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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.

Please note that this resource requires at least version 1.7 of Java (JRE).
View the source code document attached to this resource
Subjects Levels Resource Types
Modern Physics
- Condensed Matter
= Crystal Structure
Oscillations & Waves
- Oscillations
= Coupled Oscillations
= Normal Modes
- Upper Undergraduate
- Instructional Material
= Simulation
Intended Users Formats Ratings
- Learners
- Educators
- application/java
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Access Rights:
Free access
License:
This material is released under a GNU General Public License Version 3 license.
Rights Holder:
Richard Andrew
Record Creator:
Metadata instance created October 8, 2013 by Wolfgang Christian
Record Updated:
June 10, 2014 by Andreu Glasmann
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Record Link
AIP Format
R. Andrew, Computer Program NORMAL MODES ON 1D MONATOMIC LATTICE MODEL (2013), WWW Document, (http://www.compadre.org/Repository/document/ServeFile.cfm?ID=13029&DocID=3592).
AJP/PRST-PER
R. Andrew, Computer Program NORMAL MODES ON 1D MONATOMIC LATTICE MODEL (2013), <http://www.compadre.org/Repository/document/ServeFile.cfm?ID=13029&DocID=3592>.
APA Format
Andrew, R. (2013). Normal Modes on 1D Monatomic Lattice Model [Computer software]. Retrieved October 30, 2014, from http://www.compadre.org/Repository/document/ServeFile.cfm?ID=13029&DocID=3592
Chicago Format
Andrew, Richard Charles. "Normal Modes on 1D Monatomic Lattice Model." http://www.compadre.org/Repository/document/ServeFile.cfm?ID=13029&DocID=3592 (accessed 30 October 2014).
MLA Format
Andrew, Richard Charles. Normal Modes on 1D Monatomic Lattice Model. Computer software. 2013. Java (JRE) 1.7. 30 Oct. 2014 <http://www.compadre.org/Repository/document/ServeFile.cfm?ID=13029&DocID=3592>.
BibTeX Export Format
@misc{ Author = "Richard Charles Andrew", Title = {Normal Modes on 1D Monatomic Lattice Model}, Year = {2013} }
Refer Export Format

%A Richard Charles Andrew
%T Normal Modes on 1D Monatomic Lattice Model
%D 2013
%U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=13029&DocID=3592
%O application/java

EndNote Export Format

%0 Computer Program
%A Andrew, Richard Charles
%D 2013
%T Normal Modes on 1D Monatomic Lattice Model
%U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=13029&DocID=3592


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The AIP Style presented is based on information from the AIP Style Manual.

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Normal Modes on 1D Monatomic Lattice Model:

Is Based On Easy Java Simulations Modeling and Authoring Tool

The Easy Java Simulations Modeling and Authoring Tool is needed to explore the computational model used in the Normal Modes on 1D Lattice Model.

relation by Wolfgang Christian

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