2.6.3 ADVANTAGES AND DISADVANTAGES OF NEUTRON DIFFRACTION 86
2.6.4 APPLICATIONS TO COORDINATION CHEMISTRY 87
2.6.4.1 Single Crystal Neutron Diffraction in Coordination Chemistry 87
2.6.4.2 Powder Neutron Diffraction in Coordination Chemistry 88
2.6.5 REFERENCES 89
2.6.1 INTRODUCTION
Although the neutron is stable when incorporated into a nuclide, a free neutron is unstable and decays into an electron, a proton, and an antineutrino with a half-life of 13 minutes. As a consequence, neutron diffraction experiments must be carried out with neutrons from either a nuclear reactor or a spallation source. In either case the high kinetic energy of the neutrons that result from the nuclear fission or spallation must be reduced, i.e., the neutrons must be thermal- ized, through collisions with a moderator such as light or heavy water. The resulting thermal neutrons have an energy of ca. 101 to 103eV or a wavelength, as derived from the de Broglie equivalence, of ca. 1–5 A˚. Thus thermalneutrons have wavelengths appropriate for diffraction by an atomic or molecular lattice. As a consequence, neutron diffraction is closely related to X-ray diffraction, and typically neutron diffraction studies are preceded by X-ray diffraction structuralstudies. Neutron diffraction does, however, have certain advantages over X-ray diffraction, advantages which will be discussed herein.
The neutron is a neutral particle that has a nuclear spin of 1=2 and hence a magnetic moment,, of 1.913 N, where Nẳeh/2mpẳ5.0511027J T1 is the nuclear Bohr magneton. A com- parison of the fundamentalproperties of neutrons and X-rays is given inTable 1.
2.6.2 NEUTRON INTERACTIONS WITH MATTER
The fundamentalaspects of neutron diffraction and its use in the study of materials has been covered in detail in several excellent books which should be consulted for details.1–8 Neutrons interact with matter in a variety of ways which make neutron diffraction both similar to and yet different from X-ray diffraction.
First, because the neutron is uncharged it can easily approach the point-like atomic nuclei found in a materialandnuclearscattering occurs at very short distances of ca. 1014to 1015m. It is this scattering from an ordered crystalline material that produces coherent Bragg scattering and yields either the intensity of the various hkl reflections from a single crystal or the powder diffraction pattern; results that are familiar from X-ray diffraction and provide essentially the same structuralinformation. However, there is a distinct difference in the scattering lengths for
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X-ray and neutron scattering. Because X-ray diffraction results from scattering by the electrons, atoms of similar atomic number exhibit very similar scattering and it is hard to distinguish between them by X-ray diffraction. In contrast, neutron scattering depends upon the nature of the scattering nuclide and, as a consequence, atoms of similar atomic number often have quite different neutron scattering lengths9(seeFigure 1). This difference8is also apparent inTable 2for the first row transition metals. Further, in contrast to X-ray scattering, which is highly dependent upon the scattering angle, neutron scattering by a nuclide is virtually independent of scattering angle,, a difference which is easily observed in the angular dependence of the form factor for the different scattering processes (see Figure 2).
Second, because the neutron has a magnetic moment, it also is scattered by interaction with any magnetic moments found within a material; the resulting coherent scattering, the magnetic scattering, is superimposed upon the nuclear scattering in any magnetic material. This magnetic scattering may or may not result in a reorientation of the neutron spin. Because the magnetic neutron scattering results from an interaction with both the spin and orbital components of the magnetic moments, moments that result from the unpaired valence electrons, magnetic scattering has an angular dependence that is similar to that of X-ray scattering by electrons (seeFigure 2).
Thus, in contrast to the nuclear scattering, the magnetic scattering of neutrons is highly dependent upon the scattering angle as is apparent inFigure 2which shows the typicalangular dependence of the spin, orbital, and nuclear form factors for neutron scattering by chromium as well as, for comparison, the form factor for X-ray scattering. The difference in the angular dependence is one way in which the magnetic and nuclear neutron scattering can be distinguished. Other possible
Table 1 Fundamentalproperties of X-rays and neutrons.
X-rays Neutrons
Nature Electromagnetic Particle wave
Mass (1027kg) 0 1.6749286(10)
Charge 0 0
Spin 1 1=2
Magnetic moment (N) 0 1.91304275(45)
Typicalenergy (eV) 8042 0.036
Typicalwavelength (A˚) 1.5418 1.50
Velocity (m s1) 3.0108 2.6103
Figure 1 The scattering length of thermal neutrons as a function of atomic number for the natural abundance elements.
methods would be a study of the temperature dependence of the magnetic scattering or the use of polarized neutron scattering.
Third, for some nuclei the neutron will actually interact with the nuclide to form a short-lived compound nucleus, a process that often results in isotropic incoherent scattering with a negative scattering length; this interaction may also be associated with a neutron spin reorientation.
Neutron scattering by hydrogen is a special case in which the incoherent scattering is especially strong because the scattering proton may have either the same or the opposite spin to that of the scattered neutron.9 These two different types of scattering, singlet or triplet scattering, lead to strong incoherent scattering by hydrogen. Fortunately, this does not apply to neutron scattering
Table 2 Selected elastic scattering lengths and cross-sections.
Atom bcoh(1012cm) coh(1024cm2) incoh(1024cm2) abs (1024cm2)
Hydrogen 0.3739 1.7568 80.26 0.3326
Deuterium 0.6671 5.592 2.05 0.000519
Boron-10 0.01 0.144 3 3835
Boron 0.530 3.54 1.7 767
Carbon 0.6646 5.551 0.001 0.0035
Titanium 0.3438 1.485 2.87 6.09
Vanadium 0.03824 0.0184 5.08 5.08
Chromium 0.3635 1.66 1.83 3.05
Manganese 0.373 1.75 0.4 13.3
Iron 0.945 11.22 0.4 2.56
Cobalt 0.249 0.779 4.8 37.18
Nickel1.03 13.3 5.2 4.49
Copper 0.7718 7.485 0.55 3.78
Zinc 0.5680 4.054 0.077 1.11
Cadmium 0.487 3.04 3.46 2 520
Gadolinium 0.65 29.3 151 49 700
Figure 2 The angular dependence of the normalized form factor for nuclear, and spin and orbital magnetic scattering for chromium metal. The comparable values for X-ray scattering are given for comparison.
Neutron Diffraction 85
by deuterium and many neutron diffraction studies require the replacement of hydrogen by deuterium.
Fourth, most atoms have nuclei which consist of several isotopes, isotopes that usually have different neutron scattering lengths and cross-sections.10 As a result, unless a material is made with a single isotope of a given atom, neutron scattering from the various isotopes results, in part, in isotropic incoherent nuclear scattering. The values for the different isotopes of nickel are given in Table 3along with that of natural abundance nickel. The differences in scattering lengths for nickelisotopes given in Table 3 show that different but pure isotopes can be used to provide contrast with other elements in a compound, a contrast that is impossible to obtain with X-ray diffraction.