Hysteretic phononic band structures arising from martensitic phase transformations

Thermal tuning of phononic crystals typically treats each constituent's elastic modulus as a single-valued function of temperature. Here we show that when one constituent undergoes a first-order martensitic transformation (NiTiCu), paired with a Parylene C spacer in a thin one-dimensional composite rod, the intrinsic thermal hysteresis of the transformation is transferred to the collective acoustic response, making it depend on thermal history. Transfer-matrix calculations performed separately along the heating and cooling branches reveal that the same temperature within the transformation interval can correspond to two distinct Bloch band structures and two distinct transmission spectra. As temperature is cycled, stop-band edges trace closed loops in the temperature-frequency plane, producing hysteretic phononic band structures. At a fixed probe frequency, the rod can switch between transmitting and strongly attenuating states depending solely on whether the sample was last heated or cooled, with transmission contrasts exceeding 50 dB in a six-cell structure, thereby realizing a form of acoustic memory. The filling fraction of the active segment provides an independent geometric control parameter that modifies the width of the hysteresis loops and the positions of gap closures. These predictions can be tested directly using immersion-ultrasonic measurements on NiTiCu/Parylene C composite rods.