Comparison of the characteristics of X-ray and neutron beams

The formalism that will be developed in this chapter will apply equally to X-ray or neutron diffraction, and many experiments involving the two types of

Bank 4 (50−75°) Bank 5 (79−104°)

Bank 6 (142−169°)

Bank 2 (14−21°) Bank 1 (6−13°)

Bank 3 (25−45°) Sample tank

Incident beam direction

Fig. 6.10 State-of-the art neutron powder diffractometer at the ISIS spallation neutron source. (Photograph and diagram by courtesy of the ISIS Facility.)

radiation are very similar in concept. As noted above, laboratory X-ray sources have many operational advantages over synchrotron X-rays and neutrons.

However, X-ray and neutron diffraction have complementary strengths and weaknesses, depending on the actual system under study, and there may often be compelling reasons to choose one type of radiation over the other, or to obtain data from both types of radiation in a single study.

0.5 1 1.5 2 2.5 3

d-spacing (Å)

Intensity

×2.5

Fig. 6.11 Neutron powder diffraction data for a sample of spinel, obtained on a medium-resolution time-of-flight diffractometer at the ISIS spallation neutron source.

The primary difference between the techniques of X-ray and neutron diffraction arise from the fact that the scattering mechanisms are different.

X-rays are scattered by the electrons and will therefore provide information about the electron density in the scattering material. Neutrons are scattered by two mechanisms. First, neutrons are scattered by the atomic nuclei, and will therefore provide information about the positions of the nuclei in the scattering material. To obtain information about the shape of the electron distribution about an atomic nucleus, which is of interest in the chemistry of bonding, combined X-ray and neutron diffraction studies can be of considerable value.

Second, in magnetic materials, the neutrons can be scattering by the atomic magnetic moments through the interaction with the magnetic dipole moment of the neutron. The magnetic moments of solids, except at very low temperatures, arise from the alignment of the spins of the electrons, and so there can be a component of scattering of neutrons directly from the electrons. Unlike X-ray diffraction, the magnetic scattering of neutrons does not involve all the electrons, but only the electrons in the partially filled energy levels in which the electrons are aligned to give the magnetic moment.

Since X-rays are scattered from the electrons, it will follow (and we will show formally in Section 6.4.2) that the scattering power of each atom is proportional to the number of electrons. This means that there is a consistent variation of the scattering power with atomic number, so that heavy atoms will scatter X-rays more strongly than will light atoms. Also, the scattering of X-rays will be different from neutral atoms and their corresponding charged ions (e.g. from neutral Si or from the Si⁴⁺cation). On the other hand, there is no corresponding correlation in the power of neutron scattering from atomic nuclei and the atomic number. In fact there is a wide distribution in the scattering

power, and the sign of the scattering amplitude can be either positive or negative since the neutron–nucleus scattering may or may not give a change of phase of πto the neutron wave (Section 6.4.3).

There are three important practical implications to this comparison of the scattering power of X-rays and neutrons. First, neutrons will be better at distinguishing between atoms that have similar numbers of electrons, such as Si⁴⁺and Al³⁺cations. On the other hand, there will also be other pairs of atoms that have very similar scattering power for neutrons (e.g. Cl and Br) but very different atomic number, so these will be better distinguished by X-ray methods.

Second, in structures where there is an atom that dominates most of the X-ray scattering (these are typically atoms with a lot of electrons), the positions of the other atoms (those with few electrons, such as oxygen) may be difficult to deduce. In neutron scattering the scattering powers of most atoms are broadly in the same range, so there is rarely a problem with one atom dominating the scattering. However, there are some atoms (vanadium is an example) where the scattering power of neutrons is almost zero. Third, the hydrogen atom is virtually invisible to X-rays but will scatter neutrons with the same order of strength as any other atom. For crystallographic problems where the positions of hydrogen atoms are important, for example when there are C–H and O–H bonds, neutron scattering is the main way of providing information about the bond lengths.

We will show later (Section 6.4.2) that the X-ray scattering power of an atom falls off with increasing scattering angle to an extent that is determined by the inverse of the size of the atom, whereas with nucleus–neutron scattering the scattering power is independent of the scattering angle (because the nucleus is tiny compared to the wavelength of the neutron beam). For studies where we need scattering at high angles, for example to obtain accurate bond lengths in disordered systems, neutron scattering may be the preferred method.

The scattering of X-rays by electrons is a stronger process than the scattering of neutrons by atomic nuclei. This is coupled with the fact that X-ray beams are much more intense than neutron beams. These two factors have implications for the design of experiments. It is possible to use much smaller samples for X-ray diffraction than in neutron diffraction. For example, X-ray experiments use samples that are likely to be much smaller than 1 mm³, whereas the samples for neutron diffraction are likely to be several mm³(or even a few cm³) in size.

The other side of this issue is that neutrons can penetrate into materials much further than X-rays. For example, there may be the haunting possibility that X-ray diffraction is determined by the surface rather than the bulk. This may be important when studying phase transitions (strictly a bulk issue; see Chapter 12), which can be significantly affected by surfaces. In the design of experiments, the greater penetrating power of neutrons gives rather more flexibility in the use of complex equipment for control of the sample environment. For example, in studies of diffraction from materials at high pressures, neutrons will penetrate through the pressure-generating anvils more easily than laboratory X-rays (the solution to this problem for X-ray diffraction is to use high-energy X-ray beams generated by a synchrotron source). The need to reduce the thickness of the environment equipment will lead to the reduction in the size of this equipment, which may mean that large gradients in temperature or pressure are hard to avoid. All these difficulties can be solved by careful design of experiments, but it

does suggest that sometimes the larger scale of neutron diffraction experiments can be exploited in certain types of difficult diffraction experiments.