Packing of more than one type of sphere into unit cells:

- Packing of ions in salts- Which is usually larger, negative (anions) or positive

(cations) ions?

- Construct binary salts in lattice with anions usually occupying positions in unit cell and cations in holes in cell

NaCl

Space fill

How do you describe salts with more than one atom type? By unit cells and holes

C

H H

H H3 atomse clouds in plane

109.50

Tetrahedron – 4 identicalequilateral triangles

SF6

5 atoms/e clouds in plane

Octahedron – 8 identical triangles

Types of Holes

• What's a tetrahedron• What's an octahedron• Holes: Chemtube3D

• Cubic close packed / • Face-centred cubic (ccp/fcc)

• CCP and holes

Cube –

TETRAHEDRAL

OCT AHEDRAL

CUBIC

Ion in hole

SIMPLE CUBIC PACKINGHOLES

CC

CUBIC

CUBIC CLOSEST PACKING – FACE CENTERED CUBICHOLES

T

T T

TTO

O

O

tetrahedraloctahedral

Unit Cell Packing Eff Coord # Holes ≈ Hole Size (r=1),

Simple Cubic

0.52 6 cubic 0.732-1.00

Face centered

0.74 124

OctahedralTetrahedral

0.414-0.7320.225-.0.414

O

Example: NaCl (Jmol)

Cl- Na+

x

y

z

z=0

z=0.5

z=1

Tetrahedral Holes• How many tetrahedral holes are there in the

fcc unit cell?• Are there any Na+ ions occupying the holes?

Bottom face

Top face

Octahedral Holes• How many octahedral holes are there in one

fcc unit cell?• In what type of holes are Na+ ions in edges

throughout the whole lattice?

• What type of unit cell is defined by the Cl- ions?

Example: Nickel Arsenide (this Jmol link shows lattice based on Ni as in workbook pg 49, #4)

Unit cell: hexagonal closest packingOf Arsenide with Ni in what holes?

Z=0

Z=0.25

Z=0.5

Z=0.75

A

B

Hexagonal Closest Packing

• In what type of hole is Ni found in the structure above

• How many As are in the unit cell to the right? How many Ni?

• What is the formula for nickel arsenide?

• Locate a tetrahedral hole? Are there any Ni ions there?

Z=1 AArsenide

Nickel

Determining the empirical formula from unit cell data:

A salt must be electrically neutral. If you know the charge on the cations and anions, you can determine MxNy.

Alternatively, you can use crystal data to determine the structure of the unit cell and hence the empirical formula. Determine the number of each different ion in the following unit cells. Does it correspond to the formula from charge balance?

1. Copper (I) chloride

2. Barium Chloride

3. Rhenium oxide

4. Based on Cl- alone, what type of unit cell is this? What type of “hole” is occupied by Cu+?

Cu

Cl

Examples from Chemtube3D