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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.

								
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