A particle-like quantum of the lattice vibrations of a crystal. Phonons carry heat and heat capacity in insulators and also cause the scattering of electrons.
Japanese name: フォノン
Phonon appears in 10 practice questions across 4 topics, including Thermal properties of materials, Electronic, magnetic and optical materials, Battery and energy materials.
The atoms in a crystal are bound to one another as if joined by springs, and their vibrations can be expressed as a superposition of waves spread through the whole crystal. The energy of each wave is quantized in units of ħω, and a unit of this excitation is called a phonon, just as a photon is the quantum of an electromagnetic wave. There are acoustic phonons, in which neighboring atoms move in the same direction, and optical phonons, in which atoms within the unit cell move in opposite directions. The Debye temperature is a rough measure of the energy of the highest-frequency phonon converted to a temperature, and it is higher for stronger bonds and lighter atoms.
At high temperatures all vibrations are excited, each atom holds an energy of 3kT, and the molar heat capacity is about 3R (the Dulong–Petit law). As the temperature falls, phonons stop being excited in order from the highest energy, and the heat capacity shrinks. At temperatures well below the Debye temperature, only long-wavelength acoustic phonons are excited, and the heat capacity is proportional to T³. This quantum behavior of the heat capacity, which classical theory could not explain, was the starting point when Einstein and Debye explained the heat capacity of solids.
In insulators and semiconductors heat is carried mainly by phonons, and the thermal conductivity is expressed through the heat capacity, the speed of sound and the mean free path, as in κ = (1/3)Cvl. Phonons are scattered by other phonons, point defects and isotopes, dislocations, and grain boundaries and surfaces. At high temperatures umklapp processes between phonons dominate and κ falls roughly as 1/T, while at very low temperatures scattering at surfaces and grain boundaries dominates. Thermoelectric materials deliberately scatter phonons with nanostructures and heavy atoms to lower thermal conductivity, whereas heat-dissipating materials use crystals with little scattering instead.
Answer: C. About 46 nm
The heat capacity per unit volume is C = ρc = 2330×700 ≈ 1.63×10⁶ J/(m³·K). l = 3κ/(Cv) = 3×150/(1.63×10⁶×6000) ≈ 4.6×10⁻⁸ m, about 46 nm. About 15 nm drops the factor of 1/3 and uses κ/(Cv), and about 5.1 nm applies the 1/3 on the wrong side, giving κ/(3Cv). This estimate is an average that represents all phonons by a single speed and mean free path; in reality, low-frequency phonons with mean free paths of several hundred nm or more also carry much of the heat. For that reason, in silicon thin films and nanowires about 100 nm thick, surface scattering lowers the thermal conductivity well below the bulk value.
It is a quantum of the collective vibration of atoms, not a particle that can be taken out on its own, and it is called a quasiparticle. Even so, it carries energy and crystal momentum and collides with and scatters electrons and photons, so treating it as a particle explains many phenomena simply.
They do, but in pure metals the heat carried by conduction electrons is far larger, and the phonon share is usually only part of the total. In alloys and in intermetallic compounds with few electrons, the phonon share can become large.
The main cause of the temperature dependence of the electrical resistance of metals is the scattering of conduction electrons by phonons. As temperature rises, phonons increase and so does scattering, and near room temperature the resistivity increases nearly in proportion to temperature. The fall in semiconductor mobility with temperature has the same cause.
This estimate is an average that represents all phonons by a single speed and mean free path; in reality, low-frequency phonons with mean free paths of several hundred nm or more also carry much of the heat.
For silicon (density 2330 kg/m³, specific heat 700 J/(kg·K)…In metals the concentration of conduction electrons is nearly independent of temperature, and as temperature rises, scattering by lattice vibrations (phonons) increases and the mobility falls, so the resistivity increases roughly in proportion to temperature near room temperature.
Which correctly describes how electrical resistivity change…For an electron and hole to recombine by emitting light, a phonon must participate at the same time to make up the momentum difference, so the probability of radiative recombination is very low and most recombination is nonradiative through defect levels, producing heat.
What is the main reason silicon is hardly ever used as the …A promising strategy is therefore to scatter only the phonons, which carry most of the heat, using nanostructured interfaces or the rattling of heavy atoms, to lower the lattice thermal conductivity; this is described as “phonon glass, electron crystal.” Lowering σ and raising κ moves ZT down.
Which is a correct strategy for increasing the thermoelectr…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 …Debye temperature Wiedemann–Franz law Indirect-bandgap semiconductor Thermoelectric figure of merit Dulong–Petit law Brass Umklapp process Interatomic potential Density functional theory Molecular dynamics