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Electron microscopy of antisites (a, Mo substitutes for S) and vacancies (b, missing S atoms) in a "monolayer of "molybdenum disulfide. Scale bar: 1 nm.[1]

"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 "atoms or "molecules in most crystalline materials is not perfect. The regular patterns are interrupted by crystallographic defects.[2][3][4][5]

Contents

Point defects[edit]

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. However, these defects typically 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.

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Schematic illustration of some simple point defect types in a monatomic solid

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Schematic illustration of defects in a compound solid, using GaAs as an example.

Line defects[edit]

Line defects can be described by gauge theories.

"Dislocations are linear defects, around which (the dislocation line) some of the atoms of the crystal lattice are misaligned.[12] There are two basic types of dislocations, the edge dislocation and the screw dislocation. "Mixed" dislocations, combining aspects of both types, are also common.

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An edge dislocation is shown. The dislocation line is presented in blue, the Burgers vector b in black.

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 crystallographic 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.

"Disclinations are line defects corresponding to "adding" or "subtracting" an angle around a line. Basically, this means that if you track the crystal orientation around the line defect, you get a rotation. Usually, they were thought to play a role only in liquid crystals, but recent developments suggest that they might have a role also in solid materials, e.g. leading to the self-healing of "cracks.[13]

Planar defects[edit]

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Origin of stacking faults: Different stacking sequences of close-packed crystals

Bulk defects[edit]

Mathematical classification methods[edit]

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.[15]

Computer simulation methods[edit]

"Density functional theory, classical "molecular dynamics and "kinetic Monte Carlo [16] simulations are widely used to study the properties of defects in solids with computer simulations.[9][10][11][17][18][19][20] 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 technique for demonstrating some types of crystallographic defects.[21]

See also[edit]

References[edit]

  1. ^ Hong, J.; Hu, Z.; Probert, M.; Li, K.; Lv, D.; Yang, X.; Gu, L.; Mao, N.; Feng, Q.; Xie, L.; Zhang, J.; Wu, D.; Zhang, Z.; Jin, C.; Ji, W.; Zhang, X.; Yuan, J.; Zhang, Z. (2015). "Exploring atomic defects in molybdenum disulphide monolayers". Nature Communications. 6: 6293. "Bibcode:2015NatCo...6E6293H. "doi:10.1038/ncomms7293. "PMC 4346634Freely accessible. "PMID 25695374. 
  2. ^ Ehrhart, P. (1991) Properties and interactions of atomic defects in metals and alloys, volume 25 of Landolt-Börnstein, New Series III, chapter 2, p. 88, Springer, Berlin
  3. ^ Siegel, R. W. (1982) Atomic Defects and Diffusion in Metals, in Point Defects and Defect Interactions in Metals, J.-I. Takamura (ED.), p. 783, North Holland, Amsterdam
  4. ^ Crawford, J. H.; Slifkin, L. M., eds. (1975). Point Defects in Solids. New York: Plenum Press. 
  5. ^ Watkins, G. D. (1997) "Native defects and their interactions with impurities in silicon", p. 139 in Defects and Diffusion in Silicon Processing, T. Diaz de la Rubia, S. Coffa, P. A. Stolk, and C. S. Rafferty (eds), vol. 469 of MRS Symposium Proceedings, Materials Research Society, Pittsburgh, "ISBN "1-55899-373-8
  6. ^ 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. 
  7. ^ 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): 8527–8539. "Bibcode:1996PhRvB..54.8527H. "doi:10.1103/PhysRevB.54.8527. 
  8. ^ Lieb, Klaus-Peter; Keinonen, Juhani (2006). "Luminescence of ion-irradiated α-quartz". Contemporary Physics. 47 (5): 305–331. "Bibcode:2006ConPh..47..305L. "doi:10.1080/00107510601088156. 
  9. ^ a b Ashkenazy, Yinon; Averback, Robert S. (2012). "Irradiation Induced Grain Boundary Flow—A New Creep Mechanism at the Nanoscale". Nano Letters. 12 (8): 4084–9. "Bibcode:2012NanoL..12.4084A. "doi:10.1021/nl301554k. "PMID 22775230. 
  10. ^ a b Mayr, S.; Ashkenazy, Y.; Albe, K.; Averback, R. (2003). "Mechanisms of radiation-induced viscous flow: Role of point defects". Phys. Rev. Lett. 90 (5): 055505. "Bibcode:2003PhRvL..90e5505M. "doi:10.1103/PhysRevLett.90.055505. "PMID 12633371. 
  11. ^ a b Nordlund, K; Ashkenazy, Y; Averback, R. S; Granato, A. V (2005). "Strings and interstitials in liquids, glasses and crystals". Europhys. Lett. 71 (4): 625–631. "Bibcode:2005EL.....71..625N. "doi:10.1209/epl/i2005-10132-1. 
  12. ^ Hirth, J. P.; Lothe, J. (1992). Theory of dislocations (2 ed.). Krieger Pub Co. "ISBN "0-89464-617-6. 
  13. ^ Chandler, David L., Cracked metal, heal thyself, MIT news, October 9, 2013
  14. ^ Waldmann, T. (2012). "The role of surface defects in large organic molecule adsorption: substrate configuration effects". Physical Chemistry Chemical Physics. 14 (30): 10726–31. "Bibcode:2012PCCP...1410726W. "doi:10.1039/C2CP40800G. "PMID 22751288. 
  15. ^ Mermin, N. (1979). "The topological theory of defects in ordered media". Reviews of Modern Physics. 51 (3): 591–648. "Bibcode:1979RvMP...51..591M. "doi:10.1103/RevModPhys.51.591. 
  16. ^ Cai, W.; Bulatov, V. V.; Justo, J. F.; Argon, A.S,; Yip, S. (2000). "Intrinsic mobility of a dissociated dislocation in silicon". Phys. Rev. Lett. 84 (15): 3346–3349. "Bibcode:2000PhRvL..84.3346C. "doi:10.1103/PhysRevLett.84.3346. "PMID 11019086. 
  17. ^ Korhonen, T; Puska, M.; Nieminen, R. (1995). "Vacancy formation energies for fcc and bcc transition metals". Phys. Rev. B. 51 (15): 9526–9532. "Bibcode:1995PhRvB..51.9526K. "doi:10.1103/PhysRevB.51.9526. 
  18. ^ Puska, M. J.; Pöykkö, S.; Pesola, M.; Nieminen, R. (1998). "Convergence of supercell calculations for point defects in semiconductors: vacancy in silicon". Phys. Rev. B. 58 (3): 1318–1325. "Bibcode:1998PhRvB..58.1318P. "doi:10.1103/PhysRevB.58.1318. 
  19. ^ Nordlund, K.; Averback, R. (1998). "The role of self-interstitial atoms on the high temperature properties of metals". Phys. Rev. Lett. 80 (19): 4201–4204. "Bibcode:1998PhRvL..80.4201N. "doi:10.1103/PhysRevLett.80.4201. 
  20. ^ Sadigh, B; Lenosky, Thomas; Theiss, Silva; Caturla, Maria-Jose; Diaz De La Rubia, Tomas; Foad, Majeed (1999). "Mechanism of Boron Diffusion in Silicon: An Ab Initio and Kinetic Monte Carlo Study". Phys. Rev. Lett. 83 (21): 4341–4344. "Bibcode:1999PhRvL..83.4341S. "doi:10.1103/PhysRevLett.83.4341. 
  21. ^ Stillinger, Frank H.; Lubachevsky, Boris D. (1995). "Patterns of broken symmetry in the impurity-perturbed rigid-disk crystal". Journal of Statistical Physics. 78 (3–4): 1011–1026. "Bibcode:1995JSP....78.1011S. "doi:10.1007/BF02183698. 

Further reading[edit]

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