X-ray Diffraction

Dependence of the X-ray scattering intensity on the scattering angle and the electron count of the scattering atom.

Figure 1 Dependence of the
X-ray scattering intensity on
the scattering angle and the
electron count of the
scattering atom.

 

Different types of radiation can and have been used to perform diffraction. The most common is X-radiation, as it can be routinely generated in the laboratory using sealed X-ray tubes. Depending on the anode material, several different radiation wavelengths can be achieved with their specific advantages and drawbacks. The most common X-radiation for single crystals is possibly molybdenum Kα (λ = 0.71074 Å), while powder machines normally run with copper Kα (λ = 1.54056 Å). Other target materials include silver, iron, cobalt, nickel and zirconium. If fine-tuned wavelengths are necessary, synchrotron radiation can provide these. The use of wigglers and undulators on the modern synchrotrons generates a brilliant white X-radiation, from which the necessary wavelength can be obtained by the use of specific monochromators.

X-radiation interacts with the electron cloud of an atom due to its electromagnetic moment. Thus, atoms with many electrons will interact stronger with the radiation than those with few electrons. Since the wavelength of the used X-radiation is in the length scale of the scattering electron shell, the diffraction intensity decreases with increasing scattering angle (Figure 1).

Librational apparent shortening of bonds to hydrogen.

Figure 2 Librational apparent
shortening of bonds to hydrogen.

It is obvious that the detection of hydrogen atoms having only one electron will in the best of cases be difficult. Even if residual electron density can be seen in the Fourier maps, this will only show the position of the electron of the covalent bond of the hydrogen atom to its heavier counterpart. Since most elements are more electronegative than hydrogen, the position of the bonding electron will be biased towards the heavier atom.

In addition, hydrogen atoms move considerably more than heavier atoms, thus leading to further apparent shortening of the X-H bond as presented in Figure 2. It is therefore standard to calculate most hydrogen atom positions as riding models to the heavier atoms the hydrogen atoms are connected to, and constrain the bond geometry of hydrogen atoms, whose position can be picked directly from the Fourier maps.