Basic principles of chemical thermodynamics as applied to macro and nano-sized materials. This course will cover the fundamentals of classical thermodynamics as applied to the calculation and prediction of phase stability, chemical reactivity and synthesis of materials systems. The size-dependent properties of nano-sized systems will be explored through the incorporation of the thermodynamic properties of surfaces. The prediction of the phase stability of two and three component systems will be illustrated through the calculation and interpretation of phase diagrams for a variety of materials systems.

Text: Introduction to the Thermodynamics of Materials, D.R. Gaskell, McGraw-Hill, 4th edition. Additional lecture notes/handouts will be supplied throughout the course

1. Fundamental Principles and Laws of Thermodynamics. Review of 1st law of thermodynamics: state functions; path independence, heat and work, internal energy, enthalpy, heat capacity. Types of paths: adiabatic, isothermal, isochoric, isobaric (G2). 2nd law: reversibility; entropy; equilibrium, calculation of entropy changes, entropy and disorder. (G3 &4). Third Law: free energy, standard states, utilizing experimental data to calculate enthalpy, entropy, and free energy changes in macro-scale systems (G5). 3 weeks

2. Phase equilibrium in a one-component system. Vapor pressure, co-existence of phases, chemical potential. 1 component phase diagrams. G7 1/2 week.

3. Reaction equilibrium in gaseous systems. Standard state for a gas, partial pressure, free energy of mixing, chemical potential. Reaction equilibria; equilibrium constant; meaning of standard free energy change. Why does Le Chatelier’s principle work ? Balance between chemical stability and entropy of mixing.  G11 1/2 week

4. Heterogeneous equilibria. Standard state for solids and liquids, reaction equilibria for metal/metal oxide systems. Ellingham diagrams. Multiple oxidation states in transition metal oxide systems. G12. 1 week

5. Thermodynamics of condensed solutions. Raoult's law; ideal solutions, activity, chemical potential, free energy of mixing in solid solutions, meaning of random mixing. Non-ideal solutions; activity coefficient, excess free energy of mixing, enthalpy of mixing. Mixing models for binary systems; regular solution model, interaction parameter, stability of inorganic solid solutions; relation of mixing energetics to crystal structure.  G9 1 1/2 weeks

6. Phase stability in two-component systems. Free-energy - composition relationships; immiscibility in the solid state, common tangents. Solid-liquid equilibria, Calculation of phase diagrams for ideal solid-liquid co-existence. (G 10) Non-ideal systems; eutectic systems, peritectic systems. Free energy of mixing curves, activity-composition relations. (G 13). 1 1/2 weeks

7. Binary and Ternary Phase Diagrams. Cooling curves in binary systems, reading complex diagrams, intermediate compounds, congruent and incongruent melting.  1 week

8. Size dependent properties of nanocrystals: Surface tension, surface free energy, Kelvin effect. Variation of melting point and solid state phase transformations with particle size and shape in the nano-regime.  Changes in phase stability in the nano-regime; nano-sphere and nanowire melting. 2 weeks.

Problem sets (compulsory); 2 mid-semester examinations; final examination.

Grades: Problem sets (10%); Midterm 1 (25%); Midterm 2 (25%); Final (40%)

Note: Problem sets must be handed in on the due date; 10% of the grade will be subtracted for each day late.