Bragg's Law Calculator
The (110) peak of α-iron at 2θ = 44.67° with Cu Kα radiation gives an interplanar spacing of 2.02699 Å and a lattice parameter of 2.867 Å.
2.02699182015695 Å
Full answer, then cut to fewer decimals (not rounded):
- 2.02699182015695 Å
- 2.0269918201569 Å
- 2.026991820156 Å
- 2.02699182015 Å
- 2.0269918201 Å
- 2.026991820 Å
- 2.02699182 Å
- 2.0269918 Å
- 2.026991 Å
- 2.02699 Å
- 2.0269 Å
- 2.026 Å
- 2.02 Å
- 2.0 Å
- Cubic lattice parameter a = d√(h² + k² + l²) for (110)
- 2.866599323 Å
- θ
- 22.335 °
- h² + k² + l²
- 2
Step-by-step solution
- nλ = 2d sin θ → d = 1 × 1.5406 ÷ (2 sin 22.335°) = 2.02699182 Å
- a = d √2 = 2.866599323 Å
Bragg's Law Formula
nλ = 2d sin θ, d = a/√(h² + k² + l²)
Cu Kα₁ λ = 1.5406 Å; cubic crystals
Worked Example
The (110) peak of α-iron at 2θ = 44.67° with Cu Kα radiation:
- nλ = 2d sin θ → d = 1 × 1.5406 ÷ (2 sin 22.335°) = 2.02699182 Å
- a = d √2 = 2.866599323 Å
θ: 22.335 ° · h² + k² + l²: 2
GATE tip
For cubic crystals sin²θ ∝ h² + k² + l². The ratio of sin²θ values of successive peaks (2, 4, 6… for BCC; 3, 4, 8… for FCC) identifies the lattice.
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ρ = nA / (V_c Nₐ)
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Example: α-iron, body-centred cubic with a = 2.8665 Å: Theoretical density ρ = 7.87422 g/cm³.
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N = 2^(G − 1) grains/in² at 100×
G = −6.6439 log₁₀ ℓ − 3.288 (ℓ in mm); grains per mm² = 2^(G + 2.954)
Example: A micrograph showing 64 grains per square inch at 100×: ASTM grain size number G = 7.
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r* = 2γ/ΔG_v, ΔG* = 16πγ³/(3ΔG_v²)
ΔG_v = ΔH_f ΔT / T_m; heterogeneous S(θ) = (2 + cos θ)(1 − cos θ)²/4
Example: Copper solidifying with 200 K of undercooling: Critical radius r* = 1.27854 nm.
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σ_y = σ₀ + k_y / √d
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Example: Mild steel (σ₀ = 70 MPa, k_y = 0.74 MPa·m^½) with 25 µm grains: Yield strength σ_y = 218 MPa.
Frequently asked questions
Which reflections appear for BCC and FCC?
BCC: h + k + l even (110, 200, 211…). FCC: h, k, l all odd or all even (111, 200, 220…). Simple cubic shows all.
Why is θ half of the measured angle?
Diffractometers record 2θ, the angle between the incident and diffracted beams; Bragg’s law uses θ, the angle to the planes.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Bragg's Law Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/braggs-law-calculator/
IEEE
Scientific Converters, "Bragg's Law Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/braggs-law-calculator/