Diffusion in Solids: Fundamentals, Methods, Materials, by Helmut Mehrer
By Helmut Mehrer
Diffusion is a crucial subject in solid-state physics and chemistry, actual metallurgy and fabrics technology. Diffusion techniques are ubiquitous in solids at increased temperatures. a radical realizing of diffusion in fabrics is important for fabrics improvement and engineering. This ebook first offers an account of the critical facets of diffusion in solids, for which the required historical past is a direction in strong nation physics. It then presents easy accessibility to special information regarding diffuson in metals, alloys, semiconductors, ion-conducting fabrics, glasses and nanomaterials. numerous diffusion-controlled phenomena, together with ionic conduction, grain-boundary and dislocation pipe diffusion, are regarded as well.
Graduate scholars in solid-state physics, actual metallurgy, fabrics technology, actual and inorganic chemistry or geophysics will take advantage of this booklet as will physicists, chemists, metallurgists, fabrics engineers in educational and commercial study laboratories.
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Additional resources for Diffusion in Solids: Fundamentals, Methods, Materials, Diffusion-Controlled Processes
P. Stark, Solid-State Diﬀusion, John Wiley & Sons, New York, 1976 S. Mrowec, Defects and Diﬀusion – an Introduction, Materials Science Monographs, Vol. J. J. G. S. J. Young, Diﬀusion in the Condensed State, The Institute of Metals, London, 1987 J. R. B. S. E. S. C. Jaeger, Conduction of Heat in Solids, Clarendon Press, Oxford, 1959 J. Crank, The Mathematics of Diﬀusion, 2nd edition, Oxford University Press, 1975 R. , 1988 J. M. Mazo, Brownian Motion – Fluctuations, Dynamics, and Applications, Clarendon Press, Oxford, 2002 Specialised Books and Monographs on Solid-State Diﬀusion W.
There are thus not more than three coeﬃcients of diﬀusion. There are, however, always p ≤ 6 independent parameters; the p − 3 others deﬁne the orientations of the principal axes. 1. If x1 , x2 , x3 denote the principal diﬀusion axes and J1 , J2 , J3 the pertinent components of the diﬀusion ﬂux, Eq. 13) can be written as ∂C , ∂x1 ∂C , J2 = −D2 ∂x2 ∂C J3 = −D3 . 1. Number of parameters, p, decribing the principal diﬀusivities plus the orientations of principal axes System triclinic monoclinic orthorhombic p 6 4 hexagonal tetragonal rhombohedral (or trigonal) cubic 3 2 1 principal axes and one principal axis isotropic crystal axes coincide parallel crystal axis These equations imply that the diﬀusion ﬂux J and the concentration gradient ∇C usually point in diﬀerent directions.
16) D(α1 , α2 , α3 ) = α21 D1 + α22 D2 + α23 D3 . 16) shows that for given principal axes, anisotropic diﬀusion can be completely described by the principal diﬀusion coeﬃcients. Fig. 4. Diﬀusion direction in a single-crystal with principal diﬀusion axes x1 , x2 , x3 References 35 For crystals with triclinic, monoclinic, and orthorhombic symmetry all three principal diﬀusivities are diﬀerent: D1 = D2 = D3 . 17) Among these crystal systems only for crystals with orthorhombic symmetry the principal axes of diﬀusion do coincide with the axes of crystallographic symmetry.