# Solving Static and Dynamic Disorder in Cu4TiTe4: Crystal Structure and Thermodynamic Properties

## TL;DR

This paper investigates the structural disorder in Cu4TiTe4 and its impact on thermodynamic properties, showing that dynamic disorder leads to unique behaviors like negative thermal expansion.

## Contribution

The study introduces a method to account for dynamic disorder in Cu4TiTe4 using supercells and DFT calculations, revealing novel thermodynamic effects.

## Key findings

- Dynamic disorder in Cu4TiTe4 leads to negative thermal expansion at low temperatures.
- Energy barriers for copper diffusion are below 0.5 eV, indicating significant dynamic effects.
- Single-configuration models are inadequate for capturing the true thermodynamic behavior of Cu4TiTe4.

## Abstract

Cu4TiTe4 shows positional disorder
because
one of the copper atoms does not occupy a precise position in the
unit cell. This fact complicates the development of simple and reliable
crystalline models capable of capturing the promising thermodynamic
and optical properties of Cu4TiTe4. Here, we
select practical supercells accounting for the different Cu atomic
environments in the crystal and identify nonequivalent structural
configurations. Their electronic energies and thermodynamic properties
are calculated by coupling DFT and the quasi-harmonic approximations.
Average values corresponding to the experimentally observed Cu4TiTe4 structure are obtained introducing Boltzmann
weights based on the total energy of these configurations. For Cu4TiTe4, differences in the calculated properties
among the 16 nonequivalent configurations of its 2 × 2 ×
1 supercell demonstrate the inadequacy of focusing just on a single
configuration. After calculating the energy barriers associated with
the diffusion of the disordered copper atoms among its four equivalent
positions (lower than 0.5 eV), we evidence the importance of taking
into account this dynamic disorder, which reveals a negative thermal
expansion for this telluride at low temperatures, not found under
the static disorder approach.