NOT ALL CRYSTALS ARE CREATED EQUAL:
A HANDS-ON INVESTIGATION OF UNIT CELL
STRUCTURES
C
Susanne M. Dana
Blacksburg High School
2013 VMI STEM Education Conference:
“Science with the future in mind”
October 8, 2013
Why study crystals?
• Synthesis of several areas of STEM
• Modeling
• Symmetry and Geometry
• Periodic trends
• Connection of microscopic structure to macroscopic properties
• Current applications
• Solid-state chemistry and physics not emphasized in traditional high school
programs
• Manipulation of composition and structure creates desirable properties
• Gemstones
• Steel
• semiconductors
Self-Assembly Activity
• RULES:
• You must hold hands. No hand can be left untouched.
• Your right hand must touch someone else’s right hand and your
left hand must touch someone else’s left hand.
• You cannot cross your arms.
• RESULTS: A complete circle with each participant alternating the
direction they are facing.
What is a unit cell?
•Single unit from which structure of
compound can be predicted
•Modeling in 2-D
•Scrapbook paper, wallpaper, etc.
•Corner/vertex, edge
Investigating unit cells in 3-D
• Different types
• Simple cubic
• Face-centered cubic
• Body-centered cubic
• Investigation
• Forming cell
• Analyzing for
• # atoms per unit cell
• Coordination number
• Connection between edge length and radius of atom
• Connection to density, Avogadro’s number, molar mass
Simple Cubic
• Making a unit cell
• Use template A and block with half moon
• Align template on block and put rods in four corners of shaded area
• Place two clear atoms on each rod
• One unit cell! Expand pattern
• Investigating…
• What portion of each atom is within each unit cell?
• How many atoms are in a unit cell?
• What is the relationship between edge length and atomic radius
Geometry
Applying to a problem…
• Polonium (Po) is one of the few metals that crystallizes in
a simple cubic arrangement. It has an edge length of
334 pm.
• What percentage of the unit cell is taken up by
atoms?
Face-Centered Cubic
• Making a unit cell
• Use template C and block with half moon
• Align template on block and put nine rods in corners, edges, and center of shaded
area
• Place one clear atom in each corner and center (like an x)
• Place one on each edge (four total)
• Repeat corner and center
• One unit cell! Expand pattern
• Investigating…
• What portion of each atom is within each unit cell?
• How many atoms are in a unit cell?
• What is the relationship between edge length and atomic radius?
Geometry
Applying to a problem…
• The density of an unknown metal is 2.64 g/cm3 and its
atomic radius is 215 pm. It has a face-centered cubic
lattice.
• What is the edge length?
• What is the volume of a unit cell?
• What is the molar mass of the metal?
• Identify the metal.
Body-Centered Cubic
• Making a unit cell
• Use template F and block with full circle
• Align template on block and put five rods in shaded area (corners and center)
• Place one clear atom in each corner
• Place one in center
• Repeat corner layer
• One unit cell! Expand pattern
• Investigating…
• What portion of each atom is within each unit cell?
• How many atoms are in a unit cell?
• What is the relationship between edge length and atomic radius?
Geometry
Applying to a problem…
• Sodium has a density of 0.971 g/cm3 and crystallizes with a body-centered cubic unit
cell.
• What is the edge length of the cell in picometers?
• What is the radius of a sodium atom in picometers?
• What percent of the unit cell is taken up by sodium atoms?
Computer tutorial
• http://www.wwnorton.com/college/chemistry/gilbert2/chemtours.asp
• Chapter 11: Unit Cell
• Section 5: What are the three common cubic systems? Name and draw a rough
sketch for each one.
• Section 6: What are the four different lattice positions an atom can occupy? How
many unit cells share each one?
• Continue through the tutorial and complete questions 1-4 at the end.
Ionic compounds…
•CsCl – simple cubic
•NaCl – face centered cubic
Other ideas
•Crystal lab…integrates several areas of
chemistry (in packet)
•Rock Candy
•Bragg equation
Bragg’s Law
For more information…
• Self assembly games:
• http://pbskids.org/dragonflytv/pdf/DragonflyTV_SelfAssemblyGames.pdf
• Institute for chemical education (unit cell kits)
• http://ice.chem.wisc.edu/Catalog/SciKits.html#Anchor-Solid-31140
• Pics of geometries…thanks to
• http://penyayangbercahaya.wordpress.com/2010/03/09/packing-efficiency/
• Bragg’s law pic…thanks to
• http://www-outreach.phy.cam.ac.uk/camphy/xraydiffraction/xraydiffraction7_1.htm