TOF diffraction in reciprocal space

Time-of-flight diffraction (TOF) is done with neutrons of varying speeds (whereas constant-wavelength (CW) diffraction uses only one).  

Thermal neutrons are neutrons that have lost part of their energy to a moderator. Neutrons produced by a nuclear reactor or a spallation source are thermalised/moderated by for instance water: the neutrons will have approximately the same energy as the water molecules with which they collide (many times). In fact, the energy or speed distribution of the ‘virtual gas’ of neutrons will be a Maxwell distribution. Typical speeds are then 1000-3000m/s.

A spallation source typically produces pulses of neutrons. A continuous stream of neutrons from a reactor can also be chopped into pulses by placing a chopper (rotating disk with a hole in it) in a beam of neutrons. This chopped beam of neutrons will fly to the diffractometer and the fastest neutrons arrive first.

In the picture below these neutrons are depicted in blue in a reciprocal space diagram (the fastest neutron has the biggest ki-vector). Since Bragg scattering is elastic scattering, the scattered neutron has the same size kf and therefore also lies on the dotted blue circle.

The mesh of black dashed lines connect the reciprocal lattice points τ(h,k,l) like discussed in the post of 13 Nov 2010.

Bragg diffraction will occur when the Bragg condition is met, which is when the vector sum (Q) of ki and kf is connecting two points τ(h,k,l) in the reciprocal lattice. This condition is not met in the ‘green scheme‘, but it is met in the ‘purple scheme‘.

Note that ki and kf do not have to lie on (/connect) a lattice point: only Q has to. I’ve made them join in this diagram to show how Q is the vector-sum of them and how Q should lie on (/connect to) a lattice point in reciprocal space.

Also note that Q has no relation to the blue dotted circle: it can be bigger as well as smaller than the circle, but it cannot become more than twice the size of k.

In the diagram there are 5 incoming neutrons shown, with the diffraction scheme depicted for the first and fastest neutron. The second neutron that arrives can be drawn with a smaller dotted circle and maybe the same  τ(h,k,l)-vector (as in the purple scheme) can overlap with the Q-vector of that ki and some other kf that scatters under another angle.

In TOF-diffraction one pulse of neutrons produces several diffraction peaks (scattering in specific directions) at a given time and some time later during the arrival of the pulse it will produce another set of diffraction peaks at (typically) different angles.

The neutrons are collected by detectors that are placed at some angle 2Θ around the sample. A plot of the detected intensity versus time-of-flight (/arrival in the detector) and angle of the detector is shown below. It shows how different d-spacings in the sample produces different ‘streaks’ of intensity in the plot.

Be Sociable, Share!

Leave a Reply