The thermal conductivity of a-alumina single crystals as a function of temperature is given in Table 16 (from [2, 23]). Heat is conducted through a nonmetallic solid by lattice vibrations or phonons. The mean free path of the phonons determines the thermal conductivity and depends on the temperature, phonon-phonon interactions, and scattering from lattice defects in the solid. At temperatures below the low temperature maximum (below about 40°K), the mean free path is mainly determined by the sample size because of phonon scattering from the sample surfaces. Above the maximum, the
Table 15 The pressure of AlO vapor and total vapor pressure in equilibrium with a-Al2O3 as a function of temperature, for reducing and neutral conditions
Table 16 Thermal conductivity of single crystal a-Al2O3
From [2, 23]
conductivity decays approximately exponentially because of phonon-phonon interactions. At high temperatures (above about 800°C), the phonon mean free path is of the order of a lattice distance, and becomes constant with temperature. There is a much more detailed discussion of phonon behavior in ceramics and glasses in [23, 32]. The velocity v of a phonon or sound wave in a solid can be found from the formula
v2 = Elp (8)
in which E is Young’s modulus and p is the density, so this velocity in alumina is 10.1(10)3 m s-1 at 25°C. This result is close to the measured value of 10.845 m s-1.