Diffusion in solids

In the diffusion through solids, several distinct cases arise that depend on the nature of the diffusing species and of tiie solid medium. The diffusing 

The estimation of diffusion coefficients in solids is not accurate. In almost every case, one must use experimental results. Methods for rough estimates based on the theory for face-centered-cubic (FCC) metals are the standard by which other theories are judged. 

Note In most cases, these values are extrapolated from values at higher temperatures. 

There are two overriding considerations to keep in mind when discussing diffusion in solids the structure of the matrix across which diffusion occurs and the defects present. In a normal crystalline solid, diffusion is mediated by the defects present, and the speed of diffusion will vary significantly if the predominant defect type changes. This is because diffusion involves the movement of a species from a stable position, through some sort of less stable position or bottleneck, to another stable position. Any disorder in the solid due to defects will make this process easier. 

Movement through the body of a solid is called volume, lattice, or bulk diffusion. In a gas or liquid, bulk diffusion is usually the same in all directions and the material is described as isotropic. This is also true in amorphous or glassy solids and in cubic crystals. In all other crystals, the rate of bulk diffusion depends upon the direction taken and is anisotropic. Bulk diffusion through a perfect single crystal is dominated by point defects, with both impurity and intrinsic defect populations playing a part. 

In this chapter, to keep the material compact, only the relationship between diffusion and defects in solids will be discussed. Moreover, the diffusion coefficient will be considered as a constant at a fixed temperature, and attention is focused upon the movement of atoms and ions rather than the equally important diffusion of gases or liquids through a solid. Discussion of diffusion per se, the extensive literature on classical theories of diffusion, and diffusion when the diffusion coefficient is not a constant will be found in the Further Reading section at the end of this chapter. 

Diffusion is followed by tracking the movements of tracer species through the solid to obtain the tracer diffusion coefficient, written as D when the tracer is identical to one of the components of the crystal, and D% when an impurity or foreign atom A is the tracer. Earlier studies made extensive use of radioactive isotopes because the progress 

For a typical poly crystalline material the concentration profile is divided into three segments. Near the original surface the tracer distribution will be characteristic of volume diffusion and show a typical bell shape. The average tracer concentration 

It was indicated in Chap. I that certain of the diffusional operations such as leaching, drying, and adsorption and membrane operations such as dialysis, reverse osmosis, and the like involve contact of fluids with solids. In these cases, some of the diffusion occurs in the solid phase and may proceed according to any of several mechanisms. While in none of these is the mechanism as simple as in the diffusion through solutions of gases and liquids, nevertheless with some exceptions it is usually possible to describe the transfer of diffusing substance by means of the same basic law used for fluids, Pick s law. 

At high temperature and a higher partial pressure of oxygen (1 P(02) 20 torr), the rate of growth of the FeO layer follows the parabolic rate law. The rate of formation of FeO is determined by the rate of diffusion of Fe2+, but the rate of diffusion of O2- determines the rate at which the thickness of Fe203 increases. 

Although solids have definite shapes and the lattice members (atoms, ions, or molecules) are essentially fixed in their locations, there is still movement of units from their lattice sites. In fact, several 

When this system was studied over time, it was found that the marker wires move toward each other. This shows that the most extensive diffusion is zinc from the brass (an alloy of zinc and copper) outward into the copper. If the mechanism of diffusion involved an interchange of copper and zinc, the wires would not move. The diffusion in this case takes place by the vacancy mechanism described later, as zinc moves from the brass into the surrounding copper. As the zinc moves outward, vacancies are produced in the 

Displacements of lattice members are determined by energy factors and concentration gradients. To a considerable extent, diffusion in solids is related to the existence of vacancies. The concentration of defects, N0, (sites of higher energy) can be expressed in terms of a Boltzmann distribution as 

When a crystal is heated, lattice members become more mobile. As a result, there can be removal of vacancies as they become filled by diffusion. Attractions to nearest neighbors are reestablished that result in a slight increase in density and the liberation of energy. There will be a disappearance of dislocated atoms or perhaps a redistribution of dislocations. These events are known to involve several types of mechanisms. However, the diffusion coefficient, D, is expressed as 

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P. G. Shewmon, Diffusion in Solids, 2nd edition, TMS Publishers, Warrendale, Penn, USA, 1989. W. D. Kingery, Introduction to Ceramics, Wiley, 1960, Chap. 8. 

Chemical reaction - formation of intermetollic compounds Diffusion in solid solutions (dilute ideal solutions between solute 300 to 5 X 1 O ... 

By way of example, Volume 26 in Group III (Crystal and Solid State Physics) is devoted to Diffusion in Solid Metals and Alloys, this volume has an editor and 14 contributors. Their task was not only to gather numerical data on such matters as self- and chemical diffusivities, pressure dependence of diffusivities, diffusion along dislocations, surface diffusion, but also to exercise their professional judgment as to the reliability of the various numerical values available. The whole volume of about 750 pages is introduced by a chapter describing diffusion mechanisms and methods of measuring diffusivities this kind of introduction is a special feature of Landolt-Bornstein . Subsequent developments in diffusion data can then be found in a specialised journal. Defect and Diffusion Forum, which is not connected with Landolt-Bdrnstein. 

Shewmon, P. G., Diffusion in Solids, McGraw-Hill, New York (1963)... 

Figure 8. Three types of polarization of Mn02 (1) J]c (H+ solid), due to proton diffusion in solid (2) rja, due to the solution-solid interface (3) 7/t (ApH), due to a pH change of the electrolyte in the pores.

By defining nA as the number of A atoms present per unit volume, x as the time of stay at any given site, 1/x as the frequency of jumps and Jx- y as the number of jumps per unit time. Pick was able to derive two laws regarding diffusion in solids. To do this, he also defined ... 

We have already discussed diffusion in solids to some degree. While bulk properties such as heat capacity are not sensitive to defect concentration, many other properties such as conductivity are. Thus, the method of preparation becomes important if one wishes to obtain a conductive or... 

Multidimensional and heteronuclear NMR techniques have revolutionised the use of NMR spectroscopy for the structure determination of organic molecules from small to complex. Multidimensional NMR also allows observation of forbidden multiple-quantum transitions and probing of slow dynamic processes, such as chemical exchange, cross-relaxation, transient Over-hauser effects, and spin-diffusion in solids. 

W lost. Diffusion in Solids, Liquids, Gases. New York Academic Press, 1960, pp 8, 42-45. 

Arefian NA, Shokuhfar A, Vaezi MR, Kandjani AE, Tabriz MF (2008) Sonochemical synthesis of SnO/ZnO nano-Composite the effects of temperature and sonication power. In Ochsner A, Murch GE (eds) Defect and diffusion forum, vol 273-276, Diffusion in solids and liquids III., pp 34-39... 

How does temperature effect diffusion in solids How do defects influence diffusion in solids ... 

The first four chapters introduce basic concepts that are developed to build up a framework for understanding defect chemistry and physics. Thereafter, chapters focus rather more on properties related to applications. Chapter 5 describes diffusion in solids Chapter 6, ionic conductivity Chapters 7 and 8 the important topics of electronic conductivity, both intrinsic (Chapter 7) and extrinsic (Chapter 8). The final chapter gives a selected account of magnetic and optical defects. 

Let us assume that a sphere with radius a is immersed in a liquid of finite volume, e.g., a mineral in a hydrothermal fluid. Diffusion in liquids is normally fast compared to diffusion in solids, so that the liquid can be thought of as homogeneous. Similar conditions would apply to a sphere degassing into a finite enclosure, e.g., for radiogenic argon loss in a closed pore space. Given the diffusion equation with radial flux and constant diffusion coefficient... 

Jost, W. "Diffusion in Solids, Liquids, Gases Academic Press New York, 1960. 

Shewmon P.G. (1963) Diffusion in Solids. New York McGraw-Hill. 

Experiments snch as the one illnstrated in Fignre 4.38 not only give us self-diffusion coefficients for certain snbstances, bnt as the temperatnre of the experiment is varied, they give us the temperature dependence of the process and a measurement of the activation energy barrier to diffnsion. Diffusion in solid systems, then, can be modeled as an activated process that is, an Arrhenius-type relationship can be written in which an activation energy, Ea, and temperatnre dependence are incorporated, along with a preexponential factor. Do, sometimes called ht frequency factor ... 

As a reaction medium, solvents are used to bring reactants at suitable concentrations. For endothermic reactions, heat can be supplied readily by heating the solvent for exothermic reactions, the solvent can act as a heat sink. If necessary, surplus heat can be removed by allowing the solvent to boil. After the reaction, products have to be freed of solvent. As diffusion in solids is slow, solid-solid reactions are slow at room temperature. To get reactants to mix at a molecular level requires use of the gas phase. 

Bennett, . H., Exact Defect Calculations in Model Substances, In Diffusion in Solids Recent Developments Eds. Nowick, A. S. Burton, J. J. Academic Press, New York, 1975 p. 73. 

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