Table of Contents
X-ray diffraction (XRD) is a technique used to analyze the crystal structure of materials. It provides data that can be used to calculate interplanar spacings, which are distances between atomic planes in a crystal. Understanding how to interpret XRD data is essential for material characterization and analysis.
Understanding X-ray Diffraction Data
XRD data is typically presented as a diffraction pattern, showing peaks at specific angles. These peaks correspond to the diffraction of X-rays by the crystal planes. The position of each peak is related to the interplanar spacing through Bragg’s Law.
Calculating Interplanar Spacings
Bragg’s Law is the fundamental equation used to calculate interplanar spacings. It is expressed as:
nλ = 2d sin θ
Where:
- n is the order of diffraction (usually 1)
- λ is the wavelength of the X-ray
- d is the interplanar spacing
- θ is the Bragg angle (half of the diffraction angle)
Rearranging the equation to solve for d gives:
d = λ / (2 sin θ)
Applying the Calculation
To determine the interplanar spacing, measure the diffraction angle (2θ) from the pattern. Divide this angle by 2 to find θ. Use the known wavelength of the X-ray source, typically 1.54 Å for Cu Kα radiation. Plug these values into the formula to calculate d.
For example, if a peak appears at 2θ = 30°, then θ = 15°. Using λ = 1.54 Å:
d = 1.54 Å / (2 sin 15°) ≈ 1.54 Å / (2 × 0.2588) ≈ 1.54 Å / 0.5176 ≈ 2.97 Å