Q1(c). Accuracy at high diffraction angle

Answer in brief

For a fixed small angular error, |δ d|/d=|cot θ δθ|, which decreases as θ approaches 90°.

Key points

• From Bragg' s law, d=nλ/(2sin θ). With wavelength fixed, logarithmic differentiation gives dd/d=-cot θ dθ.
• In a cubic crystal a=d√(h²+k²+l²), so the relative error in a equals that in d for a known reflection.
• At higher Bragg angle, cot θ is smaller and the same angular uncertainty produces a smaller relative lattice-parameter uncertainty.
• This concerns angular-error propagation; wavelength calibration, specimen displacement and instrumental systematics still require correction.