Solids lattice defects

Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

An additional problem is encountered when the isolated solid is non-stoichiometric. For example, precipitating Mn + as Mn(OH)2, followed by heating to produce the oxide, frequently produces a solid with a stoichiometry of MnO ) where x varies between 1 and 2. In this case the nonstoichiometric product results from the formation of a mixture of several oxides that differ in the oxidation state of manganese. Other nonstoichiometric compounds form as a result of lattice defects in the crystal structure. ... 

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... 

Various types of intermediate behaviour embodying features of more than one of these effects can be visualized. In addition to the considerations (i)—(iii) above, the interface may behave as a source or sink for the creation and/or annihilation of imperfections such as lattice defects and electrons, which can be important participants in the overall change (for clarity, such effects have not been included in Fig. 8). The decomposition characteristics of many solids are influenced by externally supplied energy such as irradiation, cold working, etc. 

The second significant factor arises from the fact that no solid is ever 100% pure. It is this lack of purity which gives rise to lattice defects. Consider the fact that those inorganic compounds which are of the highest purity known to date are about 99.99999999% pure. That is, the purity is about 1/10 part per billion, i.e.- 1 x lO i But, the compound still contains about lO atoms per mole, i.e.- per 6.02 x 1023 atoms, i.e.-in terms of atoms actually present in a mole ... 

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. 

X-Ray irradiation of quartz or silica particles induces an electron-trap lattice defect accompanied by a parallel increase in cytotoxicity (Davies, 1968). Aluminosilicate zeolites and clays (Laszlo, 1987) have been shown by electron spin resonance (e.s.r.) studies to involve free-radical intermediates in their catalytic activity. Generation of free radicals in solids may also occur by physical scission of chemical bonds and the consequent formation of dangling bonds , as exemplified by the freshly fractured theory of silicosis (Wright, 1950 Fubini et al., 1991). The entrapment of long-lived metastable free radicals has been shown to occur in the tar of cigarette smoke (Pryor, 1987). 

Alkaline earth oxides (AEO = MgO, CaO, and SrO) doped with 5 mol% Nd203 have been synthesised either by evaporation of nitrate solutions and decomposition, or by sol-gel method. The samples have been characterised by chemical analysis, specific surface area measurement, XRD, CO2-TPD, and FTIR spectroscopy. Their catalytic properties in propane oxidative dehydrogenation have been studied. According to detailed XRD analyses, solid solution formation took place, leading to structural defects which were agglomerated or dispersed, their relative amounts depending on the preparation procedure and on the alkaline-earth ion size match with Nd3+. Relationships between catalyst synthesis conditions, lattice defects, basicity of the solids and catalytic performance are discussed. 

At variance with the evaporated samples, Am and did not change much for the sol-gel ones, in spite of the difference between AE cation radii size (Fig. lb, c). It can be suggested that the sol-gel method succeeded in better introduction of Nd into a solid solution (supported by the TPD results) which also depended to a lower extent on the cation radii size match. The increase of the lattice anisotropy AO (Fig. Id) and the trend of the local strain values to decrease or remain about constant (Fig. lc) indicated that there was competition between disorder sources of different nature dispersed lattice defects and Nd3+ agglomerates. 

Solids possess an energy unknown in typical liquids. This cuticular energy exists because the surface region of innumerable solids has a chemical composition, a frequency of lattice defects, and so on, different from those in the bulk. 

You now have enough experience with DFT calculations to imagine how calculations could be performed that would be relevant for each of the three examples listed above. For instance, DFT calculations could be used to determine the relative energy of various kinds of lattice defects that could potentially exist in a solid material. Similar calculations could be used to determine the equilibrium positions of reactive molecules on the surfaces of ice crystals that could be thought of as mimics for polar stratospheric clouds. 

Non-stoichiometry is a very important property of actinide dioxides. Small departures from stoichiometric compositions, are due to point-defects in anion sublattice (vacancies for AnOa-x and interstitials for An02+x )- A lattice defect is a point perturbation of the periodicity of the perfect solid and, in an ionic picture, it constitutes a point charge with respect to the lattice, since it is a point of accumulation of electrons or electron holes. This point charge must be compensated, in order to preserve electroneutrality of the total lattice. Actinide ions having usually two or more oxidation states within a narrow range of stability, the neutralization of the point charges is achieved through a Redox process, i.e. oxidation or reduction of the cation. This is in fact the main reason for the existence of non-stoichiometry. In this respect, actinide compounds are similar to transition metals oxides and to some lanthanide dioxides. 

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