Topology and Martensitic Phase Transformations

Triply periodic minimal surfaces (TPMS) are discovered to conform to surfaces of given charge density distributions embedded in crystals [Z. Kristallogr. $\mathbf{\text{170}}$, 138 (1985)]. Based on our previous work [Phys. Rev. Mater. $\mathbf{\text{9}}$, 073802 (2025)], we discovered that crystals can have surfaces of a given charge density converging to TPMS. We also discovered that end states connected by a martensitic phase transformation should have their corresponding TPMS being topologically equivalent. In this work, we gave an explanation for the topological continuity of a martensitic phase transformation and studied how TPMS indicate whether a non-magnetic crystal can undergo a martensitic phase transformation or not.