How does an ideal diffraction angle respond to spacing?
Bragg’s condition is 2d sinθ = nλ. With first order n = 1 and an authored wavelength λ = 1.54 Å, d = 2.00 Å gives calculated 2θ ≈ 45.29°, while d = 3.00 Å gives about 29.74°. The angle displayed on a powder scan is commonly 2θ.
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EXPLORE THE MODEL
Repeating planes and a diffraction condition
Inspect the structure; select a site or component for its label.
What this representation means
Illustrative plane spacing; this is not a measured mineral pattern. One angle cannot identify a mineral. Intensities, atomic basis, texture and peak widths are omitted.
- Interplane separation
- 0.3 nm
- Within-plane spacing
- Illustrative, not calibrated
- Atomic identities
- Unspecified in this geometric model
nλ = 2d sin θ; n = 1
Read sampled numerical values
| Plane spacing d (nm) | Allowed 2θ |
|---|---|
| 0.12 | 79.83 |
| 0.155 | 59.57 |
| 0.19 | 47.82 |
| 0.225 | 40.02 |
| 0.26 | 34.45 |
| 0.295 | 30.26 |
| 0.33 | 26.99 |
| 0.365 | 24.36 |
| 0.4 | 22.2 |
| 0.435 | 20.39 |
| 0.47 | 18.86 |
| 0.5 | 17.72 |
The displayed planes are separated by the chosen d. θ is the angle to a plane; instruments commonly report the scattering angle 2θ. Different structures can share a spacing, so this condition alone cannot identify a mineral.
What this model can establish
Illustrative plane spacing; this is not a measured mineral pattern. One angle cannot identify a mineral. Intensities, atomic basis, texture and peak widths are omitted.
Optional: check your understanding
MAKE THE CONNECTION
At fixed λ and n, increasing d has which effect on the allowed θ?
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HISTORY THROUGH EVIDENCE
Bragg turned patterns into structure
W. L. Bragg’s recollections describe testing sodium chloride and potassium chloride crystals in late 1912 and early 1913.
Explore how the evidence changed the explanation →