Materials Included In Kit

Additional Materials Required

Prelab Preparation

1. 2-inch Connectors: Take one 18-inch floral wire and cut it into 2-inch lengths using a wire cutter. Repeat this for seven more wires to produce 72 2-inch connectors.
2. 1-inch Connectors: Take one 18-inch floral wire and cut it into 1-inch lengths using a wire cutter. Repeat this for five more wires to produce 108 1-inch connectors.

Safety Precautions

While the activity is considered nonhazardous, protective eyewear is recommended. Caution students to use care when handling the cloth wire connectors; the ends may have sharp points. Remind students to wash their hands thoroughly with soap and water before leaving the laboratory.

Disposal

The spheres and connectors can be stored for later use.

Lab Hints

• Enough materials are provided in this kit for 24 students working in groups of four. All materials are reusable. Both parts of this laboratory activity can reasonably be completed in one 50-minute class period.
• This experiment may be carried out as a series of five to six activity stations, with groups of students rotating between the stations.
• Each group has enough spheres to assemble each structure, but not all at once. Once the students are confident of their lattice and the data, they can disassemble the spheres and connectors to use in subsequent constructions.
• The list of ionic crystals can be expanded to compounds other than the two group 1 chlorides. For example, copper(I) oxide, Cu₂O, has a face-centered cubic lattice for copper with two oxide ions wholly in the unit cell, each connected to four Cu.
• Show students a copy of Figure 21 or have one group construct this unit cell. Students would then calculate the number of each ion in the unit cell.
  {13538_Hints_Figure_21}
  [Copper(I) ion has the same number as any FCC unit cell, 4. There are 2 oxide ions in the unit cell, giving the correct ratio of copper(I) ions to oxide ions, 2:1.]

Teacher Tips

• Metals that crystallize in the body-centered cubic structure include vanadium, chromium, manganese, iron and all the alkali metals. Metals that crystallize in the face-centered cubic crystal structure include aluminum, lead, copper, silver and gold.
• The hexagonal closest packing ABAB structure and the hexagonal closest packing ABCABC (face-centered cubic) structure are examples of closest packing of solids—identical atoms are packed as closely as possible into a given space. If one assumes that the atoms behave as small spheres, the atoms occupy 74% of the volume of the crystal structure and have a coordination number of 12. This is the maximum coordination number and maximum density for atoms in a solid lattice composed of “spheres.”

Sample Data

Part 1

Hexagonal Closest Packing ABABAB... ___12___ coordination number
Hexagonal Closest Packing ABCABC... ___face-centered___ unit cell

Part 2

References

This laboratory activity has been adapted from Flinn ChemTopic™ Labs, Volume 5, Chemical Bonding, Cesa, I., Flinn Scientific, Batavia, IL, 2004.

Introduction

How are the atoms arranged in a metallic solid and in an ionic crystal? Are the arrangements of atoms random or is there some kind of “system” to it with regular “repeating units”? Discover the structures of these solid state materials using polystyrene foam spheres and wire “bond connectors” to build models of different crystal structures.

Concepts

• Crystal lattice
• Simple cubic
• Body-centered cubic
• Unit cell
• Face-centered cubic
• Hexagonal closest packing

Background

The atoms of most solid elements, molecules and ionic compounds are fixed in a regular pattern that repeats itself throughout the entire solid. Solid ionic compounds contain ions arranged in an orderly and repeatable pattern called a crystal lattice. The smallest repeatable arrangement of the lattice is called the unit cell.

Many metals and ionic compounds have unit cells with a cubic structure, that is, have atoms or ions occupying the eight corners of a cube. If only the corners of the cube are occupied, the unit cell is referred to as a simple cubic unit cell (see Figure 1).

If the center of the cube is also occupied, the unit cell is called body-centered cubic (see Figure 2). When atoms or ions occupy the center of each “face” of the cube, the result is a face-centered cubic arrangement of the unit cell (see Figure 3).  In addition to these structures, metal atoms can also be arranged in a pattern called hexagonal closest packing. The atoms are arranged in layers in which each atom is surrounded by six other atoms in a hexagonal arrangement. The layers above and below every layer fit into the openings between the atoms in the “middle” layer (see Figure 4). The total number of each type of atom or ion in a cubic unit cell is determined by adding together the “fractions” of each atom or ion that occupy the unit cell. The fractional amount of each ion in the unit cell is determined based on its location in the cell (see Figure 5). Any ion in the center of the cube (1) is wholly in the unit cell and its “fractional amount” is 1. Each ion in the center of a face (2) is part of two unit cells, so that ½ of the ion is “counted” as being part of each unit cell. Ions in a “center edge” of the cube (3) belong to four unit cells and have a unit cell “fraction” of ¼. Ions at the corners of the cells (4) are shared by 8 unit cells, and therefore only ⅛ of each corner ion is “counted” in the unit cell.

Experiment Overview

The purpose of this activity is to build models of various crystal structures and closest packed arrangements using polystyrene foam spheres and wire connectors. The models will be analyzed to determine the total number of atoms or ions in each unit cell.

Materials

Safety Precautions

While the activity is considered nonhazardous, protective eyewear is recommended. Use care when handling the floral wire connectors; the ends may have sharp points. Wash hands thoroughly with soap and water before leaving the laboratory.

Procedure

Part 1. Cubic Unit Cells and Hexagonal Closest Packing

Simple Cubic Unit Cell

1. Use the 2-inch connectors and the 2-inch spheres to construct the two layers of “atoms” shown in Figure 6.
   {13538_Procedure_Figure_6}
2. Using the 2-inch connectors, attach one of the four-sphere layers directly on top of the other. Determine the number of “atoms” in the unit cell and record this value in the data table.

Face-Centered Cubic Unit Cell

1. Use the 2-inch connectors and the 2-inch Styrofoam spheres to construct the three layers of “atoms” shown in Figure 7.
   {13538_Procedure_Figure_7}
2. Attach the four-sphere ring to one of the five-sphere rings so that each sphere is over a space of the five-sphere ring.
3. Now place the other five-sphere ring over the four-sphere layer so that each sphere is over a space of the four-sphere ring (see Figure 8).
   {13538_Procedure_Figure_8}
4. Determine the number of “atoms” in the unit cell and record this value in the data table.

Body-Centered Cubic Unit Cell

1. Use the 2-inch connectors and the 2-inch spheres to construct the two layers shown in Figure 9.
   {13538_Procedure_Figure_9}
2. Attach a single sphere into the center space in the middle of one of the four-sphere rings.
3. Attach the second four-layer ring on top of the center sphere so that its spheres are aligned directly over the spheres in the bottom layer.
4. The unit cell should resemble Figure 10.
   {13538_Procedure_Figure_10}
5. Determine the number of atoms in the unit cell and record this value in the sata table.

Hexagonal Closest Packing ABAB...

1.  Use the 2-inch connectors and the 2-inch Styrofoam spheres to construct the three layers in Figure 11.
   {13538_Procedure_Figure_11}
2. Place the seven-sphere ring on top of one of the three-sphere rings so the spheres in the bottom ring occupy or sit over every other “hole” or space in the seven-sphere ring (see Figure 12).
   {13538_Procedure_Figure_12}
3. Attach the remaining three-sphere ring to the seven-sphere ring so that its spheres are aligned directly over those in the first layer (see Figure 13).
   {13538_Procedure_Figure_13}
4. When every other layer in a crystal structure is identical, the structure is referred to as an ABABAB... structure. Many metals have this arrangement. The number of spheres touching a single sphere is called its coordination number. Count the number of spheres that touch the central sphere and record this number in the data table.

Hexagonal Closest Packing ABCABC...

1. Use the 2-inch connectors and the 2-inch Styrofoam spheres to construct the two layers of “atoms” shown in Figure 14.
   {13538_Procedure_Figure_14}
2. Attach the two layers together so that their triangular shapes point away from each other.
3. Attach a single sphere to the center opening of each layer, one on top and one on bottom (see Figure 15).
   {13538_Procedure_Figure_15}
4. Hold the structure by the top and bottom spheres with the point of the bottom triangle pointing towards you. Rotate the structure forward 45º towards you, then counter-clockwise 45º (see Figure 16). Observe the structure. What type of unit cell is the ABCABC... structure? Record this answer in the data table.
   {13538_Procedure_Figure_16}

Part 2. Sodium Chloride and Cesium Chloride Unit Cells

Sodium Chloride Unit Cell—Face-Centered Cubic Lattice

1. Use both the 2-inch and 1-inch connectors and the 2-inch and 1-inch spheres to construct the three layers shown in Figure 17. The 2-inch spheres represent chloride ions and the 1-inch spheres represent the sodium ions.
   {13538_Procedure_Figure_17}
2. Attach the ring with four large spheres between the other two rings so that the large spheres in the middle layer are “sandwiched” between the small spheres of the other two rings above and below (see Figure 18).
   {13538_Procedure_Figure_18}
3. Count the number of sodium ions in the center of the cube, in the middle of each face of the cube, along the “center edges” of the cube, and in the corners of the cube. Enter these values in the data table and determine the total number of sodium ions in the unit cell.
4. Repeat step 3 for the chloride ions.

Cesium Chloride Unit Cell

1. Use the 2-inch connectors and the 2-inch spheres to construct the two layers shown in Figure 19. All of the four spheres represent chloride ions.
   {13538_Procedure_Figure_19}
2. Attach a single sphere, representing a cesium ion, into the middle space of one of the four-sphere rings.
3. Attach the second four-layer ring, also representing chloride ions, on top of the center sphere so that its spheres are aligned directly over the spheres in the bottom layer (see Figure 20).
   {13538_Procedure_Figure_20}
4. Count the number of each type of ion in each category of the cube (see the data table). Record these values in the data table.
5. Disassemble the models and put away the spheres and connectors as directed by your teacher.

Student Worksheet PDF

13538_Student1.pdf