Interactive Bragg's Law Calculator
How to Use This Calculator
This calculator uses Bragg's Law (nλ = 2d sinθ) to determine parameters related to X-ray diffraction from crystal lattices.
- Select which variable you want to calculate: Bragg Angle (θ), Interplanar Spacing (d), or Wavelength (λ).
- Enter the order of diffraction (n), which must be a positive integer (e.g., 1, 2, 3...).
- Enter the known values for the other two parameters, selecting appropriate units for wavelength and spacing.
- If providing the Bragg Angle, enter it in degrees.
- Click the "Calculate" button.
- Results, including the calculated variable, maximum diffraction order, and a step-by-step solution, will be displayed.
Theory: Bragg's Law
Bragg's Law, formulated by Sir William Lawrence Bragg and Sir William Henry Bragg in 1913, describes the condition for constructive interference of X-rays scattered by crystal planes. When X-rays strike a crystal, they are scattered by the atoms in the crystal lattice. If the scattered waves interfere constructively, a diffracted beam is observed at a specific angle.
The law states that constructive interference occurs when the path difference between X-rays reflecting from successive crystal planes is an integer multiple of the X-ray wavelength. The path difference is 2d sin(θ), where 'd' is the spacing between the crystal planes and 'θ' is the glancing angle (Bragg angle) between the incident X-ray beam and the crystal planes.
Bragg's Law is fundamental in X-ray crystallography and solid-state physics for determining crystal structures, identifying materials, and measuring atomic spacing.
Formulas Used
Bragg's Law:
nλ = 2d sin(θ)
n= Order of diffraction (a positive integer: 1, 2, 3, ...)λ(lambda) = Wavelength of the X-rays (e.g., in meters, Angstroms)d= Interplanar spacing (distance between crystal planes)θ(theta) = Bragg angle (glancing angle) of incidence and diffraction
Rearranged forms for calculation:
- To find θ:
sin(θ) = nλ / (2d)=>θ = arcsin(nλ / (2d)) - To find d:
d = nλ / (2 sin(θ)) - To find λ:
λ = 2d sin(θ) / n
Maximum order of diffraction (nmax): nmax = floor(2d / λ) (since sin(θ) ≤ 1)