Linear free energy relationships in solid state diffusion processes

Abstract

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 Ki or the free energy of transformation, $G_i^0$, via a transfer coefficient γ, through the expression ln Di = γ ln Ki + constant $( = - \gamma \Delta G_i^0/{\text{R}}{T_p} + {\text{constant)}}$. The system investigated here is the series of suboxide intermediates of vanadium pentoxide formed during temperature-programmed synthesis of vanadium nitride. The value of γ 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 α = 0.53, is also shown to exist for the above system. The discrepancy between α and γ is resolved by using the Horiuti concept of the stoichiometric number of the rate-determining step.