Assessment Of Interdiffusion Coefficient Through Spreadsheet Implementation

Abstract

In intermediate materials science laboratory courses the analysis of experimental data is heavily dependent on the students’ proficiency in the use of commercial softwares. In such courses, the students are required to apply theoretical principles and analyze the corresponding experimental results. In the present article, a spreadsheet implementation results in a simplified alternative to analyze experimental data when numerical techniques are required. Numerical integration and differentiation are performed by using Microsoft Excel™ 7.0 for Windows. Finally the resulting analysis is contrasted against literature data and important conclusions are drawn.

Cookbook-type of data analysis can help those students with less computer skills catch up with the rest of the class and comply with the requirements of the course. However, when dealing with mathematical problems that cookbook approach can hinder the understanding of the physical or chemical principles on which the analysis is based (1). In addition the application of numerical analysis techniques and their limitations may not be evident if no breakdown of the problem mechanics is provided. As a worthy example of an alternative approach, the study of chemical diffusion in the copper-nickel binary system is presented as set up in a college Physical Metallurgy laboratory course offered at the Dept. of Materials Science and Engineering of the University of Wisconsin-Madison every Spring semester. As prerequisite for this laboratory there is an introductory Phase Transformation course. Therefore the students are supposed to be familiar with the phenomenological viewpoint of chemical diffusion in a metallic system. In addition, some knowledge of numerical analysis is beneficial for the complete understanding of the present experiment.

2. Basics of Diffusion and Matano-Boltzmann’s Analysis

Diffusion in an A-B substitutional metallic system comprises the analysis of atom mobility as affected by temperature and chemical potential differences across an interface (Figure 1). In this case the non-steady diffusion process is described by Fick’s Second Law:

† Teaching Assistant ‡ Associate Professor

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