Theoretical | Practical | Study | Duration | Total | Credits |
---|---|---|---|---|---|

4 hours/week | 0 hours/week | 8 hours/week | 15 weeks | 180 hours | 12 |

97135 - Magnetism and Superconductivity

Provide the student with the main concepts in Statistical Thermodynamics oriented to materials. After a review of the fundamental concepts of Classical Thermodynamics, the theoretical foundations of Statistical Physics and their application to material properties, such as modeling of thermal capacity, solid solutions and chemical-magnetic ordering, are treated. Throughout the course, a modern approach will be adopted, with the contextualized use of traditional methods in the area, such as Monte Carlo, Molecular Dynamics and Cluster Variation (CVM), in the form of application examples. The course will also address the calculation by first principles of thermochemical properties of materials, such as phase diagrams or thermal capacities of compounds.

Statistical thermodynamics, as a discipline of Physics, has little more than a century of existence, having developed from the framework created by Josiah Willard Gibbs and Ludwig Boltzmann at the end of the 19th century, completed by seminal works by Planck, Einstein, Debye , Bohr, among other early 20th century physics pioneers. Its popularization in Engineering, however, occurred in the 1980s with the spread of personal computers. Nowadays Statistical Mechanics provides the theoretical foundation for numerous models used in engineering to investigate material properties. The course seeks to develop these theoretical foundations using examples of calculations using the Monte Carlo Method, the Cluster Variation Method and the Molecular Dynamics Method, discussing topics such as partition functions, critical phenomena and thermodynamic potentials in a concrete way.

- Review of the principles of classical thermodynamics and the principle of maximum entropy
- Statistical Thermodynamics: ensembles and their connection with the concepts of isolated, closed and open systems
- Partition function, fundamental identities
- Exact solutions: Boltzmann distributions (principle of equipartition of energy)
- Exact solutions: quantum statistics (Fermi-Dirac and Bose-Einstein), superconductivity, superfluidity and other critical phenomena
- Thermal capacity of crystalline solids: vibrational, electronic and magnetic, models by Einstein and Debye.
- Chemical balance and solutions; chemical potentials, modeling phase diagrams
- Order-disorder transitions
- Application: calculation of a phase diagram using the Variable Cluster Method and data obtained by first principles
- Application: Monte Carlo modeling of gaps in solids
- Application: molecular dynamics modeling of iron alpha / gamma transition

The arithmetic mean of exercises (weight 1) and a written assignment (weight 2) must be equal to or greater than 5, on a scale from 0 to 10.

- F. Reif, Fundamentals of Statistical and Thermal Physics, Waveland, 1965 (reissued 2009).
- H. B. Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd ed, Wiley, 1985.
- R. D. Reed e R. R. Roy, Statistical Physics for Students of Science and Engineering, Dover, 1995.
- S. A. Salinas, Introdução à Física Estatística, EDUSP, 1997.
- J. P. Sethna, Entropy, Order Parameters and Complexity, Oxford University Press, 2006.
- K. Stowe, An Introduction to Thermodynamics and Statistical Mechanics, 2nd ed, Cambridge University Press, 2007.
- Papers published in Intermetallics, Calphad, J. Phys. Chem. Solids, among other journals.