Interstitial diffusion coefficient

In normal tissues vascular and interstitial oncotic pressures (ttv and 77 ) are approximately 20-25 and 5-15 mm Hg, respectively (Baxter and Jain, 1989). Although there are no direct measurements of in tumors, based on high vascular permeability and high interstitial diffusion coefficient in tumors, one would expect higher concentration of endogenous plasma proteins in the tumor interstitium than in normal interstitium. This hypothesis is supported by the data in the literature (Sylven and Bois, 1960). As a result, in tumors may be higher than that in normal tissues. 

The diffusion of implanted Zn was studied, at 625 to 850C, by means of secondary ion mass spectrometry. A substitutional-interstitial diffusion mechanism was suggested to explain how deviations of the local Ga interstitial concentration from its equilibrium value regulated Zn diffusion. The Ga interstitial diffusion coefficient was described by ... 

Transition metals in amorphous samples exhibit a direct interstitial diffusion behavior which was retarded by temporary trapping at defects that were intrinsic to the amorphous structure. Diffusion was investigated here by means of Rutherford back-scattering spectrometry. It was found that the data could be fitted by using foreign-atom interstitial diffusion coefficients for crystaHine Si modified by the presence of... 

When one considers interstitial diffusion of an interstitially dissolved species in dilute solid solution, essentially all the nearest neighbour interstitial sites of the same type are unoccupied and available for occupancy by the diffusing interstitial atoms. Thus the interstitial atom may jump to any of the nearest neighbour interstitial sites and in this case Nd is equal to unity. The interstitial diffusion coefficient is then given by... 

For an ion to move through the lattice, there must be an empty equivalent vacancy or interstitial site available, and it must possess sufficient energy to overcome the potential barrier between the two sites. Ionic conductivity, or the transport of charge by mobile ions, is a diffusion and activated process. From Fick s Law, J = —D dn/dx), for diffusion of a species in a concentration gradient, the diffusion coefficient D is given by... 

In tire transition-metal monocarbides, such as TiCi j , the metal-rich compound has a large fraction of vacairt octahedral interstitial sites and the diffusion jump for carbon atoms is tlrerefore similar to tlrat for the dilute solution of carbon in the metal. The diffusion coefficient of carbon in the monocarbide shows a relatively constairt activation energy but a decreasing value of the pre-exponential... 

Just as in the case of (16), an equation of the form (20) applies to any other association-dissociation reaction in which one of the dissociated species is mobile, the other fixed. When the two species are distinct but both mobile, as for hydrogen combining with, say, an interstitial silicon, a similar line of reasoning, whose details we omit, leads to equations of the same form as (16) and (20) but with D+ replaced by the sum of the diffusion coefficients of the two species. When the two mobile species are the same, as for the reaction H° + H° 5H2, it turns out that nA and n+ should each be replaced by the monatomic density n, D+ by the monatomic diffusion coefficient, and 4ir by 8tt in (16) but not in (20). 

The material would be expected to be a hole (p-type) semiconductor. However, in this compound the interstitial oxygen ions can diffuse fairly quickly, and the oxygen diffusion coefficient is higher than normal, so that the compound shows both high oxygen diffusivity and electronic conductivity, a situation referred to as mixed conductivity (Section 8.7). 

Interstitial Water. The differentiation between solutes and particles is of great importance in the sampling of interstitial water. Most conveniently so-called peepers are used. These consist usually of plexiglass plates in which small compartments (0.5 cm deep and 0.5 - 1 cm high) are separated from the sediments by a dialysis membrane. The compartments are initially filled with degassed distilled water. After 1 - 2 weeks for equilibration subsequent to the retrieval of the peeper, the "dissolved" components are measured in each component. For this type of application the pore size does not seem to be very critical colloids do not seem to accumulate in the compartments (low diffusion coefficients). 

Such a mechanism is not incompatible with a Haven ratio between 0.3 and 0.6 which is usually found for mineral glasses (Haven and Verkerk, 1965 Terai and Hayami, 1975 Lim and Day, 1978). The Haven ratio, that is the ratio of the tracer diffusion coefficient D determined by radioactive tracer methods to D, the diffusion coefficient obtained from conductivity via the Nernst-Einstein relationship (defined in Chapter 3) can be measured with great accuracy. The simultaneous measurement of D and D by analysis of the diffusion profile obtained under an electrical field (Kant, Kaps and Offermann, 1988) allows the Haven ratio to be determined with an accuracy better than 5%. From random walk theory of ion hopping the conductivity diffusion coefficient D = (e /isotropic medium. Hence for an indirect interstitial mechanism, the corresponding mobility is expressed by... 

An example of a material (Li3Sb) with a very large Wagner factor is shown in Fig. 8.3. The effective chemical diffusion coefficient is compared with the diffusivity as a function of non-stoichiometry. These data were determined by electrochemical techniques (see Section 8.5). An increase of the diffusion coefficient is observed at about the ideal stoichiometry which corresponds to a change in the mechanism from a predominantly vacancy to interstitial mechanism. The Wagner factor W is as large as 70 000 at the ideal stoichiometry. This gives an effective diffusion coefficient which is more typical of liquids than solids. It is a common... 

Transport of cations in glass is controlled by the defect mechanism where the defects are cations in interstitial positions [78], The diffusion coefficient is given by the product... 

The diffusion coefficient for a given ion in a crystal is determined, as we have seen, by the atomistic properties of the ion in the structural sites where the vacancy (or interstitial) participating in the migration process is created (see eq. 4.71). The units of diffusion (and/or self-diffusion ) are usually cm sec . Pick s first law relates the diffusion of a given ion A (Jf) to the concentration gradient along a given direction X ... 

The studies on Cu2 aO mentioned above concluded that CujO is a metal-deficient p-type semiconductor with cation vacancies. It was not established, however, which kinds of defects (Vcu, Vcu) were dominant and what the effect of Q (interstitial oxygen) was on non-stoichiometry. To clarify these points, Peterson and Wiley measured the diffusion coefficient, D, of Cu in Cu2 O, by use of "Cu as a tracer over the temperature range 700-1153 °C and for oxygen partial pressures, greater than 10 atm. It has been widely accepted that lattice defects play an important role in the diffusion of atoms or ions. Accordingly it can be expected that the measurement of D gives important information on the lattice defects. 

Effective Diffusivity. The effective diffusivity for N2/He at 25° C was calculated from the slope of the straight-line portion obtained in the high velocity region of a van Deemter plot [height of an equivalent plate vs. interstitial velocity 14, 15)]. A binary diffusion coefficient for N2-He of 0.717 cm2/sec was computed from Ref. 21, and the partition coefficient was taken as the reciprocal of the particle porosity (Table III) on the assumption that the adsorption of N2 at 25° C can be neglected. The calculated diffusivities are listed in Table III. 

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