Association point defects

Issues associated with order occupy a large area of study for crystalline matter [1, 7, 8]. For nearly perfect crystals, one can have systems with defects such as point defects and extended defects such as dislocations and grain... 

If tlie level(s) associated witli tlie defect are deep, tliey become electron-hole recombination centres. The result is a (sometimes dramatic) reduction in carrier lifetimes. Such an effect is often associated witli tlie presence of transition metal impurities or certain extended defects in tlie material. For example, substitutional Au is used to make fast switches in Si. Many point defects have deep levels in tlie gap, such as vacancies or transition metals. In addition, complexes, precipitates and extended defects are often associated witli recombination centres. The presence of grain boundaries, dislocation tangles and metallic precipitates in poly-Si photovoltaic devices are major factors which reduce tlieir efficiency. 

At the beginning of the century, nobody knew that a small proportion of atoms in a crystal are routinely missing, even less that this was not a mailer of accident but of thermodynamic equilibrium. The recognition in the 1920s that such vacancies had to exist in equilibrium was due to a school of statistical thermodynamicians such as the Russian Frenkel and the Germans Jost, Wagner and Schollky. That, moreover, as we know now, is only one kind of point defect an atom removed for whatever reason from its lattice site can be inserted into a small gap in the crystal structure, and then it becomes an interstitial . Moreover, in insulating crystals a point defect is apt to be associated with a local excess or deficiency of electrons. 

Sinee there are six unknowns and three equations, there are three independent variables. We ean associate these with any three elementary independent modes of point defect formation which conserve the numbers of atoms. These are like basis vectors for representing arbitrary point defect concentrations. Let us define them as follows ... 

Point defects are changes at atomistic levels, while line and volume defects are changes in stacking of planes or groups of atoms (molecules) m the structure. Note that the curangement (structure) of the individual atoms (ions) are not affected, only the method in which the structure units are assembled. Let us now examine each of these three types of defects in more detail, starting with the one-dimensional lattice defect amd then with the multi-dimensional defects. We will find that specific types have been found to be associated with each t3rpe of dimensional defect which have specific effects upon the stability of the solid structure. 

Note that we can use the same statistical mechanical approach to calculate SchottslQi" pairs, Frenkel pairs, divancies (which are associated vacancies), impurity-vacancy complexes, and line dislocation-point defect complexes. 

The intensity of the dicarbonyl at 2116cm is considerably reduced as compared to the 90 K deposit, indicating that the amount of metal atoms trapped at point defects is reduced for growth at 60 K. The difference in the nucleation sites is also reflected by the lower thermal stability of the systems, which decompose between 80 and 150 K as compared to 200 to 250 K for the 90 K deposits. With isotope mixing experiments the peak at 2087 cm was assigned to a carbonyl with three or more CO ligands, while the peak at 1999 cm is associated to a monocarbonyl [32]. 

Although this estimate of the interaction energy between defects is simplistic, it demonstrates that a fair number of defects may cluster together rather than remain as isolated point defects, provided, of course, that they can diffuse through the crystal. It is difficult, experimentally, to determine the absolute numbers of point defects present in a crystal, and doubly so to determine the percentage that might be associated rather than separate. It is in both of these areas that theoretical calculations are able to bear fruit. 

Point defects of opposite charges tend to be reciprocally attracted, forming the so-called associate defects. 

Let us consider the general case of two point defects A and B forming an associate defect (AB) according to the process... 

Reif 97) has observed the effects of point defects on nuclear resonance lines of Br , Br, Na , and Li in cubic crystals. The effect of temperature on the line widths and spin-lattice relaxation times was investigated for various impurity levels in AgBr and found to be quite pronounced due to vacancy association and diffusion. 

Next let us discuss the electronic defects associated with point defects in semiconductive or insulating compounds, which lead to non-stoichiometry. Consider a NiO crystal, which has a NaCl-type structure, as NiO can be regarded as an ionic crystal, the valence states of Ni and O are Ni and O , respectively. We assume that the non-stoichiometry originates only from metal vacancies. Generation of metal defects in NiO may be expressed by a chemical reaction similar to eqn (1.119), i.e. 

Let. us finally include higher clusters in the discussion. In kinetics, they are mainly relevant because the mobility of clustered point defects is quite different from the mobility of single defects. We shall treat the simplest possible situation. A matrix crystal A contains impurities B which form associates B, n = 2,3,. ... The total impurity content N% is given by n-Ns. The formation equation of B is... 

We remember that minority point defect concentrations in compounds depend on the activity of their components. This may be illustrated by the solubility of hydrogen in olivine since it depends on the oxygen potential in a way explained by the association of the dissolved protons with O" and O- as minority defects [Q. Bai, D. L. Kohlstedt (1993)]. Similarly, tracer diffusion coefficients and mobilities of Si and O are expected to depend on the activity of Si02. The value (0 lnDf/0 In aSio2)> = Si and O, should give information on the disorder type as discussed in Section 2.3. 

A dislocation is generally subjected to another type of force if nonequilibrium point defects are present (see Fig. 11.2). If the point defects are supersaturated vacancies, they can diffuse to the dislocation and be destroyed there by dislocation climb. A diffusion flux of excess vacancies to the dislocation is equivalent to an opposite flux of atoms taken from the extra plane associated with the edge dislocation. This causes the extra plane to shrink, the dislocation to climb in the +y direction, and the dislocation to act as a vacancy sink. In this situation, an effective osmotic force is exerted on the dislocation in the +y direction, since the destruction of the excess vacancies which occurs when the dislocation climbs a distance Sy causes the free energy of the system to decrease by 8Q. The osmotic force is then given by... 

This model has a number of limitations, including the fact that only point defects are considered. As discussed below, there is some evidence that more complex defect pairs or clusters may occur in BaTi03. In addition, the model requires that photocarriers are associated with only a single partially filled level in thermal equilibrium and cannot account for light-induced charge redistribution among multiple levels. Several studies (13-15) have suggested the possible importance of the latter effect, based on observations of intensity-dependent absorption and the sublinear intensity-dependence of the response time in many crystals. 

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