Solid State Physics Lecture 8 – The Debye model Professor Stephen Sweeney Advanced Technology Institute and Department of Physics University of Surrey, Guildford, GU2 7XH, UK
[email protected] Solid State Physics - Lecture 8 Recap from Lecture 7 • Concepts of “temperature” and thermal Dulong-Petit equilibrium are based on the idea that individual particles in a system have some form of motion • Heat capacity can be determined by considering vibrational motion of atoms • We considered two models: • Dulong-Petit (classical) • Einstein (quantum mechanical) • Both models assume atoms act independently – this is made up for in the Debye model (today) Solid State Physics - Lecture 8 Summary of Dulong-Petit and Einstein models of heat capacity Dulong-Petit model (1819) Einstein model (1907) • Atoms on lattice vibrate • Atoms on lattice vibrate independently of each independently of each other other • Completely classical • Quantum mechanical • Heat capacity (vibrations are quantised) independent of • Agreement with temperature (3NkB) experiment good at very • Poor agreement with high (~3NkB) and very low experiment, except at (~0) temperatures, but high temperatures not inbetween Solid State Physics - Lecture 8 A more realistic model… • Both the Einstein and Dulong-Petit models treat each atom independently. This is not generally true. • When an atom vibrates, the force on adjacent atoms changes causing them to vibrate (and vice-versa) • Oscillations can be broken down into modes 1D case Nice animations here: http://www.phonon.fc.pl/index.php