Linear free energy relationships in solid state diffusion processes

This paper presents a new form of linear free energy (LFE) relationship for diffusive mass transport in oxides and other binary compounds. The relationship applies to a family of related compounds. For a given substance, i, solid-state diffusivity is related to the equilibrium constant 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 investigated here is the series of suboxide intermediates of vanadium pentoxide formed during temperature-programmed synthesis of vanadium nitride. The value of gamma for this series is 0.27. The diffusivity values are determined by fitting a mathematical model to the experimental data. Diffusivity data are presented graphically in contour diagrams which correlate pre-exponential values, activation energies, particle sizes, 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 transformation, Delta H-i(0), via a transfer coefficient alpha = 0.53, is also shown to exist for the above system. The discrepancy between alpha and gamma is resolved by using the Horiuti concept of the stoichiometric number of the rate-determining step.