Simulations of Lattice Vibrations in a One-Dimensional Triatomic Network

A. JUAN

Physchem

Multidisciplinary Digital Publishing Institute (MDPI)

Año: 2023 vol. 3 p. 440 - 450

Using equivalent electrical circuits (EEC) is not common practice in several areas of physicalchemistry. The phonon concept is used in solid-state works but much less frequently in branchesof chemistry. Lattice vibration phenomena present a high complexity when solving equations inreal systems. We present here a methodology that crosses disciplines and uses EEC that can beanalyzed and solved using freely downloaded computer codes. To test our idea, we started with aone-dimensional lattice dynamics problem with two and three masses. The initial mechanical modelis numerically solved, and then an equivalent circuit is solved in the framework of electrical networktheory through the formalism of transfer function. Our lattice model is also solved using circuitanalysis software. We found the dispersion relationship and the band gaps between acoustical andoptical branches. The direct solution of a mechanical model gives the correct answers, however, theelectrical analogue could give only a partial solution because the software was not designed to beconverted into an analogue simulator. Due to the finite size of the circuit elements, the number ofcomputed frequencies is less than those expected for two unit cells and right for eight. On the otherhand, by using a huge number of electrical components, the network behaves like a low-pass filter,filtering higher frequencies.