Expt8-07 - _University of Puget Sound Department of...

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Models: Crystals and the Solid State _____University of Puget Sound Department of Chemistry Chem 110 E XP . 8–M ODELS : C RYSTALS AND THE S OLID S TATE I NTRODUCTION Crystalline solids are characterized by distinctive faces which arise from the orderly arrangements of the constituent atoms. The order of the arrangement can be represented by the unit cell. The unit cell is defined as the smallest portion of the space lattice which, repeated in all three directions, generates the whole space lattice of the crystal. In this experiment we will first construct models of various unit cells and then, assuming that atoms can be represented as rigid spheres, we will calculate the fraction of the volume that is empty space. Simple Cubic Face–centered Cubic Body–centered Cubic Figure 1. Cubic unit cells Cubic Systems The basic lattice of a crystal involves three sets of parallel planes. Intersections of the lattice planes produce three-dimensional parallelepipeds having six faces arranged in three sets of parallel planes; a unit cell is the simplest such parallelepiped that when translated will generate the entire lattice. If the planes are equidistant and mutually perpendicular (intersect at 90° angles), it forms a cubic lattice (cubic unit cells are shown in Figure 1). A cubic cell can be used to describe some, but by no means all, crystals. For many crystals the appropriate lattice may involve planes that are not equidistant or that do not intersect at 90° angles. In all there are seven possibilities, leading to seven crystallographic systems; we will emphasize only the cubic system. In describing a crystal, it is convenient to arrange the three-dimensional space lattice so that the structural particles of the crystal (i.e., atoms, ions or molecules) are situated at the corners of the unit cell (or lattice points) whenever possible. A unit cell having structural particles only at the corners is called a primitive unit cell, or simple cubic if the cell is cubic (it is the simplest unit cell that can be considered). Sometimes a unit cell involving more structural particles is necessary to describe the structure. In the body-centered cubic (bcc) structure, a structural particle is found at the center of the cube as well as at each corner. In a face-centered cubic (fcc) structure there is a structural particle at the center of each face as well as at each corner. These three unit cells are depicted in Figure 1. Closest Packed Structures Considerable insight into the structures of crystals can be gained by considering the way in which identical spheres—marbles, cannonballs, metal atoms—can be stacked. Unlike the case of cubes, there is no way of stacking spheres to fill all space, but there are certain arrangements in which the spheres come into as close contact as possible
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Models: Crystals and the Solid State and the holes or voids are kept to a minimum. These are known as closest packed structures. Two such structures are presented in Figure 2.
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