Defects and density

The theoretical density of a solid with a known crystal structure can be determined by dividing the mass of all the atoms in the unit cell by the unit cell volume, (Chapter 1, Section 1.12). This information, together with the measured density of the sample, can be used to determine the notional species of point defect present in a solid that has a variable composition. However, as both techniques are averaging techniques they say nothing about the real organisation of the point defects. The general procedure is  

The method can be illustrated by reference to a classical study of the defects present in iron monoxide1. Iron monoxide, often known by its mineral name of wiistite, has the halite (NaCl) structure. In the normal halite structure, there are four metal and four non-metal atoms in the unit cell, and compounds with this structure have an ideal composition MX 0, (see Chapter 1, Section 1.8). Wiistite has an oxygen-rich composition compared to the ideal formula of FeOi.o- Data for an actual sample found an oxygen iron ratio of 1.059, a density of 5728 kg m 3, and a cubic lattice parameter, a, of 0.4301 nm. Because there is more oxygen present than iron, the real composition can be obtained by assuming either that there are extra oxygen atoms in the unit cell, as interstitials, or that there are iron vacancies present. 

Model A Assume that the iron atoms in the crystal are in a perfect array, identical to the metal atoms in the halite structure and an excess of oxygen is due to interstitial oxygen atoms over and above those on the normal anion positions. The ideal unit cell of the structure contains 4 Fe and 4 O, and so, in this model, the unit cell must contain 4 atoms of Fe and 4(1+x) atoms of oxygen. The unit cell contents are Fc404+4a and the composition is FeOi.059- 

The volume, V, of the cubic unit cell is given by a3, thus  

The density, p, is given by the mass mA divided by the unit cell volume, V  

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Lester Guttman, Relation between the Atomic and the Electronic Structures A. Chenevas-Paule, Experiment Determination of Structure 5. Minomura, Pressure Effects on the Local Atomic Structure David Adler, Defects and Density of Localized States... 

S. Minomura, Pressure Effects on the Local Atomic Structure David Adler, Defects and Density of Localized States... 

Stampfl C, van de Walle C G, Vogel D, Kruger P and Pollmann J 2000 Native defects and impurities in InN First-principles studies using the local-density approximation and self-interaction and relaxation-corrected pseudopotentials Phys. Rev. B 61 R7846-9... 

Heterogeneous surface areas consist of anodic regions at corrosion cells (see Section 2.2.4.2) and objects to be protected which have damaged coating. Local concentrations of the current density develop in the area of a defect and can be determined by measurements of field strength. These occur at the anode in a corrosion cell in the case of free corrosion or at a holiday in a coated object in the case of impressed current polarization (e.g., cathodic protection). Such methods are of general interest in ascertaining the corrosion behavior of metallic construction units... 

Uniformity characterization of luminescent materials (e.g., mapping of defects and measurement of their densities, and impurity segregation studies)... 

We can anticipate that the highly defective lattice and heterogeneities within which the transformations are nucleated and grow will play a dominant role. We expect that nucleation will occur at localized defect sites. If the nucleation site density is high (which we expect) the bulk sample will transform rapidly. Furthermore, as Dremin and Breusov have pointed out [68D01], the relative material motion of lattice defects and nucleation sites provides an environment in which material is mechanically forced to the nucleus at high velocity. Such behavior was termed a roller model and is depicted in Fig. 2.14. In these catastrophic shock situations, the transformation kinetics and perhaps structure must be controlled by the defective solid considerations. In this case perhaps the best published succinct statement... 

Table 2 Restricted Hartree-Fock energies (Hartrees) for Ceo and C70 and their muon adducts. AE is the difference in energy between the carbon allotrope and its adduct. In all cases, except where indicated by f, only the six carbon atoms in the immediate vicinity of the muon have had there positions optimised, f means that a full geometry optimisation has been carried out. The type specifies the defect and for C70 is identified in Table 1. is the spin density at the muon in atomic units (and the hyperfine coupling constant in MHz). JMuon constrained to lie in equatorial plane. indicates geometry not fully optimized.

Stranski-Krastanov growth has been documented for copper on Au(lll) [101, 102], Pt(100) and Pt(lll) [103], for silver on Au(lll) [104, 105], for cadmium on Cu(lll) [106] and for lead on Ag(100) and Ag(lll) [107-109]. In all of these examples, an active metal is deposited onto a low-index plane of a more noble metal. Since the substrate does not undergo electrochemical transformations at the deposition potential, a reproducible surface can be presented to the solution. At the same time, the substrate metal must be carefully prepared and characterized so that the nucleation and growth mechanisms can be clearly identified, and information can be obtained by variation of the density of surface features, including steps, defects and dislocations. 

Hydrogenation has been found to reduce defect state densities and potential barriers associated with grain boundaries in Si (Johnson et al.,... 

As described earlier, the covalently bonded hydrogen, by passivating dangling bond defects and removing strained weak Si—Si bonds from the network, dramatically improves the semiconducting quality of amorphous silicon. Hence without the presence of hydrogen, effective amorphous semiconductor devices such as solar cells or thin film transistors would not be possible. Unfortunately, low defect density, high electronic quality... 

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