Diffraction methods experimental limitations

METHODS OF OBTAINING atomically-clean surfaces of solids are listed with comments on their advantages and limitations. The method of argon-ion bombardment is reviewed with a discussion of the operating conditions and precautions necessary for successful results. The low-energy electron-diffraction method is used to determine the condition of the surface. Experimental results indicate that the relative positions of the atoms in the clean (100) surface planes of germanium and silicon are not the same as those of similar planes in the bulk crystals. 

In spite of these caveats, there is intense activity in the application of these methods to polymorphic systems and considerable progress has been made. Two general approaches to the use of these methods in the study of polymorphism may be distinguished. In the first, the methods are utilized to compute the energies of the known crystal structures of polymorphs to evaluate lattice energies and determine the relative stabilities of different modifications. By comparison with experimental thermodynamic data, this approach can be used to evaluate the methods and force fields employed. The ofher principal application has been in fhe generation of possible crystal structures for a substance whose crystal structure is not known, or which for experimental reasons has resisted determination. Such a process implies a certain ability to predict the crystal structure of a system. However, the intrinsically approximate energies of different polymorphs, the nature of force fields, and the inherent imprecision and inaccuracy of the computational method still limit the efificacy of such an approach (Lommerse et al. 2000). Nevertheless, in combination with other physical data, in particular the experimental X-ray powder diffraction pattern, these computational methods provide a potentially powerful approach to structure determination. The first approach is the one applicable to the study of conformational polymorphs. The second is discussed in more detail at the end of this chapter. 

From the arguments presented in the previous sections, it is clear that informations on the exact molecular structure that are obtainable by experimental methods are limited and sometimes even ambiguous limited because of technical difficulties and conditions inherent to the methods (e.g. the electron diffraction technique is applicable only to symmetric molecules. X-ray analysis only to crystals, etc.), ambiguous because of imposed constraints and also because of thermal vibration effects. 

As noted in previous sections, the development of life prediction models for the reliability of patterned features such as periodic lines on substrates inevitably requires knowledge of intrinsic stress and mismatch stress generated during film growth, patterning, passivation and service. In this section, three prominent experimental methods for determining stress in thin films with patterned lines are considered the substrate curvature method, the x-ray diffraction method, and the micro-Raman spectroscopic method. The advantages and limitations of each of these techniques are also briefly addressed. 

The main experimental studies in the far-IR or THz regions performed nowadays involve spectroscopy and the imaging of materials, in particular those of biomedical interest. Given the intrinsic long wavelength of this radiation (1 THz is equivalent to 33 cm or 300 pm), diffraction plays a major role and the optical detection method intrinsically limits its use to sub-millimetre types of spectroscopy. On the other hand, when new detection systems are applied, such as with near field or non-optical methods, the spatial resolution limitation can be overcome, provided that a brilliant IR source is used, in the case of SR especially with coherent emission mode. For example. Figure 3.18 demonstrates the feasibility of the use of intense THz radiation for... 

As anticipated in the experimental part, from the limit constant value of the sediment weight the volume increase ratio of the materials is calculated. The relationship between the volume increase ratio obtained by centrifugation and that obtained by laser diffraction method is given in Figure 3. 

In this way and by numerical evaluation, Driessens (2) proved that the experimental activities could be explained on the basis of substitutional disorder, according to Equation (27), within the limits of experimental error. It seems, therefore, that measurements of distribution coefficients and the resulting activities calculated by the method of Kirgintsev and Trushnikova (16) do not distinguish between the regular character of solid solutions and the possibility of substitional disorder. However, the latter can be discerned by X-ray or neutron diffraction or by NMR or magnetic measurements. It can be shown that substitutional disorder always results in negative values of the interaction parameter W due to the fact that... 

In amorphous solids there is a considerable disorder and it is impossible to give a description of their structure comparable to that applicable to crystals. In a crystal indeed the identification of all the atoms in the unit cell, at least in principle, is possible with a precise determination of their coordinates. For a glass, only a statistical description may be obtained to this end different experimental techniques are useful and often complementary to each other. Especially important are the methods based on diffraction experiments only these will be briefly mentioned here. The diffraction pattern of an amorphous alloy does not show sharp diffraction peaks as for crystalline materials but only a few broadened peaks. Much more limited information can thus be extracted and only a statistical description of the structure may be obtained. The so-called radial distribution function is defined as ... 

In addition to these limited procedures a number of experimental methods (vibrational spectroscopy, dipole moment measurements, electron diffraction, NMR, etc.) have been employed to determine the relative stabilities of these complexes.11,23 Intense effort has been directed towards establishing some kind of correlation between NMR parameters and stability of the borane complexes. The chemical shifts alone rarely show good correlation. However, complexation shifts (the chemical shift difference between the free and complexed borane or ligand) and various spin-spin coupling constants correlate better with calorimetric data, especially for ligands or boranes belonging to structurally similar series (Table 2).10,24... 

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