Marker diffusion constant

The squared step length divided by the fundamental time scale r necessary for one step of movement.) The number 6 comes from the space dimensions d multiplied by 2 for the directions. The diffusion of a marked particle obtained in such a way is the self-diffusion constant or marker diffusion constant. 

The diffusion constant obtained by tracing the selected particle among many is the marker diffusion constant. The marker diffusion constant is indicated by the labeling symbol, as D. In contrast, the diffusion constant in Pick s law is defined for the many particles involved in the local concentration, and is called the concentration diffusion coefficient. In dilute solutions where particles move independently of each other, these two diffusion constants are the same. In concentrated solutions, the assumption of independent motion of the particles breaks down by molecular interaction, so that the two diffusion coefficients are not identical. 

Darken assumed that the accumulated vacancies were annilrilated within the diffusion couple, and that during tlris process, tire markers moved as described by Smigelskas and Kirkendall (1947). His analysis proceeds with the assumption tlrat the sum of tire two concenuations of the diffusing species (cq - - cq) remained constant at any given section of tire couple, and tlrat the markers, which indicated the position of tire true interface moved with a velocity v. 

Oxide movements are determined by the positioning of inert markers on the surface of the oxideAt various intervals of time their position can be observed relative to, say, the centreline of the metal as seen in metal-lographic cross-section. In the case of cation diffusion the metal-interface-marker distance remains constant and the marker moves towards the centreline when the anion diffuses, the marker moves away from both the metal-oxide interface and the centreline of the metal. In the more usual observation the position of the marker is determined relative to the oxide/ gas interface. It can be appreciated from Fig. 1.81 that when anions diffuse the marker remains on the surface, but when cations move the marker translates at a rate equivalent to the total amount of new oxide formed. Bruckman recently has re-emphasised the care that is necessary in the interpretation of marker movements in the oxidation of lower to higher oxides. 

Equation 3.23 for the velocity of a local C-frame with respect to the E-frame is therefore the velocity of any inert marker with respect to the E-frame. The assumptions that fli and il2 are each constant throughout the material, and thus that there are no changes in overall specimen volume during diffusion, permit the use of Eq. 3.19 to derive the unique choice of the E-frame. 

The rate of diffusion is proportional to the concentration gradient, and the proportionality constant is defined as the diffusion coefficient (D) in Fick s first law of diffusion. Experimental determination of D is commonly performed ex vivo due to the difficulty of measuring concentration gradients in the interstitium. In vivo measurement can be performed in specific tissues, using transparent chamber preparations in combination with the FRAP technique (Berk et al., 1997 Jain et al., 1997 Pluen et al, 2001). However, the in vivo approach is limited only to fluorescent molecules or solutes whose D is not affected by labeling with fluorescent markers. 

TDFRS allows for experiments on a micro- to mesoscopic length scale with short subsecond diffusion time constants, which eliminate almost all convection problems. There is no permanent bleaching of the dye as in related forced Rayleigh scattering experiments with photochromic markers [29, 30] and no chemical modification of the polymer. Furthermore, the perturbations are extremely weak, and the solution stays close to thermal equilibrium. 

A significant shift of the inert markers and the formation of porosity were observed only in the La-Ce couples. The lack of inert markers shift in the other systems was attributed to the essentially similar intrinsic diffusivities of the two components. The concentration dependence of the intrinsic diffusivities (at constant temperature) seemed to correlate with the temperature of the solidus in the binary system. In all instances precipitates containing a ternary component, most likely oxygen, appeared in the diffusion zone, their presence was attributed... 

Band spreading is also related to an obstructive factor that is not a constant in a column bed. Both Kubin [6] and Pfannkoch et al. [11] have shown that plate height varies as a function of K. It appears that as its molecular size approaches the pore dimensions, a solute experiences diffusion limitations, decreasing its effective diffusion coefficient. This influence of restricted molecular movement on plate height (//) can be readily observed in SEC profiles. The first peak to elute after the void volume marker is frequently the broadest peak in the chromatogram. If one were able to obtain columns with different pore diameters but similar plate counts, pore volumes, and calibration curve slopes, it would be best to select a column on which would be 0.2 or greater for the solutes to minimize the effect of the obstructive factor. 

From the intuitive viewpoint, it seems strange that the markers initially smear over the whole concentration range of the diffusion couple (located in quite a narrow region, though), and then gather into one plane which corresponds to only one fixed (constant) composition this plane is generally referred to as the Kirkendall plane. It is accepted [31-35] that the (K-planes is a plane of initial contact moving at parabolic dependence... 

Assume the inert markers to be homogeneously distributed over the diffusion couple before annealing. Actually, one may employ the steplike distribution (provided the markers distribution is different but constant in the left and right halves of the diffusion couple). Let... 

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