Correlation factors for diffusion in solids

Abstract

The relation of Einstein D = BkT/e, relating the diffusivity and mobility of particles (ions or atoms) must be altered where D is the diffusion constant of tracers in solids, if a vacancy mechanism holds, because there will be a correlation between successive steps of a particle, even if the steps of the vacancies themselves are uncorrelated. Certain symmetry conditions being fulfilled, the relation of Einstein must be extended with a correlation factorwhere el , i + 1 is the angle between two successive steps of a particle.The diffusion problem can be translated into the theory of electrical networks and with the help of measurements in a resistor network the value of C o S i , i + 1 is easily evaluated. This has been done for several types of lattices. Other cases, where eqn. (1) does not hold, because of lack of symmetry, are treated by similar methods.Appropriate substitutions having been made, the diffusion of associated pairs has been treated as the diffusion of a single particle in a so-called transposed lattice. * Unfortunately in their eqn. (A2), which is our eqn. (l.Z), a factor 2 was erroneously overlooked, modifying their equation 1 + OlPr 1 -&P,' (AS) into f = -~ f = -1 -&P, 1 which is our eqn. (3.4). International Meeting on Reactivity of Solids, to be held in Madrid, April, 1956.-f A discussion of these applications will be published in the proceedings of the Third

The ionic conductivity of pure and doped lead bromide single crystals

“…The theoretical correlation factor for diffusion of free vacancies in a hexagonal closed-packed structure has the value 0.78146 (19). In the diffusion experiment the displacement of the tracer is measured.…”

“…On a macroscopic scale, however, it is necessary to introduce a correlation factor,f, for diffusion. The factorfdepends on the crystal lattice as well as on the mechanism of ionic transport (19)(20)(21)(22).…”

“…The ionic conductivity in lead bromide (3, 4) is analogous to the ionic conductivity in lead chloride (5)(6)(7)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20). With the usual formulas (8) the following expressions for the temperature and concentration dependence of the ionic conductivity in lead chloride were derived by De Vries (6).…”

Correlation factor, velocity autocorrelation function and frequency-dependent tracer diffusion coefficient

“…A very simple expression for the correlation factor is obtained under the assumption that only consecutive jumps of the tracer particle are correlated, and under some simplifying assumptions concerning the types and symmetries of the jumps of the particles in the underlying lattice. The expression reads (Compaan andHaven 1956, LeClaire 1970): where (cos e) is the average angle between two successive jumps of the tracer particle.…”

Self-Diffusion in the Ionic Plastic Phase of (CH3 )3 NHClO4 Studied by 1H NMR and Electrical Conductivity

“…respectively, where /., Ze, and N are the spatial correlation factor [23,24], the electric charge of the diffusing ion, and the number of mobile ions per unit volume, respectively. The £a value of conductivity becomes 64 + 3 kJ mol -1 , being larger than the values derived from the NMR data.…”