Unit Cell of Crystal Structure 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 together in three dimensions , can generate the entire crystal structure. [2003 Paper I, Q.4(b)] p. 1

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

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

Generating of entire Lattice AL Chemistry Generating of entire Lattice p. 4

Ionic Crystals ** General Bonding considerations 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

How do the anion and cation pack together? AL Chemistry How do the anion and cation pack 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

if the cation is not small AL Chemistry Closed packed of Anions & Cation: if the cation is small if the cation is not small anions are packed in form of “FCC” anions are packed in form of “SC” 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

AL Chemistry Types of “cation site” (holes) available in 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

FCC (for small cations) 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

Stable Bonding Configuration : 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

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

Holes available in “FCC” unit cell closed packed of anions: 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

Example 1: Sodium Chloride (NaCl) AL Chemistry 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 of cation and anion = 1:1, 4 Na+ ions fit into the cell. i.e. all the octahedral sites are occupied! 6:6 coordination ! Cl- Na+ Cl- Na+ p. 13

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

Example 3: Cesium Chloride (CsCl) 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

8:8 coordination ! Simple Cubic closed packed (SC) Cl- Cs+ AL Chemistry Simple Cubic closed packed (SC) Each unit cell has 8 anions and 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! Cl- Cs+ 8:8 coordination ! p. 16

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

Practice: Calcium Fluoride (CaF2) 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 anions and 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

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

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