ1 How does the Cu diffusion mechanism evolve from solid-like to liquid-like behavior in Cu2Se and Cu2S with increasing temperature?
• RQ2 What is the role of Cu-vibrational modes and their damping in the transition from solid-like to liquid-like diffusion?
• RQ3 How do the jump-length distributions of Cu ions change across the solid-to-liquid-like transition?
• RQ4 To what extent do the simulated ionic conductivities match experimental values in Cu2X compounds?
• RQ5 Are the dynamical and structural features of the cubic and hexagonal phases of Cu2S qualitatively similar in their high-temperature behavior?

Key findings

• At 500 K in cubic-Cu2Se, Cu diffusion is solid-like with jump lengths closely matching the first-neighbor distance of ~3 Å.
• Above 700 K, the Cu-jump length distribution broadens and centers at ~4 Å, spanning first and second neighbor distances, indicating a transition toward liquid-like diffusion.
• Above 900 K, the Cu-diffusion becomes nearly liquid-like, with continuous connections between crystal sites and a broad, featureless distribution of jump lengths.
• The Cu-phonon density of states becomes strongly broadened above 700 K and highly damped above 900 K, though not fully over-damped, indicating intermediate behavior between solid and liquid.
• The ionic conductivity calculated from AIMD simulations shows fair agreement with reported experimental values for both Cu2Se and Cu2S.
• Similar solid-to-liquid-like transitions in Cu diffusion are observed in both the cubic and hexagonal phases of Cu2S, confirming the behavior is intrinsic to the superionic phase.