Some universalities in the relaxation of glasses

Abstract

Universal features of the dielectric relaxation of glasses are derived from new theories of transport in electronic and ionic conducting glasses. The fundamental concept common to both systems is the transition of relaxation processes from local (parallel) processes treatable in a ‘bare’ pair approximation at high frequencies through semi-local (predominantly parallel) processes treatable in a ‘renormalized’ pair approximation at intermediate frequencies to strongly non-local processes (with critical series characteristics) treatable using cluster statistics from percolation theory at low frequencies. The cross-over frequency, ω c , from predominantly local to strongly non-local relaxation is defined by the percolation of relevant pair processes, which defines as well the dc conductivity, σ dc , thus providing the basis for the Barton-Nakajima-Namikawa (B-N-N) relation, σ dc α ω c . The relationship, 1 − s α § −1 c , between the dc conductivity ln σ dc α § c , and the high frequency ac conductivity, σ ( ω )α ω s , is established to result from the proportionality of σ dc and ω c , i.e., the B-N-N relation. Frequency-dependent scaling is then shown to be equivalent to the B-N-N relation, making the well-known B-N-N relation and the role of the percolation of relevant pair processes the fundamental universalities in dielectric relaxation of glasses.