## How to Calculate and Solve for Normally Occupied Positions | Ceramics

The image above represents normally occupied positions.

To compute for normally occupied positions, four essential parameters are needed and these parameters are Avogadro’s number (NA), Density (ρ), Atomic weight (AK) and Atomic weights (AG).

The formula for calculating normally occupied positions:

N = NAρ / (AK + AG)

N = Normally Occupied Positions
AK, AG = Atomic Weights
ρ = Density

Let’s solve an example;
Find the normally occupied positions when the avogadro’s number is 6.022e+23, atomic weight is 12, atomic weight is 16 and the density is 10.

This implies that;

NA = Avogadro’s Number = 6.022e+23
AK, AG = Atomic Weights = 12, 16
ρ = Density = 10

N = NAρ / (AK + AG)
N = (6.022e+23)(10)/(12 + 16)
N = (6.022e+24)/(28)
N = 2.15e+23

Therefore, the normally occupied positions is 2.15e+23.

Calculating the Density when the Normally Occupied Positions, the Avogadro’s Number, the Atomic Weights is Given.

ρ = N (AK + AG) / NA

Where;

ρ = Density
N = Normally Occupied Positions
AK, AG = Atomic Weights

Let’s solve an example;
Given that normally occupied positions is 20, the avogadro’s number is 6.022e+23, atomic weights is 18, 6.

This implies that;

N = Normally Occupied Positions =20
NA = Avogadro’s Number = 6.022e+23
AK, AG = Atomic Weights = 18, 6

ρ = N (AK + AG) / NA
ρ = 20 (18 + 6) / 6.022e+23
ρ = 20 (24) / 6.022e+23
ρ = 480 / 6.022e+23
ρ = 7.970e-22

Therefore, the density is 7.970e-22.

## How to Calculate and Solve for Theoretical Density of Ceramics | Ceramics

The image above represents theoretical density of ceramics.

To compute for theoretical density of ceramics, five essential parameters are needed and these parameters are Number of formula units in unit cell (n’), Sum of atomic weights of atoms (ΣAc), Sum of atomic weights of anions (ΣAA), Unit cell volume (Vcand Avogadro’s number (NA).

The formula for calculating theoretical density of ceramics:

ρ = n'(ΣAc + ΣAA) / VcNA

Where:

ρ = Theoretical Density of Ceramics
n’ = Number of Formula Units in Unit Cell
ΣAc = Sum of Atomic Weights of Atoms
ΣAA = Sum of Atomic Weights of Anions
Vc = Unit Cell Volume

Let’s solve an example;
Find the theoretical density of ceramics when the number of formula units in unit cell is 12, the sum of atomic weights of atoms is 8, the sum of atomic weights of anions is 10, the unit cell volume is 9 and the avogadro’s number is 6.02214e+23.

This implies that;

n’ = Number of Formula Units in Unit Cell = 12
ΣAc = Sum of Atomic Weights of Atoms = 8
ΣAA = Sum of Atomic Weights of Anions = 10
Vc = Unit Cell Volume = 9
NA = Avogadro’s Number = 6.02214e+23

ρ = n'(ΣAc + ΣAA) / VcNA
ρ = (12)(8 + 10) / (9)(6.02214e+23)
ρ = (12)(18) / (5.4199e+24)
ρ = (216)/(5.4199e+24)
ρ = 3.98e-23

Therefore, the theoretical density of ceramics is 3.98e-23.