x-ray diffraction

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.

The image above represents distance of inter-atomic spacing.

To compute for distance of inter-atomic spacing, four essential parameters are needed and these parameters are Unit Cell Edge Length (a), Miller Index (h), Miller Index (k) and Miller Index (l).

The formula for calculating distance of inter-atomic spacing:

d = ^a/_{√(h² + k² + l²)}

Where:

d = Inter-atomic Spacing
a = Unit Cell Edge Length
h = Miller Index
k = Miller Index
l = Miller Index

Given an example;
Find the distance of inter-atomic spacing when the unit cell edge length is 4, the miller index is 2, the miller index is 3 and the miller index is 6.

This implies that;

a = Unit Cell Edge Length = 4
h = Miller Index = 2
k = Miller Index = 3
l = Miller Index = 6

d = ^a/_{√(h² + k² + l²)}
d = ⁴/_{√(2² + 3² + 6²)}
d = ⁴/_{√(4 + 9 + 36)}
d = ⁴/_√(49)
d = ⁴/₇
d = 0.571

Therefore, the distance of inter-atomic spacing is 0.571 m.

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

How to Calculate and Solve for Distance of Inter-atomic Spacing | X-Ray Diffusion