Vacancies and Self-Interstitials

Describe both vacancy and self-interstitial crystalline defects. 

Calculate the equilibrium number of vacancies in a material at some specified temperature, given the relevant constants. 

Name the two types of solid solutions and provide a brief written definition and/or schematic sketch of each. 

Given the masses and atomic weights of two or more elements in a metal alloy, calculate 

Describe the atomic structure within the vicinity of (a) a grain boundary and (b) a twin boundary. 

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Figure 1.28 Representation of a vacancy and self-interstitial in a crystalline solid. From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc.

Diffusion phenomena, as well as calculations of diffusion entropy and enthalpy, have been successfully explained by ascribing multiple ionization levels to vacancies that are the same as those observed for the vacancy in low-temperature irradiation experiments (14-16). Vacancies and self-interstitials are interchangeable as far as diffusion is concerned, provided that both have charge states. 

In principle, both vacancies and self-interstitials may occur simultaneously and somewhat independently. Indeed, any relationship between Cv° and C j° may be dominated by the Si surface, which can act as a source or sink for either species. If a local dynamical equilibrium exists between re-... 

Vacancies and self-interstitials can exist in equilibrium with each other in the silicon lattice. The concentration of each species can be described by equilibrium equations of the following type. 

As an example of the study of vacancies and self-interstitial impurities by the continued fraction expansion of Eq. (S.2S), we mention the work of Kauffer et al. These authors consider impurities in silicon and set up a model tight-binding Hamiltonian with s p hybridization, which satisfactorily describes the valence and conduction bands of the perfect crystal. A cluster of 2545 atoms is generated, and vacancies (or self-interstitial impurities) are introduced at the center of the cluster. One then takes as a seed state an appropriate orbital or symmetrized combination of orbitals, and the recursion method is started. Though self-consistent potential modifications are neglected in this paper, the model leads to qualitatively satisfactory results within a simple physical picture. 

Ice Ih, the proton-disordered hexagonal phase of water, has been by far the most studied phase of ice, however, a complete understanding of many of its properties still remains elusive. The role played by crystal defects is among the important issues requiring better comprehension. It is in fact quite remarkable that not even the most basic disruptions of crystalline order, the molecular vacancy and self-interstitial, are well understood. ... 

Even surfaces obtained by cleaving single crystals are not atomically smooth, because any surface undergoes relaxation and reconstruction, and contains equilibrium defects like vacancies and self-interstitials. Roughening is a fundamental process for all solid surfaces, and results in terraces, steps and kinks (see, for instance, ref. [27]). 

Voronkov, V.V. (2008). Grown-in defects in silicon produced by agglomeration of vacancies and self-interstitial. Journal Crystal Growth, Vol. 310, No. 7-9, pp. 1307-1314, ISSN 0022-0248. 

O Problem available (at instructor s discretion) in WUeyPLUS Vacancies and Self-Interstitials... 

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