In pure substances, the movement of the own particles, the so-called self-diffusion, can easily be studied by a labeled species of the substance. As mentioned in Section 8.1, both stable and radioactive isotopes can be used for labeling. In the case of stable labeling isotopes, mass spectrometry or subsequent activation is used to measure self-diffusion. Other techniques that can differentiate the isotopes with different mass numbers, such as nuclear magnetic resonance, are also used for the study of self-diffusion.

In this chapter, the application of radioactive isotopes in self-diffusion studies is discussed. As an example, the self-diffusion of metals is studied so that the bottom of

(C)

Metallic bulk phase

Figure 9.10 The distribution of the radioactive isotopes resulting in the different oxidized layer formation mechanisms. The oxidizing agent is labeled by the radioactive isotope.

(A) The oxidation process is determined by the diffusion of metal toward the solution.

(B) Both the metal and the oxidizing agent diffuse toward each other. (C) The oxidizing agent moves faster than metal atoms. (D) The oxidizing agent moves faster than metal atoms; the difference of the transport rate, however, is smaller than in C.

the metal piece is evenly covered (e. g., electrolysis) by a layer of the carrier-free radioactive isotope of the metal, and then the local distribution of the isotope is mea­sured after a given length of time. In the meantime, the temperature is kept constant. Under these conditions, the self-diffusion can be described by Eq. (9.34); thus, the self-diffusion coefficient is determined from the slope of the ln I versus x2 function. The transport of the radioactive tracer increases the mixing entropy. The change of enthalpy can be disregarded because of the very low concentration of the radiotracer. The first self-diffusion studies were done by George Hevesy and Gyula Grah.

In Table 9.1, the self-diffusion coefficients of different metals are listed. As seen, the diffusion coefficients give information on the crystal lattice, and consequently on the properties of metals. In noncubic lattices, the diffusion coefficients depend on the direction, the diffusion is anisotropic. In Table 9.1, || and _L denote the direc­tions parallel and perpendicular to the c-axis of the crystal lattice, respectively. As seen, different authors sometimes give different values, but within the same order of magnitude. This shows the uncertainty of self-diffusion measurements.

In solid crystalline substances, diffusion has two mechanisms:

• Diffusion in a crystal grain or volume diffusion. This takes place inside a crystal grain or in a single crystal.

• Grain boundary diffusion, which is characteristic in polycrystals. An example of this is shown in Figure 9.11.

The self-diffusion coefficients are suitable to study the structural changes of sub­stances under different physical effects. An example is shown in Figure 9.12, where

the effect of heat treatment and deformation by compression is seen. Primary recrystallization takes place as a result of compression, while secondary recrystalli­zation occurs by 1 h anneal at an elevated temperature.

Table 9.1 also shows the self-diffusion coefficients for some liquids. As seen, the self-diffusion coefficients of liquids are several orders of magnitude higher than those of solid substances. In addition, the activation energy of self-diffusion in liquids is less by about an order of magnitude.