Cubic Unit Cells Model

Introduction

Use this “super-size” model of the sodium chloride lattice to demonstrate the concept of the unit cell.

Concepts

• Crystal lattice
• Unit cell
• Body-centered cubic structure
• Face-centered cubic structure

Background

Solid ionic compounds contain ions arranged in an orderly and repeatable three-dimensional pattern called a crystal lattice. The smallest repeating unit or arrangement of ions in the crystal lattice is called the unit cell. Since the geometry of the unit cell is the same as that of the entire lattice, the crystalline solid will exhibit the same overall shape as the unit cell.

In this demonstration, the unit cells of sodium chloride and cesium chloride will be examined. Both solids are examples of cubic unit cells—crystal lattice with a cubic structure.

Sodium chloride forms a face-centered cubic unit cell. Chloride ions occupy the eight corners of the unit cell as well as the center of each “face” of the cube (see Figure 1).

The smaller sodium ions occupy the “voids” or spaces between the chloride ions in the cube (see Figure 2). The overall sodium chloride unit cell is shown in Figure 3. The total number of each type of ion in the unit cell is determined by adding together the “fractions” of each ion that occupy the unit cell. The fractional amount of each ion is determined by its location in the cell. Any ion in the center of the cube is wholly in the unit cell and will be counted as one in the unit cell. Each ion in the center of a face is part of two unit cells, with ½ of the ion being part of the unit cell. Any ion at the center of an edge of the cube is part of four unit cells and contributes ¼ of an ion to the unit cell. Ions at the corners of the cube are shared by 8 unit cells, and therefore only ⅛ of each corner ion is “counted” in the unit cell.

For sodium chloride the number of chloride ions in the unit cell (eight corner ions and six face ions) is equal to:

(8 x ⅛) + (6 x ½) = 4 ions

The number of sodium ions in the unit cell (12 center edge ions and one center ion) is equal to:

(12 x ¼) + 1 = 4 ions

Thus the unit cell of sodium chloride contains four chloride ions and four sodium ions. (The ratio of the ions in the unit cell must be equal to the ratio of ions in the formula of the ionic compound.)

Cesium chloride forms a body-centered cubic unit cell. In this arrangement, chloride ions occupy the eight corners of the cube, with the cesium ion located in the center of the cube. The cesium chloride unit cell contains one cesium ion and one chloride ion (see Figure 4).

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 nine rods into the holes of the base. Check to see if the rods are aligned and perpendicular to the base.

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

Procedure

Assembling the Sodium Chloride Unit Cell

1. The ions must be added one layer at a time. Start by placing one of the 3-inch balls on each corner rod and also on the center rod. Slide the balls down the rods until they reach the bottom. (The 3-inch balls represent chloride ions in the NaCl unit cell.)
2. Place a ½-inch spacer on each of the remaining rods.
3. Slide a 2-inch ball down each of the four remaining rods (see Figure 5).
   {13539_Procedure_Figure_5}
4. Slide a 2-inch ball down each of the corner rods and the center rod.
5. Slide a 3-inch ball down the remaining rods (see Figure 6).
   {13539_Procedure_Figure_6}
6. Repeat step 1.
7. Place a 2-inch ball down each of the four remaining rods (see Figure 7).
   {13539_Procedure_Figure_7}

Assembling the Cesium Chloride Unit Cell 

1. Slide a 3-inch ball down each of the four middle rods. These will represent the chloride anions in the CsCl unit cell.
2. Place a 1-inch spacer down the middle rod. Add a 3-inch ball to the middle rod. (This 3-inch ball represents a cesium ion in the CsCl unit cell.)
3. Place a 3-inch ball at each of the four middle rods.

Student Worksheet PDF

13539_Student1.pdf

Teacher Tips

• A student worksheet is included with this model kit. The worksheet may be used as a teaching tool to help students work through and review the unit cell concept or as an assessment tool.
• If it is difficult to slide the balls down the rods, apply a small amount of Vaseline^® to the rod to correct this problem.
• Other ionic compounds with the face-centered cubic unit cell include NaF, KCl, MgO and CaS.
• For NaCl, the positions of the anion and cations can be reversed, that is, the sodium ions can occupy the eight corners and the six faces of the unit cell, with the chloride ions occupying the 12-edge centers and the center of the cube.

Answers to Questions

Solid ionic compounds contain ions arranged in an orderly and repeatable pattern called a crystal lattice. The smallest repeating arrangement of the lattice is called the unit cell.

1. Examine the sodium chloride unit cell.
   1. Identify the chloride ions on each face of the cubic unit cell. How many unit cells is each “face” chloride ion part of?

      Two

   2. How many unit cells is each corner chloride ion part of?

      Eight

   3. How many unit cells is each center edge sodium ion part of?

      Four

   4. How many unit cells is the sodium ion in the center of the cube part of?

      One

The number of each ion in the unit cell is determined by adding together the fractions of each ion that occupy the unit cell. This fraction is always one ion divided by the number of unit cells the ion is part of.

2. Calculate the number of chloride ions and the number of sodium ions in the sodium chloride unit cell.

   Chloride ions: (8 x ⅛) + (6 x ½) = 4Cl^–/unit cell
   Sodium ions: (12 x ¼) + 1 = 4Na⁺/unit cell

3. Examine the cesium chloride unit cell. Calculate the number of chloride ions and the number of cesium ions in the unit cell.

   Chloride ions: (8 x ⅛) = 1Cl^–/unit cell
   Cesium ions: 1 = 1Cs⁺/unit cell