# Order–Disorder-Type Transitions Through a Multifractal Procedure in Cu-Zn-Al Alloys—Experimental and Theoretical Design

## TL;DR

This paper studies the thermal and structural behavior of Cu-Zn-Al alloys using experiments and a multifractal theoretical model to explain unusual properties like 'rubber-type behavior'.

## Contribution

A novel multifractal approach is introduced to model order–disorder transitions and thermal dynamics in Cu-Zn-Al alloys.

## Key findings

- Cu-Zn-Al alloys exhibit 'rubber-type behavior' due to micro-structural changes.
- Thermal expansion velocity reflects both phase transformation and thermal diffusion speeds.
- Self-modulated thermal fields lead to channel-type or cellular-type thermal patterns.

## Abstract

Experimental and theoretical design on thermal and structural properties of Cu-Zn-Al alloys are established. As such, from an experimental point of view, differential thermal analysis has been performed with the help of a DSC Netzsch STA 449 F1 Jupiter calorimeter with high levels of sensitivity, and the structural analysis has been accomplished through X-ray diffraction and SEM analysis. An unusual specific property for a metallic material has been discovered, which is known as “rubber-type behavior”, a characteristic determined by micro-structural changes. From the theoretical point of view, the thermal transfer in Cu-Zn-Al is presented by assimilating this alloy, both structurally and functionally, with a multifractal, situation in which the order–disorder transitions assimilated with thermal “dynamics” of Cu-Zn-Al, are mimed through transitions from non-multifractal to multifractal curves. In such a context, the thermal expansion velocity contains both the propagation speed of the phase transformation (be it a direct one: austenitic–martensitic transformation, or an indirect one: martensitic–austenitic transformation) and the thermal diffusion speed. Then, through self-modulations of the thermal field, the Cu-Zn-Al alloy will self-structure in channel-type or cellular-type thermal patterns, which can be linked to obtained experimental data. Consequently, since the thermal conductivity becomes a function of the observation scale, and heat transfer is modified to reflect the multifractal, non-differentiable paths in the material, it leads to anomalous diffusion and complex thermal behaviors.