Simple Cubic Structure

Simple Cubic (SC) Structure

• The simplest crystal structure

• Atoms are located only at the eight corners of each cube

• Atoms in one layer are directly above atoms in the layer below

Primitive Cubic Unit Cell

• Another name for the Simple Cubic Unit Cell.

• Called so because lattice points exist only at the cube's corners

• Contains the smallest repeating arrangement of a simple cubic crystal

Simple Cubic Unit Cell

• A cubic unit cell with atoms located only at the eight corners

• No atoms are present at the faces or center

• Repeating this cube in all directions forms the crystal

Simple Cubic Lattice

• A crystal lattice where every lattice point occupies one corner of a cube.

• Produces the simplest three-dimensional repeating pattern

Corner Atom

An atom located at one of the eight corners of a unit cell. Therefore, each corner atom contributes only 1/8 atom to one unit cell

Edge Length

The length of one side of the cubic unit cell

r

Symbol to represent the atomic radius

a

Symbol to represent the edge length

a = 2*r

Formula to calculate the edge length

Atomic Radius (SC)

Half the distance between the centers of two adjacent touching atoms

r = a/2

Formula to calculate the atomic radius

Coordination Number (SC)

• The number of nearest neighboring atoms touching one atom

• In a Simple Cubic crystal:

  • Four neighbors are in the same layer

  • One neighbor is directly above

  • One neighbor is directly below

6

Provide the Coordination number for the Simple Cubic Structure

Packing Efficiency (SC)

Percentage of the unit-cell volume occupied by atoms

52%

Provide the packing efficiency inside the simple cubic structure

48%

Approximately how much of the space inside the simple cubic structure is empty?

Atom per unit cell = 8×(1/8) = 1

Atom per unit cell calculation formula for a simple cubic unit cell

Polonium (Po)

The only common element that naturally crystallizes in a Simple Cubic structure

84

Atomic number of polonium

Along the edges of the cube

Where do atoms touch in a Simple Cubic crystal?

The cube edge

Which direction is used to calculate the atomic radius in SC?

Yes, it is true

Is it true that the Simple cubic structure has the lowest packing efficiency?

Because atoms occupy only 52% of the available volume, leaving large empty spaces.

Why is the Simple Cubic structure considered inefficient?

Simple Cubic Structure and Neighboring Atoms Diagram

Lattice Points

(1)

Simple cubic lattice cell

(2)

8 corners

(3)