Neutron Sciences Directorate

Description:

The resolution of conventional neutron scattering techniques can be further increased by using the Larmor labeling of neutron spin. At ORNL, Larmor labeling is available in Larmor diffraction, inelastic neutron spin echo and spin echo small angle neutron scattering, which can be used in the scientific themes including:
Lattice distortion or broadening with a resolution beyond Δd/d<10-4.
Variation of lattice spacing due to thermal expansion or stress with Δd/d~10-6. 
Phonon energy shift with a resolution below 10µeV.
Materials of strong scattering or with an extended long length scale correlation beyond 100nm.

Larmor precession

For a given magnetic field , the neutron spin  with a wavelength of λ will execute a motion called Larmor precession and the number of rotations is referred as Larmor phase . With the polarization analyzer, only the component of their polarization vectors along the analyzing direction can be picked up as P=Cos().

Larmor diffraction

When picking up the right configurations of the magnetic fields, the effective tilting angle of the setup can be set to be parallel to the crystal plane such that all the diffracted neutrons will yield the same Larmor phase independent of the beam divergence. The neutron polarization measured by the detector is the cosine Fourier transform of the distribution of all lattice spacings within the Bragg peak.

Achievable resolution:

The absolute splitting of sharp Bragg peaks: Δd/d=2x10-4.
Broadening of Bragg peak during phase transition: Δd/d<10-5.
Variation of lattice spacing due to thermal expansion or stress with Δd/d~10-6. 

Inelastic neutron spin echo

Unlike a conventional TAS experiment doing a series of constant q scans to measure the energy change, the host TAS is fixed in position and only the magnets are manipulated to perform the measurements. The measured polarization yields the cosine Fourier transform of the phonon dispersion line shape within the resolution ellipsoid. The following calculation is currently provided for non-dispersive excitations only.

Spin echo small angle neutron scattering

SESANS works in real space and the measured polarization yields the cosine Fourier transform of the scattering function of sample in reciprocal space. It provides a one to one relation between the density correlation function of the sample and the neutron polarization observed after Larmor labeling. SESANS can measure the correlations over a wide range of length scales making it suitable for measuring length scales from a few tens of nm to a few microns. It overcomes the issue of multiple scattering thus samples with strong scattering are allowed. 
*SESANS is a SANS technique thus not part of the HB1 instrument.

Point of Contacts
Fankang Li (frankli@ornl.gov)
Jaime A. Fernandez-Baca (fernandezbja@ornl.gov)
Masaaki Matsuda (matsudam@ornl.gov)

References:
1.    Li, F., et al., New capabilities in high-resolution neutron Larmor diffraction at ORNL. Journal of Applied Crystallography, 2018. 51(3).
2.    Li, F., et al., High resolution neutron Larmor diffraction using superconducting magnetic Wollaston prisms. Scientific Reports, 2017. 7(1): p. 865.
3.    Li, F. and R. Pynn, A novel neutron spin echo technique for measuring phonon linewidths using magnetic Wollaston prisms. Journal of Applied Crystallography, 2014. 47(6): p. 1849-1854.
4.    Li, F., et al., Superconducting magnetic Wollaston prism for neutron spin encoding. Review of Scientific Instruments, 2014. 85(5): p. 053303