Cubic hole

YjAlsOn)—YAG Most garnets are silicates, whereas yttrium aluminum garnet (YAG) is an aluminate. In YAG, both the tetrahedral and the octahedral holes of the garnet structure are occupied by Al-ions and the quasi-cubic holes are occupied by Y-ions. 

Arsenides. The crystal structure of Nb4As3 has been determined. It consists of a complicated arrangement of Nb As prisms, with one additional Nb in a cubic hole, and one additional As atom situated in another hole between the... 

True solid-state reactions without liquids are exothermically obtained upon heating of halogenoacetate salts (212) to 100-200 °C. Quantitative yields of polyglycolide matrices (213) with cubic holes after washing with water (when the MX dissolved away) were obtained [93] (Scheme 27). 

The fluorite structure may also be regarded as being composed of a simple cubic packing of anions, and the number of cubic holes is the same as the... 

This structure can be described as M occupying a cubic hole. Use of geometric arguments similar to those we have used for the tetrahedral and oc-... 

The guidelines for filling the tetrahedral, octahedral, and cubic holes are summarized in Table 16.6. 

The structure of sodium chloride, which is the prototype for most of the alkali halides, is best described as a cubic closest packed array of Cl- ions with the Na+ ions in all of the octahedral holes [see Fig. 16.42(b)]. The relative sizes of these ions are such that rua 0.66i ci-> so this solid obeys the guidelines given previously. Note that the CP ions are forced apart by the Na+ ions, which are too large for the octahedral holes in the closest packed array of CP ions. Since the number of octahedral holes is the same as the number of packed spheres, all the octahedral holes must be filled with Na+ ions to achieve the required 1 1 stoichiometry. Most other alkali halides also have the sodium chloride structure. In fact, all the halides of lithium, sodium, potassium, and rubidium have this structure. Cesium fluoride has the sodium chloride structure but because of the large size of Cs+ ions, in this case the Cs ions form a cubic closest packed arrangement with the F ions in all the octahedral holes. On the other hand, cesium chloride, in which the Cs+ and CP ions are almost the same size, has a simple cubic structure of CP ions, with each Cs+ ion in the cubic hole in the center of each cube. The compounds cesium bromide and cesium iodide also have this latter structure. 

For a simple cubic array, solve for the volume of an interior sphere (cubic hole) in terms of the radius of a sphere in the array. 

BaO CsCl-type structure all cubic holes filled by Ba2+ cations ... 

The crystal structure of SC2BC2 depicted in Figure 2 is related to that of CaC2.9 The metal atoms form regular 2-D square nets which stack in such a way to form bi-capped cubic holes in which symmetrical and linear C-B-C units are embedded.8 The B-C distance (1.48 A) suggests double bonds. Unprecedented for a while, such BC2 units are now commonly observed in different solid-state compounds.10 12... 

Model r(tetrahedral hole) < r (octahedral hole) < r (cubic hole))... 

By examining Figures 3.7 and 3.32, we note that the caesium cations sit on a primitive cubic unit cell (lattice type P) with chloride anion occupying the cubic hole in the body centre. Alternatively, one can view the structure as P-type lattice of chloride anions with caesium cation in cubic hole. Keep in mind that caesium chloride does not have a body centred cubic lattice although it might appear so at a first glance. The body centred lattice has all points identical, whereas in CsCl lattice the ion at fte body centre is different from those at the comers. 

The structure of Cap2 is not a closest packed structure because the Ca ions that occupy the face-centered cubic sites are smaller than the F ions. An alternative description of this structure is a simple cubic array of F ions, with Ca ions in half of the cubic holes. 

Replace the four spheres in the middle layer with four spheres of the smallest diameter. Do the smallest spheres fit snugly into these cubic holes ... 

An example of a common ionic solid that is not based on a closest-packed structure is the cesium chloride lattice shown in Figure 12.3. The cesium chloride structure consists of a body-centered cube of one type of ion with the opposite type sitting in the cubic hole at the center of the unit cell. The cubic hole is larger than... 

A space-filling representation of a cubic hole (shaded) within a simple cubic unit celL (A comer sphere has been removed for darity.)... 

---