Crystal lattice site internal

Crystal lattice site internal standards (CLIS)... 

When the concentration of an element is already known, it may be used as a variable internal standard. This enables the use of elements which occupy the same crystal lattice sites as those whose concentration is sought (e.g. one rare... 

Two types of species have been detected in the /rSR spectrum of Ceo- One shows an unreacted or meta-stable muonium state which may well correspond to an internal state, muonium is trapped inside the cage Mu Ceo in the current notation [2]. This may be compared with normal muonium (Mu ) in diamond and many other elemental and compound semi-conductors, where the trapping site is in one of the cavities of tetrahedral symmetry. This state of CeoMu is not discussed here, but it does exhibit all the characteristics expected of the internal chemistry of Ceo-The anomalous muonium state. Mu, observed in semi-conductors and generally accepted to arise from muonium being trapped within one of the chemical bonds of the crystal, is unknown in molecules [5,6]. The constraints of the crystal lattice are necessary for the bond-centred state to be stable. 

The simple CSL model is directly applicable to the cubic crystal class. The lower symmetry of the other crystal classes necessitates the more sophisticated formalism known as the constrained coincidence site lattice, or CCSL (Chen and King, 1988). In this book we treat only cubic systems. Interestingly, whenever an even value is obtained for E in a cubic system, it will always be found that an additional lattice point lies in the center of the CSL unit cell. The true area ratio is then half the apparent value. This operation can always be applied in succession until an odd value is obtained thus, E is always odd in the cubic system. A rigorous mathematical proof of this would require that we invoke what is known as O-lattice theory (Bollman, 1967). The O-lattice takes into account all equivalence points between two neighboring crystal lattices. It includes as a subset not only coinciding lattice points (the CSL) but also all nonlattice sites of identical internal coordinates. However, expanding on that topic would take us well beyond the scope of this book. The interested reader is referred to Bhadeshia (1987) or Bollman (1970). 

These crystal habits usually have the same internal structure and so have the same X-ray diffraction patterns. A more fundamental difference in properties may be found when the compounds crystallise as different polymorphs. When polymorphism occurs, the molecules arrange themselves in two or more different ways in the crystal either they may be packed differently in the crystal lattice or there may be differences in the orientation or conformation of the molecules at the lattice sites. These variations cause differences in the X-ray diffraction patterns of the polymorphs and this technique is one of the main methods of detecting the existence of polymorphs. The polymorphs have different physical and chemical properties for example, they may have different melting points and solubilities and they also usually exist in different habits. 

In our discussions of the internal structure of crystals, we have shown that each atom (or molecule) has a precise location in a repeating structure. If this structure is disrupted in some way the crystal is said to have imperfections. There are a number of different kinds of imperfections that can occur. If a foreign atom (or molecule in a molecular crystal) is present in the crystal lattice, this is known as a chemical imperfection. The foreign atom can be present at a lattice site having substituted for an atom in the structure as we saw in our brief discussion of isomorphism and solid solutions. This is called a substitutional impurity. The foreign atom can also be present in the crystal by fitting between the atoms in the lattice. This is called a interstitial impurity. Both of these types of impurities can cause the atoms in the crystal to be slightly displaced since the impurity atoms do not really fit in the perfect lattice structure. The displacement of the atoms causes a strain in the crystal. 

Dislocations, and the associated internal strains, are thermodynamically unstable as we have mentioned, and to a certain extent can be eliminated by annealing. They have a strong influence on the mobility of charge carriers and of excitons in the crystal. In any case, they disturb the periodicity of the lattice and act as scattering centres. They also modify the distribution and the concentration of impurity molecules in the crystal. It thus becomes clear with the example of step dislocations (Fig. 4.3) that the lattice above the slippage plane is compressed by the insertion of an additional lattice plane, while it is expanded below the slippage plane. Smaller molecules than those of the host can then occupy lattice sites in the upper region. 

The defects which disrupt the regular patterns of crystals, can be classified into point defects (zero-dimensional), line defects (1-dimensional), planar (2-dimensional) and bulk defects (3-dimensional). Point defects are imperfections of the crystal lattice having dimensions of the order of the atomic size. The formation of point defects in solids was predicted by Frenkel [40], At high temperatures, the thermal motion of atoms becomes more intensive and some of atoms obtain energies sufficient to leave their lattice sites and occupy interstitial positions. In this case, a vacancy and an interstitial atom, the so-called Frenkel pair, appear simultaneously. A way to create only vacancies has been shown later by Wagner and Schottky [41] atoms leave their lattice sites and occupy free positions on the surface or at internal imperfections of the crystal (voids, grain boundaries, dislocations). Such vacancies are often called Schottky defects (Fig. 6.3). This mechanism dominates in solids with close-packed lattices where the formation of vacancies requires considerably smaller energies than that of interstitials. In ionic compounds also there are defects of two types, Frenkel and Schottky disorder. In the first case there are equal numbers of cation vacancies... 

An expression for the chemical diffusion coefficient for binary diffusion by means of vacancies can be derived in a straightforward way. Assume that the molar volume is independent of concentration. Since transport occurs via vacancies, there will be a flux of vacancies in addition to the fluxes of the components 1 and 2 in the lattice system. If the jump frequency r of particles of type 1 into the vacancies is greater than that of particles of type 2, then a local flux of vacancies will occur towards the region of higher concentration of component 1. Under the assumption of internal thermodynamic equilibrium, these vacancies are removed from the crystal at sites of repeatable growth (i.e. dislocations, grain boundaries). Because of this flux... 

Crystalline solids contain different types of stractural defects. If the imperfection is limited to one stractural or lattice site and its immediate vicinity, the imperfection is termed a point defect. Vacancies and interstitial atoms are point defects. An impurity atom present in a crystal and that either occupies a lattice site or an interstitial site is also termed a point defect. But in addition to the point defects the stractural defects also comprise line and plane defects. The line defects are dislocations which are characterised by displacements in the stractirre in certain directions. The plane defects comprise stacking faults, grain boundaries, internal and external surfaces. 

As described in the previous chapter, the Schottky disorder involves the presence of equivalent amounts of cation and anion vacancies. In an oxide MO this means that the erystal contains equal concentrations of metal and oxygen vacancies. The overall formation of such a defect pair within the crystal involves the transfer of a pair of cations and anions on regular lattice sites from the bulk to the surface. In reality the defects are formed at external and internal surfaces or... 

Now it is well known that the surfaces of crystals may contain electron traps, hole traps, and/or recombination centers. Clearly the electronic processes occurring at these surface sites or surface states can release sufficient energy to produce reactions at the crystal surface. Some states ( ) can be associated with defects or impurities in the crystal lattice or one or more types of atoms chemisorbed on the crystal surface. Other surface states, the Tamm states (" ), occur in or on perfect crystals and are a consequence of the quantum mechanical nature of the electronic properties of crystals. Clearly if the surface of a crystal is being eroded by photolytic decomposition there could be ever-present Tamm states on the surface. The more important carriers, surface states, and internal states or traps which are important for photolytic decomposition are summarized in Table I. 

Hopping (diffusion) of molecules between lattice sites This kind of motion will usually occur in combination either with whole-molecule rotation on a lattice site or with internal motion in the molecules. The diffusion process will have a large effect on dipolar interactions between nuclei in different molecules. The exact magnitude of the effect will depend on the crystal structure, but it will always lead to a reduction in the intermolecular contribution to dipolar coupling. 

Raman spectroscopy of the solid state differs from that of gases or liquids. A fluid is usually considered to be an assembly of noninteracting, randomly oriented molecules. In contrast, in a solid, i.e., a molecular crystal, the molecules have essentially fixed orientation with respect to the crystal axis. Thus, the molecules lose the rotational and translational degrees of freedom found in the free molecule. In the molecular crystal, these degrees of freedom are replaced by so-called external vibrations torsional motions of the molecule about its axis at the lattice site (librations) and restricted translational excursions within the lattice site. The external vibrations give rise to many new features in the low-frequency region of the spectrum. In addition, the vibrational bands seen for the free molecule (the internal vibrations) can be perturbed in the crystal. These vibrational bands may be split, for example, due to the symmetry of the crystal site, interactions with other molecules in the unit cell, or interaction between the vibrations of the free molecule and the external vibrations in the crystal. 

Internal and Lattice Vibrations. Infrared and Raman spectroscopic investigations were only performed on crystalline NH4N3. The symmetry of free NH4 (T ) and free N3 (D ) is reduced to the site symmetry C2 and C2h in the crystal lattice. The site group analysis for the NH4 ion and the two crystallographically independent N3 ions is given in [4]. 

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