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Neutron Scattering and MagnetismAt the top of the page on magnetism that leads into this one, you should have noticed that the discussion began with the statement that the only stable elementary particles are protons and electrons, but that astrophysical processes crushed some protons together, converting some of them into neutrons while forming nuclei of elements heavier than hydrogen. A neutron has similar mass, spin and nuclear-interaction properties to a proton, but it has no electric charge. In the language of yet-more-elementary particles, they are both 3-quark states. "Quarks" along with "gluons" are the elementary entities of "quantum chromodynamics (QCD)" the nuclear-interaction part of The Standard Model of elementary particle physics, which is a different field of physics research, but we use its results, because all physics is inter-related. Quarks interact so strongly that an isolated quark cannot be produced: as you try to pull a lone quark away from others, it will literally pull new quarks out of the vacuum to dress itself up as a meson (2-quark state) or nucleon (3-quark state). The 3 quarks in a neutron themselves each have a fraction of an electron charge, but the sum of the 3 charges is zero. Just like the proton, as described on the >magnetism< page, the neutron also has Spin ½, and again this means the internal charges are effectively orbiting to create a magnetic dipole field, so despite having no net charge, the neutron has a magnetic moment similar to the proton's. We use neutrons' magnetic moments to probe magnetic states in materials by scattering neutrons from the materials. The neutron by itself is "almost" stable in that it has a mean lifetime of 11 minutes before it decays (into a proton, electron and neutrino) which is a long time by particle-physics standards, and it is stabilized by combining roughly equal numbers of neutrons and protons in a nucleus of an element. That instability nonetheless means that neutrons must be produced in order to be used. Neutrons are produced copiously in the cores of nuclear reactors, and when particle accelerator main beams (usually protons or electrons) strike a target. In most nuclear reactors, neutrons are prevented from escaping by the radiation shielding. To get neutrons suitable for studying magnetism out, a research reactor must have relatively neutron-transparent tubes through the shielding. A number of reactors around the world produce neutron beams for condensed matter research. The most intense (most desirable) reactor neutron beams are at In other places, "spallation sources" supply neutrons from accelerated beams striking targets. The most intense sources are at The neutrons useful for determining magnetic ordering structures have energies corresponding to thermal equilibrium at room temperature (or colder), and those are what are produced in a nuclear reactor running at room temperature. These have >de Broglie wavelengths< of a couple of Angstroms (10-10 meters, not quite a standard metric unit), comparable to interatomic spacings in materials. It turns out that the vast, overwhelming majority of non-organic solid materials are crystalline lattices on at least the microscopic scale: their atoms are arranged in huge numbers of precisely-spaced repetitions of a very simple basis unit called the unit cell, precisely-stacked rows and columns of the unit cell precisely assembled into planes, which are precisely stacked to make a 3D crystallite. It is the precise stacking of planes of atoms that is important at the moment. When a beam of thermal neutrons (X-rays will also work) is directed onto the surface of a crystal lattice, it does not reflect from the surface, but penetrates into the bulk. Then, when wavelength n Both X-ray diffraction and neutron diffraction are used to determine the >crystal structures of materials< (the atom positions, independent of any magnetism). X-rays are cheaper to produce, but have difficulty seeing light atoms (like hydrogen) if there are heavier atoms in a structure, and difficulty distinguishing atoms of similar atomic number. Neutrons are more expensive, and are so strongly absorbed by a few elements (boron, cadmium, gadolinium) that it is difficult to measure neutron scattering from materials containing those elements. Neutron scattering from nuclei at the center of atoms provides the information about crystal structures. Magnetic structure information is provided by neutron magnetic scattering from the magnetic moments of electrons in atoms. (There is very weak magnetic scattering of X-rays, which it is now feasible to use at synchrotron X-ray "light" sources, but so far this is a very specialized technique. Neutrons also scatter from the magnetic moments of nuclei, but nuclei do not undergo magnetic ordering by themselves except at temperatures of fractions of a degree above absolute zero) . When a material has ferromagnetic ordering, as described in the >magnetism< page, the magnetic lattice is the same as the atom lattice, and no new "Bragg reflections" are created (the intensities of existing Bragg reflections change). For an antiferromagnetic state, however, the magnetic lattice is not the same as the atom lattice, and new, purely-magnetic Bragg reflections occur. From the pattern of the magnetic Bragg reflections, the details of the antiferromagnetic ordering structure can be deduced, in the same way that crystal structures are solved from the pattern of the (non-magnetic) Bragg peaks in X-ray diffraction and (nuclear) neutron diffraction. To read about the sequence of discoveries that finally led to the discovery of antiferromagnetic ordering with magnetic neutron diffraction, >click here< More to come ! dnoakes@vsu.edu |
matches the spacing between planes d in just the right way (at a particular angle
), wave diffraction occurs, according to the Bragg formula: