Martindale Geoff Tuesday 1:00 Lab MASC 110L Lab #4 Objective: The objective of this lab is to understand the crystal structures of metals, and to understand the hexagonal closest packed structure and the cubic closest packed structure using plastic foam balls and toothpicks. Also to find the symmetry of the two structures. Theory: This experiment includes some basic concepts of crystal structure. The meanings of crystal, lattice, unit cell, closest packing, hexagonal closest packed (hcp) structure (abab arrangement) and cubic closest packed (ccp) structure (abcabc arrangement or face-centered cubic (fcc) unit cell). Many metals crystallize in these structures. Also, the coordination number was determined by finding the total number of atoms any single atom would have in contact with those surrounding it. Axis of symmetry were also determined and the number of n-degrees a unit cell has. Results:
This is the HCP arrangement.
This is the CCP arrangement. Discussion: Question 1: Is this the closest packing of balls (atoms) in one plane? How many atoms are in contact with one atom? Can you find a way to have more than six atoms in contact with any one atom? Why? Yes, this is the closest packing of atoms in one plane. There are six atoms in contact with any one atom. There is no better way to have more than six atoms in contact with any one atom in one plane because a regular crystal pattern could not be established; hexagon a is the shape with the most sides that can form a repeating pattern by itself. Any more atoms would result in blank spaces in between atoms. Question 2: Why does the atom of the second sheet have to sit in the dimple position of the first sheet? The atom of the second sheet has to sit in the dimple pattern of the first sheet because if it sat on the atom it would just be a repetition of the first sheet making a pattern of (aaaa), not (abab). In addition to this it would be touching not as many atoms at a time of the corresponding atoms. Question 3: What kind of rotation symmetry does a planar hexagonal structure that you built in step 1, have? Why does a hcp structure formed by stacking these sheets lose the rotation symmetry and have only 3-fold symmetry? The planar hexagonal structure in step one has 6 fold symmetry. The (hcp) structure has a 3 fold symmetry because the atoms filling the gaps in the first layer have to undergo a 120 rotation instead of a 60 rotation to return to the original structure. The formula for calculating is (360/n). Conclusion: The objective of this lab was, "to study and understand two different close packed crystal structures and analyze how their structures were different and how that might affect their physical properties." Bibliography: Goo, Edward; Bosze, Eric J. Materials Science 110L Laboratory Manual; Thomson Custom Publishing, 2005.