Chemistry Ch. 13 - Cubic Unit Cells

When calculating the number of atoms in a cubic unit cell, the multiplying factor for an atom on the corner of the unit cell is _____.

1/8

When calculating the number of atoms in a cubic unit cell, the multiplying factor for an atom on the face of the unit cell is _____.

1/2

When calculating the number of atoms in a cubic unit cell, the multiplying factor for an atom on the edge of the unit cell is _____.

1/4

When calculating the number of atoms in a cubic unit cell, the multiplying factor for an atom inside of the unit cell is _____.

1

Simple Cubic: Coordination Number

6

Simple Cubic: Atoms per Unit Cell

1

Simple Cubic: Edge Length in Terms of r

2r

Simple Cubic: Packing Efficiency

52%

Body-Centered Cubic: Coordination Number

8

Body-Centered Cubic: Atoms per Unit Cell

2

Body-Centered Cubic: Edge Length in Terms of r

4r/√3

Body-Centered Cubic: Packing Efficiency

68%

Face-Centered Cubic: Coordination Number

12

Face-Centered Cubic: Atoms per Unit Cell

4

Face-Centered Cubic: Edge Length in Terms of r

2√2r

Face-Centered Cubic: Packing Efficiency

74%

What is meant by a “close-packed structure” in crystalline solids?

An arrangement where layers of spheres are packed as efficiently as possible by offsetting rows to minimize gaps.

What is the difference between the AA and AB patterns in close-packed structures?

AA stacking places the second layer directly above the first, while AB stacking places the second layer over the holes of the first layer.

In close-packed structures, why is the AB pattern more efficient than the AA pattern?

Because offsetting layers reduces empty space, increasing packing efficiency.

What is the stacking pattern of hexagonal close-packed?

ABAB

What is the stacking pattern of cubic close-packed?

ABCABC

Are hcp and ccp equally efficient?

Yes — both pack 74%.

Which close-packed structure corresponds to an Face-Centered Cubic cell?

ccp

Which close-packed structure uses a hexagonal unit cell?

hcp

Which pattern repeats every 2 layers?

hcp

Which pattern repeats every 3 layers?

ccp