C NOT ALL CRYSTALS ARE CREATED EQUAL: A HANDS-ON INVESTIGATION OF UNIT CELL STRUCTURES 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/cm 3 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 g/cm 3 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 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: Institute for chemical education (unit cell kits) Pics of geometries…thanks to Bragg’s law pic…thanks to