Lab Ch. 15 – Crystal Structures

 

PURPOSE      To investigate the arrangement of atoms in crystalline solids.

 

BACKGROUND

 

The regular geometric shapes of crystals reflect the orderly arrangement of the atoms, ions, or molecules making up the crystal lattice.  In this experiment, you will gain insight into the ways crystals are formed.  To do this, you will model crystal structures using balls of Play-Doh.  Using the models, you will determine the number of nearest neighbors (the coordination number) of particles in each of these structures.  The effect of the size of the cations and anions in the crystal structures will also be investigated. 

 

MATERIALS

 

 

PROCEDURE

 

As you complete each sections of the experiment, answer the corresponding questions in the Analyses and Conclusions sections.

 

IMPORTANT – After you are done the lab, take all toothpicks out of the Play-Doh and put the Play-Doh back into the containers.  Make sure the lids are on tight!!!  Be considerate, other students will need to use these supplies and your teacher purchased them with her own hard-earned cash.

 

Part A.  Hexagonal Closest Packing

 

  1. Roll Play-Doh into 13 spheres (all of the same color), 2 cm in diameter.  Use the vernier calipers to measure the diameter of the spheres.
  2. Connect three sets of these spheres as in Fig. 1.  Use broken-off pieces of toothpicks to help secure the spheres.

 

layer 1             layer 2            layer 3

 

Figure 1

 

  1. Place one of the sets of 3 spheres on the table.  This is the first layer.
  2. Place the set of 7 spheres on the 3 spheres so that its center sphere fits snugly into the depression in the first layer.
  3. Place the second set of 3 spheres over the center sphere of the second layer.  The spheres in this third layer should be directly above the spheres in the first layer.  Record the number of nearest neighbors (the coordination number) of the central sphere in the structure you formed.  Retain your model for Part C.  The arrangement you have constructed, hexagonal closest packing, is found in the crystals of zinc, magnesium, and many other metals.  There is a cool model of a magnesium lattice at the website below.  Left-click it and move the mouse around to rotate it in 3-D. 

 

http://www.le.ac.uk/eg/spg3/atomic.html

 

 

Part B.  Face-centered Cubic Packing

 

  1. From 14 more 2-cm spheres (all the same color), construct the layers shown in Fig. 2. Again, use toothpicks to help secure the spheres.

 

layer 1             layer 2            layer 3

 

Figure 2

 

  1. Place the first layer of 5 spheres on the table.  Place the second layer (4 spheres) over the first so that its spheres rest in the spaces between the corner spheres of the first layer.
  2. Place the third layer so that the spheres line up with those of the first layer.  Study this model carefully to determine why crystals with this structure are described as face-centered cubic packing.  This is the type of packing found in copper, silver, aluminum, and many other metals.

 

Part C.  Comparison of Hexagonal Closest Packing  & Face-centered Cubic Packing

 

  1. Make a fourth layer for model B exactly like layer 2.  Before putting it on top of layer 3, count the number of nearest neighbors to the center sphere in layer 3.  Now add layer 4.  How many nearest neighbors does the center sphere of layer 3 have now?  This is the coordination number.
  2. Compare models A and B.

 

Part D.  Body-centered Cubic Packing

 

  1. Use 2-cm spheres to construct the layers shown in Fig. 3.  Leave a space of approximately 2 mm between the spheres.

 

layer 1             layer 2            layer 3

 

Figure 3

 

  1. Place the single sphere in the center of the first layer, and them position the third layer so that it lines up with the first layer.  Examine the symmetry of this model and comment on the term body-centered cubic.  This type of packing is typical of the alkali metals, which include sodium and potassium.

 

Part E.  The Sodium Chloride Lattice

 

  1. Ionic crystals are formed by packing positive and negative ions alternately into a lattice.  A single sodium ion has a diameter of 0.19 nm, a chloride ion has a diameter of 0.36 nm.  Because the diameters are in a ratio of roughly 1:2, the relative sizes of Na+ and Cl- can be approximated by using 1-cm and 2-cm spheres.
  2. Use model B, with its 2-cm spheres, to represent the face-centered cubic arrangement of the chloride ions in a sodium chloride crystal.  Make 13 1-cm spheres of a different color to represent the sodium ions.  Take the layers in model B apart, and put the 1-cm spheres into the holes between the chloride ions in each layer. Put the layers back together.  Note that the NaCl lattice is an interpenetrating set of face centered cubes, one set of cubes made up of Na+ ions and the other made up of Cl- ions.

 

Part F.  The Zinc Sulfide (Wurtzite) Lattice

 

  1. Because each zinc ion has a diameter of 0.15 nm and the diameter of the sulfide ion is 0.37 nm (a ratio of about 1:2.5), you can use 2-cm spheres for the S2- ions and 0.8-cm spheres for the Zn2+ ions.  You will need to make 13, 0.8-cm spheres of a different color for the zinc ions.
  2. Use model A, with its hexagonal closest-packing orientation, to represent the lattice of the larger sulfide ions.  Secure one 0.8-cm sphere directly above each of the larger spheres in each of the three layers of model A. Use small pieces of toothpick to help.
  3. Place the largest layer of spheres on the table with the small spheres down.  Place one of the smaller layers on the top of this layers so the smaller spheres fit into alternate depressions.  Invert the two layers and place the other small layer, with the small spheres upward, above the larger layer so that the spheres in the top layer are directly above the spheres in the bottom layer.

 

ANALYSES AND CONCLUSIONS

 

Part A.  Hexagonal Closest Packing

 

  1. What is the coordination number of the central atom in the model of hexagonal closest packing?

 

 

 

Part B.  Face-centered Cubic Packing

 

  1. Explain the appropriateness of this name for describing the model you constructed.

 

 

 

Part C.  Comparison of Hexagonal Closest Packing  & Face-centered Cubic Packing

 

  1. Compare the coordination numbers for the two types of closest packing.

 

 

 

  1. If both a hexagonal-closest packed model and a cubic closest packed model were constructed from spheres of the same size and mass, would the densities of the models differ?  Explain.  (Hint: Think about how much volume an equal number of spheres would take up in each case.)

 

 

 

 

Part D.  Body-centered Cubic Packing

 

  1. Below 906oC, metallic iron crystallizes in a body-centered cubic form which is called alpha-ferrite (a-ferrite). Above this temperature, the stable form is gamma-ferrite (g-ferrite), which is a face-centered cube.  At 140oC, the crystal form changes back to a body-centered cubic form called delta-ferrite (d-ferrite).  What is the coordination number of iron in each of these forms?

 

 

 

 

Part E.  The Sodium Chloride Lattice

 

  1. What ions most closely surround each Na+ ion?  What ions most closely surround each Cl- ion?

 

 

  1. What is the coordination number of the Na+ ions?  What is the coordination number of the Cl- ions?

 

 

 

Part F.  The Zinc Sulfide (Wurtzite) Lattice

 

  1. What is the coordination number of the Zn2+ ions?  What is the coordination number of the S2- ions?