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Electrons and Disorder in Solids$
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V. F. Gantmakher

Print publication date: 2005

Print ISBN-13: 9780198567561

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198567561.001.0001

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Electrons and Disorder in Solids

V.F. Gantmakher

Oxford University Press

This chapter demonstrates approaches to the treatment of macroscopically inhomogeneous materials. The conception and criteria of granularity are introduced and experimental examples of metal-insulator transition are presented. The nature of the transition is tightly connected to the phenomenon of Coulomb blockade: electron tunneling between the grains is blocked because charging of small grains requires Coulomb energy larger than the temperature. The concept of a granular material is not restricted to cermets — a mixture of metallic and insulating grains of different sizes but quasi-spherical in shape. It can be extended to materials with fractal grains where the insulating volume resembles a loose glomus of thin insulating sheets.

Keywords:   cermet, Coulomb blockade, granulation, phase transition, tunneling, fractal grains

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