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Defect Equilibria in Solids

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The Chemical Structure of Solids

Part of the book series: Treatise on Solid State Chemistry ((TSSC,volume 1))

Abstract

An ideal crystal consists of a perfectly ordered arrangement of atoms, ions, or molecules. However, in any real crystal, at temperatures above absolute zero, there are always imperfections or defects in the crystal lattice, as discussed in Chapter 5. This chapter will deal with defects whose distribution and concentration in the lattice are governed by the laws of thermodynamics.† In pure crystals such defects are called native defects. The existence of native defects in a lattice arises from a tendency of a crystal to increase its entropy or degree of disorder. As defects are introduced into a crystal, the entropy ΔS will increase. The number of defects will be limited, however, by the enthalpy necessary to form the defects, ΔH. The actual number of defects present at any temperature is that which gives a minimum in the free energy G of the crystal according to the relation

$$G = G^* + \Delta H - T\Delta S = G^* + N_D \Delta H_D - TN_D \Delta S_u - T\Delta S_c (N_D )$$
((1))

where G* is the free energy of the theoretically perfect crystal, N D is the number of defects, ΔH D is the enthalpy change per defect, ΔS V is the change in vibrational entropy per defect, and ΔS c(N D) is the change in configurational entropy, which is a function of the number of defects.

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Authors and Affiliations

  1. Materials Research Center, Allied Chemical Corporation, Morristown, New Jersey, USA

    George G. Libowitz

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  1. Research and Patents, Bell Laboratories, Murray Hill, New Jersey, USA

    N. B. Hannay (Vice President) (Vice President)

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Libowitz, G.G. (1973). Defect Equilibria in Solids. In: Hannay, N.B. (eds) The Chemical Structure of Solids. Treatise on Solid State Chemistry, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-2661-8_6

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  • DOI: https://doi.org/10.1007/978-1-4684-2661-8_6

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