X-ray calculator.
Set the beam energy once and every calculator below follows it. Results update as you type; tap a result to copy it. The full offline set, with a beamtime logbook, is at xray.ooguy.com.
Beam
Bragg angle, q and d-spacing
Type any one of the three; the others follow. Change the energy and d stays put while 2θ moves.
λ = 2d sin θ and q = 4π sin θ / λ = 2π / d. For reflectivity, θ is the grazing angle and q = qz.
Beam footprint
Check whether the beam spills past the sample at low angle.
L = h / sin α. Below the angle where sin α = h / sample length, part of the beam misses the sample and the measured intensity drops.
Transmission
How much beam gets through a filter, a window or the sample.
T = exp(−t / ℓ). Look the attenuation length up for your material and energy in the CXRO tables.
Film thickness from Kiessig fringes
Enter the spacing between neighbouring fringes on a reflectivity curve.
t = 2π / Δq. Δ2θ is converted with the small-angle form Δq ≈ 2π Δ2θ / λ. Fringes just above the critical angle are stretched by refraction, so read the spacing further out in q.
Crystallite size (Scherrer)
Estimate crystallite size from the width of a diffraction peak.
τ = K λ / (β cos θ), with β in radians. Subtract the instrument width first; strain broadening makes the size come out too small.