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## Über dieses Buch

This book offers detailed descriptions of the methods available to predict the occurrence of diffusion in alloys subjected to various processes. Major topic areas covered include diffusion equations, atomic theory of diffusion, diffusion in dilute alloys, diffusion in a concentration gradient, diffusion in non-metals, high diffusivity paths, and thermo- and electro-transport.

## Inhaltsverzeichnis

### 1. Diffusion Equations

Abstract
Changes in the structure of metals and their relation to physical and mechanical properties are the primary interest of the physical metallurgist. Since most changes in structure occur by diffusion, any real understanding of phase changes, homogenization, spheroidization, etc., must be based on a knowledge of diffusion. These kinetic processes can be treated by assuming that the metal is a continuum, that is, by ignoring the atomic structure of the solid. The problem then becomes one of obtaining and solving an appropriate differential equation. In this first chapter the basic differential equations for diffusion are given, along with their solutions for the simpler boundary conditions. The diffusion coefficient is also defined, and its experimental determination is discussed.
Paul Shewmon

### 2. Atomic Theory of Diffusion

Abstract
If a drop of a dilute mixture of milk in water is placed under a microscope and observed by transmitted light, small fat globules can be seen. These globules are about 1 µm in diameter and continually make small movements hither and yon. These movements, which are called Brownian motion, give a continual mixing and are the cause, or mechanism, of the homogenization, whose rate could be measured in a macroscopic diffusion experiment. For example, if a drop of the same milky solution is placed in water, it will tend to spread out, and the mixture will ultimately become homogeneous. In this latter experiment a concentration gradient is present, a flux of fat globules1 exists, and a diffusion coefficient could be measured. This is not quite an after-lunch experiment though, since turbulent mixing must be avoided and diffusion occurs quite slowly (D = 10−8 cm2/sec).
Paul Shewmon

### 3. Diffusion in Dilute Alloy

Abstract
The next degree of complexity after studying diffusion in pure metals is to study the diffusion in dilute alloys. The simplest problem in this area arises in interstitial alloys. Here the solute atoms diffuse on a sublattice whose sites are essentially all vacant, and the only role played by the solvent atoms is to form the barriers which define the sublattice of the interstitial sites. Because the two types of atoms do not share the same sites, the theory of interstitial diffusion is relatively simple and has been discussed in Chap. 2. The use of relaxation or resonance techniques to measure D for interstitials in bcc metals is introduced as a representative of a family of techniques in which the mean jump frequency of the interstitials is obtained from some relaxation phenomenon. This frequency is then combined with a model and random-walk theory to give values of D.
Paul Shewmon

### 4. Diffusion in a Concentration Gradient

Abstract
In the preceding chapter our discussion of diffusion in substitutional alloys was limited to self-diffusion experiments. In such experiments the specimen is, or is assumed to be, chemically homogeneous. Such studies showed that the self-diffusion coefficients are, in general, different for the two elements in a substitutional alloy. Yet, if two semiinfinite bars of differing proportions of components 1 and 2 are joined and diffused, the Boltzmann-Matano solution gives only one diffusion coefficient D(c) which completely describes the resulting homogenization. Thus the problem is to relate this single diffusion coefficient to the self-diffusion coefficients at the same composition. To do this two new effects must be understood. The first of these concerns the kind of matter flow which is to be classified as diffusion. In a binary diffusion couple with a large concentration gradient we shall see that diffusion gives rise to the movement of one part of the diffusion couple relative to another. The coordinate system used in the Boltzmann-Matano solution is fixed relative to the end of the specimen, and the chemical diffusion coefficient is given by the equation1
$$\tilde D = - J/(\partial c/\partial x)$$
(4-1)
Thus any movement of lattice planes relative to the ends of the diffusion couple is recorded as a flux and affects Ď even though such translation does not correspond to any jumping of atoms from one site to another.
Paul Shewmon

### 5. Diffusion in Nonmetals

Abstract
In the preceding chapters, the specific examples used concerned metals. This stems partly from the author’s experience but also from the fact that the majority of the research on diffusion in solids has been done with metals. There is reason to believe that all the general theory and most of the physical phenomena discussed in the earlier chapters applies equally well to nonmetals, although well-studied examples are often not available. With the change in electronic structure in going from metals to nonmetals, several new effects arise. In insulators the electrons are bound so tightly to the atoms that the principal means of carrying electric current at elevated temperature is by the movement of ions. In oxides and sulfides of transition metals the charge is carried by electrons, or electron holes, but charge conservation dictates that deviations from stoichiometry are accompanied by large increases in the concentration of the point defects that aid diffusion. In elemental semiconductors like silicon and germanium the bonding leads to both special electronic effects and the relatively easy accommodation of host and solute atoms on interstitial sites. This chapter deals with the phenomena which are unique to nonmetals, and ordered alloys.
Paul Shewmon

### 6. High Diffusivity Paths

Abstract
In the preceding chapters the only defects which aided diffusion through the crystal were vacancies and interstitials. Dislocations, free surfaces, and grain boundaries entered only to help attain the equilibrium defect concentration. However, it is now well established that the mean jump frequency of atoms at dislocations, boundaries, or surfaces is much higher than that of the same atom in the lattice. The diffusivity is therefore higher in these regions. This higher diffusivity is of interest for several reasons. First, there is the question of what error these paths introduce in the measurement of the lattice diffusion coefficient. Also, with properly designed experiments it is possible to determine the diffusion coefficients in each of these high diffusivity regions, allowing one to learn more about the structure of these paths and about how the atoms move in them. Finally, there are a group of kinetic processes which are limited by such diffusion, for example diffusional creep, structural changes in thin films, or the stability of fine catalysts.
Paul Shewmon

### 7. Thermo- and Electro-Transport in Solids

Abstract
If a current of electricity, or a flux of heat, is passed through an initially homogeneous alloy an unmixing occurs, that is a concentration gradient develops. These effects are called electro-transport and thermotransport, respectively. In electro-transport the atomic redistribution is similar to that studied in ionic conductors. However, in metals electrons carry essentially all of the electric current, and the ratio of electron to atomic currents is high. It appears that most of the atomic transport results from the impact of the large flux of electrons on the solute atoms making diffusive jumps. In thermo-transport, the redistribution of solute which occurs is analogous to the more widely studied thermoelectric effects that arise from the redistribution of electrons in a solid in a temperature gradient. The origin of the force driving the atoms is not clear.
Paul Shewmon

### Backmatter

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