MRSEC Teacher Institute 15 March 2005

1. MRSEC Teacher Institute15 March 2005 Introduction to Crystal Structures Janet Rankin Division of Engineering

2. Objectives By the end of this session, participants will: have considered how the arrangement of atoms in crystals influences material properties be able to recognize a few simple crystal structures have learned how to designate the positions of atoms within a crystal structure, be acquainted with the rules for specifying direction within a crystal structure have considered ways in which the introduction of crystal structures into K-12 curricula can help students learn a variety of mathematical and scientific concepts

3. How are atoms arranged in solids?? 3 phases or states of matter Solid Liquid Gas The solid state Atoms in solids may be randomly positioned (as in a liquid) � Amorphous Solids (e.g. glasses) or Arranged in an orderly, repeating pattern within the material � Crystalline Solids

4. How do we describe the arrangement of atoms in crystals? Specify a LATTICE Specify the POSITIONS of atoms in the lattice

5. What�s a Lattice? There are 14 (only) Bravais Lattices there are only 14 unique ways to fill space with a periodic arrangement of points. A lattice is like scaffolding Once you specify the lattice, you can then �decorate� your lattice with a collection of atoms. Each lattice point must be decorated with the same collection of atoms.

6. �Constructing� a Crystal Once you specify the lattice, you can then �hang� a collection of atoms off of each position in the lattice Important: every lattice point (point on the scaffold) must have the exact same enviroment. i.e. the structure must possess translational symmetry from point to point. Look at 2-D examples: Escher prints

7. 2-D �Crystals� M.C. Escher: http://home.comcast.net/~eschermc/ Sea horses Bugs Moths Fish Flying Fish Birds Menagerie Butterflies

8. Metallic Crystals

9. Metallic Crystal Structures The atoms in most simple metals are arranged in one of the configurations below Simple Cubic (sc) - Po Body-Centered Cubic (bcc) � Ba, Cs, Cr Face-Centered Cubic (fcc) � Cu, Ag, Hexagonal Close-Packed (hcp) � Zn, Co Nearest-neighbors atoms �touch� in all of these cases.

10. Characteristics of Selected Elements at 20C

11. Specifying Directions in a (cubic) Crystal Choose a right-handed coordinate system Pick an origin for your set of axes the x-axis is the vector (100) the y-axis is the vector (010) the z-axis is the vector (001) Any direction in the crystal can be defined using the basis above.

12. Materials Science Links Crystal Structures Naval Research Labs � �interactive� crystal structure http://cst-www.nrl.navy.mil/lattice/ University of Arizona � Geology Department http://www.geo.arizona.edu/AMS/amcsd.php More Crystal Structures http://www.chem.ox.ac.uk/icl/heyes/structure_of_solids/Strucsol.html Stereo Pairs http://www.chem.lsu.edu/htdocs/people/sfwatkins/ch4570/lattices/lattice.html MERLOT http://wb.chem.lsu.edu/htdocs/people/sfwatkins/MERLOT/flattice/00lattice.html

13. Construction of a Crystal Model Supplies needed: Styrofoam, clay, or candy spheres (atoms) Wood or plastic connectors, e.g. dowels or toothpicks, coffee stirrers, spaghetti (bonds). Choose fcc, or bcc structure.

14. Construction of a Crystal Model Things to consider: Which atoms are touching in your structure? What is the Coordination Number (CN) in your crystal? (How many nearest neighbors does each atom have?) Can you identify a line (direction) in which the atoms touch? Can you relate the size of the atom to the size of the unit cell? (i.e. write an expression for a = f(r))

15. Crystals as Building Blocks

16. Polycrystalline Materials

17. Single v. Polycrystals

18. Break-Out Session:How might you use this in your classroom? suggestions for student activities: Model construction and analysis Identify coordinates (positions) of atoms in various structures I.D directions Geometry exercises (distances in unit cells) I.D. symmetry operators (translation, rotation, mirror) Notes from discussions

19. Materials Science Links General Links Materials Research Society (http://www.mrs.org/microworld) University of Arizona�s science e-zine (see the �gallery� on the left side-bar) http://researchmag.asu.edu/materials_4.html University of Connecticut - simulations of a variety of phenomena in materials science (p.c. - only) http://ims.uconn.edu/centers/simul/movie CS 92 - Educational Software Seminar http://www.cs.brown.edu/courses/cs092/2001/splash/ (see Spring 2001 projects for �Splash� [p.c.- only, < XP])

20. Contact Information Janet_Rankin@brown.edu 863-9192

21. SIMPLE CUBIC STRUCTURE (SC)

22. Hexagonal Close-Packed Structure (hcp)

23. Body-Centered Cubic (BCC)

24. Face-Centered Cubic (FCC)

25. Hexagonal Close-Packed

26. Specifying Directions in Crystals

27. Notes from Discussion In order to use these concepts effectively in K-12 classes, more background knowledge would be necessary (i.e. teachers would have to do more research into crystalline structures). Felt that this could be used as a �real life� application of Pythagorean Theorem Could be used in chemistry classes: e.g. make NaCl, ZnI2, crystals and then consider various aspects of crystallography, compare, contrast, etc. Different models for solid, liquid and gaseous states Could be used to present vectors in algebra II classes.