Normal Modes on 1D Monatomic Lattice Model Documents

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Main Document

Normal Modes on 1D Lattice Model 

written by Richard Charles Andrew

The Normal Modes on 1D Monatomic Lattice Model shows the motion and the dispersion relation of N identical ions of mass M separated by a lattice distance a. 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 relation between the vibrational frequencies and the allowed wave vectors can be analytically solved for the simple one dimensional case.  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 solution by graphically representing these modes.  The analytical form of the dispersion relation is 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 from unit cell to unit cell.

The Normal Modes on 1D Monatomic Lattice 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.

Last Modified October 14, 2013

This file has previous versions.

Source Code Documents

Normal Modes on 1D Lattice Source Code 

The source code zip archive contains an XML representation of the Normal Modes on 1D Lattice Model.   Unzip this archive in your Ejs workspace to compile and run this model using Ejs.

Last Modified October 14, 2013

This file has previous versions.