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Linear free energy relationships in solid state diffusion processes

Published online by Cambridge University Press:  26 July 2012

Rajat Kapoor and
S. T. Oyama
Rajat Kapoor
Affiliation:
Department of Chemical Engineering, Virginia Polytechnic, Blacksburg, Virginia 24061-0211
S. T. Oyama*
Affiliation:
Department of Chemical Engineering, Virginia Polytechnic, Blacksburg, Virginia 24061-0211
*
a)Author to whom correspondence should be addressed.
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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, , via a transfer coefficient γ, through the expression ln Di = γ ln Ki + 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, , relating activation energy, Ei, to enthalpy change of transformation, , 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.

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Articles
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Journal of Materials Research , Volume 12 , Issue 2 , February 1997, pp. 474 - 479
Copyright
Copyright © Materials Research Society 1997

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References

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