Measurement of solid state diffusion coefficients by a temperature-programmed method

Abstract

This paper presents a method for determining diffusivities in solids where the diffusing species desorbs or reacts at the external surfaces, and where the diffusivity does not vary appreciably with concentration. The method involves measuring the flux of the diffusive species out of the solid under the influence of a temperature program. A general model is developed, based on nonisothermal Fickian diffusion, which is applicable to solid particles with slab or spherical geometry. The solution is presented both as an analytical expression and as correlation charts of experimentally observable quantities. These charts are contour diagrams of the temperatures of peak diffusion rate with ln(E/R) and ln(D ₀/h ²) as the axes, where E and D ₀ are the activation energy and pre-exponential terms of the diffusivity expression D = D ₀ exp(−E/RT), where R is the gas constant, and h the size of the particles. This paper deals exclusively with the case of oxygen diffusion in the vanadium oxide system. In this case, vanadium oxide was reduced in a reactive ammonia stream at conditions in which the surface reaction was fast compared to the diffusive transport process. Using this method the diffusion parameters were found to be D ₀ = 1.9 × 10⁻⁵ cm² s⁻¹ and E = 101 kJ/mol. The method was checked by varying the crystallite size of the vanadium oxide sample in the range 2h = 0.14−0.29 μm.