Thermal conduction model of metal and ceramics

Abstract

A theoretical analysis of the thermal conductivity ( κ v ) of metals and ceramics from their Young's modulus ( E), atomic weight ( M) and density ( ρ) based on a harmonic oscillator model is presented. The κ v value is expressed as ( A g N 0 ) 3 ρ ( 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/ r 0, 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 A g value is proportional to ρ. The κ 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 ρ( E/ M) 3/2 contributes to increase κ v . A good agreement was shown between the measured and calculated κ v values in a wide range from 1 to 2310 J/smK.