The highest frequency of lattice vibration converted, via its energy, to a temperature. Well below it, the lattice heat capacity is proportional to T³, and at high temperatures it approaches about 3R.
Japanese name: デバイ温度
Debye temperature appears in 4 practice questions across 1 topic, including Thermal properties of materials.
Answer: B. It decreases in proportion to the cube of the temperature
The energy of lattice vibrations is quantized, and vibrations whose energy unit ħω is larger than kT are hardly excited. At temperatures well below the Debye temperature, only low-energy, long-wavelength acoustic phonons are excited, and their number grows with temperature, so the lattice heat capacity is proportional to T³ (the Debye T³ law). A nearly constant 3R is the classical limit at high temperatures comparable to or above the Debye temperature, corresponding to the Dulong–Petit law. A heat capacity proportional to temperature is the signature of the electronic heat capacity from conduction electrons in metals, which arises because only electrons near the Fermi level are thermally excited.
Answer: B. The number of phonons grows, and with it the phonon–phonon scattering that does not conserve total momentum (umklapp processes)
Among phonon collisions, normal processes, which conserve the total momentum, hardly impede the flow of heat, whereas umklapp processes, in which the total momentum changes by a reciprocal lattice vector, act against the heat flow and are the main source of thermal resistance. At high temperatures the number of phonons grows in proportion to temperature, so the mean free path shortens roughly as 1/T, and since the heat capacity is nearly constant, κ ∝ 1/T. Above the Debye temperature the heat capacity stays near 3R per mole of atoms; a sharp drop happens on the low-temperature side instead. Scattering at surfaces and grain boundaries hardly depends on temperature and dominates at very low temperatures, where the phonon mean free path is long; there κ falls with decreasing temperature, as the heat capacity does.
At temperatures well below the Debye temperature, only low-energy, long-wavelength acoustic phonons are excited, and their number grows with temperature, so the lattice heat capacity is proportional to T³ (the Debye T³ law).
At temperatures well below the Debye temperature, how does …Above the Debye temperature the heat capacity stays near 3R per mole of atoms; a sharp drop happens on the low-temperature side instead.
The lattice thermal conductivity of an insulating single cr…Because diamond has light atoms and strong bonds, its Debye temperature is high, about 1900–2200 K, its speed of sound is large, and at room temperature phonons rarely scatter off each other, so l is long.
Diamond is an electrical insulator, yet its thermal conduct…At temperatures well below the Debye temperature the heat capacity shrinks in proportion to T³, so the linear expansion coefficient of an insulator also approaches 0 in proportion to T³.
According to the Grüneisen relation, the volume expansion c…Phonon Dulong–Petit law Umklapp process Coefficient of linear thermal expansion Invar Thermal diffusivity Wiedemann–Franz law