Lattice failure

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Any irregularity in an otherwise periodic crystal lattice is referred to as a lattice defect (also known as a lattice defect or crystal (structural) defect ) . The existence of lattice defects distinguishes the real crystal from the theoretical model of the ideal crystal . Lattice defects are of fundamental importance for many properties of a crystal , in particular for chemical reactivity, mass transport and diffusion in the crystal as well as for its mechanical properties.

The classification of the grid defects is based on the spatial extent of the defect area. One characterizes the number of spatial dimensions in which the lattice defect has more than an atomic size. In this way, zero to three-dimensional lattice defects are distinguished.

Zero-dimensional lattice errors

Point defects in a two-dimensional crystal lattice and the like a. with a self-interstitial atom (top left)

Point defects are defects that are the size of a single atom. Formally, they are limited to a single grid location. Three cases can be distinguished.

  • Vacancy ( vacancies ) are free lattice sites occupied in the regular lattice.
  • Interstitial atoms ( interstitials ) sitting on seats that are vacant in the regular lattice. Such defects are also known as interstitial defects .
  • Substitution atoms ( antisites ) sit on lattice sites that are occupied by another type of atom in the regular lattice. A special case are color centers in which an anion is replaced by an electron .

Point errors differ from the higher-dimensional errors in that they are the only ones to occur in thermodynamic equilibrium. Since they are a necessary prerequisite for mass transport and thus for chemical reactivity in a crystal, a separate branch of thermodynamics has developed in physical chemistry , the so-called point defect thermodynamics .

Different point defects are linked to one another in a crystal by charge and structure conditions and therefore often occur in certain combinations. Some important combinations have been given their own names. Schottky disorder , Frenkel disorder , intercalation solid solution and substitution solid solution should be mentioned . In order to be able to set up formal reaction equations with point defects, the Kröger-Vink notation is used.

Point defects can be divided into intrinsic and extrinsic defects. One speaks of intrinsic defects when the defects occur in the thermodynamic equilibrium of the pure crystal. Extrinsic defects, on the other hand, are caused by the presence of a second phase. For example, the Schottky disorder of a sodium chloride crystal is intrinsic. However, if the crystal is doped with small amounts of potassium chloride, the resulting potassium substitution atoms on sodium sites are referred to as extrinsic defects. The intrinsic and extrinsic conductivity are based on this difference in the type of charge carriers .

One-dimensional lattice defects

A step shift.

Line errors are commonly referred to as dislocations or dislocation lines . There are two types: step dislocations and screw dislocations. Both are crucial for the mechanical properties of the crystal and are therefore of great importance in materials science . But they can also be "paths" of increased atomic or ion mobility and thereby influence the transport of substances and the reactivity of the crystal.

The Burgers vector , which is perpendicular to the dislocation line in the case of a step dislocation, is used to characterize the dislocation. In the case of screw dislocation, it is parallel to the dislocation line.

Two-dimensional lattice defects

A real crystal inevitably has a finite size and therefore a surface. This represents an interruption of the translation symmetry and thus the simplest surface error. For the same reason, interfaces to other phases count as surface errors. The atomic structure in the vicinity of an interface depends very much on the state of aggregation, the chemical composition and possibly the crystallographic orientation of the second phase.

All other two-dimensional defects only occur inside the crystal under consideration.

  • Grain boundaries separate two grains of a crystal, i.e. two areas with different spatial orientation of the lattice. Depending on the angle by which the two grids are rotated against each other, one speaks of small- angle grain boundaries (sub-grain boundaries) or large-angle grain boundaries.
  • A twin boundary is the interface between the two parts of a crystal twin .
  • Stacking faults occur when the periodic “stacking” of the individual levels of a crystal is disturbed. This is a common mistake, especially with metals.
  • At an antiphase boundary, a part of the crystal is (formally) offset by translation with respect to the other part of the crystal. The translation is only part of the lattice constant.

Furthermore, the walls between ferromagnetic or ferroelectric domains of a crystal are also counted as surface defects.

Three-dimensional lattice defects

Volume error (also inclusions ) are full of foreign phases in the interior of the crystal.

  • Pores are open or closed cavities in the crystal that are filled with gas or liquid.
  • Inclusions are solid foreign phases.
  • Excretions (precipitates) are special cases of inclusion in which the foreign phase is formed from the crystal itself. This is e.g. This is the case, for example, when the minority component in the interior of the crystal forms its own phase when a solid solution cools (see also precipitation hardening ).

Since volume defects distort the surrounding crystal, they are surrounded by a zone with a higher concentration of low-dimensional lattice defects.

Structural disorder

The so-called structural disorder that occurs in some ion crystals is a special case . In such crystals, a single partial lattice has completely lost its translational symmetry. The ions of this partial lattice have an extremely high mobility. One speaks of a quasi-melted partial lattice. The crystals become very good solid ion conductors, so-called superion conductors . A prerequisite for structural disorder is that very large ions with large spaces are present alongside small ions that can move in these spaces. The disordered partial lattice is therefore always a cation lattice.

Examples of crystals with structural disorder are certain modifications of silver sulfide , silver iodide and rubidium silver iodide , in each of which the partial silver lattice is structurally disordered.

Classification method

A successful mathematical method for the classification of physical lattice defects, which are not only found in the dislocation theory of ordinary crystals, but also in a. also for the description of so-called disclinations in liquid crystals and with excitations of the superfluid states of has proven the topological homotopy theory .

See also

literature

Individual evidence

  1. ^ ND Mermin: The topological theory of defects in ordered media . In: Reviews of Modern Physics . tape 51 , no. 3 , 1979, pp. 591-648 , doi : 10.1103 / RevModPhys.51.591 .