Faces of a crystal

X-ray spectrometer An apparatus used in the X-ray study of crystals in which a fine beam of monochromatic X-rays impinges at a measured angle on the face of a crystal mounted in its path, and in which the intensity of the X-rays diffracted in various directions by the crystal is measured with an ionization chamber mounted on an arm of the spectrometer table, or is recorded photographically. 

Morphology. A crystal is highly organized, and constituent units, which can be atoms, molecules, or ions, are positioned in a three-dimensional periodic pattern called a space lattice. A characteristic crystal shape results from the regular internal stmcture of the soHd with crystal surfaces forming parallel to planes formed by the constituent units. The surfaces (faces) of a crystal may exhibit varying degrees of development, with a concomitant variation in macroscopic appearance. 

Crystal growth is a diffusion and integration process, modified by the effect of the solid surfaces on which it occurs (Figure 5.3). Solute molecules/ions reach the growing faces of a crystal by diffusion through the liquid phase. At the surface, they must become organized into the space lattice through an... 

S. R. Coriell, B. T. Murray, A. A. Chernov, G. B. McFadden. Step bunching on a vicinal face of a crystal growing in a flowing solution. J Cryst Growth 169 773, 1996. 

Spectral data from a (111) face of a crystal of magnesium stannide are given in Table I. Using the value of 3.591 for the density,2 these data place nz/m = 0.248 for the first reflection. No reflections were found on the Laue photographs with values of n less than 0.26 A. U., calculated for the unit containing four Mg2Sn, with n — 1, and di0o = 6.78 0.02 A. U. 

Fast-growing faces of a crystal disappear during the growth process... 

The habit of pharmaceutical compounds has been used for purposes of identification, although the method can only be reliably used when the crystallization solvent used to generate the test crystals is carefully controlled. Since the faces of a crystal must reflect the internal structure of the solid, the angles between any two faces of a crystal will remain the same even if the crystal growth is accelerated or retarded in one direction or another. Toxicologists have made extensive use of microscopy following multiple recrystallization, and they have developed useful methods for compound identification [5]. 

Screw dislocations play an important part in crystal growth. The theoretical background to this fact was first developed in 1949 by Frank and colleagues. It was apparent that crystal growth was rapid as long as ledges and similar sites existed on the face of a crystal because these form low-energy positions for the addition of new atoms or... 

Figure 3.34 Faces of a crystal of the sodium chloride type. Faces of the 100 type contain both atom species (a) while planes of 111 type contain one atom type (b) or the other (c).

Figure 12 (continued) (c) Optical micrograph of the (101) face of a crystal of (R)-asparagine etched by (/ )-/V-methylasparagine. 

If a crystal siirlace bo exposed to a supersaturated solution the surface will commence to grow. As has already been noted the surface energy of a crystal is dependent n<)t only on the nature of the substance but also on the packing in the space lattice, the rate of growth will thus vary with the crystal face, e.g. the faces of a crystal of the cubic class will possess different growth rates depending on whether the 1, 0, 0 or 1, 1, 1 face is exposed to the solution. 

Fig. 6.8. (a) The spherical projection of the faces of a crystal. The numbers indicate the Miller indices of the corresponding planes, (b) Photomicrograph of a polycrystalline brass. (Reprinted with permission from Elizabeth A. Wood in Crystals and Light. An introduction to Optical Crystallography, 2nd ed., Dover, 1977, Plate lll(2) and Fig. 4.5.)... 

Fig. 7.108. The structure of a single face of a crystal with a simple cubic lattice at lower temperatures. (Reprinted from E. Budevski, G. Staikov, and W. J. Lorenz, Electrochemical Phase Formation and Growth, p. 17, copyright 1996 John Wiley Sons. Reproduced by permission of John Wiley Sons, Ltd.)...

Ill plane for this reason. (Remember, three indices are necessary to describe the planar face of a crystal.)... 

The rate of solution of the different faces of a crystal of rock-salt is slightly different, being rather faster on the octohedral face than on a cubic face, and intermediate between these two rates on the dodecahedral face.41 A. Ritzel has shown that in the absence of urea, the octohedral faces dissolve fastest, and in the presence of urea, the cubic faces. W. Poppe found that with 0"5 and 1"0 per cent, under-sat. soln, each crystal face dissolves at a characteristic rate, but with a 2 per cent, under-sat. soln., all the faces dissolve at approximately the same rate. The solubility of cubic and octohedral crystals per 100 c.c. of water at the end of a given time is ... 

Nevertheless, the broad generalization is of the greatest value for we can measure the angles between the faces of a crystal, and, assuming that these faces are simple—that is, they are densely packed with lattice points and are either parallel to the unit cell faces or are related in some simple way to the unit cell—we can usually deduce the type of unit cell, and very often calculate its relative dimensions and angles. 

According to Jannettaz,6 the thermal conductivity perpendicular to the (111) face of a crystal of metallic arsenic is nearly twice as great as it is parallel to the chief axis. Little7 gives the coefficient of thermal conductivity in absolute units at 20° C. to be 3-68 xlO6. 

BRAGG SPECTROMETER. An instrument for the x-ray analysis of crystal structure, in which a homogeneous beam of x-rays is directed on the known face of a crystal, C. and the reflected beam detected in a suitably placed ionization chamber, E. As the crystal is rotated, the angles at which... 

The foregoing electrostatic calculations hold, moreover, only for positions in the middle of a cubic face of a crystal of the NaCl type. Any deviation from this situation may result in a stronger electrostatic bond. Corners and edges of crystals, other crystallographic faces, lattice disturbances, etc., may all form active spots where the electrostatic adsorption of ions is relatively strong. We shall return to the problem of active spots in Sec. V,12. 

In 1784, Haiiy formulated the Law of Rational Indices, which states that all faces of a crystal can be described by Miller indices (hid), and for those faces that commonly occur, h, k, and l are all small integers. The eight faces of an octahedron are (111), (111), (ill), (111), (111), (111), (III), and (III). The form symbol that represents this set of eight faces is 111. The form symbol for the six faces of a cube is 100. Some examples in the cubic system are shown in Figs. 9.1.3. and 9.1.4. 

In the reciprocal space in three dimensions the zones, instead of line sections, become geometrical bodies determined by the values of the three integers h, k, and l instead of by m. They are just such polyhedra (Brillouin zones) in the reciprocal lattice as the faces of a crystal in ordinary space which correspond to the same hkl (e.g. 100 is the cube, 111 the octahedron, etc. in the cubic system). 

The term crystal habit is often used to describe the relative sizes of the faces of a crystal. Crystal habit is readily modified by conditions of nucleation and growth, and it is rather difficult to prepare ciystals with all faces of the same form equally developed (M2). Small amounts of soluble impurities, especially dyes, which may be adsorbed selectively on the different faces of a crystal, cause these faces to be suppressed in favor of others. This can alter the external geometry of a crystal completely, except for its interfacial angles. Many examples of crystal habit modification are reported in the literature (B8), and in some commercial... 

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