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MAP An Article from the December 2003 JOMe: A WebOnly Supplement to JOM 


ZiKui Liu, LongQing Chen, and Karl E. Spear are with the Department of Materials Science and Engineering and Carlee Pollard is with the Department of Educational and School Psychology and Special Education at Pennsylvania State University.

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Thermodynamics and kinetics of materials are two critical components in materials design,^{1,2} but have long been viewed as two of the most difficult subjects to both teach and learn in materials science and engineering. Thermodynamics is generally considered to be abstract and kinetics to be highly mathematical. Many undergraduate and graduate students, after taking the two courses, still lack the necessary skills to apply fundamental thermodynamic and kinetic principles to quantitatively solve practical materials research and engineering problems. Based on recent developments in computational thermodynamics and computational kinetics and their proven success in research and industrial applications, the authors proposed to the Division of Materials Research at the National Science Foundation (NSF) in 1999 to improve the student learning experience and educator teaching experience in thermodynamics and kinetics by integrating fundamental principles and advanced computational approaches. A threeyear project was consequently established from 2000–2003 at Pennsylvania State University (Penn State) with the enthusiastic support of the university’s Department of Material Science and Engineering. A computer teaching facility was immediately set up and first used for teaching in fall 2000, equipped with stateoftheart computational tools. This facility has been used not only for courses related to this project, but also for other courses taught in the department.
Additionally, national initiatives and workshops^{2–5} enabling students to practice project design, project management, and interpersonal communication skills were introduced. System materials design integrates fundamental principles of processing, structure, and properties through computational thermodynamics, kinetic simulations, and engineering system design methodology^{1} and contributes to the education of new generations of scientists and engineers. A new team and projectbased graduate course on System Materials Design was thus developed with faculty from Penn State’s Engineering Design and Graphics Department teaching project design and project management. Furthermore, a new computational course on continuum and mesoscale simulations was developed to focus on computational techniques and fundamentals of phase transformation simulations on the continuum, mesoscale level. This course introduces the evolution of simulation techniques and integrates fundamental principles in thermodynamics and kinetics with advanced computational approaches. Some of the teaching materials were also applied in upperlevel undergraduate courses.
A comprehensive teaching assessment approach was developed in association with the Schreyer Institute for Innovation in Learning at Penn State. The Schreyer Institute is an applied research laboratory that seeks more effective ways for students to learn and for instructors to teach. Its mission is to promote a partnership between students and faculty to design, conduct, and engage in problemfocused, problemframing learning experiences that foster inquiry, initiative, and teamwork.
The teaching activities of the past three years are presented in this article, along with the assessment results of the program.
Thermodynamics and kinetics, two core components of materials science and engineering, are not reflected in the traditional materials science and engineering tetrahedron that relates processing, structure, property, and performance. Thus, the authors developed the schematic relationship among the key components in materials science and engineering shown in Figures 1a and 1b. Figure 1a represents the physical space of materials. The outermost circle is the performance circle, which characterizes how a material behaves in given environments. The performance is realized by a set of properties, in the second circle, relevant to those environments. Those properties are achieved by an agglomeration of phases with various structures and their morphologies in the third circle. The structures are obtained through proper processing in the fourth circle with accurate chemical compositions in the fifth circle. While the two outermost circles are environmentdependent, the three inner circles can be directly related to the three key components in materials science and engineering, crystallography, kinetics, and thermodynamics, as shown in Figure 1b. This diagram demonstrates the core importance of thermodynamics and kinetics in the discipline and also outlines the foundation of the recent multiscale, multicomponent materials simulations and design projects described in Reference 6. The offcenter feature of the circles implies one’s subjective view on the degree of difficulties in the multiscale integration.


a  b 
Figure 1. The schematic relationship of key components in materials science and engineering. 


The authors believe that two of the main reasons for thermodynamics and kinetics of materials being viewed as difficult subjects are the available teaching tools and the opportunity for application. In the past, the fundamental abstract concepts in thermodynamics could only be quantified for binary or ternary systems with one or two possible reactions; more complicated cases could not be calculated due to the lack of thermodynamic data and minimization tools. Typically, after taking the thermodynamic and kinetic courses, graduate students have no further opportunities to practice the subjects in other courses, and few students use thermodynamics and kinetics in their thesis research projects as they have not learned to deal with multicomponent systems. Thus, the authors developed a course that allows students to apply fundamental thermodynamic and kinetic principles to quantitatively address industrialrelated, openended problems.
Thermodynamics of Materials
Thermodynamics of Materials is a course taken by almost every materials science and engineering graduate student at Penn State. An undergraduate course in thermodynamics of materials (or equivalent) is a prerequisite. The major thrust in this course is to integrate the computational thermodynamics with the classic approaches through the computational software ChemSage/FACT^{7} and ThermoCalc^{8} for thermodynamic calculations. Students examine the use of equilibrium calculations for explaining and predicting dynamic reactions of systems at high temperatures and their limiting maximum rates as a function of experimental variables. Local (partial) equilibrium concepts are used for calculations in dynamic systems, and methods for deducing mechanistic ratelimiting steps are illustrated.
In this project, the course objectives are to:
The approaches used in this course include modifications of lecture notes, homework assignments, midterm and final exams, and quizzes. The following specific measures were taken:
One example of a homework question is: Can an Ni(s) crucible be used to contain Fe_{2}O_{3}, FeO, or Fe_{3}O_{4} without reactions at 1,000 K or 1,500 K? Students can solve this problem by constructing all possible chemical reactions and calculating the Gibbs energy changes of these reactions or by calculating the isothermal sections of the FeNiO ternary systems with all binary and ternary oxides (Figure 2). For multicomponent systems, this type of problem becomes very difficult to solve as it becomes harder to list all possible reactions. With the computational approach, one can include either all compounds for a complete equilibrium state or subsets of compounds for metastable equilibrium states.


Figure 2: The calculated FeNiO ternary isothermal section at 1,500 K. 
Figure 3: The carbon concentration profiles in a diffusion couple of two FeSiC alloys with 3.80%Si0.49%C and 0.05%Si0.45%C, respectively. 


Kinetics of Materials Processes
Kinetics of Materials Processes is another course taken by almost every materials science and engineering graduate student at Penn State. First, the fundamental kinetic principles of diffusional processes and phase transformations are covered with the following outline:
The computational materials of the course are mostly drawn from the extensive computational research in the last five to ten years on the kinetics of phase transformations and microstructure evolution in materials. Particularly, this course uses the Dictra program^{8} that shares the same thermodynamic databases as the ThermoCalc program used in the computational thermodynamics of materials course, plus has a mobility/diffusivity database. A number of computer experiments were designed to teach students how to conduct process modeling such as homogenization, diffusional phase transformations, and diffusion couples. For example, students are asked to reproduce the results for the uphill diffusion in the FeSiC system (Figure 3). They are then asked to explain, thermodynamically and kinetically, why carbon diffuses from the low carbon concentration region (A) to the high carbon concentration region (B) and to simulate the times needed to homogenize the carbon concentration at a number of different temperatures.
The course also briefly discusses both the microscopic and continuum phasefield kinetic models that have been applied to a wide range of phase transformation and microstructure evolution kinetic problems including precipitation, phase separation, structural transformations, coarsening, and grain growth.^{9,10} A set of visualFortranbased executable Windowsbased software was developed by modifying the research computer codes. Using these codes, students are able to conduct virtual experiments on a computer and watch the realtime microstructure evolution for the most common phase transformations. These codes have also been used in the mesoscale modeling graduate course discussed in this article. Figures 4a and 4b show examples of understanding the spinodal decomposition process using the code. Students are able to study the effect of composition, elastic inhomogeneity, lattice mismatch, and applied strain on the morphological evolution by changing the parameters in a dialog box (Figure 4a). They can watch the realtime evolution process as well as take snapshots of the images during evolution. The students are assigned homework problems that require using the visualFortran codes. The comments from students on the use of visualFortran codes are very positive.
System Materials Design
System Materials Design is a team and projectbased course. Knowledge and skills students learned from Thermodynamics of Materials and Kinetics of Materials Processes are the foundation for this course. Figure 5 shows the relationships among thermodynamics, kinetics, and system materials design. The ideas of the Materials Design course taught at Northwestern University^{1} were integrated into this course as well as the engineering design methodologies from Penn State’s College of Engineering.
This course started with the introduction of materials property maps developed by M.F. Ashby.^{11} The materials property maps provide a menu of existing engineering materials and the ranges and various combinations of their intrinsic properties. Following a discussion of design principles based on the textbook by N.P. Suh,^{12} the concepts of the functional requirements and design parameters in design principles were introduced in terms of design objectives defined by performance and physical embodiments defined by properties. The design process involves relating these functional requirements of the functional domain to design parameters in the physical domain. The hierarchy of functional requirements and design parameters was explored through the two principal axioms, the independence axiom in maintaining the independence of functional requirements and the information axiom in minimizing the information content. Tools for computational thermodynamics and kinetic simulations were introduced and utilized during design projects whenever applicable.
The following design projects were carried out by two groups of students:
During the semesterlong project activities, individual reports and team reports were interwoven. In team reports, students were required to state the team’s organization and to identify contributions from individual members, and a five to ten minute presentation was required with each report. When students gave a presentation, other students used a rubric to evaluate the presentation for content, organization, delivery, and visual aids. The details of the evaluation were then given to presenting students for review.
Continuum, Mesoscale Simulations
This course, focused on computational techniques and fundamentals of phase transformation simulations on the continuum, mesoscale level, was taught using the computer teaching facility established in this project. The objective was to introduce the evolution of simulation techniques and integrate fundamental principles in thermodynamics and kinetics with advanced computational approaches. The teaching was problemoriented, using publications and handson computer exercises to give students experience in presenting problems to the computer and interpreting the results. This course was aimed at students who would like to explore the power of computational approaches and understand the thermodynamic and kinetic principles behind computational phase transformations. Thermodynamics of Materials, or an equivalent course, and knowledge of phase transformations were prerequisites for this course.
The topics covered in this course include:
Preliminary Expansion to Undergraduate Classes
Several attempts were made to expand computational approaches to undergraduate classes (i.e., Thermodynamics of Materials taught to juniors, Phase Transformations in Metals and Alloys taught to juniors and seniors, and Metallurgy Lab taught to seniors).
In Thermodynamics of Materials, computational tools were used to calculate the thermodynamic properties and phase diagrams of pure substances and binary systems and to demonstrate the relationship between Gibbs energy diagrams, phase diagrams, and concept of reference states.
In Phase Transformations in Metals and Alloys, other types of phase diagrams in addition to those used in Thermodynamics of Materials were introduced by plotting conjugate quantities of temperature and compositions (i.e., entropy and chemical potentials or activities). This further reiterates the concept of reference states.
In Metallurgy Lab, a computational lab based on the following ThermoCalc example was developed: A manufacturer wanted to increase the chromium content of a material from 18 to 25 weight percent. However, clogging starts to occur during the continuous casting of this material because solid Cr_{2}O_{3} is formed. By calculating the equilibria in the steel/slag system, a simple modification could be found through the adjustment of the steel melt composition.
The objectives of the computational lab are to have students experience the efficient computational approach to solving practical problems and understand the thermodynamic fundamentals behind the computational approach. Students were challenged to find the maximum chromium content one could have without clogging during continuous casting with the given composition of the steel melt and to show if one can adjust the temperature to do the same.
To determine the effectiveness of the project, an assessment plan was designed and implemented over the course of several semesters. This plan was developed around the objectives of the courses as well as the objectives of the project in order to identify strengths and weaknesses in the program and work with these to enhance the new program.
Methods of Evaluation
An overall assessment plan was developed for this project. The plan involved the utilization of existing and new assessment methods that focused on three major areas: student learning, student attitude, and program implementation.
Several methods were used to measure student learning including:
The methods that were used to measure student attitudes included:
The methods used to measure the program implementation included:
Results of Evaluation
The students involved in the program showed improvement in many areas over the course of the project. For example, the students showed significant improvement on knowledge tests across the semester (see Appendix D). Several students also showed improvement in their peer presentation and teamwork scores across the semester. In addition, the student attitudes showed improvement across the semester. A statistically significant positive relationship was found between course grades and selfreported student attitudes.
When student feedback was implemented as improvements made by the course instructor, this was reflected in continued improvements in student learning. The students were provided the opportunity to give feedback about the program through focus groups and openended surveys. Their comments and suggestions were then converted into recommendations that were given to the course instructors. Examples of these comments included requests for more practical examples during class lectures and for better stepbystep solutions for homework problems.
An additional important finding from the surveys and focus groups was the apparent awareness of the significance of the new computational approach in educating the students. While this was evident in the quantitative data (for example, see Figure 7), it was more obvious in the qualitative data provided by both students enrolled in the relevant courses and those who had taken the traditional courses. Students from previous years indicated that a computer laboratory portion of the courses would have been beneficial to them in their current research. Students who were given the opportunity to learn the computational techniques over the course of the project commented on its usefulness and practical nature.
The results of the evaluation of the program implementation also showed evidence that the participants understood the vital nature of the computational core of this project. For example, the enrollment numbers in the new course developed as a result of the NSF grant were encouraging, and the workshops for those outside the university were filled to capacity. In addition, the workshop participants showed strong interest in furthering their newly acquired knowledge in future workshops. The results of observations of the students’ computer lab time and the workshops were used to improve learning and teaching while using the computers. For example, it was found that teaching assistants were needed to assist students with minor problems in order to minimize the distractions for both the students and the instructor.


Figure 7: Student attitudes that computers can expand the complex of problems tackled in the classroom at pretest. 
Figure 8: An example of pretest and posttest responses to the following item: Thermodynamic concepts are difficult to understand. A) Strongly Disagree B) Disagree C) Neutral D) Agree E) Strongly Agree 


It appears that in this project, the quantitative and qualitative data complemented each other well. The quantitative data provide a numeric account of the attitudes and performance of students in the larger courses. The qualitative data narrow down areas in need of improvement and allow students to provide suggestions for future semesters. It also allows for a better source of data collection in smaller classes. Students in these smaller courses should be encouraged to take better advantage of these opportunities to provide feedback.
It was found in this study that student feedback could be used to enhance the student learning and educator teaching experiences. In addition, it appeared that this project was successful in assisting the students to view thermodynamics and kinetics as more useful and less difficult and abstract (Figure 8).
Based on information gathered through the various aspects of the project evaluation, recommendations were made to the educators and project investigators for future implementation into the graduate and undergraduate programs.
One weakness of this study was the lack of an adequate control group. It is difficult to make valid posthoc comparisons between students who had taken the traditional courses and those who have taken the computationally based courses.
The evaluation component has been a very important part of the project. It has allowed the instructors to gain feedback on an experimental program, which is necessary to improve both their teaching and the students’ learning. Several themes resounded in the data. One was that the students showed continued support for the program throughout this project and believed it to be beneficial to them. Another was that the students desired a great deal of structure in order to successfully integrate the knowledge that they acquired from their coursework into their research. This structure includes taking steps such as having the instructors provide a framework for the lecture information, stepbystep solutions to homework problems, and outside resources such as books, web materials, computer program manuals, and teaching assistants when the students encounter problems they are not equipped to solve.
The authors are thankful for the financial support of the National Science Foundation through the grant DMR0073836. The Department of Materials Science and Engineering at Penn State enthusiastically provided a wide range of services for the project and is highly appreciated.
1. G.B. Olson, "Computational Design of Hierarchically Structured Materials," Science, 277 (1997), pp. 1237–1242.
2. Report of a workshop sponsored by the U.S. National Science Foundation, "New Directions in Materials Design Science and Engineering (MDS&E)", Georgia Institute of Technology Materials Council and Morehouse College, 1998.
3. Committee on Science, Engineering, and Public Policy, Reshaping the Graduate Education of Scientists and Engineers, (Washington, DC: National Academy Press, 1995), www.nap.edu/books/0309052858/html/index.html.
4. U.S. Department of Energy, DOE Initiative in Computational Materials Science, 1998, www.er.doe.gov/production/bes/May4Report.htm.
5. U.S. Department of Defense’s Defense Advanced Research Projects Agency, Accelerated Insertion of Materials (AIM), 1999, www.darpa.mil/dso/thrust/matdev/aim.htm.
6. L.Q. Chen, C. Wolverton, V. Vaithyanathan, and Z. K. Liu, "Modeling SolidState Phase Transformations and Microstructure Evolution," MRS Bull., 26 (2001), pp. 197–202.
7. C. Bale, P. Chartrand, S.A. Degterov, G. Eriksson, K. Hack, R. Ben Mahfoud, J. Melancon, A.D. Pelton, and S. Petersen, "FactSage Thermochemical Software and Databases," CALPHAD, 26 (2002), pp. 189–228.
8. J.O. Andersson, T. Helander, L.H. Hoglund, P.F. Shi, and B. Sundman, "THERMOCALC & DICTRA, Computational Tools for Materials Science", CALPHAD, 26 (2002), pp. 273–312.
9. L.Q. Chen and Y. Wang, "The Continuum Field Approach to Modeling Microstructural Evolution," JOM, 48 (1996), pp. 13–18.
10. L.Q. Chen, "PhaseField Models for Microstructure Evolution," Annual Review of Materials Research, 32 (2002), pp. 113–140.
11. M.F. Ashby, Materials Selection in Mechanical Design, 2nd ed. (Oxford, U.K.: ButterworthHeinemann, 1999).
12. N.P. Suh, The Principles of Design, (New York: Oxford University Press, 1990).
13. J.D. Novak, "Concept Maps and Vee Diagrams: Two Metacognitive Tools to Facilitate Meaningful Learning," Instructional Science, 19 (1990), pp. 29–52.
For more information, contact ZiKui Liu at Pennsylvania State University, 209 Steidle Bldg., University Park, PA 16802; (814) 8651934; fax (412) 2913185; email liu@matse.psu.edu.
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