Alkali halide crystal

The MR approximation was applied for electronic structure calculations of both perfect crystals (alkali halides [222], MgO and CaO [226], PbO [227], corundum [228]), point defects in solids ( [229-234]) and surfaces [224]. 

Materials that contain defects and impurities can exhibit some of the most scientifically interesting and economically important phenomena known. The nature of disorder in solids is a vast subject and so our discussion will necessarily be limited. The smallest degree of disorder that can be introduced into a perfect crystal is a point defect. Three common types of point defect are vacancies, interstitials and substitutionals. Vacancies form when an atom is missing from its expected lattice site. A common example is the Schottky defect, which is typically formed when one cation and one anion are removed from fhe bulk and placed on the surface. Schottky defects are common in the alkali halides. Interstitials are due to the presence of an atom in a location that is usually unoccupied. A... 

Slides Plastic cavitation around inclusions in metals (e.g. metallographic section through neck in tensile specimen) SEM pictures of fracture surfaces in ductile metals, glass, alkali halide crystals. 

Turning next to an ionic crystal, where the ions may be regarded as spheres, the total volume of the crystal is equal to the volumes of these spheres, together with the appropriate amount of void space between the spheres. To take the simplest case, it is convenient to discuss a set of substances, all of which have the same crystalline structure—for example, the 17 alkali halide crystals that have the NaCl structure. 

The structures of LiCl and NaCl are typical of all the alkali halides (Group 1 cation, Group 17 anion) except those of cesium. Because of the large size of the Cs+ ion, CsCl crystallizes in a quite different structure. Here, each Cs+ ion is located at the center of a simple cube outlined by Cl- ions. The Cs+ ion at the center touches all the Cl- ions at the comers the Cl- ions do not touch each other. As you can see, each Cs+ ion is surrounded by eight Cl- ions, and each Cl- ion is surrounded by eight Cs+ ions. 

In the phosphor-photoelectric detector used as just described, the x-ray quanta strike the phosphor at a rate so great that the quanta of visible light are never resolved they are integrated into a beam of visible light the intensity of which is measured by the multiplier phototube. In the scintillation counters usual in analytical chemistry, on the other hand, individual x-ray quanta can be absorbed by a single crystal highly transparent to light (for example, an alkali halide crystal with thallium as activator), and the resultant visible scintillations can produce an output pulse of electrons from the multiplier phototube. The pulses can be counted as were the pulses-from the proportional counter. 

Sometimes the atomic arrangement of a crystal is such as not to permit the formulation of a covalent structure. This is the case for the sodium chloride arrangement, as the alkali halides do not contain enough electrons to form bonds between each atom and its six equivalent nearest neighbors. This criterion must be applied with caution, however, for in some cases electron pairs may jump around in the crystal, giving more bonds than there are electron pairs, each bond being of an intermediate type. It must also be mentioned that determinations of the atomic arrangement are sometimes not sufficiently accurate to provide evidence on this point an atom reported equidistant from six others may be somewhat closer to three, say, than to the other three. 

A normal crystal is one in which contact (that is, strong repulsion) occurs only between adjacent anions and cations, and in which there is only so much deformation as that shown by the alkali halides. 

The crystal radii for eight-shell ions are in agreement with the observed inter-atomic distances for normal alkali halide crystals, showing that the... 

The elucidation of the factors determining the relative stability of alternative crystalline structures of a substance would be of the greatest significance in the development of the theory of the solid state. Why, for example, do some of the alkali halides crystallize with the sodium chloride structure and some with the cesium chloride structure Why does titanium dioxide under different conditions assume the different structures of rutile, brookite and anatase Why does aluminum fluosilicate, AljSiCV F2, crystallize with the structure of topaz and not with some other structure These questions are answered formally by the statement that in each case the structure with the minimum free energy is stable. This answer, however, is not satisfying what is desired in our atomistic and quantum theoretical era is the explanation of this minimum free energy in terms of atoms or ions and their properties. 

Fig. 2.—The arrangement of ions in cube-face layers of alkali halide crystals with the sodium chloride structure.

Heating of certain alkali halides with elemental sulfur also produces colored materials containing the anions 82 or 83 which replace the corresponding halide ions. For example, NaCl and KI crystals when heated in the presence of sulfur vapor incorporate di- and trisulfide monoanions [116-119] which can be detected, inter alia, by resonance Raman spectroscopy [120, 121] ... 

The (lOO)-oriented crystals of various alkali halides were prepared by cleavage and placed in a humidity-controlled chamber housing the SPFM microscope. Two types of ex-... 

One method we might use is to cool the melt to incipient nuclei-formatlon. toss in the seed-crystal, and allow the melt to freeze into a single crystal. This is the KYROPOULOS method which we will discuss in detail later. Alas, this method only works for a few systems, notably alkali halides (cubic) and the like. We find that we can use a seed-crystal to grow single crystals, but only if we use it under carefully defined conditions. A modified K5rropoulos method has been used for many years to form single-crystal sapphire up to 13.0 inches in dieimeter. Plates cut from such crystals are used as windows and substrates for all sorts of integrated circuits, as well as watch "crystals". 

Dick BG, Overhauser AW (1958) Theory of the dielectric constants of alkali halide crystals. Phys Rev 112(1) 90-103... 

Figure 3.9 C44 elastic moduli vs. reciprocal polarizabilities for prototype alkali halide crystals.

Figure 9.2 is schematic diagram of the crystal structure of most of the alkali halides, letting the black circles represent the positive metal ions (Li, Na, K, Rb, and Cs), and the gray circles represent the negative halide ions (F, Cl, Br, and I).The ions lie on two interpenetrating face-centered-cubic lattices. Of the 20 alkali halides, 17 have the NaCl crystal structure of Figure 9.1. The other three (CsCl, CsBr, and Csl) have the cesium chloride structure where the ions lie on two interpenetrating body-centered-cubic lattices (Figure 9.3). The plastic deformation on the primary glide planes for the two structures is quite different.

As mentioned above alkali halide crystals are strongly hardened by small additions of divalent impurities. Data are available for 12 cases, the host crystals NaCl, NaBr, KC1, and KBr with additions of Ca2+, Sr2+, and Ba2+ (Chin, et al., 1973). It was found that the hardness increases depend only on the concentrations of the additions and not on the divalent specie (Ca, Sr, or Ba). However, a dependence on the valence (1, 2, or 3) is observed. It was also found that hardness increment is proportional to the square root of the concentration, (C1/2). 

In alkali halide crystals containing color-centers (F-centers) illumination with light of appropriate energy causes transient changes of hardness (Nadeau, 1964). This effect apparently results from changes in the effective sizes of the F-centers when they become excited. 

A. R. Ruffa, Theory of the Electronic Polarizabilities of Ions in Crystals Application to the Alkali Halide Crystals, Phys. Rev., 130,1412 (1963). 

As we have seen, several atomic properties are important when considering the energies associated with crystal formation. Ionization potentials and heats of sublimation for the metals, electron affinities, and dissociation energies for the nonmetals, and heats of formation of alkali halides are shown in Tables 7.1 and 7.2. 

When a crystal of an alkali halide has the vapor of the alkali metal passed over it, the alkali halide crystal becomes colored. The reason for this is that a type of defect that leads to absorption of light is created in the crystal. Such a defect is known as an F-center because the German word for "color" is Farbe. It has been shown that such a defect results when an electron occupies a site normally occupied by an anion (an anion "hole"). This arises as a result of the reaction... 

In this equation, N is the number of ions per cm3, q is the charge on the ion, and a is a factor that varies from about 1 to 3 depending on the mechanism of diffusion. Because conductivity of a crystal depends on the presence of defects, studying conductivity gives information about the presence of defects. The conductivity of alkali halides by ions has been investigated in an experiment illustrated in Figure 8.11. 

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