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Course Detail

Course Name Thermodynamics of Defects and Phase Transitions in Solid State
Course Code 22PHY549
Credits 3


Unit 1

Defect Chemistry
Learning Objectives
Learn different types of defects present in solids and differentiate between thermodynamically permitted defects and other types of defects and their energies and optimal concentration in a solid; Deduce the connection between defects and defect compensations.

Point and electronic defects; Kröger-Vink notation; Effective charge on a defect; Frenkel and Schottky defects; Defect formation and reaction equations; Extended defects – Line and planar defects; Population and energy of defects: Equilibrium population of vacancies, Schottky and Frenkel defects; Energy of a point defect and a line defect; Non-stoichiometric defects – the phase diagram.

Unit 2

Thermodynamics of Solid Solutions
Learning Objectives
Review basic thermodynamic potentials and calculate them using appropriate formulas. Understand the relevant thermodynamic models and concepts necessary to understand the formation of solids.

Review of basic thermodynamic functions – heat capacities, enthalpy, entropy, chemical potential, activity and activity coefficients; Statistical definition of entropy; Thermodynamics of solutions – entropy, enthalpy and free energy of solution and mixtures; First order and second order phase transitions; Approximations to the free energy function – Ideal solution, Regular solution and Sub-lattice model; the calculation of Phase Diagrams (CALPHAD) technique using the sub-lattice model.

Unit 3

Binary Phase Diagrams
Learning Objectives
Learn how to interpret a practical phase diagram and gleaning information from published phase diagrams.

The Gibbs phase rule; the common tangent rule; the Lever rule; understanding the binary phase diagram; Miscibility gap.

Unit 4

Learning Objectives
Review solution techniques of differential equations describing diffusional phenomena using Fick’s laws.

Basic review of parabolic partial differential equations (PDEs); solution by analytical and numerical methods; Fick’s laws; solution of the Fick’s diffusion equation; Mechanisms of diffusion; Kirkendall effect.

Unit 5

Non-classical diffusion
Learning Objectives
Understand the limitations of the classical Fick’s laws; Introduction to the two C-H and A-H equations describing non-classical diffusion and solution method(s).

Overview of the types of solid state phase transitions; Failure of the classical Fick’s law; Spinodal decomposition; Cahn-Hillard (C-H) equation; Solution of the C-H equation using the semi-implicit Fourier spectral method; Using the C-H equation for understanding microstructural evolution in solids.

Objectives & Outcomes

Prerequisites: The student is expected to have covered topics in basic solid-state physics/ crystal physics and a basic course in thermodynamics.

Course Objectives:
1. Present a general outline of solid-state phase transitions in materials starting from point defects to phase diagrams
2. Understand how to calculate free energy of a solid using various approximations and construct a simple phase diagram for a binary alloy
3. Description of diffusion and how to solve diffusion problems
4. Combining thermodynamics and kinetics to understand how microstructures develop in real materials

Course Outcomes:
CO1. Understand the concept of crystalline defects in solids and their implications in phase diagrams
CO2. Apply the notion of effective charges to write defect chemistry equations
CO3. Understand how to construct binary phase diagrams
CO4. Understand the concept of diffusion in solids and their implications in phase transitions.

Skills: The student will develop a better understanding of thermodynamics by applying it to the formation of solids. Problem solving skills and analytical thinking skills will also be enhanced.

CO-PO Mapping

CO1 3
CO2 3 2 2
CO3 3
CO4 3


  1. “Physical metallurgy principles” by Robert E Reed-Hill and Reza Abbaschian, Chapters 3-5.
  2. “Defects in Solids” by Richard J Tilley, Chapters 2-4.
  3. “Thermodynamics of materials”, by Gaskell.
  4. “Thermodynamics of microstructures” by Taiji Nishizawa
  5. “Statistical Thermodynamics and model calculations” by Tetsuo Mohri-Chapter 10 of “Alloy Physics”.
  6. “Mathematics of diffusion” by J. Crank, Oxford University Press
  7. “Physical metallurgy principles” by Robert E Reed-Hill and Reza Abbaschian.

Evaluation Pattern

Assessment Internal External Semester
Periodical 1 (P1) 15
Periodical 2 (P2) 15
*Continuous Assessment (CA) 20
End Semester 50

Justification for CO-PO Mapping

Mapping Justification Affinity level
CO1-PO1 CO1 is related to a particular aspect of understanding of solids (namely, defects), while PO1 is related to basic sciences. The basic physics and thermodynamics of defect formation in solids will be discussed in this course. Hence, they are mapped at the highest level of 3.
CO2-PO1 CO2 is application of the methods developed in this course to describe the behaviour of solids (both electrical and mechanical). This is related to fundamental science and hence is mapped with level 3 with PO1.
CO2-PO2 CO2 pertains to application of certain methods to describe the complicated behaviour of solids. PO2 is about developing methods to formulate and analyze complex behaviour. Hence they are mapped at level 2.
CO2-PO4 The methods studied in this course also form a primary basis of many research methods which is relevant to PO4 which suggests using research-based methods for arriving at the solution to a problem.
CO3-PO1 CO3 refers to a basic application of fundamental thermodynamics to construct phase diagrams. It is strongly correlated to fundamental sciences as mentioned in PO1. Hence it is mapped at level 3.
CO4-PO1 CO4 also refers to the basic concept of diffusional movement in solids. This is related to basic kinetic processes in solids that is correlated with fundamental science and its relevance in the course. Hence mapped at level 3.

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