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Beam and crystal
Slow neutrons have wavelengths of a few angstroms, the same as atomic spacings, so crystals diffract them. A reflection appears only when n times the wavelength does not exceed twice the plane spacing.
Model checks
The science
What is modelled
A monoenergetic neutron beam of kinetic energy E meets a set of parallel lattice planes. The de Broglie wavelength follows from the neutron speed, and the Bragg condition fixes the angle at which the planes reflect the beam. The scattering triangle shows the incident and final wave vectors and their difference, the momentum transfer Q.
Equations
v = √(2E/mn),λ = h / (mn v), soE[meV] = 81.80 / λ[Å]².- Bragg:
n λ = 2 d sin θ, scattering angle2θ. Q = 4 π sin θ / λ = 2 π n / d; elastic:|ki| = |kf| = 2π/λ.- Time of flight over a path L:
t = L / v.
Checks run in the page
- Thermal neutron: 25.3 meV gives 2200 m/s and 1.798 A.
- The energy-wavelength constant 81.80 meV A^2.
- Q from the Bragg angle equals 2 pi n / d.
- Closure of the scattering triangle for elastic scattering.
Honest simplifications
A single ideal crystal and a perfectly monochromatic, collimated beam. There is no mosaic spread, energy resolution, structure factor, absorption, inelastic scattering or detector efficiency, and the time of flight is for free flight without moderator pulse width.
What to try
- Press Cold neutron: the longer wavelength gives a larger Bragg angle.
- Press No reflection: when the wavelength exceeds 2d the beam is not diffracted.
- Press Second order and compare the angle with the first order.