Thin crystallization

For cubic crystals, which iaclude sUicon, properties described by other than a zero- or a second-rank tensor are anisotropic (17). Thus, ia principle, whether or not a particular property is anisotropic can be predicted. There are some properties, however, for which the tensor rank is not known. In addition, ia very thin crystal sections, the crystal may have two-dimensional characteristics and exhibit a different symmetry from the bulk, three-dimensional crystal (18). Table 4 is a listing of various isotropic and anisotropic sUicon properties. Table 5 gives values for the more common physical properties and for some of the thermodynamic properties. Figure 5 shows some thermal properties. 

E B. Hirsch, A. Howie, R. B. Nicholson, D. W. Pashley, and M. J. Whelan. Electron Microscopy of Thin Crystals. Butterworth, Washington, 1965, Chapter 4. This sometimes incomprehensible volume is the classic textbook in the field ofTEM. 

Hirsch, P.B., Nicholson, R.B., Howie, A., Pashley, D.W. and Whelan, M.J. (1965) Electron Microscopy of Thin Crystals (Butterworth, London). 

Hirsch, P. B. (ed). Electron Microscopy of Thin Crystals, Butterworths, London (1965) Bunshah, R. F. (ed). Techniques of Metals Research, Vol. IIC, Handbook of Melallographic Techniques, Interscience Publishers, New York (1969)... 

Mile. Cauchois20 used in transmission with a convergent beam a thin crystal bent cylindrically with the Bragg planes about as shown in Figure 4-11. Mica, gypsum, and quartz proved suitable materials. The action of the crystal is shown graphically in Figure 4-11, and it can be demonstrated analytically as well.22... 

Small, very thin crystals of molybdenite may be made by fusing together ammonium molybdate, sulfur and potassium carbonate.6 We have ex-... 

The diffraction pattern obtained in the detector plane when the beam scan in a STEM instrument is stopped at a chosen point of the image comes from the illuminated area of the specimen which may be as small as 3X in diameter. In order to form a probe of this diameter it is necessary to illuminate the specimen with a convergent beam. The pattern obtained is then a convergent beam electron diffraction (CBED) pattern in which the central spot and all diffraction spots from a thin crystal are large discs rather than sharp maxima. Such patterns can normally be interpreted only by comparison with patterns calculated for particular postulated distributions of atoms. This has been attempted, as yet, for only a few cases such as on the diffraction study of the planar, nitrogen-rich defects in diamonds (21). 

Fig. 2.4. Microphotographs of sintered ZnO films with different structures a - structure consists of microcrystals connecting each other by thin crystal bridges b - lace structure is characterized by variety of branch thickness. Magnification 2 1(H.

In one of the first attempts to produce a systematic procedure for the identification of compounds based upon crystal morphology, Shead proposed to use profile angles as the analytical parameter [6,7]. This method was based on the use of sublimation to obtain thin crystal plates of simple geometrical forms. 

Stoichiometric variations in compositions of a material and of surface layers can be revealed by AEM. Because a relatively small amount of scattering occurs through a thin HRTEM specimen, X-rays are generated from a volume that is considerably less than in the case of electron microprobe analysis (EPMA). For quantitative microanalysis, a ratio method for thin crystals (57) is used, given by the equation ... 

Scattering from Thin Crystals. The simple arguments given above hold only if samples are amorphous. Although some catalyst supports are non-crystalline, such as charcoal and silica, others such as alumina are not. Furthermore, the metal catalyst clusters themselves are generally crystalline and thus the above arguments must be modified to account for Bragg reflections from crystalline areas. 

H.P. Boehm, A. Ciauss, G. Fischer, U. Hofmann, Surface Properties of Extremely Thin Crystals, in Proceedings of the Fifth Conference on Carbon, (1962) 73-80. 

Structure refinement based on kinematical scattering was already applied by the Russian scientist 60 years ago. Weirich et al. (1996) first solved the structure of an unknown TinSe4by HREM combined with crystallographic image processing. Then they used intensities extracted from selected area electron diffraction patterns of a very thin crystal and refined the structure to a precision of 0.02 A for all the atoms. Wagner and Terasaki et al. (1999) determined the 3D structure of a new zeolite from selected area electron diffraction, based on kinematical approach. 

The effects of crystal tilt on phases is quite different. The phases are practically unaffected for small tilts and thin crystals. However, as long as the product t-siny is small, the phases are unchanged. Both phase relations and phase restrictions are still valid. Thus, it is possible to determine the (projected) crystal symmetry also from an image of a tilted crystal, using the phases. 

For most thin crystals, the distortion of the image due to crystal tilt can be compensated by imposing the crystal symmetry on the amplitudes and phases extracted from the image. 

D reconstruction can be performed by restoring the 3D Fourier space of the object from a series of 2D Fourier transforms of the projections. Then the 3D object can be reconstructed by inverse Fourier transformation of the 3D Fourier space. For crystalline objects, the Fourier transforms are discrete spots, i.e. reflections. In electron microscopy, the Fourier transform of the projection of the 3D electrostatic potential distribution inside a crystal, or crystal structure factors, can be obtained from HREM images of thin crystals. So one can obtain the 3D electrostatic potential distribution (p(r) inside a crystal from a series of projections by... 

To obtain good HREM images and electron diffraction patterns is one to the most important step in 3D reconstruction. The data should be as kinematical as possible, so HREM images and electron diffraction (ED) patterns should only be taken from very thin crystals. 

Although the d5mamic dififaction has the disadvantage that the intensities of the reflections depend on the thickness, which make the conventional kinematic dififaction sofiware only valid for very thin crystals, is has on the other hand some major advantages, some of which will be discussed in the next chapters. 

From soluble compounds like FAPPO, crystals of approx. 100-200 A thickness have been grown from thin solutions directly on a carbon coated copper grid (3mm/300 mesh) at room temperature by evaporation. With this method thin crystals with less dynamical effects are usually obtained which he flat on the grid providing a view along the thinnest direction. 

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