Defects relaxation

Tompre I have a question concerning the knockout mice that show defective relaxation. How can this be related to the work of Shull s group (Liu et al 1997) on the SERCA3-defective mice They also see that the endothelial-dependent relaxation is depressed in these mice. 

Figure 1-4. The A/AX interface during flow of A-cations across the boundary (g = 0) into the (semiconducting) compound AX. Point defect relaxation reaction between 0< < R reads V + A- = Aa. hit = width of relaxation zone.

Transport plays the overwhelming role in solid state kinetics. Nevertheless, homogeneous reactions occur as well and they are indispensable to establishing point defect equilibria. Defect relaxation in the (p-n) junction, as discussed in the previous section, illustrates this point, and similar defect relaxation processes occur, for example, in diffusion zones during interdiffusion [G. Kutsche, H. Schmalzried (1990)]. 

In physical and chemical metallurgy, the Kirkendall effect, which is closely related to point defect relaxation during interdiffusion, has been studied extensively. It can be quantitatively defined as the internal rate of production or annihilation of vacan-... 

Following these introductory remarks, the next sections are devoted to a detailed discussion of defect relaxation phenomena. 

Since these considerations are independent of the nature of the sample, the results are valid for all crystals which are exposed to a sudden change of intensive state variables. The meaning of the chemical diffusion coefficient D must, however, be carefully investigated in each case (see Section 5.4.4). At 1000°C, Dv for simple transition-metal oxides is on the order of 10 7 cm2/s. This gives for cubic samples of 10-3 cm3 a defect relaxation time of approximately 1 h according to Eqn. (5.86). 

When the point defect relaxation is diffusion controlled, we can use Eqn. (5.89) to determine k. After setting rAB = aAX (= unit cell dimension), it is found that at even moderate temperatures (= 100°C), x is on the order of a millisecond or less. This r is many orders of magnitude shorter than relaxation times for nonstoichiometric compounds where the point defect pairs equilibrate at external surfaces (Section 5.3.2). In other words, intrinsic defects equilibrate much faster than extrinsic defects if, during the defect equilibration, the number of lattice sites is conserved. 

In formulating Eqn. (5.101) and the following flux equations we tacitly assumed that they suffer no restrictions and so lead to the individual chemical diffusion coefficients >(/). If we wish to write equivalent, equations for,/(A) and/(B), and allow that v(A) = = v(B), then according to Eqn. (5.103), /(A) /(B) since Ve(A) = ]Vc(B)j. However, the conservation of lattice sites requires that j/(A) j = /(B), which contradicts the previous statement. We conclude that in addition to the coupling of the individual fluxes, defect fluxes and point defect relaxation must not only also be considered but are the key problems in the context of chemical diffusion. Let us therefore reconsider in more detail the Kirkendall effect which was introduced qualitatively in Section 5.3.1. It was already mentioned that this effect played a prominent role in understanding diffusion in crystals [A. Smigelskas, E. Kirkendall (1947) L.S. Darken (1948)]. 

Before we discuss point defect relaxation phenomena which occur during matter transport in inhomogeneous crystals with different sublattices, let us resume the quantitative treatment of diffusional transport in an inhomogeneous single sublattice crystal occupied with components A and B as well as vacancies. 

The second condition for bulk transport in AX is A > A in accordance with our assumptions. The point defects relax by a bimolecular reaction mode (see Section 5.3.3). In order to simplify the formal treatment, we linearize the recombination rate... 

AC/ is known as the overpotential in the electrode kinetics of electrochemistry. Let us summarize the essence of this modeling. If we know the applied driving forces, the mobilities of the SE s in the various sublattices, and the defect relaxation times, we can derive the fluxes of the building elements across the interfaces. We see that the interface resistivity Rb - AC//(F-y0) stems, in essence, from the relaxation processes of the SE s (point defects). Rb depends on the relaxation time rR of the (chemical) processes that occur when building elements are driven across the boundary. In accordance with Eqn. (10.33), the flux j0 can be understood as the integral of the relaxation (recombination, production) rate /)(/)), taken over the width fR. 

The reaction scheme at and near the phase boundary during the phase transformation is depicted in Figure 10-14. The width of the defect relaxation zone around the moving boundary is AifR, it designates the region in which the relaxation processes take place. The boundary moves with velocity ub(f) and establishes the boundary conditions for diffusion in the adjacent phases a and p. The conservation of mass couples the various processes. This is shown schematically in Figure 10-14b where the thermodynamic conditions illustrated in Figure 10-12 are also taken into account. The transport equations (Fick s second laws) have to be solved in both the a and p... 

Proceeding systematically, diffusion controlled a-fi transformations of binary A-B systems should be discussed next when a and / are phases with extended ranges of homogeneity. Again, defect relaxations at the moving boundary and in the adjacent bulk phases are essential for their understanding (see, for example, [F. J. J. van Loo (1990)]). The morphological aspects of this reaction type are dealt within the next chapter. 

Keywords superheated crystals, molecular dynamics, defects, relaxation, cuboctahedral clusters... 

Fig. 11. Series of pictures showing the ring defect relaxation once the electric field has been tiuned off. 1 Saturn ring 2 and 3 intermediate configurations 4 dipole. Drop diameter 35 pm...

The determination of the equilibrium geometry, that is the evaluation of structural effects on the surroundings because of the presence of the defect (relaxation/reconstruction). 

Defect relaxation times for homogeneous reactions in solids can be calculated essentially by the methods of homogeneous chemical kinetics [2, 3]. For the sake of illustration, let us consider more closely the equilibration of Frenkel defects in silver bromide following a sudden change in temperature. 

One final important example of a defect relaxation process should be mentioned in this section. This is the recombination of excess electrons and electron holes m elemental and compound semiconductors following optical excitation (i.e. absorption of light). Very small concentrations of impurities can greatly reduce the relaxation time for this process, since the dissolved impurity atoms (e. g. Ni in Ge) can act as recombination centers. 

Chemical diffusion coefficients were deduced from studies of point defect relaxation in magnetite. The vacancy and interstitial tracer diffusion coefficients could be described by ... 

At the same time a clinic status of patients was characterized by beginning of epithelization which expressed in active migration of epithelial cells in a region of the corneal defect place, decrease of square of this defect, relaxation of eye inflammation and pain syndrome. The improvement was better pronounced at the control and the first experimental group than at the second group. 

R. D. Carahan and J. O. Brittain, Point-Defect Relaxation in Rutile Single Crystals, J. Appl. Phys. 34(10) 3095-3104 (1963). 

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