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written by Richard Charles Andrew
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).
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
- Graduate/Professional
- 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 Charles Andrew
Record Cloner:
Metadata instance created October 14, 2013 by Wolfgang Christian
Record Updated:
June 10, 2014 by Andreu Glasmann
ComPADRE is beta testing Citation Styles!

Record Link
AIP Format
R. Andrew, Computer Program NORMAL MODES ON 1D DIATOMIC LATTICE MODEL (2013), WWW Document, (http://www.compadre.org/Repository/document/ServeFile.cfm?ID=13031&DocID=3598).
AJP/PRST-PER
R. Andrew, Computer Program NORMAL MODES ON 1D DIATOMIC LATTICE MODEL (2013), <http://www.compadre.org/Repository/document/ServeFile.cfm?ID=13031&DocID=3598>.
APA Format
Andrew, R. (2013). Normal Modes on 1D Diatomic Lattice Model [Computer software]. Retrieved December 19, 2014, from http://www.compadre.org/Repository/document/ServeFile.cfm?ID=13031&DocID=3598
Chicago Format
Andrew, Richard Charles. "Normal Modes on 1D Diatomic Lattice Model." http://www.compadre.org/Repository/document/ServeFile.cfm?ID=13031&DocID=3598 (accessed 19 December 2014).
MLA Format
Andrew, Richard Charles. Normal Modes on 1D Diatomic Lattice Model. Computer software. 2013. Java (JRE) 1.7. 19 Dec. 2014 <http://www.compadre.org/Repository/document/ServeFile.cfm?ID=13031&DocID=3598>.
BibTeX Export Format
@misc{ Author = "Richard Charles Andrew", Title = {Normal Modes on 1D Diatomic Lattice Model}, Year = {2013} }
Refer Export Format

%A Richard Charles Andrew
%T Normal Modes on 1D Diatomic Lattice Model
%D 2013
%U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=13031&DocID=3598
%O application/java

EndNote Export Format

%0 Computer Program
%A Andrew, Richard Charles
%D 2013
%T Normal Modes on 1D Diatomic Lattice Model
%U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=13031&DocID=3598


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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 Diatomic 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 Diatomic Lattice Model.

relation by Wolfgang Christian

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