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Properties of MaterialsAnisotropy, Symmetry, Structure$
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Robert E. Newnham

Print publication date: 2004

Print ISBN-13: 9780198520757

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780198520757.001.0001

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Diffusion and ionic conductivity

Diffusion and ionic conductivity

Chapter:
(p.211) 19 Diffusion and ionic conductivity
Source:
Properties of Materials
Author(s):

Robert E. Newnham

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198520757.003.0021

The phenomenon of atomic and ionic migration in crystals is called solidstate diffusion, and its study has shed light on many problems of technological and scientific importance. Diffusion is intimately connected to the strength of metals at high temperature, to metallurgical processes used to control alloy properties, and to many of the effects of radiation on nuclear reactor materials. Diffusion studies are important in understanding the ionic conductivity of the materials used in fuel cells, the fabrication of semiconductor integrated circuits, the corrosion of metals, and the sintering of ceramics. When two miscible materials are in contact across an interface, the quantity of diffusing material which passes through the interface is proportional to the concentration gradient. The atomic flux J is given by where J is measured per unit time and per unit area, c is the concentration of the diffusing material per unit volume, and Z is the gradient direction. The proportionality factor D, the diffusion coefficient, is measured in units of m2/s. This equation is sometimes referred to as Fick’s First Law. It describes atomic transport in a form that is analogous to electrical resistivity (Ohm’s Law) or thermal conductivity. There are several objections to Fick’s Law, as discussed in Section 19.5. Strictly speaking, it is valid only for self-diffusion coefficients measured in small concentration gradients. Since J and Z are both vectors, the diffusion coefficient D is a second rank tensor. As with other symmetric second rank tensors, between one and six measurements are required to specify Dij, depending on symmetry. The relationship between structure and anisotropy is more apparent in PbI2. Lead iodide is isostructural with CdI2 in trigonal point group.m. The self-diffusion of Pb is much easier parallel to the layers where the Pb atoms are in close proximity to one another. Diffusion is more difficult along Z3 = [001] because Pb atoms have a very long jump distance in this direction. The mineral olivine, (Mg, Fe)2SiO4, is an important constituent of the deeper parts of the earth’s crust.

Keywords:   Batteries, Chemical potential, Electrical conductivity, Fuel cells, Ionic conductivity, Measurements, Nernst-Einstein Relation, Pressure Dependence, Solid solutions

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