Presets
Playback
Instrument and sample
A neutron of wavelength lambda travels the path L in t = m L lambda / h. A powder plane spacing d scatters it through 2 theta when lambda = 2 d sin(theta), so every d appears at its own arrival time. Cubic lattices differ in which reflections are allowed.
Model checks
The science
What is modelled
A cubic powder: every set of planes (hkl) with spacing d = a / sqrt(h2+k2+l2) that the lattice type allows gives one peak at the flight time that satisfies Bragg's law at the fixed bank angle. Peak intensities use the multiplicity, a thermal-like flux factor and a Lorentz-type wavelength factor and are illustrative only; counts are drawn with Poisson noise.
Equations
- de Broglie:
lambda = h / (m v), solambda = h t / (m L)(3956 A m/s). - Bragg:
lambda = 2 d sin(theta), hencet = 2 m L d sin(theta) / h. - Energy:
E = h2 / (2 m lambda2) = 81.8 meV A2 / lambda2. - Resolution:
(Δd/d)2 = (Δt/t)2 + (Δtheta cot theta)2 + (ΔL/L)2. - Frame band:
Δlambda = h T / (m L)for pulse period T.
Checks run in the page
- de Broglie wavelength of a 2200 m/s neutron.
- Bragg round trip from flight time back to d.
- Neutron energy from speed and from wavelength.
- The (111)/(200) flight-time ratio of a face-centred lattice.
- Frame-overlap wavelength band.
Honest simplifications
Cubic lattices only, no thermal factors or absorption, simplified intensities, Gaussian peaks with a single resolution formula, a point sample and a flat background. Illustrative, not a data-reduction code.
What to try
- Press Iron (bcc) and see that fewer reflections are allowed than for a simple cubic lattice.
- Press Coarse resolution: neighbouring peaks merge.
- Raise the bank angle to 150 deg: the peaks move to short times and the resolution improves.