Crystallographic defect

Crystalline solids exhibit a periodic crystal structure. The positions of atoms or molecules occur on repeating fixed distances, determined by the unit cell parameters. However, the arrangement of atom or molecules in most crystalline materials is not perfect. The regular patterns are interrupted by crystallographic defects.[1][2][3][4]

Contents

Point defects

Point defects are defects that occur only at or around a single lattice point. They are not extended in space in any dimension. Strict limits for how small a point defect is, are generally not defined explicitly, but typically these defects involve at most a few extra or missing atoms. Larger defects in an ordered structure are usually considered dislocation loops. For historical reasons, many point defects, especially in ionic crystals, are called centers: for example a vacancy in many ionic solids is called a luminescence center, a color center, or F-center. These dislocations permit ionic transport through crystals leading to electrochemical reactions. These are frequently specified using Kröger–Vink Notation.

Line defects

Line defects can be described by gauge theories.

There are two basic types of dislocations, the edge dislocation and the screw dislocation. "Mixed" dislocations, combining aspects of both types, are also common.

Edge dislocations are caused by the termination of a plane of atoms in the middle of a crystal. In such a case, the adjacent planes are not straight, but instead bend around the edge of the terminating plane so that the crystal structure is perfectly ordered on either side. The analogy with a stack of paper is apt: if a half a piece of paper is inserted in a stack of paper, the defect in the stack is only noticeable at the edge of the half sheet.

The screw dislocation is more difficult to visualise, but basically comprises a structure in which a helical path is traced around the linear defect (dislocation line) by the atomic planes of atoms in the crystal lattice.

The presence of dislocation results in lattice strain (distortion). The direction and magnitude of such distortion is expressed in terms of a Burgers vector (b). For an edge type, b is perpendicular to the dislocation line, whereas in the cases of the screw type it is parallel. In metallic materials, b is aligned with close-packed crytallographic directions and its magnitude is equivalent to one interatomic spacing.

Dislocations can move if the atoms from one of the surrounding planes break their bonds and rebond with the atoms at the terminating edge.

It is the presence of dislocations and their ability to readily move (and interact) under the influence of stresses induced by external loads that leads to the characteristic malleability of metallic materials.

Dislocations can be observed using transmission electron microscopy, field ion microscopy and atom probe techniques. Deep level transient spectroscopy has been used for studying the electrical activity of dislocations in semiconductors, mainly silicon.

Planar defects

Bulk defects

Mathematical classification methods

A successful mathematical classification method for physical lattice defects, which works not only with the theory of dislocations and other defects in crystals but also, e.g., for disclinations in liquid crystals and for excitations in superfluid 3He, is the topological homotopy theory.[9]

Computer simulation methods

Simulating jamming of hard spheres of different sizes and/or in containers with non-commeasurable sizes using the Lubachevsky-Stillinger algorithm can be an effective techniques for demonstrating some types of crystallographic defects. [10]

See also

References

  1. ^ P. Ehrhart, Properties and interactions of atomic defects in metals and alloys,volume 25 of Landolt-Börnstein, New Series III, chapter 2, page 88, Springer, Berlin, 1991
  2. ^ R. W. Siegel, Atomic Defects and Diffusion in Metals, in Point Defects and Defect Interactions in Metals, edited by J.-I. Takamura, page 783, North Holland, Amsterdam, 1982
  3. ^ J. H. Crawford and L. M. Slifkin, ed (1975). Point Defects in Solids. New York: Plenum Press. 
  4. ^ G. D. Watkins, Native defects and their interactions with impurities in silicon, in Defects and Diffusion in Silicon Processing, edited by T. Diaz de la Rubia, S. Coffa, P. A. Stolk, and C. S. Rafferty, volume 469 of MRS Symposium Proceedings, page 139, Materials Research Society, Pittsburgh, 1997
  5. ^ Mattila, T; Nieminen, RM (1995). "Direct Antisite Formation in Electron Irradiation of GaAs.". Physical review letters 74 (14): 2721–2724. Bibcode 1995PhRvL..74.2721M. doi:10.1103/PhysRevLett.74.2721. PMID 10058001. 
  6. ^ Hausmann, H.; Pillukat, A.; Ehrhart, P. (1996). "Point defects and their reactions in electron-irradiated GaAs investigated by optical absorption spectroscopy". Physical Review B 54 (12): 8527. Bibcode 1996PhRvB..54.8527H. doi:10.1103/PhysRevB.54.8527. 
  7. ^ Lieb, Klaus-Peter; Keinonen, Juhani (2006). "Luminescence of ion-irradiated α-quartz". Contemporary Physics 47 (5): 305. Bibcode 2006ConPh..47..305L. doi:10.1080/00107510601088156. 
  8. ^ a b J. P. Hirth and J. Lothe (1992). Theory of dislocations (2 ed.). Krieger Pub Co. ISBN 0894646176. 
  9. ^ Mermin, N. (1979). "The topological theory of defects in ordered media". Reviews of Modern Physics 51 (3): 591. Bibcode 1979RvMP...51..591M. doi:10.1103/RevModPhys.51.591. 
  10. ^ F. H. Stillinger and B. D. Lubachevsky (1995). Patterns of Broken Symmetry in the Inpurity-Perturbed Rigid Disk Crystal, J. Stat. Phys. 78, 1011-1026

Further reading