Bragg's Law Calculator
Calculate diffraction angles for X-ray crystallography using Bragg's law
Common X-ray wavelengths: Cu Kα = 154 pm, Mo Kα = 71 pm
Interplanar spacing in the crystal
Usually 1 for first-order diffraction
How to Use This Calculator
Enter the Wavelength
Input the wavelength of the X-rays in meters. Common X-ray sources use Cu Kα (154 pm = 0.000000000154 m) or Mo Kα (71 pm = 0.000000000071 m).
Enter the Lattice Spacing
Input the interplanar spacing (d) between crystal planes in meters. Typical values range from 0.1 to 1 nanometer (0.0000000001 to 0.000000001 m).
Enter the Diffraction Order
Input the order of diffraction (usually 1 for first-order diffraction). Higher orders (2, 3, etc.) produce diffraction at different angles.
Calculate
Click the "Calculate Bragg Angle" button to get the diffraction angle in degrees and radians.
Formula
nλ = 2d sin(θ)
Where:
- n = Order of diffraction (1, 2, 3, ...)
- λ = Wavelength of the X-rays (in meters)
- d = Interplanar spacing (lattice spacing) in meters
- θ = Bragg angle (angle between incident X-rays and crystal planes, in degrees or radians)
Solving for θ:
θ = arcsin(nλ / (2d))
Example Calculation:
For Cu Kα X-rays (λ = 154 pm) diffracting from a crystal with d = 200 pm spacing:
λ = 0.000000000154 m (154 pm)
d = 0.0000000002 m (200 pm)
n = 1 (first order)
sin(θ) = (1 × 0.000000000154) / (2 × 0.0000000002) = 0.385
θ = arcsin(0.385) = 22.6°
About Bragg's Law Calculator
Bragg's law is a fundamental principle in X-ray crystallography that describes the conditions for constructive interference when X-rays are scattered by crystal planes. Discovered by William Lawrence Bragg and his father William Henry Bragg in 1913, this law is essential for determining crystal structures and understanding how X-rays interact with crystalline materials. The law relates the wavelength of X-rays, the spacing between crystal planes, and the angle at which diffraction occurs.
When to Use This Calculator
- X-ray Crystallography: Calculate diffraction angles for crystal structure determination
- Material Science: Analyze crystal structures and lattice parameters
- Research: Plan X-ray diffraction experiments and determine optimal angles
- Education: Understand the principles of X-ray diffraction and crystal structures
- Quality Control: Verify crystal structures and detect defects in materials
Why Use Our Calculator?
- ✅ Instant Results: Get accurate Bragg angles immediately
- ✅ Easy to Use: Simple interface requiring wavelength, spacing, and order
- ✅ Multiple Units: Results displayed in both degrees and radians
- ✅ Validation: Checks for physically meaningful values
- ✅ Educational: Includes formula explanations and worked examples
- ✅ 100% Free: No registration or payment required
Common Applications
Crystal Structure Determination: X-ray crystallographers use Bragg's law to determine the three-dimensional structure of crystals. By measuring diffraction angles, they can calculate interplanar spacings and reconstruct the crystal lattice.
Material Analysis: Engineers and scientists use X-ray diffraction to identify unknown materials, analyze phase composition, and study crystal defects. Bragg's law helps them interpret diffraction patterns.
Drug Discovery: Pharmaceutical researchers use X-ray crystallography to determine the structure of proteins and drug molecules, which is crucial for understanding drug-target interactions and designing new medications.
Tips for Best Results
- Use consistent units (meters for both wavelength and spacing)
- Common X-ray wavelengths: Cu Kα = 154 pm, Mo Kα = 71 pm, Cr Kα = 229 pm
- Remember that sin(θ) cannot exceed 1, so nλ/(2d) ≤ 1 must be satisfied
- For most applications, first-order (n=1) diffraction is most commonly used
- Typical lattice spacings range from 0.1 to 1 nm for most crystals
Frequently Asked Questions
What is Bragg's law used for?
Bragg's law is used in X-ray crystallography to determine crystal structures. It relates the angle at which X-rays are diffracted by crystal planes to the spacing between those planes and the X-ray wavelength. This information is essential for understanding the atomic structure of materials.
Why do we need the diffraction order (n)?
The diffraction order represents how many wavelengths of path difference occur between X-rays scattered from different crystal planes. First-order (n=1) diffraction is most common, but higher orders (n=2, 3, etc.) also occur at different angles and provide additional information about the crystal structure.
What happens if sin(θ) > 1?
If the calculated sin(θ) exceeds 1, it means the combination of wavelength, spacing, and order is physically impossible. This occurs when nλ > 2d. No diffraction will occur for that combination, so you need to use a shorter wavelength, larger spacing, or lower order.
Can Bragg's law be used for other types of radiation?
While Bragg's law was developed for X-rays, similar principles apply to electron diffraction and neutron diffraction. However, the specific formulas and applications may differ slightly for these other types of radiation.
What's the difference between Bragg's law and the general diffraction formula?
Bragg's law is a specific application of the general diffraction condition for crystal planes. It simplifies the general case by considering the specific geometry of crystal planes and the path difference between waves scattered from adjacent planes.