Diffusivity interdiffusion coefficient

Mutual Diffusivity, Mass Diffusivity, Interdiffusion Coefficient. 5-46... 

Mutual Diffusivity, Mass Diffusivity, Interdiffusion Coefficient Diffusivity is denoted by D g and is defined by Tick s first law as the ratio of the flux to the concentration gradient, as in Eq. (5-181). It is analogous to the thermal diffusivity in Fourier s law and to the kinematic viscosity in Newton s law. These analogies are flawed because both heat and momentum are conveniently defined with respec t to fixed coordinates, irrespective of the direction of transfer or its magnitude, while mass diffusivity most commonly requires information about bulk motion of the medium in which diffusion occurs. For hquids, it is common to refer to the hmit of infinite dilution of A in B using the symbol, D°g. 

The resolution of infra-red densitometry (IR-D) is on the other hand more in the region of some micrometers even with the use of IR-microscopes. The interface is also viewed from the side (Fig. 4d) and the density profile is obtained mostly between deuterated and protonated polymers. The strength of specific IR-bands is monitored during a scan across the interface to yield a concentration profile of species. While in the initial experiments on polyethylene diffusion the resolution was of the order of 60 pm [69] it has been improved e.g. in polystyrene diffusion experiments [70] to 10 pm by the application of a Fourier transform-IR-microscope. This technique is nicely suited to measure profiles on a micrometer scale as well as interdiffusion coefficients of polymers but it is far from reaching molecular resolution. 

By selecting the reference properly, the diffusion coefficients DA and DB can be made equal to each other. This value is termed the mutual diffusion (or interdiffusion) coefficient Dab- The reference frame is one across which no change in volume occurs (fixed volume) ... 

The above sections have focused upon homogeneous systems with a constant composition in which tracer diffusion coefficients give a close approximation to selfdiffusion coefficients. However, a diffusion coefficient can be defined for any transport of material across a solid, whether or not such limitations hold. For example, the diffusion processes taking place when a metal A is in contact with a metal B is usually characterized by the interdiffusion coefficient, which provides a measure of the total mixing that has taken place. The mixing that occurs when two chemical compounds, say oxide AO is in contact with oxide BO, is characterized by the chemical diffusion coefficient (see the Further Reading section for more information). 

If there is simultaneous diffusion of more than one component in the crystal, the flux of A in direction X depends on the individual diffusivities of all diffusing components (Darken, 1948), and the individual diffusivity coefficient in equations 4.87 and 4.88 is replaced by interdiffusion coefficient D i.e., for the simultaneous diffusion of two ions A and B,... 

Mn Mgi )2Si04 olivine mixture obtained by Morioka (1981). The concentration profiles are symmetric, indicating that the diffusivities are independent of the concentration of the diffusing ion. On the contrary, possible asymmetry in the diffusion profiles indicate that concentration depends significantly on the diffusing cations. In this case, the interdiffusion coefficient can be obtained by the Boltzmann-Matano equation ... 

Unfortunately, the interpretation of Giletti et al. (1978) does not solve the problem of differential diffusivities of 0 and To do this, their experimental results should be interpreted in terms of interdiffusion of 0 and O. Application of Pick s first law to interdiffusion of the two species would in fact lead to the definition of an interdiffusion coefficient/), so that... 

This coefficient describes a diffusion process under the influence of a gradient in the chemical composition. When two diffusing species mix together, their rate of mixing depends on the diffusion rates of both species. Consequently, the interdiffusion coefficient is defined to measure this rate of mixing in relation to a laboratory frame of reference [13]. In this sense, the relation defining the interdiffusion coefficient, deduced by Darkens [29], is... 

As we have commented previously for metals, the diffusion in concentration gradients is described with the chemical diffusion coefficient, or interdiffusion coefficient. In this case, it is possible to consider that the interdiffusion and the intrinsic diffusion coefficients are equivalent, since we have only the movement of one species, that is, oxygen, by the vacancy mechanism. Subsequently, applying the Einstein relation... 

Lawrence Stamper Darken (1909-1978) subsequently showed (Darken, 1948) how, in such a marker experiment, values for the intrinsic diffusion coefficients (e.g., Dqu and >zn) could be obtained from a measurement of the marker velocity and a single diffusion coefficient, called the interdiffusion coefficient (e.g., D = A ciiD/n + NznDca, where N are the molar fractions of species z), representative of the interdiffusion of the two species into one another. This quantity, sometimes called the mutual or chemical diffusion coefficient, is a more useful quantity than the more fundamental intrinsic diffusion coefficients from the standpoint of obtaining analytical solutions to real engineering diffusion problems. Interdiffusion, for example, is of obvious importance to the study of the chemical reaction kinetics. Indeed, studies have shown that interdiffusion is the rate-controlling step in the reaction between two solids. 

Charge balance requires that the outward flux of cations from the silicate be balanced by the inward flux of hydrogen ions. For example, the apparent sodium diffusion coefficient in equation 5 is therefore really the interdiffusion coefficient, +,... 

Interdiffusion coefficients of gases are much larger than those of liquids. The diffusion coefficients of most gases are of the order of a few tenths of a square centimeter per second, cm /s, at the standard temperature and pressure, whereas diffusion coefficients of liquids are less than 10 cm /s. The diffusion coefficient D at pressure p (torr) and temperature T (ZT) can be derived from the diffusion coefficient Z)o at the standard temperature and pressure (po = 760 torr, ro = 273K) by... 

Most of the known IE kinetic problems have been solved by the use of a single mass-balanced diffusion equation [1-3,7-11,14-24,34-43]. They are, on this basis, identified as one component systems and the diffusion rate for the invading B ion is controlled by the concentration gradient of this ion alone. In these cases the effective interdiffusion coefficient depends on the ion concentrations and the equilibrium constants of the chemical reaction between both ions in the ion exchanger [2-3,7-12,16-22,23,23,30,32,34,42,32-34]. 

Solid-phase interdiffusion coefficient of counterions i and j Scale diffusion coefficient (cmVs )... 

In the two-component system gas + zeolite, in parallel with a general two-component system, one may consider 5 diffusion coefficients Dab (interdiffusion coefficient of sorbate and zeolite) Da, Db (intrinsic diffusion coefficients, respectively, of sorbate and zeolite) and Da, Db (tracer diffusion coefficients, respectively, of sorbate and zeolite). However, because Db and Db are effectively zero, as for a nonswelling crystal. 

In addition, a model has been formulated to predict the self-diffusion coefficient of diffusing species, which are hydrogen and aluminum ions. The interdiffusion coefficient value for the coupled transport of these two ions is also determined for the two types of membranes. 

---