A Fractal Approach to Evaluating the Thermal Conductivity of ZrB2–C Composite Ceramic Materials

A pressing issue in materials science is the controlled application of ceramic composite materials at high temperatures in modern technologies, particularly in nuclear physics, atomic energy, aerospace, and rocket engineering. This study investigates the correlation between the thermal conductivity of synthesized ZrB2–C ceramic composites and their microstructural features using fractal analysis. The composites were produced via high-temperature reactive synthesis from boron and zirconium carbide powders. Scanning electron microscopy (SEM) and backscattered electron (BSE) modes was used to obtain micrographs of the fracture surfaces. These images were analyzed using the Box Counting method with ImageJ and FracLac software to determine two fractal parameters: fractal dimension and lacunarity. A strong inverse correlation was observed between lacunarity and thermal conductivity. The study demonstrates that fractal analysis, particularly the lacunarity parameter, can serve as a useful tool for assessing heat transfer potential in two-phase ceramic composites, especially when conventional measurement methods are impractical.