The Normal Modes on 1D Diatomic Lattice Model shows the motion and the dispersion relation of N diatomic unit cells. Ionic vibrations in a crystal lattice form the basis for understanding many thermal properties found in materials.  These vibrations are described as displacement waves traveling through the lattice.    These vibrational modes can also be described as bosonic particles called phonons which have quantized energy in much the same way photons do for light.  Using a spring model for the inter-ionic interactions, the dispersion relations between the vibrational frequencies and the allowed wave vectors can be analytically solved for the simple one dimensional case with a two atom basis.  It is sometimes difficult for students to visualize these modes of vibration and how they relate to the resulting ionic motions in the underlying crystal lattice.  This simulation facilitates the understanding of the analytical solutions by graphically representing these modes.  The analytical forms of the two dispersion relations (the optical and acoustic branches) are shown along with the allowed normal mode points.  Based on the chosen normal mode, the motion of the ions as a function of time is displayed to help visualize the mode.  It is easy to see how the chosen mode affects the ion motions inside a unit cell as well as the motions from unit cell to unit cell.  Also, the optical and acoustic motions can be readily compared.  

This model was developed by Richard Charles Andrew using the Easy Java Simulations (EJS) modeling tool.  It is distributed as a ready-to-run (compiled) Java archive.  Double clicking the jar file will run the program if Java is installed.

Please note that this resource requires at least version 1.7 of Java (JRE).