Simulations of Lattice Vibrations in a One-Dimensional Triatomic Network

Abstract

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