Thermal Physics of Nanosystems (in Russian)
Course Overview
This course offers a systematic exploration of thermal physics at the nanoscale. It integrates classical continuum theories with cutting-edge atomistic simulations to explain heat transport mechanisms in solids.
Students will master the theoretical framework of Lattice Dynamics and Phonon Transport, while developing practical skills in First-Principles Calculations. By the end of the course, students will be proficient in calculating phonon spectra, density of states, and thermal conductivity for bulk and low-dimensional materials using industry-standard computational tools.
Access the companion computational code and notebooks.
Syllabus
| Date / Week | Topic | Description | Materials |
|---|---|---|---|
| February 11 Week 1 | Basic Definitions | Introduction to nanothermophysics. | Lecture 1 (Slides) |
| February 18 Week 2 | Theory of Elasticity | Kinematics of deformation, stress, and Hooke’s Law. Wave equations, dispersion, reflection of elastic waves from boundaries, and Kapitza conductance. | Lecture 2 (Slides) |
| February 25 Week 3 | Crystal Structure Fundamentals | Bravais lattices, primitive and conventional cells, Wigner-Seitz cells, and cubic lattices. | Lecture 3 (Slides) |
| March 4 Week 4 | Introduction to Lattice Dynamics | Crystallographic directions, reciprocal lattice, Brillouin zone. Harmonic approximation basics. | Lecture 4 (Slides) |
| March 11 Week 5 | Lattice Dynamics | Phonon dispersion in 1D mono/diatomic chains and real 3D crystals. | Lecture 5 (Slides) |
| March 18 Week 6 | Ab Initio Calculation of Interatomic Potentials | Many-body Schrödinger equation, Born-Oppenheimer approximation, and Density Functional Theory (DFT). | Lecture 6 (Slides) |
| March 25 Week 7 | Force Constants & Density of States | Finite displacement method, DFPT, Phonon Density of States (DOS), and lattice dynamics in nanostructures. | Lecture 7 (Slides) |
| April 1 Week 8 | Heat Capacity of Crystals | Classical theory, Einstein model (1907), Debye model (1912), and modern refinements. | Lecture 8 (Slides) |
| April 8 Week 9 | Thermal Conductivity (BTE & RTA) | Anharmonicity, Boltzmann Transport Equation (BTE), Relaxation Time Approximation (RTA), and iterative solutions. | Lecture 9 (Slides) |
| April 15 Week 10 | Scattering Mechanisms & Monte Carlo Analysis | Ab initio approach to scattering, empirical models, and analyzing N/U processes using Monte Carlo. | Lecture 10 (Slides) |
| April 22 Week 11 | Classical Size Effects & Roughness | Specularity parameters, BMSTU roughness models, and numerical modeling via Monte Carlo methods. | Lecture 11 (Slides) |
| April 29 Week 12 | Phonon Spectrum Calculation | Calculation of Silicon phonon spectrum using Quantum Espresso. | Lecture 12 (Slides) Tutorial Code |
| May 6 Week 13 | Graphene & Thermal Conductivity | Calculating Graphene spectrum (VASP + Phonopy) and thermal conductivity (VASP + Phono3py). | Lecture 13 (Slides) |
| May 13 Week 14 | Machine Learning Potentials | Calculation of phonon spectra and DOS using Neural Evolution Potentials (NEP). | Lecture 14 (Slides) |