Debye temperature
The characteristic temperature above which a solid behaves classically and below which its heat capacity collapses toward zero.
Definition
The Debye temperature Θ_D is the characteristic temperature of a solid's lattice vibrations, set by the maximum phonon frequency: k_BΘ_D = ħω_max. Above Θ_D the vibrational modes are fully excited and the solid obeys the classical Dulong–Petit law, with molar heat capacity near 3R. Below Θ_D the high-frequency modes freeze out, and the heat capacity falls — toward zero as T → 0, following Debye's celebrated T³ law at the lowest temperatures.
The Debye temperature ranges widely: about 105 K for soft, heavy lead, around 343 K for copper, and over 2000 K for stiff, light diamond, whose strong bonds make it behave 'cold' even at room temperature. A high Θ_D signals stiff bonds and light atoms; it correlates with hardness, melting point, and the speed of sound in the material.
Introduced by Peter Debye in 1912, the concept improved on Einstein's 1907 model by treating the lattice vibrations as a spectrum of sound-like waves rather than a single frequency, correctly reproducing the low-temperature behaviour of real solids.
History
Introduced by Peter Debye in 1912, refining Einstein's 1907 quantum model of specific heats; both were responses to the failure of classical equipartition at low temperature.