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

April 14, 2020March 30, 2024 Loveth Idoko

Last Updated on March 30, 2024

To calculate the 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 (ΣA_c), Sum of atomic weights of anions (ΣA_A), Unit cell volume (V_c) and Avogadro’s number (N_A).

The formula for calculating theoretical density of ceramics:

ρ = ^{n'(ΣA_c + ΣA_A)} / _{V_cN_A}

Where:

ρ = Theoretical Density of Ceramics
n’ = Number of Formula Units in Unit Cell
ΣA_c = Sum of Atomic Weights of Atoms
ΣA_A = Sum of Atomic Weights of Anions
V_c = Unit Cell Volume
N_A = Avogadro’s Number

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
ΣA_c = Sum of Atomic Weights of Atoms = 8
ΣA_A = Sum of Atomic Weights of Anions = 10
V_c = Unit Cell Volume = 9
N_A = Avogadro’s Number = 6.02214e+23

ρ = ^{n'(ΣA_c + ΣA_A)} / _VcNA
ρ = ^{(12)(8 + 10)}/ _{(9)(6.02214e+23)}
Then, 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.

Calculating the Number of Formula Units in Unit Cell when the Theoretical Density of Ceramics, the Sum of Atomic Weights of Atoms, the Sum of Atomic Weights of Anions, the Unit Cell Volume and the Avogadro’s Number are Given

n’ = ^{p x V_cN_A} / _{(ΣA_c + ΣA_A)}

Where;

n’ = Number of Formula Units in Unit Cell
ρ = Theoretical Density of Ceramics
ΣA_c = Sum of Atomic Weights of Atoms
ΣA_A = Sum of Atomic Weights of Anions
V_c = Unit Cell Volume
N_A = Avogadro’s Number

Let’s solve an example;
Find the number of formula units in unit cell when the How to Calculate and Solve for Theoretical Density of Ceramics | Ceramics is 20, the sum of atomic weights of atoms is 12, the sum of atomic weights of anions is 10, the unit cell volume is 5 and the avogadro’s number is 6.022e+23.

This implies that;

ρ = Theoretical Density of Ceramics = 20
ΣA_c = Sum of Atomic Weights of Atoms = 12
ΣA_A = Sum of Atomic Weights of Anions = 10
V_c = Unit Cell Volume = 5
N_A = Avogadro’s Number = 6.022e+23

n’ = ^{p x V_cN_A} / _{(ΣA_c + ΣA_A)}
Then, n’ = ^{20 x 5 x 6.022e+23} / _{(12 + 10)}
n’ = ^6.022e+25 / ₍₂₂₎
n’ = 2737.72

Therefore, the number of formula units in unit cell is 2737.72.

Calculating the Sum of Atomic Weights of Atoms when the Theoretical Density of Ceramics, the Sum of Atomic Weights of Anions, the Number of Formula Units in Unit Cell, the Unit Cell Volume and the Avogadro’s Number are Given

ΣA_c = ^{p x V_cN_A} / _n’ – ΣA_A

Where;

ΣA_c = Sum of Atomic Weights of Atoms
ρ = Theoretical Density of Ceramics
n’ = Number of Formula Units in Unit Cell
ΣA_A = Sum of Atomic Weights of Anions
V_c = Unit Cell Volume
N_A = Avogadro’s Number

Let’s solve an example;
Find the sum of atomic weights of atoms when the theoretical density of ceramics is 24, the number of formula units in unit cell is 18, the sum of atomic weights of anions is 12, the unit cell volume is 8 and the avogadro’s number is 6.022e+23.

This implies that;

ρ = Theoretical Density of Ceramics = 24
n’ = Number of Formula Units in Unit Cell = 18
ΣA_A = Sum of Atomic Weights of Anions = 12
V_c = Unit Cell Volume = 8
N_A = Avogadro’s Number = 6.022e+23

ΣA_c = ^{p x V_cN_A} / _n’ – ΣA_A
ΣA_c = ^{24 x 8 x 6.022e+23} / ₁₈ – 12
So, ΣA_c = ^1.156224e+23 / ₁₈ – 12
ΣA_c = 642346.6 – 12
ΣA_c = 642334.6

Therefore, the sum of atomic weights of atoms is 642334.6.

Calculating the Sum of Atomic Weights of Anions when the Theoretical Density of Ceramics, the Sum of Atomic Weights of Atoms, the Number of Formula Units in Unit Cell, the Unit Cell Volume and the Avogadro’s Number are Given

ΣA_A = ^{p x V_cN_A} / _n’ – ΣA_c

Where;

ΣA_A = Sum of Atomic Weights of Anions
ρ = Theoretical Density of Ceramics
n’ = Number of Formula Units in Unit Cell
ΣA_c = Sum of Atomic Weights of Atoms
V_c = Unit Cell Volume
N_A = Avogadro’s Number

Let’s solve an example;
Find the sum of atomic weights of anions when the theoretical density of ceramics is 32, the number of formula units in unit cell is 2, the sum of atomic weights of atoms is 6, unit cell volume is 10 and the avogadro’s number is 6.022e+23.

This implies that;

ρ = Theoretical Density of Ceramics = 32
n’ = Number of Formula Units in Unit Cell = 2
ΣA_c = Sum of Atomic Weights of Atoms = 6
V_c = Unit Cell Volume = 10
N_A = Avogadro’s Number = 6.022e+23

ΣA_A = ^{p x V_cN_A} / _n’ – ΣA_c
ΣA_A = ^{32 x 10 x 6.022e+23} / ₂ – 6
That is, ΣA_A = ^1.92704e+25 / ₂ – 6
ΣA_A = 9.6352e-24 – 6
ΣA_A = 3.6352e-24

Therefore, the sum of atomic weights of anions is 3.6352e-24.

Calculating the Unit Cell Volume when the Theoretical Density of Ceramics, the Sum of Atomic Weights of Atoms, the Sum of Atomic Weights of Anions, the Number of Formula Units in Unit Cell and the Avogadro’s Number are Given

V_c = ^{n'(ΣA_c + ΣA_A)} / _{p x N_A}

Where;

V_c = Unit Cell Volume
ρ = Theoretical Density of Ceramics
n’ = Number of Formula Units in Unit Cell
ΣA_c = Sum of Atomic Weights of Atoms
ΣA_A = Sum of Atomic Weights of Anions
N_A = Avogadro’s Number

Let’s solve an example;
Find the unit cell volume when the theoretical density of ceramics is 10, the number of formula units in unit cell is 8, the sum of atomic weights of atoms is 3 and the sum of atomic weights of anions is 2.

This implies that;

ρ = Theoretical Density of Ceramics = 10
n’ = Number of Formula Units in Unit Cell = 8
ΣA_c = Sum of Atomic Weights of Atoms =3
ΣA_A = Sum of Atomic Weights of Anions = 2
N_A = Avogadro’s Number = 6.022e+23

V_c = ^{n'(ΣA_c + ΣA_A)} / _{p x N_A}
V_c = ^{8 (3 + 2)} / _{10 x 6.022e+23}
So, V_c = ^{8 (5)} / _{10 x 6.022e+23}
V_c = ⁴⁰ / _6.022e+24
V_c = 6.642e-23

Therefore, the unit cell volume is 6.642e-23.

How to Calculate and Solve for Theoretical Density of Ceramics Using Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the theoretical density of ceramics.

To get the answer and workings using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

Web – https://www.nickzom.org/calculator-plus

To get access to the professional version via web, you need to register and subscribe for NGN 1,500 per annum to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator

Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Materials & Metallurgical under Engineering.

Now, Click on Ceramics under Material & Metallurgical

Now, Click on Theoretical Density of Ceramics under ceramics

The screenshot below displays the page or activity to enter your values, to get the answer according to the respective parameters which are the Number of formula units in unit cell (n’), Sum of atomic weights of atoms (ΣA_c), Sum of atomic weights of anions (ΣA_A), Unit cell volume (V_c) and Avogadro’s number (N_A).

Now, enter the values appropriately and accordingly for the parameters as required by the Number of formula units in unit cell (n’) is 12, Sum of atomic weights of atoms (ΣA_c) is 8, Sum of atomic weights of anions (ΣA_A) is 10, Unit cell volume (V_c) is 9 and Avogadro’s number (N_A) is 6.022e+23.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the theoretical density of ceramics and presents the formula, workings and steps too.