MECH 530 - MATERIALS SCIENCE LABORATORY:
Lab #1 - CRYSTAL STRUCTURES
INTRODUCTION:
The crystal structure of several metals is comprised of a unit cell of cubic geometry with atoms
located at all corners of the cube as well as the center of all faces. Such an arrangement is referred to as
a face-centered cubic (FCC) crystal structure. Common metals exhibiting the FCC structure include
copper, aluminum, silver, and gold. Each corner atom in the FCC structure is shared by eight
neighboring unit cells, and each face-centered atom is shared by two unit cells.
Another common metallic crystal structure known as the body-centered cubic (BCC) is also
comprised of a unit cell of cubic geometry with atoms located at the corners of the cube and a single
atom in the center of the cube. Similar to the FCC structure, the corner atoms of the BCC crystal are
shared by eight unit cells, while the center atom is not shared at all.
The last common crystal structure exhibited by metals is not based on a cubic structure. Instead
of a cubic geometry, the hexagonal-close packed (HCP) structure consists of three planes of atoms
stacked together. The top and bottom planes are symmetrical and consist of six atoms arranged in a
hexagon with an additional atom in the center of the hexagonal face. The midplane consists of 3 interior
atoms that complete the stacking arrangement.
OBJECTIVE:
To study the atomic arrangements of BCC, FCC, and HCP crystals with the aid of hard-sphere
representations. Through building the crystal models with readily obtainable spheres, such as marbles
and/or ping-pong balls, students will obtain a tangible grasp of the similarities and differences among
each of the three most common metallic crystal structures.
EQUIPMENT:
Hard sphere objects to represent atoms, positioning fixtures, glue or other adhesive, and a dial
caliper or similar measuring instrument.
SAFETY:
When using hot-melt glue guns, be extremely careful when handling the glue gun as the tip will
likely exceed 1600F, and can cause burns. Also, be cautious of recently dispensed glue as it will also be
hot and has the potential to cause burns.
PROCEDURE:
To make the three crystal structures assigned to your group, you will need 40 hard sphere
atomic models. Several of the aluminum spheres or marbles should be measured to determine an
accurate average value for the diameter. Record this value. Also, be sure to choose spheres that are as
close to the same diameter as possible.
FCC Model: - 14 balls/marbles required.
1. Using the supplied positioning fixtures, assemble the top and bottom of the FCC structure using
5 spheres for each. Orient the spheres in the shape of a plus-sign “+” using the straight line and
900 positioning fixture.
2. Assemble the remaining four spheres in the shape of a perfect square.
3. Complete the model by combining the three sections together.
BCC Model: - 9 balls/marbles required.
1. Using the supplied positioning fixtures, assemble the diagonal plane of the BCC structure using 5
spheres. Orient the spheres in a flattened “x”-shape using the straight line and 700 positioning
fixture.
2. While holding this assembly at an incline of 450, position two additional spheres in the correct
location on the bottom of the structure.
3. Reposition the assembly consisting of 7 spheres to facilitate adding the last two spheres to
complete the BCC structure.
HCP Model: - 17 balls/marbles required.
1. Using the supplied positioning fixtures, assemble the top and bottom of the HCP structure using
7 spheres for each. Start with a triangle comprised of three spheres, and then add a fourth
sphere to form an elongated diamond. A fifth sphere will form a stacking arrangement of two
spheres on the bottom, and three spheres on the next level. Two additional spheres on top of
the row with three will form a hexagon with an additional 7th sphere in the center. Repeat the
steps above for the top of the model.
2. Assemble the remaining 3 spheres in the shape of a triangle.
3. Complete the model by combining the three sections together.
RESULTS:
 Measure the actual lattice constant, a0 for each model (FCC, BCC, and HCP) and compare this to
the calculated lattice value based on the average radius of the “atoms”.
 Using the measured lattice constants and average “atomic” radii, calculate the atomic packing
factor for your group’s BCC and FCC structure and compare this to published values.
 Sketch a unit cell of each of the crystal structures. CAD models are preferred, though hand
drawings, done neatly will be acceptable.
 If we were to assemble our models in a different manner, what would be the required inner
dimensions of a box to construct the BCC structure based on the diameter of the spheres your
group used? The height of the box is not critical as long as it is tall enough to hold all of the
spheres.
CONCLUSIONS:
 Which of these three crystal structures are most similar and why?
 Based on a given atomic radius, which crystal would have the largest volume?
 List a few of the common metals that occur with each structure, and discuss whether or not a
general correlation can be made between crystal structure and mechanical, electrical, and
thermal properties.
FCC Unit Cell Structure.
(a) Hard sphere unit cell, (b) Reduced sphere unit cell,
(c) FCC unit cell in an aggregate of atoms – from W.G. Moffat, et al, The Structure and Properties of Materials,
John Wiley & Sons, New York.
BCC Unit Cell Structure.
(a) Hard sphere unit cell, (b) Reduced sphere unit cell,
(c) BCC unit cell in an aggregate of atoms – from W.G. Moffat, et al, The Structure and Properties of Materials,
John Wiley & Sons, New York.
HCP Unit Cell Structure.
(a) Reduced sphere unit cell, (b) HCP unit cell in an aggregate of atoms – from W.G. Moffat, et al, The Structure
and Properties of Materials, John Wiley & Sons, New York.