Crystalline Solids Model

Introduction

Use this large-sized ball model to demonstrate the principle of closest packing for the arrangement of metal atoms in a crystal.

Concepts

• Hexagonal closest packing
• Cubic closest packing
• Face-centered cubic unit cell

Background

Metallic crystals can be visualized as consisting of spheres of atoms packed together in the most efficient way possible, so that the atoms occupy the greatest percentage of the available space. This type of arrangement is called closest packing.

For all closest packed metals, within every layer of atoms, each atom is surrounded by six other atoms (see Figure 1).

If this layer of atoms is placed on top of a second layer of closest packed atoms, the atoms of the second layer occupy every other depression between the atoms in that first layer. If we consider these two layers of atoms, there are nine atoms surrounding each atom. These layers are labeled A and B, respectively (see Figure 2). If a third layer of atoms is placed on top of the AB layer so that each atom in the third layer is directly over each atom in the first layer (A), the resulting arrangement is referred to as an ABAB... pattern and is called hexagonal closest packing (hcp). If we consider all three layers of atoms, there are 12 atoms surrounding each atom. Every other layer is identical (see Figure 3). When the third layer of atoms is placed on top of the AB layer so that atoms are not directly over any atoms in the first layer, the resulting arrangement is labeled an ABCABC... pattern and is called cubic closest packing (ccp). This structure, along with hcp, are the most efficient arrangements, occupying 74% of the space within the structures. Again, there are 12 atoms surrounding each atom (see Figure 4). If the cubic closest packing structure is rotated properly, it is evident that the cubic closest packing arrangement is identical to the face-centered cubic unit cell or crystal lattice (see Figure 5).

Materials

Safety Precautions

The materials in this demonstration are considered nonhazardous. Wear eye protection when using the rubber mallet.

Prelab Preparation

Assemble the platform by inserting the 13 steel rods supplied with the kit into the holes of the base. Check to see that the rods are aligned parallel to one another and perpendicular to the base.

Worksheet (Optional)
Make copies of the demonstration worksheet. Pass out a worksheet to each student before beginning the demonstration.

Procedure

Assembling the ABAB... (hcp) Structure

1. The spheres must be added one layer at a time. Place one sphere on each of the three rods shown in Figure 6. Slide each sphere down the rod until it reaches the bottom.
   {12528_Procedure_Figure_6}
2. Slide one sphere down the center rod. Slide six of the spheres down the adjacent rods shown in Figure 7.
   {12528_Procedure_Figure_7}
3. Slide one sphere down each of the rods used in step 1. The completed hcp structure is shown in Figure 8.
   {12528_Procedure_Figure_8}

Assembling the ABCABC... (ccp) Structure

1. Repeat steps 1 and 2 of the procedure for assembling the hcp structure.
2. Slide a sphere down each of the rods shown in Figure 9.
   {12528_Procedure_Figure_9}
   The completed structure shown in Figure 10 is the ccp.
   {12528_Procedure_Figure_10}

Student Worksheet PDF

12528_Student1.pdf

Teacher Tips

• A student worksheet is included with the kit. Use this as a teaching tool to explain the closest packing concept.
• If it is difficult to slide the balls down the rods, applying a small amount of Vaseline^® or petroleum jelly to the rod should correct this problem.
• The ccp structure can be rotated to show the face-centered cubic unit cell arrangement (see Figure 11).
  {12528_Tips_Figure_11}

Answers to Questions

1. There are six atoms surrounding every atom in the simple cubic structure
   {12528_Answers_Figure_12}
2. There are eight atoms surrounding every atom in the body-centered cubic structure.
   {12528_Answers_Figure_13}
3. The packing efficiency appears to correlate with the number of adjacent atoms or the coordination number. Because the body-centered cubic structure has a coordination number of eight and the simple cubic has a coordination number of only six, the body-centered cubic structure has a greater packing efficiency.