Diffusivity sample composition dependence

The above data relate to very pure iron samples with low dislocation densities. In real steels the trapping effects result in much lower apparent diffusivities, which are dependent on the metallurgical state of the steel, as well as its chemical composition. Typical values for the apparent diffusion coefficient of hydrogen in high-strength alloy steel at room temperature are in the region of 10" mVs. 

The experimental a versus x dependence for these samples, together with the fitting curves, are shown in Fig. 53. Note that in contrast to the previous example, these data are obtained at a constant sample composition. Now, Variations of the parameters a and x are induced by temperature variation. As mentioned above, the exponents a as well as the relaxation time x are functions of different experimentally controlled parameters. The same parameters can affect the structure or the diffusion simultaneously. In particular, both a and x are functions of temperature. Thus, the temperature dependence of the diffusion coefficient in (144) should be considered. Let us consider the temperature dependence of the diffusion coefficient D ... 

In electron-probe x-ray spectroscopy (EPXS), an electron beam of moderate energy, 10 to 50 keV, is focused on the sample at the location where elemental composition is to be determined. The atoms in a minute volume, one-half to several ftm in diameter and one or more /xm in depth, are excited by the incident electrons and, upon returning to the ground state, emit x-rays characteristic of the excited elements. The actual volume of sample analyzed depends on such variables as the diameter and energy of the electron beam, the diffusion of electrons in the sample, and the path length of the scattered primary and secondary x-rays. 

IR spectroscopy is one of the few analytical techniques that can be used for the characterization of solid, liquid, and gas samples. The choice of sampling technique depends upon the goal of the analysis, qualitative identification or quantitative measurement of specific analytes, upon the sample size available, and upon sample composition. Water content of the sample is a major concern, since the most common IR-transparent materials are soluble in water. Samples in different phases must be treated differently. Sampling techniques are available for transmission (absorption) measurements and, since the advent of FTIR, for several types of reflectance (reflection) measurements. The common reflectance measurements are attenuated total reflectance (ATR), diffuse reflectance or diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS), and specular reflectance. The term reflection may be used in place of reflectance and may be more accurate specular reflection is actually what occurs in that measurement, for example. However, the term reflectance is widely used in the literature and will be used here. 

The form or packing of the sample is another factor that will determine excess of the degree of contact with gaseous environment and the rate of escape of the volatile products. Thus, decomposition may be diffusion controlled and dependent on the sample geometry instead of chemically controlled and dependent only on the sample composition. Packing will also affect the thermal gradients in the sample. Thus, results for a single lump of a sample, rather than a powder, may differ. 

Collection of particles is based on filtration, gravitational and centrifugal sedimentation, inertial impaction and impingement, diffusion, interception, or electrostatic or thermal precipitation (e.g., see Spurny, 1986, Chapter 3). The choice of method depends on a number of parameters such as the composition and size of the particles, the purpose of the sample, and acceptable sampling rates. Table 11.10 summarizes some of the commonly used methods and the size ranges over which they are effective. 

Six samples were taken daily during three non-consecutive days within one week to achieve an average weekly composition. The sample size of every subsample of BA had to be defined based on considerations of a particulate pollutant (e.g., heavy metals) concentration rather than that of a diffusive pollutant distribution. A sample size reduction scheme (Fig. 1) was defined according to the study of Bunge Bunge (1999) depending on grain size and concentration of particulate pollutants. From the 18 collected subsamples,... 

Many techniques are based on this principle and can be used for the analysis of all types of samples. The spectrum obtained from reflected light is not identical to that obtained by transmittance. The spectral composition of the reflected beam depends on the variation of the refractive index of the compound with wavelength. This can lead to specular reflection, diffuse reflection or attenuated total reflection. Each device is designed to favour only one of the above. The recorded spectrum must be corrected using computer software. 

As an illustration, consider the isothermal, isobaric diffusional mixing of two elemental crystals, A and B, by a vacancy mechanism. Initially, A and B possess different vacancy concentrations Cy(A) and Cy(B). During interdiffusion, these concentrations have to change locally towards the new equilibrium values Cy(A,B), which depend on the local (A, B) composition. Vacancy relaxation will be slow if the external surfaces of the crystal, which act as the only sinks and sources, are far away. This is true for large samples. Although linear transport theory may apply for all structure elements, the (local) vacancy equilibrium is not fully established during the interdiffusion process. Consequently, the (local) transport coefficients (DA,DB), which are proportional to the vacancy concentration, are no longer functions of state (Le., dependent on composition only) but explicitly dependent on the diffusion time and the space coordinate. Non-linear transport equations are the result. 

Several points are to be noted. Firstly, pores and changes of sample dimension have been observed at and near interdiffusion zones [R. Busch, V. Ruth (1991)]. Pore formation is witness to a certain point defect supersaturation and indicates that sinks and sources for point defects are not sufficiently effective to maintain local defect equilibrium. Secondly, it is not necessary to assume a vacancy mechanism for atomic motion in order to invoke a Kirkendall effect. Finally, external observers would still see a marker movement (markers connected by lattice planes) in spite of bA = bB (no Kirkendall effect) if Vm depends on composition. The consequences of a variable molar volume for the determination of diffusion coefficients in binary systems have been thoroughly discussed (F. Sauer, V. Freise (1962) C. Wagner (1969) H. Schmalzried (1981)]. 

Figure 5-11 illustrates the results of an oxide interdiffusion experiment. Clearly, the transport coefficients are not single valued functions of composition. From the data, one concludes that for a given composition, the chemical diffusion coefficients depend both on time and location in the sample [G. Kutsche, H. Schmalzried (1990)]. Let us analyze this interdiffusion process in the ternary solid solution Co. O-Nq. O, which contains all the elements necessary for a phenomenological treatment of chemical transport in crystals. The large oxygen ions are almost immobile and so interdiffusion occurs only in the cation sublattice of the fee crystal. When we consider the following set ( ) of structure elements... 

Even when composition is fixed, viscosity and other rheological properties may depend on the size and arrangement of aligned domains within a sample of liquid crystalline material. No studies of this matter seem to have been made, however. Such structural characteristics do influence electrical conduction and diffusion in liquid crystals, as discussed further below. 

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