Neutron Scattering

scattered beam behind the sample, the energy resolution AE/E of a 2-axes diffractometer is
not well defmed (typically of the order of some %) . In addition to the dominant elastic
scattering also quasi-elastic and some inelastic scattering contributions are to be taken into
account. The narre 2-axes-diffractometer results from its two axes of rotation, the
monochromator axis defining 20m and the sample axis (20) .
In the case of energy dispersive diffraction, the time-of-flight diffractometer uses the
complete energy spectrum of a pulsed neutron beam and the wavelengths of the scattered
neutrons are determined by velocity analysis . The measurement ofthe neutron intensity as a
function of velocity at fixed scattering angle 20 has to be calibrated according to the energy
spectrum of the neutron beam. Assuming no energy transfer at the sample the time-of-flight
diffraction yields again I(Q) (and for a polycrystalline sample I( I Q 1 ) .
7 .2 Reciprocal lattice and Ewald construction
Bragg scattering (diffraction) means coherent elastic scattering of a wave by a crystal . The
experimental information consists of the scattering function S(Q,ca = 0) with no change of
energy or wavelength of the diffracted beam . For an ideal crystal and an infmite lattice with
the basis vectors a,, 22, a 3 , there is only diffraction intensity 1(H) at the vectors
H = hai*+ka2*+la3* (2)
of the reciprocal lattice . h,k l are the integer Miller indices and al*, g2*, a3*, the basis vectors
of the reciprocal lattice, satisfying the two conditions
a l **a l = a2 * .a2 =a3 * *a3 = 1 and a l*.22 = a l **a3 = ~!2
*al = . . . = 0,
or in ternis ofthe Kronecker symbol with i, j and k = 1, 2, 3
Sij = 0 for i -7~ j and Sii = 1 for i = j with Si, = a* . ai* . (3)
The basis vectors of the reciprocal lattice can be calculated from those of the unit cell in real
space
a,* = (axa