Unit Cell of Crystal StructureUnit Cell of Crystal Structure

# Definition of “Unit Cell”:

AL Chemistry

p. 1

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)]

Common Types of Unit CellCommon Types of Unit Cell# 2 common types for Ionic Crystals … AL Chemistry

p. 2

Face-centered Cubicclosed packed (fcc)

Simple Cubicclosed packed (sc)

Counting Ions in a Unit CellCounting Ions in a Unit Cell

p. 3

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

total no. = 4

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at corners = 8(1/8) = 1

along edges = 0

in faces = 0

at cubic centre = 0

total no. = 1

SCFCC

Generating of entire LatticeGenerating of entire Lattice

p. 4

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Ionic CrystalsIonic Crystals

the 3-dimensional arrangement of ions.

** General Bonding considerations

The bonding forces should be maximized by packing as many cations around each anion, andas many cations around each anion as is possible.

but it depends on the relative size of cation and anion.

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p. 5

To visualize the structures in terms of a closed packed arrangement of the larger anions (FCC or SC),

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p. 6

How do the anion and cationpack together?

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.

anions are packed in form

of “FCC”

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p. 7

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”

governed by the “radius ratio” of cation and anion !

Stacking of two closed packed anion layers produces2 types of “holes”.

p. 8

Types of “cation site” (holes) availablein closed packed anions arrays:

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(a) octahedral hole ---- coordinated by 6 anions

(b) tetrahedral hole ---- coordinated by 4 anions

p. 9

“Stuffing” the holes by Cations:

AL ChemistryOctahedral or Tetrahedral hole?► determined by the radius ratio (= rcation / ranion)

[radius ratio rule]

FCC (for small cations)

SC

p. 10

Stable Bonding Configuration :AL Chemistry

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. 11

AL Chemistry# If the cation is too small …

► cation would not be in contact with the surrounding anion. repulsion between anions UNSTABLE!

p. 12

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

# “O” – octahedral hole : The unit cell has 4 octahedral sites.

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# “T” – tetrahedral hole : The unit cell has 8 tetrahedral sites.

p. 13

Example 1: Sodium Chloride (NaCl)

radius: Na+ = 1.02nm, Cl- = 1.81nmAL Chemistry

radius ratio = 0.563 FCC

4 Cl- packed in FCC,Na+ will fit into the

octahedral hole of the anion arrays.

Cl-

Na+

Cl-

Na+

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. 14

Example 2: Zinc Blende (ZnS)

radius: Zn2+ = 0.60nm, S2- = 1.84nm AL Chemistry

radius ratio = 0.330 FCC

4 S2- packed in FCC,Zn2+ will fit into the tetrahedral hole of the anion arrays.

Since stiochiometry ofcation 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. 15

Example 3: Cesium Chloride (CsCl)

radius: Cs+ = 1.74nm, Cl- = 1.81nmAL Chemistry

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. 16

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8:8 coordination !

Simple Cubic closed packed (SC)

Cl-

Cs+

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!

Each unit cell has 8 anionsand 8 cubic centre sites.

p. 17

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Cl-

Cs+

Two Inter-penetrating Lattices in CsCl:

unit cell of CsClunit cell of CsCl

p. 18

Practice: Calcium Fluoride (CaF2)

radius: Ca2+ = 1.12nm, F- = 1.31nm AL Chemistry

radius ratio = 0.850

Simple Cubic (SC) closed packed

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!

Each unit cell has 8 anionsand 8 cubic centre sites.

p. 19

(CaF2)

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Coordination no.: each Ca2+ surrounded by 8 F-,each F- surrounded by 4 Ca2+.

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p. 20

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”

Conclusion …..Conclusion …..

e.g. NaCl

e.g. ZnS

e.g. CsCl, CaF2