RDGcrystalstruct - Reading Crystal Structures with Cubic Unit Cells Revised CRYSTAL STRUCTURES WITH CUBIC UNIT CELLS Crystalline solids are a three

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Reading: Crystal Structures with Cubic Unit Cells Revised 5/3/04 1 CRYSTAL STRUCTURES WITH CUBIC UNIT CELLS Crystalline solids are a three dimensional collection of individual atoms, ions, or whole molecules organized in repeating patterns. These atoms, ions, or molecules are called lattice points and are typically visualized as round spheres. The two dimensional layers of a solid are created by packing the lattice point “spheres” into square or closed packed arrays. (Figure 1). Which packing arrangement makes the most efficient use of space? square array close-packed array Figure 1: Two possible arrangements for identical atoms in a 2-D structure Stacking the two dimensional layers on top of each other creates a three dimensional lattice point arrangement represented by a unit cell. A unit cell is the smallest collection of lattice points that can be repeated to create the crystalline solid. The solid can be envisioned as the result of the stacking a great number of unit cells together. The unit cell of a solid is determined by the type of layer (square or close packed), the way each successive layer is placed on the layer below, and the coordination number for each lattice point (the number of “spheres” touching the “sphere” of interest.) Primitive (Simple) Cubic Structure Placing a second square array layer directly over a first square array layer forms a "simple cubic" structure. The simple “cube” appearance of the resulting unit cell (Figure 3a) is the basis for the name of this three dimensional structure. This packing arrangement is often symbolized as "AA. ..", the letters refer to the repeating order of the layers, starting with the bottom layer. The coordination number of each lattice point is six. This becomes apparent when inspecting part of an adjacent unit cell (Figure 3b). The unit cell in Figure 3a appears to contain eight corner spheres, however, the total
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Reading: Crystal Structures with Cubic Unit Cells Revised 5/3/04 2 number of spheres within the unit cell is 1 (only 1/8 th of each sphere is actually inside the unit cell). The remaining 7/8 ths of each corner sphere resides in 7 adjacent unit cells. Figure 3a: Square Array Layering Figure 3b: Simple Cubic Figure 3c: Space Filling Simple Cubic The considerable space shown between the spheres in Figures 3a is misleading: lattice points in solids touch as shown in Figure 3b. For example, the distance between the centers of two adjacent metal atoms is equal to the sum of their radii.
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This note was uploaded on 11/20/2010 for the course CHEMISTRY Chem 1LE taught by Professor Dr.kimberlyedwards during the Spring '10 term at UC Irvine.

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RDGcrystalstruct - Reading Crystal Structures with Cubic Unit Cells Revised CRYSTAL STRUCTURES WITH CUBIC UNIT CELLS Crystalline solids are a three

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