materials and metallurgical

How to Calculate and Solve for Inter-atomic Spacing | Bragg’s Law

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The image above represents inter-atomic spacing.

To compute for inter-atomic spacing, three essential parameters are needed and these parameters are Order of Reflection (n), Wavelength (λ) and Angle of Diffraction (θ).

The formula for calculating inter-atomic spacing:

d = nλ/2sinθ

Where:

d = Inter-atomic Spacing
λ = Wavelength
n = Order of Reflection
θ = Angle of Diffraction

Let’s solve an example;
Find the inter-atomic spacing when the wavelength is 12, order of reflection is 4 and the angle of diffraction is 6.

This implies that;

λ = Wavelength = 12
n = Order of Reflection = 4
θ = Angle of Diffraction = 6

d = nλ/2sinθ
d = (12)(4)/2sin(6°)
d = 48/2(0.104)
d = 48/0.209
d = 229.6

Therefore, the inter-atomic spacing is 229.6 m.

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How to Calculate and Solve for Conversion of Volume Fraction to Mass Fraction | Phase Transformation

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The image above represents the conversion of volume fraction to mass fraction.

To compute for volume fraction to mass fraction, four essential parameters are needed and these parameters are α-phase Volume Fraction (Vα), β-phase Volume Fraction (Vβ), α-phase Density (ρα) and β-phase Density (ρβ).

The formula for calculating volume fraction to mass fraction:

Wα = Vαρα/(Vαρα) + (Vβρβ)

Wβ = Vβρβ/(Vαρα) + (Vβρβ)

Where:

Wα = α-phase Weight/Mass Fraction
Wβ = β-phase Weight/Mass Fraction
Vα = α-phase Volume Fraction
Vβ = β-phase Volume Fraction
ρα = α-phase Density
ρβ = β-phase Density

Let’s solve an example;
Find the conversion of volume fraction to mass fraction when the α-phase volume fraction is 4, the β-phase volume fraction is 7, the α-phase density is 11 and the β-phase density is 10.

This implies that;

Vα = α-phase Volume Fraction = 4
Vβ = β-phase Volume Fraction = 7
ρα = α-phase Density = 11
ρβ = β-phase Density = 10

Wα = (4)(11)/((4)(11)) + ((7)(10))
Wα = (44)/(44) + (70)
Wα = (44)/(114)
Wα = 0.38

Therefore, the α-phase mass fraction, Wα is 0.38.

Wβ = (7)(10)/((4)(11)) + ((7)(10))
Wβ = (70)/(44) + (70)
Wβ = (70)/(114)
Wβ = 0.614

Therefore, the β-phase mass fraction, Wβ is 0.614.

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How to Calculate and Solve for Net Force between Two Atoms | Crystal Structures

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The image above represents net force between two atoms.

To compute for net force between two atoms, two essential parameters are needed and these parameters are Attractive Force (FA) and Repulsive Force (FR).

The formula for calculating net force between two atoms:

FN = FA + FR

Where:

FN = Net Force between Two Atoms
FA = Attractive Force
FR = Repulsive Force

Given an example;
Find the net force between two atoms when the attractive force is 15 and the repulsive force is 3.

This implies that;

FA = Attractive Force = 15
FR = Repulsive Force = 3

FN = FA + FR
FN = 15 + 3
FN = 18

Therefore, the net force between two atoms is 18 N.

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How to Calculate and Solve for Planar Density | Crystal Structures

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The image above represents planar density.

To compute for planar density, two essential parameters are needed and these parameters are Number of Atoms Centered on the Plane (N) and Area of the Plane (A).

The formula for calculating planar density:

PD = N/A

Where:

PD = Planar Density
N = Number of Atoms Centered on the Plane
A = Area of the Plane

Given an example;
Find the planar density when the number of atoms centered on the plane is 24 and the area of the plane is 3.

This implies that;

N = Number of Atoms Centered on the Plane = 24
A = Area of the Plane = 3

PD = N/A
PD = 24/3
PD = 8

Therefore, the planar density is 8 atoms/m².

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