<p>The study of topological behavior, which originally developed based on the electron as a particle, has rapidly extended to the field of electromagnetic and acoustical/elastic waves due to the similarity of the wave function. Phonons, as quasi-particles collectively excited by the crystal structures, play a crucial role in understanding the quantum behavior of materials as well as the interaction between topological mechanics and ferroelectric polarization. In this paper, we have developed a one-dimensional diatomic spring–mass model based on the real material (ferroelectric hafnium oxide) and then investigated its dispersion spectroscopy, including the wave-like properties of its vibrations and the phonon topological behavior, at both classical mechanics and quantum mechanics levels. The results demonstrate that in this material, the structural phase transition process of polarization switching is accompanied by a topological phase transition based on the X²-mode reversal mechanism and undergoing the intermediate T phase. Our study serves as an essential guide for modulating the properties of ferroelectrics and designing new functional devices from the perspective of topological mechanics and phonons.</p>