Boltzmann-Matano analysis

Figure 3-8 Concentration plots in Boltzmann-Matano analysis of an experimental diffusion-couple profile, (a) Plot of x versus C for the calculation of the integral Jx dC. (b) C versus x. The slope can be evaluated using this plot. As x approaches -co (that is, for large negative x<-500 /im), C is roughly 0.003. As x approaches co (that is, for large x> 2000 /im), C approaches 0.108. The data and the fit (using Dqh = 0 and Du om = oexp(aXH20t) see Section 3.3.1) are for exp Rhy-DC9 from Zhang and Behrens (2000).

Consider the Boltzmann-Matano analysis leading to Eq. 4.51. Explain why the condition imposed by Eq. 4.50 determines the location of the x = 0 plane (i.e., the position of the original interface). 

The diffiisivity versus composition has been investigated for 5-TiNi j, 5-HfNi j, and 5-NbNi j. A modified Boltzmann-Matano analysis, carried out on nitrogen diffusion profiles measured by EPMA, yielded a composition-dependent diffusion coefficient for N diffusion expressed as... 

Fig. 5-9, The Boltzmann-Matano analysis of a concentration profile as given in [24].

The chemical diffusion coefficient can be experimentally determined as described in section 5.5.6 with the aid of the Boltzmann-Matano analysis. The atomistic interpretation of this diffusion coefficient will be illustrated by two examples. 

A and B should form a complete range of solid solutions. This means that they should have the same crystal structure as well as similar molar volumes. The phenomenological transport problem here is concerned with the solution of Fick s laws for the given experimental conditions in this inhomogeneous system. The atomistic problem is concerned with the interpretation of the chemical diffusion coefficient which, for example, might have been determined by a Boltzmann-Matano analysis. It was shown in section 5.5.3 that, for the case of binary diffusion via vacancies, the chemical diffusion coefficient may be written as ... 

In this section we shall consider first of all reactions of the type nA + mB A B in which the reaction product A B has a narrow range of homogeneity. An example would be the reaction A1 H- Sb = AlSb at 350 °C. In general, we shall not be concerned with determining the chemical diffusion coefficient by a Boltzmann-Matano analysis, since in the limiting case the diffusion profile in the diffusion couple consists of a pure step function. Reactions of this type parallel reactions between ionic crystals as discussed in section 6.2. Two situations must be separately discussed ... 

On the basis of a Boltzmann-Matano analysis of measured impurity-atom concentration profiles, it was concluded that the diffusion coefficient was concentration-dependent at high As concentrations. 

One can extract the diffusion coefficient from the Boltzmann-Matano technique (ID analysis) [50,52,73] ... 

On the other hand, the diffusion coefficient can be evaluated from Eq. (4). This 1-D analysis is called the Boltzmann-Matano technique ... 

FIGURE 2.3-10 Matano-Boltzmann analysis of tree-diffusion experiment. Matano plane (2 = 0) Located by area ABC — area CDE. 

---