LINEAR FREE-ENERGY RELATIONSHIPS IN SOLID-STATE DIFFUSION-PROCESSES

This paper presents a new form of linear free energy (LFE) relationshi p for diffusive mass transport in oxides and other binary compounds. T he relationship applies to a family of related compounds. For a given substance, i, solid-state diffusivity is related to the equilibrium co nstant K-i or the free energy of transformation, Delta G(i)(0), via a transfer coefficient gamma, through the expression ln D-i = gamma ln K -i + constant (= -gamma Delta G(i)(0)/RT(p) + constant). The system in vestigated here is the series of suboxide intermediates of vanadium pe ntoxide formed during temperature-programmed synthesis of vanadium nit ride. The value of gamma for this series is 0.27. The diffusivity valu es are determined by fitting a mathematical model to the experimental data. Diffusivity data are presented graphically in contour diagrams w hich correlate pre-exponential values, activation energies, particle s izes, and heating rates used in the temperature-programmed syntheses. An Evans-Polanyi linear relation, Delta E(i) = alpha Delta(Delta H-i(0 )), relating activation energy, E(i), to enthalpy change of transforma tion, Delta H-i(0), via a transfer coefficient alpha = 0.53, is also s hown to exist for the above system. The discrepancy between alpha and gamma is resolved by using the Horiuti concept of the stoichiometric n umber of the rate-determining step.