Thermal conduction model of metal and ceramics

摘要

A theoretical analysis of the thermal conductivity (kappa_v) of metals and ceramics from their Young's modulus (?), atomic weight (M) and density (rho) based on a harmonic oscillator model is presented. The kappa_vvalue is expressed as (A (gN_0)~(1/3)) RHO (E/M)~(3/2)/2, where A is the maximum displacement of a harmonic oscillator and equals the mean free path of lattice vibration, g is the size factor (g = s/r0, s: cross sectional area of atom acted by force applied, r_0 : distance between two atoms in equilibrium state), and N_0 is the Avogadro number. The Ag~(1/2) value is proportional to p. The kappa_v value of a metal is strongly dominated by the mean free path (A) and decreases when E increases as a consequence of the formation of partial covalent and ionic bond in metal bond. On the other hand, the mean free path of non-oxide and oxide ceramics becomes significantly small as compared with metals. The structure factor p(E/M)~(3/2) contributes to increase kappa_v. A good agreement was shown between the measured and calculated kappa_v values in a wide range from 1 to 2310 J/smK.