X-rays can be used in a variety of ways, depending on the information required. They have been used in connection with art since 1896.
X-rays can penetrate solid objects in much the same way as they do a human body, seeing through layers of paint to reveal earlier works, sketches or repairs. Artists would often use a canvas or wood panel many times over as they were very expensive. These under paintings as they are called are present in both fake and real paintings so do not by themselves indicate a forgery. X-rays of the Mona Lisa reveal that Leonardo painted three different versions before settling on the one we know today.
Crystalline solids act as three-dimensional diffraction gratings for x-rays. This is because the distances between planes of particles in a crystalline solid are of the same order as the wavelengths of x-rays. As an x-ray meets a solid it interacts with electrons and is scattered. This produces a pattern which is distinct for individual crystal structures. To see the pattern, it must be made visible; this is done by using a photographic film. Using this pattern the structure of the solid is estimated and the diffraction pattern this model would produce is compared with the experimental one. If the model is not correct it is altered until a better match is found. Using this iterative method a structure is arrived at.
The main use of electron diffraction is to analyze the components of a pigment which are crystalline.
X-Ray Fluorescence (XRF)
XRF is a technique used to analyze which elements are present in both a qualitative and a quantitative way. If it is used for qualitative analysis then it is non-destructive, this is often essential when analyzing an important piece of work. A qualitative analysis can often be sufficient to classify a piece of work as either fake or genuine, if it uses materials unavailable for the time it purports to be from then it is almost certainly a fake.
XRF uses the Photoelectric Effect. A sample is bombarded with x-rays and instead of the x-rays being scattered as above, they are absorbed. The energy is transferred to an electron in one of the inner shells, this electron is then ejected leaving a vacancy. As it is unfavorable for an atom to be in this high energy state, an electron transfers from an outer shell to the vacancy in the inner shell returning the atom to its ground state. In this way the atom emits an x-ray characteristic of a particular element. The energy of the x-ray corresponds to the binding energy between the outer and inner shells. The atom is said to fluoresce.
One example where XRF is particularly useful is ascertaining whether metal objects are modern or ancient. Over the years methods of production and refining have changed and improved. Metal made more recently, particularly silver, is much purer than it was in antiquity. Therefore the presence of many trace elements is a major clue to the time of origin.