Lattice Layout

Unit Cells & 3D Coordinate Geometry

NAME:

01 Atom Contribution Theory

In a repeating crystal lattice, atoms are shared between neighboring unit cells. Use the rules below to calculate the total number of atoms per unit cell.

Corner Atom

1/8

Shared by 8 cells

Face Atom

1/2

Shared by 2 cells

Body Atom

1

Wholly inside 1 cell

Lattice Type	Calculation (Corners + Faces + Body)	Total Atoms
Simple Cubic (SC)	Example: (8 corners × 1/8) = 1 atom	1
Body-Centered (BCC)
Face-Centered (FCC)

02 Coordinate Mapping

Identify the fractional coordinates (x, y, z) for the specified positions in a cubic unit cell of side length 1.

A

Origin Corner

(

,

,

)

B

Body-Center Position

(

,

,

)

C

Center of the Top Face

(

,

,

)

A

B

C

Z

Y

03 Lattice Comparison

Predict which cubic lattice (SC, BCC, or FCC) would result in the highest density material if the same type of atom was used for all three. Justify your answer using the concept of atom packing.

Lattice Layout Activity Worksheet

Lattice Layout Activity Worksheet