steeply as X-rays. There is no simple relationship linking the scattering factors of
atoms and their place in the periodic table. This makes it necessary to use larger
crystals than those commonly used in X-ray diffractions studies, but nonetheless it
has proved invaluable for determining the geometries of metal hydrides’ agostic
interactions involving C–H bonds and transition metals, the location of bridging
hydrides in boranes and carboranes and molecules exhibiting hydrogen bonding
interactions [85, 86]. Although the scattering power of an atom is directly related to
the number of electrons in the neutral atom, there is no simple relationship between
the neutron scattering power and the atomic number. The neutron scattering powers
vary erratically, and there may be large differences between adjacent atoms, and
different isotopes of the same atom may show different scattering powers. The phase
of the scattering may have positive and negative signs, for example, D has a positive
scattering factor of 6.7, whereas for hydrogen it is À3.7. To generalise neutron
diffraction is very useful for locating the positions of light atoms more accurately,
e.g. the location of H and D in partially deuterated compounds. The technique has
proved to be particularly important for studying and defining the nature of the
interactions in hydrogen-bonded systems [89–94]. For such studies the bond length
involving hydrogen determined from neutron data will differ from that derived from
X-ray data because the former locates the nucleus, whereas the latter locates the
electron density which is not completely localised on the hydrogen but shifted
towards the atom to which it is bonded as a result of covalency effects. For example,
a C–H bond which has a length of 1.08 Å in a neutron study would have length of
0.98 Å by X-ray diffraction.
More generally the careful determination of a structure using X-ray and neutron
data may be used to more carefully map the electron density and lead to conclusions
about bonding effects. However, it must be noted that if the valence electrons
represent only a small amount of the total number of electrons, then these studies
have to be completed with great care [90–95]. The neutrons define accurately the
positions of the nuclei, and the X-ray data provides information concerning the
distribution of electron density throughout the molecule and consequently provides
an insight on how the electron density has been modified as a result of ionic and
covalent bonding effects. This area which was pioneered by P. Coppens [95, 96] and
many of these studies have used the R. Bader’s quantum mechanical analysis of the
topology of the electron density function for interpreting the three-dimensional space
electron density [97, 98].
Although neutrons are uncharged, they carry a magnetic moment and therefore
interact with magnetic moments associated with the target crystal, including those
arising from the electron cloud around an atom. Neutron diffraction can therefore
reveal the microscopic magnetic structure of a material. Magnetic scattering does
require an atomic form factor as it is caused by the much larger electron cloud around
the tiny nucleus. The intensity of the magnetic contribution to the diffraction peaks
will therefore decrease towards higher angles [99].
One major advantage of neutron diffraction over X-ray diffraction is that the latter
is rather insensitive to the presence of hydrogen (H) in a structure, whereas the nuclei
1H and 2H (i.e. Deuterium, D) are strong scatterers for neutrons. The greater
Early History of X-Ray Crystallography
31
atoms and their place in the periodic table. This makes it necessary to use larger
crystals than those commonly used in X-ray diffractions studies, but nonetheless it
has proved invaluable for determining the geometries of metal hydrides’ agostic
interactions involving C–H bonds and transition metals, the location of bridging
hydrides in boranes and carboranes and molecules exhibiting hydrogen bonding
interactions [85, 86]. Although the scattering power of an atom is directly related to
the number of electrons in the neutral atom, there is no simple relationship between
the neutron scattering power and the atomic number. The neutron scattering powers
vary erratically, and there may be large differences between adjacent atoms, and
different isotopes of the same atom may show different scattering powers. The phase
of the scattering may have positive and negative signs, for example, D has a positive
scattering factor of 6.7, whereas for hydrogen it is À3.7. To generalise neutron
diffraction is very useful for locating the positions of light atoms more accurately,
e.g. the location of H and D in partially deuterated compounds. The technique has
proved to be particularly important for studying and defining the nature of the
interactions in hydrogen-bonded systems [89–94]. For such studies the bond length
involving hydrogen determined from neutron data will differ from that derived from
X-ray data because the former locates the nucleus, whereas the latter locates the
electron density which is not completely localised on the hydrogen but shifted
towards the atom to which it is bonded as a result of covalency effects. For example,
a C–H bond which has a length of 1.08 Å in a neutron study would have length of
0.98 Å by X-ray diffraction.
More generally the careful determination of a structure using X-ray and neutron
data may be used to more carefully map the electron density and lead to conclusions
about bonding effects. However, it must be noted that if the valence electrons
represent only a small amount of the total number of electrons, then these studies
have to be completed with great care [90–95]. The neutrons define accurately the
positions of the nuclei, and the X-ray data provides information concerning the
distribution of electron density throughout the molecule and consequently provides
an insight on how the electron density has been modified as a result of ionic and
covalent bonding effects. This area which was pioneered by P. Coppens [95, 96] and
many of these studies have used the R. Bader’s quantum mechanical analysis of the
topology of the electron density function for interpreting the three-dimensional space
electron density [97, 98].
Although neutrons are uncharged, they carry a magnetic moment and therefore
interact with magnetic moments associated with the target crystal, including those
arising from the electron cloud around an atom. Neutron diffraction can therefore
reveal the microscopic magnetic structure of a material. Magnetic scattering does
require an atomic form factor as it is caused by the much larger electron cloud around
the tiny nucleus. The intensity of the magnetic contribution to the diffraction peaks
will therefore decrease towards higher angles [99].
One major advantage of neutron diffraction over X-ray diffraction is that the latter
is rather insensitive to the presence of hydrogen (H) in a structure, whereas the nuclei
1H and 2H (i.e. Deuterium, D) are strong scatterers for neutrons. The greater
Early History of X-Ray Crystallography
31