Diffusivities in metals

Materials handbooks list data for Dq and Q for various atoms diffusing in metals and ceramics Table 18.1 gives some of the most useful values. Diffusion occurs in polymers, composites and glasses, too, but the data are less reliable. 

The practical importance of vacancies is that they are mobile and, at elevated temperatures, can move relatively easily through the crystal lattice. As illustrated in Fig. 20.21b, this is accompanied by movement of an atom in the opposite direction indeed, the existence of vacancies was originally postulated to explain solid-state diffusion in metals. In order to jump into a vacancy an adjacent atom must overcome an energy barrier. The energy required for this is supplied by thermal vibrations. Thus the diffusion rate in metals increases exponentially with temperature, not only because the vacancy concentration increases with temperature, but also because there is more thermal energy available to overcome the activation energy required for each jump in the diffusion process. 

Several topics in diffusion have arbitrarily been excluded from the following discussion diffusion in electrolytic solutions (F3, G9, HI, 02, R3, Yl), diffusion in ionized gases (K4), diffusion in macromolecular systems (W2), diffusion through membranes (F14), use of diffusional techniques in isotopic separations (S18), diffusion in metals (S8), and neutron diffusion (F2, G5, H15, W15). 

J.L, Bocquet, G. Brebec, and Y. Limoge. Diffusion in metals and alloys. In R.W. Cahn and P. Haasen, editors, Physical Metallurgy, pages 535-668. North-Holland, Amsterdam, 2nd edition, 1996. 

A. Horner. Self-diffusion in metallic glasses Approximation of the effective medium and molecular simulation. PhD thesis, Stuttgart University, 1993. In German. 

B.G. Guy and H. Oikawa. Calculations of two-phase diffusion in metallic systems including the interfacial reactions. Trans. AIME, 245(10) 2293-2297, 1969. 

The main observation from Table 2.1 is the enormous range of values of diffusion coefficients—from 10 1 to 10 30 cm2/s. Diffusion in gases is well understood and is treated in standard textbooks dealing with the kinetic theory of gases [24,25], Diffusion in metals and crystals is a topic of considerable interest to the semiconductor industry but not to membrane permeation. This book focuses principally on diffusion in liquids and polymers in which the diffusion coefficient can vary from about 10 5 to about 10-10 cm2/s. 

In this chapter, diffusion in solid materials, that is, metals, oxides, and nanoporous crystalline, ordered, and amorphous materials is discussed. We first study diffusion in a phenomenological, general form afterward the diffusion of atoms in crystals by means of knowledge obtained from studies of diffusion in metals is discussed. Thereafter, those phenomena that are exclusive to oxides are separately discussed. Finally, diffusion in nanoporous materials is described. 

Majer, G., Eberle, U., Kimmerle, F., Stanik E. and Orimo, S. (2003) Hydrogen diffusion in metallic and nano structured materials, Physica B 328, 81-89. 

Hydrogen diffusion within metals is also known to be governed by the stress-strain state therein. Roughly, it may be considered that hydrogen diffuses in metals obeying a Fick type diffusion law including additional terms to account for the effect of the stress-strain state. Concerning the role of stress, this is... 

While considering the influence of sound on the mobility of protons, their peculiar position should be taken into account, because in a solid they are specified both by the quantum features (the availability of the overlap integral between the nearest-neighbor sites in crystal with hydrogen bonds) and by classical ones (a large mass and hence a usual diffusion in metals and nonpolar semiconductors). The peculiar position occupied by the charge carriers in a hydrogen-bonded chain enables us to point out a specific mechanism of the proton conductivity stimulation by ultrasound. 

However it turned out that the structural, chemical and dynamical details are essential for complex descriptions of long-range proton transport. These parameters appear to be distinctly different for different families of compounds, preventing proton conduction processes from being described by a single model or concept as is the case for electron transfer reactions in solutions (described within Marcus theory [23]) or hydrogen diffusion in metals (incoherent phonon assisted tunneling [24]). 

In this section we present a brief overview of experimental methods used to study hydrogen motion in metals. The methods giving microscopic information on the hydrogen jump motion are emphasized. We restrict ourselves to a discussion of the basic principles of these methods only. More detailed consideration of the application of different methods to studies of the hydrogen diffusion in metals can be found in the reviews [7-14]. 

Extensive compilations of experimental data on hydrogen diffusion coefficients in binary metal-hydrogen systems have been published by Volkl and Alefeld [9] and Wipf [42]. These reviews can be referred to as sources of information on H diffusivities in different M-H systems. In this section we shall discuss some general features of H diffusivity in metals resulting from numerous experimental studies. 

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