Transition metals diffusion coefficients

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... 

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). 

The purpose of this paper is to (1) document published studies of vaporization in vacuum of the Group 4 and 5 transition metal carbides and uranium carbide, and determine the temperature dependence of their equilibrium CVCs (C/MeCVC) and vaporization rates (Vecvc, g/cmzs) (2) document published studies on chemical diffusion of these carbides, and develop and compare data to a model describing the concentration dependence of the chemical diffusion coefficients and (3) develop diffusion-coupled vaporization equations which predict changes of surface composition (Cs, units of C/M and g/cm3 of C), average composition (Cavg units of C/M and g/cm3 of C), and C mass loss (M, units of g/cm2 of C). 

Knowing an experimental value of k, it is possible to evaluate the diffusion coefficient of the atoms of a dissolving solid substance across the diffusion boundary layer at the solid-liquid interface into the bulk of the liquid phase using equations (5.6) and (5.7). Its calculation includes two steps. First, an approximate value of D is calculated from equation (5.6). Then, the Schmidt number, Sc, and the correction factor, /, is found (see Table 5.1). The final, precise value is evaluated from equation (5.7). In most cases, the results of these calculations do not differ by more than 10 %. Values of the diffusion coefficient of some transition metals in liquid aluminium are presented in Table 5.9.303... 

As illustrated in Fig. 5.10, the temperature dependence of the diffusion coefficient of transition metals into liquid aluminium is well described by the Arrhenius equation, D = D0 exp (-E/R.T), giving a linear plot of In I) against T l. Values of the pre-exponential factor, D0, and the activation energy, E, for some of them are given in Table 5.10. 

Table 5.9. Diffusion coefficients of transition metals, D (MO-9 m2 s 1), across the diffusion boundary layer at the solid-liquid interface into liquid aluminium.303 The mean relative error of their determination is around 10%...

Table 5.10. Parameters of the Arrhenius equation, D = D0 exp ( /CRT), describing the temperature dependence of the diffusion coefficient of some transition metals into liquid aluminium303...

In oriented metallic conducting polymers, with large anisotropy in conductivity, the anisotropic diffusion coefficient factor should be taken into account in the above model. The robustness of this metallic state can be verified from the field dependence of conductivity at low temperatures. For example, in the case of sample E with oj 2 200 S/cm (see Fig. 3.4), which is just on the metallic side of the M-I transition, a field of 8 T can induce a transition to the insulating state, as shown in Fig. 3.7. The corresponding W vs. T plot (Fig. 3.7a) is consistent with the fact that the system has moved from the metallic to the critical/insulating side. This is a typical example... 

The Warburg coefficient can be experimentally determined from the average value for the slope ofthe Z versus co plot, and for the slope of the -Z" versus co plot. In many reports, the diffusion coefficients of lithium ions have been determined for various transition metal oxides [13, 97, 113, 114] and graphite [59] electrodes by using EIS. 

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