# Unavoidable disorder and entropy in multi-component systems

## TL;DR

This paper investigates the balance between enthalpy and entropy in multi-component materials, revealing a threshold where disorder becomes unavoidable as the number of species increases.

## Contribution

It provides a statistical analysis identifying a critical number of species beyond which disorder dominates in multi-component systems.

## Key findings

- Entropy gain surpasses enthalpy gain at a specific number of species.
- Disorder becomes unavoidable in systems with many components.
- Ordered compounds are rare beyond four or more species.

## Abstract

The need for improved functionalities is driving the search for more complicated multi-component materials. Despite the factorially increasing composition space, ordered compounds with 4 or more species are rare. Here, we unveil the competition between the gain in enthalpy and entropy with increasing number of species by statistical analysis of the AFLOW data repositories. A threshold in the number of species is found where entropy gain exceeds enthalpy gain. Beyond that, enthalpy can be neglected, and disorder - complete or partial - is unavoidable.