by Mike Craven (resume)
Additional comments by Justin Gravatt (resume)
Modified by R.D. Kriz (5/18/95).
The term project for this class was to produce a diffusion tutorial with the intent of aiding students, in particular introductory Materials Science and Engineering (MSE) students. Students will be able to refer to this tutorial through the MSE2034 Notebook under the Virginia Tech Materials Science and Engineering Department's page. This project was a team effort by the eleven members of the 1995 spring term MSE2094 class.
The Graphics Team consisted of two sophomore MSE students, Justin Gravatt and Michael Craven. Dr. Ron Kriz served as an advisor for the Graphics team since the programs required a deep understanding of scientific visualization. The Graphics Team was responsible for handling all of the graphics throughout the tutorial. Any and all visualization requests were directed to this team.
The Graphics Team was responsible for the graphs, equations, plots, and MPEG movies located throughout the tutorial. The small document under the Scientific Visualization heading is also a result of the work of this team. The document, titled Making Movies , describes the process of creating animation sequences using PV-Wave. These sequences can be played on Macintosh and Window computers, with a larger goal of distribution on the world wide web. This document outlines a procedure that can be executed using PV-Wave on a Unix Workstation. The Graphics Team used a Sun workstation located in the scientific visualization laboratory to complete the programs necessary to achieve the proper byte files. The document also describes the procedure needed to transfer the sequence from the Unix workstation to either a Mac or Windows machine. Allowing the students to see the methodology which was used to create these sequences might spur ideas within them that will permit the passage of more information over the world wide web.
The Graphics Team was responsible for scanning graphs, equations, and plots for other members of the group. The goal of this was to produce gif images that can be referred to easily within an html document. Fortunately, the Graphics Team had access to color scanners which produced high-quality gif files. Scanmaker by AdobePhotoShop was used through a Macintosh machine to produce these files. Once generated, the gif files were distributed to the proper directories in order to aid the group in organizing files for html reference purposes. Communication was especially vital in this portion of the project since images had to change hands among group members. The group members also needed to communicate with the Graphics Team about how they wanted the images to appear and to coordinate the nomenclature involved with naming the files.
The final achievement of the Graphics Team was the production of three MPEG movies. The first movie is a very simple model of vacancy diffusion which gives a very basic picture of the definition of diffusion. This movie was made by scanning a photo of a grid of atoms and using AdobePhotoShop to edit, cutting and pasting the diffusing atom. A series of these 'cut and paste' actions were saved and made into a sequence that was converted into a QuickTime movie and then finally an MPEG movie. The Graphics Team used the last few steps of the Making Movies document in order to form this simple animation sequence.
The final two MPEG movies are true depictions of the possibilities of scientific visualization. These movies vary only in the boundary conditions imposed on the diffusing species. The first movie shows carbon diffusing into iron where only a small area is exposed to carbon impurities and the other movie shows what happens when a larger area is exposed to carbon impurities where all other conditions remain the same. These movies are visual aids that corresponds to Example 2 in Chapter 5 of Materials Science and Engineering - An Introduction, by William D. Callister, Jr. This is the textbook that is used by MSE2034 students. This animation sequence uses different colors to depict a substance diffusing through the surface of the host material. The sequence is also accompanied by a graph that shows the concentration's dependence upon distance from the surface, and this relationship's behavior with time. The exact solution to the problem has been plotted on the movies so that the students can watch the numerical solution approach the exact solution. The Graphics Team was able to place the exact solution on the graphs by inserting the equation used to solve the problem in the text into the PV-Wave program, and then plotting that equation on the same graph as the numerical solution. These MPEG movies are excellent visualizations of the diffusion process.
As a student observes these movies, two things should become immediately apparent. The first 'discrepancy' is that the numerical solution never reaches the exact solution. This can be explained in terms of the boundary conditions imposed on the diffusing species, which is carbon in this example. The equation that is used for the exact solution assumes an ideal condition where the carbon is distributed evenly over an infinite area of steel. Using this model, the carbon tends to diffuse 'directly' into the steel, meaning that the concentration distribution would appear linear. The concentration at a certain depth into the steel would appear constant for the entire steel specimen. The numerical solutions that have been proposed show carbon diffusing over a certain finite area of the steel surface. Therefore, the numerical solutions are lower in concentration since the carbon does not diffuse directly into the steel. When carbon is distributed over a finite area, some of it diffuses at angles to the surface forming a circular concentration distribution. This affects the concentration at distances below the steel surface. This causes the numerical solution to fall short on its approach of the exact solution, in terms of composition of carbon.
The next 'discrepancy' is the difference in concentrations of the different solutions at a distance of two millimeters below the surface (the extreme right side of the graph). Again this is a result of the boundary conditions imposed on the carbon. The concentration of carbon at a distance of two millimeters from the surface, for the numerical solutions, will be the original concentration of carbon in steel. This occurs since the carbon does not diffuse 'directly' into the steel. As was mentioned before, a distinct amount of carbon diffuses at an angle to the surface and keeps the numerical solution from behaving like the exact solution. For the exact solution, the original concentration of carbon in the steel will not be reached until a distance of infinity into the steel since the carbon tends to diffuse straight into the steel. Analyzing these small differences aids in understanding the true behavior of diffusion.
Communication is always the integral part of a team project. The Graphics Team was in contact with the Group Leader, Dan Ruddick. We discussed overall file organization with him and tried to keep him updated on our progress. Susan Holt, who work with the numerical solutions, will use our movies in her portion of the tutorial. The Graphics Team conferred with her since the MPEG movies dealt with her work on the project. Brett Hull, John Stuecker, Paul Myslinski, and Susan Holt were prompt and efficient with providing images that they wanted the Graphics Team to scan. Rob Becker had images that were contained in journal papers and therefore under copyright. Rob decided against having these images scanned. Unfortunately, not all the group members contacted the Graphics Team with images to scan. The phone numbers of the Graphics Team were posted at the organization meeting on 26 April and images were requested to be provided by last friday. Dr. Kriz was referred to frequently for answers concerning the intricacies of creating graphics in general. Overall, this project proved to be an excellent lesson of the importance of communication in group projects.
written by: Michael Craven