Crystal Structures and Close-packing of Spheres

Atoms and ions can be considered to be spheres which pack together in special and reproducible patterns to form solid state crystalline materials. The patterns of the spheres repeat in all three directions. The simplest, basic repeating unit in a crystalline solid is called the unit cell. It is of importance to realize that all crystalline solids, no matter how complex, are described by unit cells. The unit cell must be consistent with the chemical formula of the solid, must indicate the coordination number and geometry of each type of atom or ion, and must generate the crystal structure by simple translation or displacement of the unit cell in three dimensions. 

When spheres of a given size are close-packed, the spaces between the layers of spheres (the voids or interstices) can be filled with smaller spheres. If the spheres represent cations and anions, the structures of ionic solids can be visualized. There are two types of interstices between layers of close-packed atoms - tetrahedral holes or interstices and octahedral holes or interstices. Tetrahedral holes are formed when one sphere in a layer fits over or under three spheres in a second layer. Octahedral holes are formed when three spheres in one layer fit over or under three spheres in a second layer. The two types of holes have different numbers per close-packed sphere, different sizes, and different coordination numbers and coordination geometries. The coordination number of the anion would be the number of cations in contact with the anion. The coordination geometry of the anion would be the geometrical arrangement of the cations which surround the anion. Related statements can be made regarding the coordination number and coordination geometry of the cation. 

In this experiment you will build models of the simple cubic, body-centered cubic, and face-centered cubic unit cells, of hexagonal close-packed structures and cubic close-packed structures, and of simple ionic solids. 

Your laboratory kit contains styrofoam and/or cork balls of three different sizes and wires for connecting the balls. You should carefully insert the wires into the centers of the balls. At the conclusion of the experiment, place the balls and wires in the plastic bag, and return it to your instructor or the stockroom, as appropriate. 

As you perform the experiment, answer each question in the space provided. After you have completed all parts of the experiment, remove the DATA section (TABLE 18.1) of the experiment from your laboratory notebook, and submit it to your instructor. The experiment has no PRE-LABORATORY QUESTIONS or POST-LABORATORY QUESTIONS. 

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