Neutrons possess unique properties for probing structures and dynamics of crystals, liquids or soft matter. Neutrons either interact through the strong force with the nuclei of the sample or through dipole interactions with the spin or even nuclear moments of the ions in the sample. Due to this latter interaction neutrons are the tiniest probes for the investigation of magnetic order and interactions on the microscopic level. Both interactions are weak, which allows neutrons to penetrate deeply into the samples and even penetrate heavy sample environment as cryostates, cryo-magnets, furnaces or pressure cells.
The kinetic energy of neutrons - typically in the meV range - is similar to the energy scales of collective excitations in condensed matter like phonons or magnons. Throughout the scattering process between the sample and neutrons an energy transfer between a fraction of the incoming neutron beam and the matter takes place. The energy and momentum transfer of neutrons is traceble, which allows to deduce the dynamics inside the atomic and magnetic systems. Two main techniques have been developped for inelastic neutron measurements: the time of flight (TOF) technique, which - as indicated by the name - measures the differencies in velocity and therefore kinetic energy of neutrons before and after the scattering process and three-axis spectroscopy (TAS) exploited in our group.
What is TAS ?The name TAS comes from the three rotation axis of the spectrometer.
The monochromator - typically an array of graphite or silicon single crystals - selects a narrow wave-length band around the mean wavelength of an incident white neutron beam by rotating the reflection plane of the crystals with respect to the incident beam.
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| The relation between the reflection angle and wavelength is given by Bragg's law : 2dsinΘ=λ where d is the lattice spacing of the crystals. The selected monochromatic neutron beam impinges on the sample - the second axis -, where parts of the neutrons interact with the sample material. |
The neutrons thereby change in general their energies and directions, of course, under respecting energy and momentum conservation of the total system. The scattered neutron are analyzed by, yes, the analyzer, where again Bragg's law is used to identify the energy or wavelength of the scattered neutrons.
To keep trace of neutrons in scattering angles and energies we rely on the formalism of the reciprocal space. The sample itself with its reciprocal lattice provides us with the necessary map for orienting and driving the spectrometer. This contains an important point for a successfull experiment on a three-axis spectrometer. The crystallographic structure of the sample has to be determined beforehand, otherwise measurements make no sense. The incident neutron beam and the scattered beam accepted by the analyzer are represented in the reciprocal space - a vector space - by the wave-vektors ki and kf, respectively. Both vectors span the scattering plane. By rotating the sample around the sample axis or by tilting the sample with the help of goniometers, the scattering plane can be adjusted to the plane of interest of the reciprocal lattice. By definition, the origin of this plane is the end-point of ki. Within the geometrical restrictions of the instruments any lattice point Q in the scattering plane can be individually adressed. If the lengths of ki and kf are equal, the scattering is called elastic. Is there a difference in length, the scattering is inelastic with the energy transfer E=const.(ki-kf). In this way E=E(Q), the dispersion relations of magnons or phonons can be traced throughout, typically, several Brillouin zones.
The number of possibilities for combining ki and kf in the way that - in typical TAS language - the vector triangle ki-kf=Q can close, is in principal infinite. Changing ki and kf, changes the energy.
General introduction to neutron scattering : | Brückel T., Heger G., Richter D., Zorn R., Neutron scattering. Lectures of the Laboratory course, Jülich, Germany, Publisher Forschungszentrum Juelich GMBH, 2005. (ISBN 3-89336-395-5). | | Shirane G., Shapiro S.M., Tranquada J.M., Neutron scattering with a triple-axis spectrometer : basic techniques, Cambridge, United Kingdom, Cambridge University Press Publication, 2002. | | Janot C., Buettner H.G., CNRS. CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE, LABORATOIRE LEON BRILLOUIN, INSTITUT LAUE-LANGEVIN (ILL), Ecole de printemps Diffusion des neutrons et sciences de materiaux, 1997. | | Furrer A., Introduction to neutron scattering. Lecture notes of the introductory course 1. European Conference on neutron scattering (ECNS '96), Villingen, Switzerland, Paul Scherrer Institute, 1996. | | Springer T., Kehr K., Schilling W., 27. IFF-Ferienkurs. Streumethoden zur Untersuchung kondensierten Materie, Juelich, GE, KFA, Forschungszentrum Juelich GMBH, 1996 (ISBN 3-89336-180-4). | | Dobrzynski L., Blinowski K., Neutrons and solid state physics, London, GBR, Ellis Horwood, 1994, Collection ELLIS HORWOOD SERIES IN PHYSICS AND ITS APPLICATIONS Editor Cooper M., Mason J.W. (ISBN 0-13-617192-3). | | Izyumov Y.A., Chernoplekov N.A., Neutron spectroscopy, New York, USA, Consultant Bureau, 1994 (ISBN 0-306-11033-4). | | Pynn R., Neutron scattering, Los Alamos National Laboratory Publication, 1990, Collection LOS ALAMOS SCIENCE Volume 19. | | Moon R.M., Neutron scattering. Vol. 1, Oak ridge National Laboratory Publication Date 1977 Conference Location Gatlinburg, Tennessee, USA Conference Date 1976-06-6 / 1. | | Moon R.M., Neutron scattering. Vol. 2, Oak ridge National Laboratory Publication Date 1977 Conference Location Gatlinburg, Tennessee, USA Conference Date 1976-06-6 / 10. |
| | More theory : | | Lovesey S.W., Theory of neutron scattering from condensed matter. Vol. 1 Nuclear scattering., Oxford University Press Publication, 1986, Collection THE INTERNATIONAL SERIES OF MONOGRAPHS ON PHYSICS Volume 72 Editor Adair R.K., Elliott R.J., Krumhansl J.A., Marshall W., Wilkinson D.H. (ISBN 0-19-852028-X). | | Lovesey S.W., Theory of neutron scattering from condensed matter. Vol. 2 Polarization effects and magnetic scattering., Oxford University Press Publication, 1986, Collection THE INTERNATIONAL SERIES OF MONOGRAPHS ON PHYSICS Volume 72 Editor Adair R.K., Elliott R.J., Krumhansl J.A., Marshall W., Wilkinson D.H. (ISBN 0-19-852029-8). | | Squires G.L., Introduction to the theory of thermal neutron scattering, Cambridge, UK, Cambridge University Press, 1978. (ISBN 0-521-21884-5). | | | Instrumentation : | | Anderson I.S., Guérard B., Advances in neutron scattering instrumentation, Washington, USA, SPIE, 2002, Collection PROCEEDINGS OF THE SPIE Volume 4785, Conference Title Advances in Neutron Scattering Instrumentation Conference Location Seattle, WA, USA Conference Date 2002-07-07 / 08 (ISBN 0-8194-4552-5). | | Magerl A., Wagner V., Focussing Bragg optics. Proceedings of the Workshop, Amsterdam, NLD, North-Holland, 1994, Collection NUCLEAR INSTRUMENTS AND METHODS IN PHYSICS RESEARCH A Volume 338, Conference Title Workshop on Focusing Bragg optics Conference Location Braunschweig, Germany Conference Date 1993-05-10 / 11. |
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