Crystal Structure Activity Learning Objectives After this activity, students should be able to

1. Identify different layering patterns that lead to the cubic unit cells, determine coordination

numbers, and compute packing efficiencies for atomic solids.

2. Determine the empirical formula of an ionic compound from its crystal structure.

Overview Use the visualization tool found at https://atom.calpoly.edu/crystal/ and answer the following

questions. Many of the functions in the simulation are bound to keys; look at Key Controls for the list.

The simulation starts by default with the Simple cubic lattice screen. The drop-down menu allows you

to view other lattice structures. You can rotate the structure and view it from different sides by holding

the mouse and dragging the structure. You can also zoom in and out with the mouse wheel. There are

two important modes that are controlled with the Expansion slider at the bottom of the screen. In

Layering mode, you can see how the 3D crystal lattice can be made by stacking layers of atoms. In Unit

Cell mode, you can see how the 3D lattice is composed of repeating unit cells with fractional atoms.

Lattice Structures of Atomic Solids

Layering We will begin this activity by looking at the layering pattern of particles that gives rise to each of the

cubic unit cells. A unit cell is the smallest unit in a repetitive pattern that makes the 3-dimensional lattice

structure. As shown in Figure 1, there are two basic 2D patterns for layers of atoms. The atoms in each

layer can be packed in a square array, or “close-packed” with a rhombus representing the simplest

repeating pattern. When multiple layers of a particular 2D pattern are stacked together, they can

generate a variety of 3D patterns, depending on how the layers are shifted relative to each other. If the

layers repeat identically as they stack, this can be described as “aa” stacking. If the second layer is

staggered relative to the first layer, but the third layer is stacked directly above the first layer, this

stacking pattern is described as “aba.” You can explore this layering effect by selecting Layering on the

left of the visualization tool and using the Expansion slider.

Figure 1. Square and rhombic unit cells in 2D layers.

For each of the cubic lattices (simple cubic, body-centered cubic, and face-centered cubic), answer the

following ques