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INTRODUCTION

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 three-year 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 state-of-the-art 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 methodology¹ and contributes to the education of new generations of scientists and engineers. A new team- and project-based 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 upper-level 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 problem-focused, problem-framing 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.

TEACHING ACTIVITIES

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 environment-dependent, 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 off-center 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 industrial-related, open-ended 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/FACT⁷ and ThermoCalc⁸ 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 rate-limiting steps are illustrated.

In this project, the course objectives are to:

• Understand fundamental principles of thermodynamics of materials from a practical viewpoint—thermodynamics as a toolbox to help study chemical behavior of materials
• Integrate chemistry, phase equilibria, and thermodynamics of a materials system as different means of describing the same chemical behavior with quantitative relationships among them
• Define thermodynamic terms/values in terms of measurable quantities such as temperature, pressure, and compositions to understand thermodynamics in depth
• Emphasize problem solving and, more specifically, develop explanations and understanding of chemical and thermal behavior observed in the laboratory/industry
• Learn the use of state-of-the-art equilibrium thermodynamics computer software as an aid in performing calculations, particularly those involving chemically complex systems with many species

The approaches used in this course include modifications of lecture notes, homework assignments, mid-term and final exams, and quizzes. The following specific measures were taken:

• One lecture hour each week was devoted to applications of computational activities.
• Many homework assignments were solved both by hand and by computer software.
• Quizzes for calculations of thermodynamic properties and phase diagrams were introduced.
• Exam problems were created from the output of computer software.

One example of a homework question is: Can an Ni(s) crucible be used to contain Fe₂O₃, FeO, or Fe₃O₄ 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 Fe-Ni-O 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 Fe-Ni-O ternary isothermal section at 1,500 K.	Figure 3: The carbon concentration profiles in a diffusion couple of two Fe-Si-C alloys with 3.80%Si-0.49%C and 0.05%Si-0.45%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:

• Introduction to generalized Onsager fluxes for diffusion in multicomponent systems
• Thermodynamics of irreversible processes, frames of reference, and linear theory
• Diffusion in simple phases, complex phases, and ionic phases
• Thermodynamics and kinetics of phase transformations
• Simulations of diffusional processes and phase transformations

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 program⁸ that shares the same thermodynamic databases as the Thermo-Calc 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 Fe-Si-C 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.

a

b

Figure 4. The phase-field simulation tools applied to the spinodal decompositions, (a) the interface, (b) the microstructure.

Figure 5. The schematic relationships between thermodynamics/kinetics and system materials design.

Figure 6: Alloy development history.

The course also briefly discusses both the microscopic and continuum phase-field 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 visual-Fortran-based executable Windows-based 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 real-time 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 real-time evolution process as well as take snapshots of the images during evolution. The students are assigned homework problems that require using the visual-Fortran codes. The comments from students on the use of visual-Fortran codes are very positive.

System Materials Design

System Materials Design is a team- and project-based 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 University¹ 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:

• Research data demonstrate that 80–96% of air pollution due to vehicle exhaust is generated within 200 s between a vehicle start and the time the catalyst reaches its optimal operating temperature (around 340°C). This is particularly a problem for vehicles used for delivery as they are switched on and off frequently each day. Students were asked to develop an optimal solution for this case using the system materials design approach.
• Today’s commercial high-strength low alloys (HSLA) have a typical yield strength of 80 ksi (about 56 kgf/mm² or 550 MPa). Figure 6 shows the development of HSLA in the past half century. With the ocean exploration of gas and petroleum going to deeper and deeper water and the increase of pipeline pressure, a yield strength as high as 120 ksi (about 84 kgf/mm² or 827 MPa) is desirable. Students were asked to design such an alloy using the system materials design approach with other properties balanced based on the application.

During the semester-long 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 problem-oriented, using publications and hands-on 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:

• Review of thermodynamic and kinetic principles
• Modeling of atomic mobility
• Simulation of diffusional phase transformations with simple geometries
• Time-temperature-transformation simulation for inclusions
• Monte-Carlo simulation of grain growth
• Kinetic Monte-Carlo simulation: ordering and phase separation
• Microscopic diffusion equation modeling of diffusional processes
• Time-dependent Ginzburg-Landau equations: order parameters, Landau expansions, and antiphase domain coarsening
• Cahn-Hilliard equations: phase separation and precipitate coarsening
• Coherency strain energy and applied stress: coherent precipitate morphologies and ferroelectric and ferroelastic domains
• Phase-field simulation: solidification and grain growth
• Project of the course

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 Thermo-Calc 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 Cr₂O₃ 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.

EVALUATION

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:

• Outside Evaluation—Outside evaluators from academia and industry rated the students’ written reports and oral presentations. This was used to evaluate how well the students were able to apply their knowledge of fundamental principles; demonstrate project design and management skills; provide optimal, cost-effective solutions; and show their communication skills.
• Peer Evaluation—The students evaluated members of their own groups and other groups on their communication skills, either in a group setting or during presentations.
• Pre/Post Tests of Students’ Knowledge of Specific Course Content—Knowledge comes in many forms, such as concepts, definitions, rules, and relationships between these items. When students build and understand relationships between concepts, they will then be better prepared to apply this learning to other situations.¹³ The project activities students engaged in were designed to help them form a stronger understanding of relationships between concepts. The pre/post tests evaluated the changes in students’ understanding of these relationships.
• Comparison—A comparison of student performance on tests, quizzes, and projects with those from previous years was performed.

The methods that were used to measure student attitudes included:

• Pre/post test surveys of student attitudes toward thermodynamics and kinetics and a comparison in following years with those from previous years
• Surveys of students’ perceptions of how well-prepared they were for subsequent academic or industrial applications to the complexity of materials behavior
• Focus groups to further explore the experiences of students in the program and elicit feedback on the implemented components (see Appendix A)

The methods used to measure the program implementation included:

• The number of students, educators, and non-residential students taking the courses
• Student surveys of classroom processes including the impact of the technology classroom (see Appendix B)
• Observation of actual classroom sessions in order to determine potential areas of strengths and weaknesses in the educator’s teaching experience (see Appendix C)
• Evaluation to examine how industrial and academic workshop participants plan to use the computational techniques in their research and development and curriculums

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 self-reported 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 open-ended 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 step-by-step 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 pre-test.	Figure 8: An example of pre-test and post-test responses to the following item: Thermodynamic concepts are difficult to understand. A) Strongly Disagree B) Disagree C) Neutral D) Agree E) Strongly Agree

DISCUSSION

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 post-hoc comparisons between students who had taken the traditional courses and those who have taken the computationally based courses.

CONCLUSION

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, step-by-step 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.

ACKNOWLEDGEMENTS

The authors are thankful for the financial support of the National Science Foundation through the grant DMR-0073836. The Department of Materials Science and Engineering at Penn State enthusiastically provided a wide range of services for the project and is highly appreciated.

References

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 Solid-State 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, "THERMO-CALC & 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, "Phase-Field 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.: Butterworth-Heinemann, 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 Zi-Kui Liu at Pennsylvania State University, 209 Steidle Bldg., University Park, PA 16802; (814) 865-1934; fax (412) 291-3185; e-mail liu@matse.psu.edu.