Disturbed and scattered: The Path of thermal conduction through diamond lattice

Abstract

With more phonons carrying the energy in the lattice, the phonon density of states in diamond extends to a much higher frequencies than that of any other material. This is related to the Debye temperature of diamond, being the highest of any bulk materials and of having the highest sound velocity of any known bulk materials. However, the thermal conductivity not only depends on the number of phonons and how fast they are, but also on how long they can travel without being disturbed or scattered. The measurement of this length of travel is the Mean Free Path of the phonons, l, which depends on the number of phonons in the lattice through the 3-phonon processes (Normal and Umpklapp), and the imperfections in the lattice (boundaries, grain boundaries, non sp3 bonds, isotopes, impurities, extended defects, dislocations, etc.). Consequently, the “real world” thermal conductivity of a given piece of diamond will depend on the “quality” of the lattice, yielding values from 1 W/m°K (ultra-nanocrystalline diamond) to more than 3400 W/m°K for isotopically pure single crystal diamond.