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Tutorial Modules For The Study Of Phase Equilibrium Diagrams

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2001 Annual Conference


Albuquerque, New Mexico

Publication Date

June 24, 2001

Start Date

June 24, 2001

End Date

June 27, 2001



Page Count


Page Numbers

6.1073.1 - 6.1073.9



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Paper Authors

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Roger Smith

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Holly Bentley

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William G. Fahrenholtz

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NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

Session 3464

Tutorial Modules for the Study of Phase Equilibrium Diagrams William G. Fahrenholtz, Holly R. Bentley, and Roger M. Smith Department of Ceramic Engineering University of Missouri-Rolla


Understanding and interpreting phase equilibrium diagrams is an essential skill for materials engineers. Extensive collections of diagrams are available, making this a resource that can be used to design process cycles, determine reaction paths, and predict thermodynamic compatibility. Hence, courses in phase equilibria are ubiquitous in materials programs. The most difficult skills to master in these classes involve the visualization of the response of complex systems to changes in temperature and composition.

At the University of Missouri-Rolla (UMR), students have developed a series of computer-based tutorial modules that cover topics from the undergraduate course in phase equilibria. Students designed the modules to help future classes understand difficult concepts. Each student selected a subject, outlined the approach, prepared a detailed plan, and then constructed the presentation. Students were also required to present their modules to the class. Individual modules cover one, narrow topic that is important when studying one, two, or three component phase diagrams. Topics range from the use of the lever rule to the construction of vertical sections in ternary systems. With student permission, the modules were posted on the class web page.1

This past year, students prepared twenty-two tutorial modules. Because the tutorials are graphics-intensive, they provide the greatest help when they cover topics that require visualization skills. After posting on-line, the modules are a source of help that supplements material covered in lectures and in the text. The modules are available for students in future classes and for anyone else that needs to learn to interpret or analyze phase diagrams.

I. Introduction

Phase diagrams provide fundamental information on the equilibrium relations among different elements and compounds.2 All materials scientists and engineers, particularly those that deal with high temperature materials, must understand how temperature, pressure, and concentration affect the kind and amount of different phases present at equilibrium.3,4 The discipline of ceramic engineering is uniquely focussed on the development and utilization of materials that are used at high temperatures or that undergo high temperature processing. 5

Most often, ceramists deal with "condensed" phases, i.e., liquids and solids. Pressure is generally assumed to be one atmosphere, although many diagrams exist for higher and lower pressures. The assumption of constant pressure simplifies diagrams by one dimension, shown by the example of a two component system. To fully describe the stable phases for two different

Proceedings of the 2001 American Society for Engineering Education Annual Conference & Exposition Copyright  2001, American Society for Engineering Education

Smith, R., & Bentley, H., & Fahrenholtz, W. G. (2001, June), Tutorial Modules For The Study Of Phase Equilibrium Diagrams Paper presented at 2001 Annual Conference, Albuquerque, New Mexico. 10.18260/1-2--9922

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