materials and metallurgical

How to Calculate and Solve for Linear Density | Crystal Structures

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The image above represents linear density.

To compute for linear density, two essential parameters are needed and these parameters are Number of Atoms Centered on Direction Vector (N) and Length of Direction Vector (L).

The formula for calculating linear density:

LD = N/L

Where:

LD = Linear Density
N = Number of Atoms Centered on Direction Vector
L = Length of Direction Vector

Given an example;
Find the linear density when the number of atoms centered on direction vector is 10 and the length of direction vector is 2.

This implies that;

N = Number of Atoms Centered on Direction Vector = 10
L = Length of Direction Vector = 2

LD = N/L
LD = 10/2
LD = 5

Therefore, the linear density is 5 atoms/m.

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How to Calculate and Solve for Hexagonal Crystals | Crystal Structures

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The image above represents hexagonal crystals.

To compute for hexagonal crystals, two essential parameters are needed and these parameters are Miller Index (h) and Miller Index (k).

The formula for calculating hexagonal crystals:

i = -(h + k)

Where:

i = Hexagonal Crystals
h = Miller Index
k = Miller Index

Given an example;
Find the hexagonal crystals when the miller index is 22 and the miller index is 11.

This implies that;

h = Miller Index = 22
k = Miller Index = 11

i = -(h + k)
i = -(22 + 11)
i = -(33)
i = -33

Therefore, the hexagonal crystals is -33.

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How to Calculate and Solve for Theoretical Density of Metals | Crystal Structures

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The image above represents theoretical density of metals.

To compute for theoretical density of metals, four essential parameters are needed and these parameters are Number of Atoms Associated in the Cell (n), Atomic Weight (A), Volume of Unit Cell (Vc) and Avogadro’s Number (NA).

The formula for calculating theoretical density of metals:

ρ = nA/VcNA

Where:

ρ = Theoretical Denity of the Metal
n = Number of Atoms Associated in the Cell
A = Atomic Weight
Vc = Volume of Unit Cell
NA = Avogadro’s Number

Let’s solve an example;
Find the theoretical density of the metal when the number of atoms associated in the cell is 3, the atomic weight is 6, the volume of unit cell is 2 and the avogadro’s number is 6.022e+24.

This implies that;

n = Number of Atoms Associated in the Cell = 3
A = Atomic Weight = 6
Vc = Volume of Unit Cell = 2
NA = Avogadro’s Number = 6.022e+24

ρ = nA/VcNA
ρ = (3)(6)/(2)(6.0221e+23)
ρ = (18)/(1.20442e+24)
ρ = 1.49

Therefore, the theoretical density of metals is 1.49 m.

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How to Calculate and Solve for Unit Cell Edge Length | Crystal Structures

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The image above represents unit cell edge length.

To compute for unit cell edge length, one essential parameter is needed and this parameter is Radius of an Atom (R).

The formula for calculating unit cell edge length:

a = 4R/√(3)

Where:

a = Unit Cell Edge Length, BCC
R = Radius of the atom

Given an example;
Find the unit cell edge length when the radius of the atom is 6.

This implies that;

R = Radius of the atom = 6

a = 4R/√(3)
a = 4(6)/√(3)
a = 24/1.73
a = 13.85

Therefore, the unit cell edge length is 13.85 m.

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