# Non‐Equilibrium Synthesis Methods to Create Metastable and High‐Entropy Nanomaterials

## TL;DR

Non-equilibrium methods create new nanomaterials by overcoming element immiscibility, enabling advanced applications in energy and sensing.

## Contribution

Review of non-equilibrium synthesis methods that enable metastable and high-entropy nanomaterials beyond equilibrium limitations.

## Key findings

- Non-equilibrium methods allow integration of immiscible elements into metastable nanostructures.
- High configurational entropy and kinetic trapping enhance phase stability in these materials.
- These methods expand compositional space for AI-guided materials discovery and industrial production.

## Abstract

Stabilizing multiple elements within a single phase enables the creation of advanced materials with exceptional properties arising from their complex composition. However, under equilibrium conditions, the Hume–Rothery rules impose strict limitations on solid‐state miscibility, restricting combinations of elements with mismatched crystal structures, atomic radii, valence states, or electronegativities. This severely narrows the accessible compositional space for creating new inorganic materials. In this review, we highlight how non‐equilibrium synthesis methods, featuring ultrafast heating and quenching, can overcome these thermodynamic barriers, enabling integration of immiscible elements into metastable and high‐entropy nanostructures. The resulting materials benefit from both kinetic trapping and stabilization by high configurational entropy, leading to enhanced phase stability. These materials can exhibit unique structural and functional properties that are needed for advancing catalysis, energy storage, thermoelectrics, and sensing. Furthermore, the ability of non‐equilibrium methods to generate unconventional compositions and structures expands the material design space dramatically, offering rich datasets for AI‐guided materials discovery. When combined with their inherent high‐throughput and scalable characteristics, these approaches enable rapid, iterative optimization and accelerate the development and industrial production of next‐generation inorganic materials.

Synthesis of compositionally‐complex materials is limited by immiscibility of elements. Nonequilibrium synthesis methods reviewed here use ultrafast heating and cooling to overcome this limitation, creating metastable solid solutions and high‐entropy nanomaterials. This expands applications of inorganic materials in catalysis, electrochemistry, and sensors, while providing vast compositional space for material design.