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NAMES Chemistry 124 Fall 2008 SOLID STATE STRUCTURES Cubic Unit Cells Project 1: Simple (Primitive) Cubic Unit Cells z - diagram(s) stacking pattern 3D illustration of unit cell number of corner spheres net number of atoms per unit cell contribution of a corner atom to coordination number of each a single unit cell corner sphere length of one side of the unit cell in terms of atomic radius r % packing efficiency (show calculations and geometric diagrams) Find an element which crystallizes in this type of unit cell. source of information: Chemistry 124 Fall 2008 SOLID STATE MODELING EXPERIMENT page 2 Project 2: Body-Centered Cubic Unit Cells z - diagram(s) stacking pattern 3D illustration of unit cell total number of corner spheres total number of center spheres contribution of a corner sphere contribution of a center atom to a to a single unit cell single unit cell net number of atoms per unit cell coordination number of each coordination number of each corner sphere center sphere volume of the cube generated using the radius,r, of the atoms (draw a diagram and show calculations) % packing efficiency (show calculations) Find an element which crystallizes in this type of unit cell. source of information: Chemistry 124 Fall 2008 SOLID STATE MODELING EXPERIMENT page 3 Project 3: Face-Centered Cubic Unit Cells z - diagram(s) stacking pattern 3D illustration of unit cell number of corner spheres number of face spheres contribution of a corner atom contribution of a face atom to a to a single unit cell single unit cell net number of atoms per unit cell coordination number of each coordination number of each face corner sphere sphere volume of the cube generated using the radius, r, of the atoms (draw a diagram and show calculations) % packing efficiency (show calculations and geometric diagrams) Find an element which crystallizes in this type of unit cell. Chemistry 124 Fall 2008 SOLID STATE MODELING EXPERIMENT page 4 source of information: Stoichiometry Project 4: Cesium Chloride z-diagram of unit cell (be sure to distinguish different colors & atoms) Type of cubic cell generated Type of cubic cell generated only by the colorless only by the green spheres spheres Colorless sphere represents Green sphere represents which which element? element? Stoichiometry (formula) for cesium chloride. Explain how this formula corresponds to what might be predicted by the Periodic Table. Project 5: Calcium Fluoride (fluorite) z-diagram of unit cell (be sure to distinguish different colors & atoms) Type of cubic cell generated Type of cubic cell generated only by the colorless only by the green spheres spheres Colorless sphere represents Green sphere represents which which element? element? Stoichiometry (formula) for calcium fluoride. Chemistry 124 Fall 2008 SOLID STATE MODELING EXPERIMENT page 5 Explain how this formula corresponds to what might be predicted by the Periodic Table. Project 6: Lithium Nitride z-diagram of unit cell (be sure to distinguish different colors & atoms) What is the stoichiometry of To which type of cubic cell blue to green spheres? might this be related? Green sphere represents Blue sphere represents which which element? element? Stoichiometry (formula) for lithium nitride. Explain how this formula corresponds to what might be predicted by the Periodic Table. Project 7: Zinc Blende (Zinc sulfide) z-diagram of unit cell (be sure to distinguish different colors & atoms) What is the stoichiometry of To which type of cubic cell blue to colorless spheres? might this be related? Blue sphere represents which Colorless sphere represents element? which element? Stoichiometry (formula) for zinc sulfide. Explain how this formula corresponds to what might be predicted by the Periodic Table. Chemistry 124 Fall 2008 SOLID STATE MODELING EXPERIMENT page 6 Discussion Questions 1. Consider the following z diagram for a crystal structure. Determine the simplest formula for this compound. Layer sequence: Key Ti Ca O z=0 z = 0.5 What are the net contributions of each atom to the unit cell? Be explicit in your explanation. The overall simplest formula which can exist is thus Ti Ca O 2. Find the simplest formula for the following unit cell structure, showing your “work”. Put the “elements” in the formula in alphabetical order. z = 0,1 z = 0.25, 0.75 z = 0.5 A B C Chemistry 124 Fall 2008 SOLID STATE MODELING EXPERIMENT page 7 3. Draw the z-diagrams for the unit cell structures of sodium chloride and then of Cu3Au. Cu3Au alloy can be described as a simple cubic arrangement of gold atoms with copper atoms occupying face centered positions. (Look up the NaCl structure…) Sodium chloride – z-diagrams Cu3Au – z-diagrams Discussion **Briefly discuss two concepts which are now clearer to you because of this solid state modeling exercise.