Undergraduate Course MSE 130:   Phase Relations in Solids

Course Description:

This is a thermodynamics course. Thermodynamics is also being taught in Dept. of Physics, Chemistry, Chemical Engineering, and Mechanical Engineering. What will be emphasized in this course is phase equilibrium and the driving force of phase changes. We start from heat capacity (Einstein model and Debye model). Knowing heat capacity, e.g. Cp is measurable, we can calculate the enthalpy and entropy. Knowing enthalpy and entropy, we have the Gibbs free energy at constant temperature and constant pressure. Knowing Gibbs free energy per atom or per mole, we have the chemical potential. We use chemical potential to define the equilibrium condition and chemical potential gradient to define the driving force of phase change. Knowing Gibbs free energy as a function of temperature and pressure, we can determine the phase diagram of single composition phases such as ice-water-vapor. For binary elements forming phases with different compositions, we need to define enthalpy and entropy of mixing, then Gibbs free energy of mixing. Simple phase diagrams such as solid solution, miscibility gap, and eutectic system can be obtained.

Course Outline:

1. Review of thermodynamics
   • Variables: pressure, volume, entropy, temperature
   • Energy functions: internal energy, enthalpy, Helmholtz free energy, Gibbs free energy
   • 1st law, 2nd law , reversible processes
   • Microscopic interpretation of thermodynamic variables and Boltzmann's distribution function
2. Heat capacity, enthalpy, entropy, and 3rd law
3. Phase equilibria in a one-component system
4. The behavior of solution
   
5. Free energy-composition diagram and phase diagram (temperature-composition) of binary systems

Textbook:

"Introduction to materials thermodynamics," 3rd edition, David R. Gaskell, HPC, New York (1997).

Reference Book:

"Thermodynamics of materials," Vol. I and II, David V. Ragone, Wiley, New York (1995).

There will be two 2-hour mid-term exams (20% each) and one 3-hour final exam (40%), close book. Four sets of homework (20%).

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Undergraduate Course MSE 131:    Diffusion and Diffusion-Controlled Reactions

Course Description:

This is a kinetics course. The two basic concepts that are essential to the understanding of kinetic processes are atomic diffusion and interfaces. Nucleation forms a new interface. Growth is the atomic process of migration of an interface. Spinodel decomposition involves up-hill diffusion in a diffusive interface. In part A and B, we discuss diffusion and interfaces, respectively. In part C, we discuss phase changes in solidification and in solid state.

Course Outline:

1. Point defects in crystalline solids
2. Fisk's first law of diffusion
   • Concept of atomic flux and flux equation
   • Chemical potential and driving force
   • Diffusivity; prefactor and activation enthalpy
3. Atomic (vacancy) mechanism of diffusion
   • Atomic jump frequency and exchange frequency
   • Measurement of formation and migration enthalpy of vacancy
   • Random walk
4. Fisk's second law of diffusion
   • Solutions of continuity equation;

     Homogenization of a periodic structure

     Diffusion profile of a finite source

     Diffusion profile of a constant source

     Bulk interdiffusion couple

5. Kirkendall effect in interdiffusion
6. Boltzmann-Matano analysis of interdiffusion coefficient
7. Darken's analysis of marker motion
8. Diffusion-controlled and interfacial-reaction-controlled growth

1. Type of interfaces; What changes across an interface?
2. Structure of interfaces
   • Tilt-type grain boundary
   • Twist-type grain boundary
   • Coherent interfaces (homo- and hetero-epitaxial interfaces)
3. Thermodynamics of interfaces
   
   • Surface and interfacial energy
   • Measurement of surface energy
   • Potential of surface curvature
   • Impurity segregation at interfaces
   • Equilibrium shape of crystals
4. Kinetics of interfaces
   • Diffusion along small and large angle grain boundaries
     
   • Grain growth
     
   • Grain boundary grooving
     
   • Kinetics of migration of an interface
     

C. Phase Transformations

1. Solidification
   • Homogeneous and heterogeneous nucleation
   • Dendritic growth and zone refining
   • Constitutional super-cooling
2. Diffusional transformations
   • Overall transformation kinetics - JMA theory and TTT diagram
   • Guinier-Preston zone precipitation (homogeneous nucleation and growth)
   • Cellular precipitation (heterogeneous nucleation and growth)
   • Spinodel decomposition
   • Ordering transformation

Textbook:

"Phase transformations in metals and alloys," by D. A. Porter and K. E. Easterling, 2nd edition, Chapman and Hall, London (1992).

Reference books

"Diffusion in solids," by P. G. Shewmon, 2nd edition, The Minerals, Metals, and Materials Society, Warrendale, PA (1989).

"Interfaces in crystalline materials," by A. P. Sutton and R. W. Balluffi, Oxford Science Publication, Oxford (1995).

"Thermodynamics of materials," vol. II, by D. V. Ragone, Wiley, New York (1995).

There will be two 2-hour mid-term exams (20% each) and one 3-hour final exam (40%), close book. Four sets of homework (20%).

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Undergraduate Laboratory Course MSE 131L:   Diffusion and Diffusion-Controlled Reactions Laboratory

Course Outline:

Experiment I: Grain Growth in Deformed and Un-deformed Cu

Sample: A used 3" or 4" diameter Cu gasket 0-ring from a UHV system. The Cu 0-ring has been indented or deformed with v-groove on both surfaces. The flat surfaces of the Cu 0-ring are un-deformed.

1. One centimeter long pieces are cut from the 0-ring. One piece is mounted and its cross-section is polished and etched for microstructure observation and hardness measurement.
   
2. Other pieces are encapsulated and annealed at 700, 800 and 900 ^oC for 1, 10 and 60 minutes. Then they are mounted , polished, etched for microstructure and hardness measurements.
   
3. X-ray diffraction can be used to show texture changes before and after annealing.

1. Grain growth rate and abnormal grain growth
2. Texture change by comparing the (111) and (200) peak intensity before and after annealing
3. Detect any lattice parameter change by using Bragg's equation to calculate and to extrapolate the lattice parameter from (111) to (420) reflections.
4. Any hardness change before and after annealing.

Experiment II: Interfacial Reaction between Molten Eutectic solder and Cu with V-grooves

Samples: A Cu 0-ring with v-groove as in experiment I, also eutectic SnAg and eutectic SnPb solder and RMA flux

1. Cut the Cu 0-ring into 4 pieces
2. Place one piece of the 0-ring into a glass disk containing the RMA flux
3. Put the glass disk on a hotplate and heat to 200^oC for the SnPb and 240^oC for the SnAg.
4. Cut a tiny piece of the eutectic solder of about 0.2 mille-gram and drop the piece over the groove. The solder melts and runs along the v-groove.
5. Remove the disk from the hotplate after 1sec, 1min and 5 min.
6. Prepare the cross-section of the v-groove for microstructure observation.

1. The growth morphology and growth rate of Cu-Sn intermetallic compound formation between the Cu and solder as a function of distance from the beginning of the V-groove.
2. Using a CCD high speed camera, the speed of molten solder running along the v-groove can be measured. The horizontal capillary behavior of the molten solder along the v-groove can be analyzed.

Experiment III: Cu Thin Film Reactions

Samples: Van der Pauw patterned Cu thin films of 1 cm2 in area and 100nm in thickness, deposited on 4" diameter oxidized Si wafers and 4" diameter bare Si wafers.

1. Cut the van der Pauw patterned test samples into about 1 cm2 pieces for in-situ electrical resistivity measurement and RBS measurement.
2. To study the oxidation of Cu films, annealed the Cu/SiO₂ samples in air and ramp the temperature from room temperature to 300^oC at various rates from 2^oC/min to 20^oC/min, at the same time the resistance change is recorded.
3. To study the Cu silicide formation, annealed the Cu/Si sample in Ar ambient and ramp the temperature from room temperature to 300^oC at various rates from 2^oC/min to 20^oC/min and the resistance change of the film is recorded.
4. To study the effect of Cu silicide on Si oxidation, re-annealed the Cu-silicide/Si sample in air.

1. Determine the activation energy of oxidation of Cu
2. Determine the activation energy of Cu₃Si formation
3. Compare the Si dioxide formation with and without Cu3Si

(Note: For those students who are taking this course, a more detailed description of these experiments and references is available.)

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Graduate Course MSE 201:   Principle of Materials Science (Solid State phase change)

Course Description:

To study kinetic processes in nanoscale materials, we need to know the kinetic processes in bulk-scale materials and thin films. When nanotechnology becomes mature and is in wide application, stability and reliability of nanoscale phases may be important. Even in the processing and fabrication of nanoscale devices, phase formation and transformation may be required

Course Outline:

1. Uni-molecular process in solids, and transition state theory of the activated state
2. Thermodynamic factor (Chemical potential gradient) and kinetic factor (Diffusivity) in atomic diffusion
3. Linear and non-linear diffusion equations and solutions
4. Spinodel decomposition (Cahn and Hilliard theory) and interdiffusion in man-made superlattice
5. Continuity equation in size space
6. Classical theory of nucleation, and growth equation (Hamˇ¦s theory)
7. Johnson-Mehl-Avrami theory of volume fraction of transformation by nucleation and growth
8. Ripening (LSW theory)
9. Theory of grain growth, grain boundary diffusion, diffusion induced grain boundary migration, and cellular precipitation
10. Nanoscale kinetic processes

Reference Book:

J. W. Christian, "The Theory of Transformations in Metals and Alloys; Part I Equilibrium and General Kinetic Theory," 2nd edition, Pergamon Press, Oxford, 1975.

K. N. Tu, J. W. Mayer, and L. C. Feldman, ˇ§Electronic thin film science,ˇ¨ MacMillan, New York, 1993.

There will be one 2-hour midterm exam and one 3-hour final exam.
A presentation (four students as a team) of one hour on a selected topic.
A term paper of less than 10 pages on a selected topic.
Three to four sets of homework will be given.

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Graduate Course MSE 223:   Thin Film Materials Science

Course Outine:

1. Thin film deposition
2. Review of surface energy, diffusion, and stress in thin films
3. Chemical potentials and surface kinetic processes
4. Homo-epitaxy and hetero-epitaxy growth
5. Irreversible processes
6. Schottky barrier and ohmic contacts
7. Silicide formation and thin film reactions
8. Electromigration in VLSI interconnects
9. Flip chip technology and thin film under-bump-metallization

Reference book:

K. N. Tu, J. W. Mayer, and L. C. Feldman, "Electronic Thin Film Science," MacMillan, New York 1992. (ISBN 0-02-421575-9, now Prentice Hall).

There will be a 2-hour mid-term exam and a 3-hour final exam.
Students are required to make a case study presentation of 15 to 20 minutes on a current research topic related to electronic thin films.
Three to four sets of homework problems.