# Three-Particle Correlations in Liquid and Amorphous Aluminium

## TL;DR

This paper investigates three-particle correlations in liquid and amorphous aluminium through simulations, introduces a new correlation function, and compares theoretical solutions with simulation data, revealing how correlations vary with temperature and structure.

## Contribution

The study introduces a novel three-particle correlation function and applies mode-coupling theory to analyze temporal evolution, comparing results with simulations for the first time in aluminium.

## Key findings

- Three-particle correlations are prominent within the second and third coordination spheres.
- Mode-coupling theory accurately reproduces the time-dependent correlation functions.
- Correlations extend over larger scales in amorphous aluminium at lower temperatures.

## Abstract

Analysis of three-particle correlations is performed on the basis of simulation data of atomic dynamics in liquid and amorphous aluminium. A three-particle correlation function is introduced to characterize the relative positions of various three particles -- the so-called triplets. Various configurations of triplets are found by calculation of pair and three-particle correlation functions. It was found that in the case of liquid aluminium with temperatures $1000\,$K, $1500\,$K, and $2000\,$K the three-particle correlations are more pronounced within the spatial scales, comparable with a size of the second coordination sphere. In the case of amorphous aluminium with temperatures $50\,$K, $100\,$K, and $150\,$K these correlations in the mutual arrangement of three particles are manifested up to spatial scales, which are comparable with a size of the third coordination sphere. Temporal evolution of three-particle correlations is analyzed by using a time-dependent three-particle correlation function, for which an integro-differential equation of type of the generalized Langevin equation is output with help of projection operators technique. A solution of this equation by means of mode-coupling theory is compared with our simulation results. It was found that this solution correctly reproduces the behavior of the time-dependent three-particle correlation functions for liquid and amorphous aluminium.