Defects energy

Figure C2.16.6. The energy states of a metastable and bistable muonium in Si are illustrated in a configuration diagram. It plots the defect energy as a function of a coordinate which combines position and all the relaxations and distortions of the crystal. The specific example, discussed in the text, illustrates acceptor and donor levels, metastability, bistability and negative- U [50] behaviour.

Table 11.1 Defect energies for various materials. Data from [Mackrodt 1982],...

Catlow C R A and W C Mackrodt 1982. Theory of Simulation Methods for Lattice and Defect Energy Calculations in Crystals. In Lecture Notes in Physics 166 (Comput. Simul. Solids), pp. 3-20. 

A useful way to approach these individual point defect energies is to define the energy per mole or cohesive energy of perfect material with respect to separated free atoms, Cmoi-We can then arbitrarily divide this between the atoms of type A and B so that ... 

In terms of the point defect energies so defined, our stoichiometry-conserving defects have formation energies given by ... 

The chemical potentials have been evaluated numerically by Hagen using embedded atom models for the defect energies [10]. An important finding was that good quantitative... 

Formula for the chemical potentials have been derived in terms of the formation energy of the four point defects. In the process the conceptual basis for calculating point defect energies in ordered alloys and the dependence of point defect concentrations on them has been clarified. The statistical physics of point defects in ordered alloys has been well described before [13], but the present work represents a generalisation in the sense that it is not dependent on any particular model, such as the Bragg-Williams approach with nearest neighbour bond energies. It is hoped that the results will be of use to theoreticians as well as... 

Active Dissolution and Crystal Defects—Energy Considerations... 

Therefore, there could exist rich defects in Ba3BP30i2, BaBPOs and Ba3BP07 powders. From the point of energy-band theory, these defects will create defect energy levels in the band gap. It can be suggested that the electrons and holes introduced by X-ray excitation in the host might be mobile and lead to transitions within the conduction band, acceptor levels, donor levels and valence band. Consequently, some X-ray-excited luminescence bands may come into being. 

Figure 2.9 Mott-Littleton method of dividing a crystal matrix for the purpose of calculating defect energies. Region I contains the defect and surrounding atoms, which are treated explicitly. Region lib is treated as a continuum reaching to infinity. Region Ha is a transition region interposed between regions I and lib.

Processes involving defect energy levels are responsible for coloration of diamonds containing races of nitrogen or boron impurities. Diamond has a band gap of about 8.65 x 10-19 J (5.4 eV), which is too large to absorb visible light and... 

The calculated low activation barrier and defect energy for Mn going Oh Td at partial lithiation is consistent with the lack of stability of 7-Li Mn02 against transformation into spinel observed experimentally. Likewise, the high activation barriers for all possible Co hops out of the TM layer are consistent with the relative stability observed experimentally for layered Li tCo02. 

The energy of all the 3d metals entering tetrahedral coordination from the /-Li rM02 structure decreases as Xu goes from 0 to 1/2. This is similar to the defect calculations on Co and Mn in section 4 that found tetrahedral defect energies in the layered structure to decrease for both as Li content increases from 0 to 1/2. 

We have already introduced the concept of ionic polarizability (section 1.8) and discussed to some extent the nature of dispersive potential as a function of the individual ionic polarizability of interacting ions (section 1.11.3). We will now treat another type of polarization effect that is important in evaluation of defect energies (chapter 4). 

An alternative (and probably more precise) method for evaluating defect energies is based on the calculation of lattice energy potentials. 

Subtracting a charge in a given lattice position also contributes to the defect energy with an induced polarization term whose significance was described in section 1.19 ... 

Table 4.2 lists defect energies calculated with the method described above in fayal-ite and forsterite crystals. Note that the energies obtained are on the magnitude of some eV—i.e., substantially lower than the energies connected with extended defects. Note also that, ionic species being equal, the defect energies depend on... 

Table 4.2 Defect energies in forsterite and fayalite based on lattice energy calcnlations. 7 = ionization potential E = electron affinity = dissociation energy for O2 A77 = enthalpy of defect process (adapted from Ottonello et af, 1990).

An alternative way of calculating defect energies on the basis of static potentials is that outlined by Fumi and Tosi (1957) for alkali halides, in which the energy of the Schottky process is seen as an algebraic summation of three terms ... 

For comparative purposes, table 4.3 lists defect energies (enthalpies) of Schottky and Frenkel processes in halides, oxides, and sulfides. The constant Kq appearing in the table is the preexponential factor (see section 4.7) raised to a power of 1/2. 

Table 4.6 shows the energy of extrinsic disorder calculated for the solid mixture (Fe, Mg)2Si04 at r = 1200 °C, based on the defect scheme of equation 4.68 and on the defect energies of table 4.2. 

We note that the defect energy contribution associated with extrinsic disorder varies considerably as a function of the partial pressure of oxygen of the system. These energy amounts may significantly affect the intracrystalline disorder, with marked consequences on thermobarometric estimates based on intracrystalline distribution. As we will see in detail in chapter 10, most of the apparent complexities affecting trace element distribution may also be solved by accurate evaluation of the defect state of the phases. 

Mackrodt W. C. and Stewart R. F. (1979). Defect properties of ionic solids, II Point defect energies based on modified electron gas potentials. J. Phys., 12C 431 49. 

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