Determination of lattice concentrations

It appears that purification of commercially available solvents is sometimes required for the complete elimination of impurity resonances. Occasionally, these impurities may be turned into advantage, as in the case of C2D2CI4 where the (known) C2DHCI4 content may be used as an internal standard for quantitation. Thus, removal of every impurity peak is not always essential for identification and quantitative analysis of stabilisers in PE. Determination of the concentration of additives in a polymer sample can also be accomplished by incorporation of an internal NMR standard to the dissolution prepared for analysis. The internal standard (preferably aromatic) should be stable at the temperature of the NMR experiment, and could be any high-boiling compound which does not generate conflicting NMR resonances, and for which the proton spin-lattice relaxation times are known. 1,3,5-Trichlorobenzene meets the requirements for an internal NMR standard [48]. The concentration should be comparable to that of the analytes to be determined. 

Because of the 100% isotopoic abundance of 27A1 and its very short spin-lattice relaxation time, even traces of aluminum are often detectable by MAS NMR. For example, Thomas et al. (156) were able to show that aluminum present as an impurity in soda glass is four-coordinated. However, quantitative determination of Al concentration in the sample is only possible when the quadrupolar effects are not so large as to affect significantly the apparent intensity of the 27A1 signal. 

An important question in characterization of high-silica molecular sieves regards die location of trivalent species, whether these are part of the lattice structure or just present as an oxide which is not part of the lattice. A number of methods are available for determining the lattice concentration, each with its own advantages and disadvantages. 

Thus, although vacancies and interstitials exist in thermal equilibrium in ice, their concentrations are small even at the melting point and for this reason the density of ice crystals, measured by macroscopic means, agrees closely with the value derived from X-ray determinations of lattice constants. 

Displacements of lattice members are determined by energy factors and concentration gradients. To a considerable extent, diffusion in solids is related to the existence of vacancies. The "concentration" of defects, N0, (sites of higher energy) can be expressed in terms of a Boltzmann distribution as... 

X-ray diffraction uses X-rays of known wavelengths to determine the lattice spacing in crystalline structures and therefore directly identify chemical compounds. This is in contrast to the other X-ray methods discussed in this chapter (XRF, electron microprobe analysis, PIXE) which determine concentrations of constituent elements in artifacts. Powder XRD, the simplest of the range of XRD methods, is the most widely applied method for structural identification of inorganic materials, and, in some cases, can also provide information about mechanical and thermal treatments during artifact manufacture. Cullity (1978) provides a detailed account of the method. 

Also, a real surface has atomic structures associated with roughness and defects and thus the atoms at these lattice structures have different bonding conditions, some are similar to those on a (100) surface in terms of bonding characteristics some are similar to a (111) surface and others are in between. Thus, a real surface may have varying degrees of reactivity determined by the concentration of the active atoms, which is a function of lattice structure determined by orientation, roughness, and type and density of defects. 

The luminescent mineral consists of a host lattice and a luminescent center, often called an activator. The determination of the nature of the center responsible for luminescence is not generally a trivial task. Correlation of the observation of the specific luminescence with a particular impurity concentration may give an indication of the source of the emission but it is not proof of the origin, and can sometimes be misleading. Furthermore, it does not give any details about the precise nature of the center. Spectroscopic studies may... 

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