Unit Cell of Crystal Structure

1. AL Chemistry Unit Cell of Crystal Structure # Definition of “Unit Cell”: A unit cell is the smallest basic portion of the crystal lattice that, repeatedly stacked togetherin three dimensions, can generate the entire crystal structure. [2003 Paper I, Q.4(b)] p. 1

2. AL Chemistry Common Types of Unit Cell # 2 common types for Ionic Crystals … Face-centered Cubicclosed packed (fcc) Simple Cubicclosed packed (sc) p. 2

3. AL Chemistry at corners = 1/8 along edges = 1/4 in faces = 1/2 at corners = 8(1/8) = 1 at corners = 8(1/8) = 1 along edges = 0 along edges = 0 at cubic centre = 1 in faces = 0 in faces = 6(1/2) = 3 at cubic centre = 0 at cubic centre = 0 Counting Ions in a Unit Cell SC FCC general principle: total no. = 1 total no. = 4 p. 3

4. AL Chemistry Generating of entire Lattice p. 4

5. AL Chemistry Ionic Crystals  the 3-dimensional arrangement of ions. ** General Bonding considerations The bonding forces should be maximized by packing as many cations around each anion, and as many cations around each anion as is possible. but it depends on the relative size of cation and anion. p. 5

6. AL Chemistry How do the anion and cationpack together? To visualize the structures in terms of a closed packed arrangement of the larger anions (FCC or SC), with the cations occupying the vacant sites between the close packed layers. The number of nearest neighbor ions of opposite charge is called the coordination number. p. 6

7. AL Chemistry if the cation is small if the cation is not small Closed packed of Anions & Cation: anions are packed in form of “SC” anions are packed in form of “FCC” cations fill into “tetrahedral holes” cations fill into the “cubic centre site” cations fill into “octahedral holes” governed by the “radius ratio” of cation and anion! p. 7

8. AL Chemistry Types of “cation site” (holes) availablein closed packed anions arrays: Stacking of two closed packed anion layers produces 2 types of “holes”. (a) octahedral hole ---- coordinated by 6 anions (b) tetrahedral hole ---- coordinated by 4 anions p. 8

9. AL Chemistry “Stuffing” the holes by Cations: Octahedral or Tetrahedral hole? ► determined by the radius ratio (= rcation / ranion) [radius ratio rule] SC FCC (for small cations) p. 9

10. AL Chemistry Stable Bonding Configuration : For a stable coordination, the bonded cation and anion must be in contact with each other. # If the cation is larger than the ideal radius ratio … ► the cation and anion remain in contact, but the cation forces the anion apart.  STABLE! p. 10

11. AL Chemistry # If the cation is too small … ► cation would not be in contact with the surrounding anion.  repulsion between anions  UNSTABLE! p. 11

12. AL Chemistry Holes available in “FCC” unit cell closed packed of anions: # “O” – octahedral hole : The unit cell has 4 octahedral sites. # “T” – tetrahedral hole : The unit cell has 8 tetrahedral sites. p. 12

13. AL Chemistry Cl- Na+ Na+ Cl- Example 1: Sodium Chloride (NaCl) radius: Na+ = 1.02nm, Cl- = 1.81nm radius ratio = 0.563  FCC 4 Cl- packed in FCC,Na+ will fit into the octahedral hole of the anion arrays. Since stiochiometry ofcation and anion = 1:1,4 Na+ ions fit into the cell.i.e. all the octahedral sites are occupied! 6:6 coordination ! p. 13

14. AL Chemistry S2- Zn2+ Example 2: Zinc Blende (ZnS) radius: Zn2+ = 0.60nm, S2- = 1.84nm radius ratio = 0.330  FCC Since stiochiometry ofcation and anion = 1:1,4 Zn2+ ions fit into the cell.i.e. half the tetrahedral sites are occupied! 4 S2- packed in FCC,Zn2+ will fit into the tetrahedral hole of the anion arrays. 4:4 coordination ! # (Cations fills in the diagonally opposite sites to minimize repulsion.) p. 14

15. AL Chemistry Example 3: Cesium Chloride (CsCl) radius: Cs+ = 1.74nm, Cl- = 1.81nm radius ratio = 0.960  SC ► Anions occupy the corners of a unit cell, the centre of the cube is larger than the tetrahedral and octahedral sites, therefore the large Cs+ ion can fit in. p. 15

16. AL Chemistry Cl- Cs+ Simple Cubic closed packed (SC) Each unit cell has 8 anionsand 8 cubic centre sites. Since stiochiometry of cation and anion = 1:1,8 Cs+ ions will fit into the cell.i.e. all the cubic center sites are occupied! 8:8 coordination ! p. 16

17. AL Chemistry unit cell of CsCl Cl- Cs+ Two Inter-penetrating Lattices in CsCl: p. 17

18. AL Chemistry Practice: Calcium Fluoride (CaF2) radius: Ca2+ = 1.12nm, F- = 1.31nm radius ratio = 0.850 Simple Cubic (SC) closed packed Each unit cell has 8 anionsand 8 cubic centre sites. Since stiochiometry of cation and anion = 1:2,only 4 Ca2+ ions will fit into the cell.i.e. half the cubic center sites are occupied! p. 18

19. AL Chemistry (CaF2) Coordination no.: each Ca2+ surrounded by 8 F-, each F- surrounded by 4 Ca2+. p. 19

20. AL Chemistry Closed packed of Anions & Cation: if the cation is small if the cation is not small anions are packed in form of “SC” anions are packed in form of “FCC” cations fill into “tetrahedral holes” cations fill into the “cubic centre site” cations fill into “octahedral holes” Conclusion ….. e.g. ZnS e.g. CsCl, CaF2 e.g. NaCl p. 20