Analyzing Art Objects

The wavelengths (700 nm to 1 mm) of infrared radiation (IR) are not detectable by the human eye and lie just outside the visible region next to red light. Infrared radiation is also known as heat radiation and can be detected by night vision goggles. IR wavelengths have energies ranging from 1.7 eV (2.7 × 10^-19 J) to 1.24 × 10^-3 eV (2.0 × 10^-22 J). Infrared radiation has the same frequencies as the vibrations of bonds in compounds and molecules and so the absorption spectrum of infrared light is typical of the types of bonds present.

Molecular vibrations can be treated as if the atoms are balls attached to springs tht are approximated as harmonic oscillators. The energies of the vibrations are inversely proportaional to the square root of the reduced masses of the atoms, where the reduced mass, μ, is defined as μ = 1/(m₁^-1 + m₂^-1), where m₁ and m₂ are the masses of the two atoms. For our purposes, this means that infrared radiation is able to determine the identity of compounds and molecules by giving information about the bonds present. In order for a particular bond vibration to be detected by IR spectroscopy, the molecule must undergo a change in dipole moment as the bond vibrates. A related technique known as Raman spectroscopy detects vibrations that cause a change in the polarizabilty of the molecule.

The infrared spectrum of polystyrene. Infrared spectra may be plotted either as absorbance (A) or transmittance (T), where A = -log₁₀T. The energy units normally used for infrared spectra are wavenumbers ν with units of cm^-1. Polystyrene is a common reference material used to calibrate the assignment of peak locations in a sample.

Many molecules are easily studied by infrared spectroscopy. In comparison to many other types of analytical instrumentation, IR spectrometers are relatively inexpensive. A beam of IR radiation is focused on a sample and the absorbed light is analyzed by a detector. This may be done either by absorption of the radiation during transmission through the sample or reflection off of the sample's surface (attenuated total reflectance, ATR). IR spectroscopy can be done on samples that are gases, liquids or solids. It is common to take spectra of solids or liquids dissolved in a solvent. Solids can also be ground into a fine powder mixed with potassium bromide and pressed into a pellet or mixed with Nujol (mineral oil) and spread on a transparent salt plate of sodium chloride or potassium bromide. This is also referred to as a Nujol mull. The advantage of using potassium bromide is that it has no absorbances from 4000 to 400 cm^-1, which is known as its spectral window, and therefore will not interfere with absorbances from the sampel. Nujol is an organic molecule but it has only a few absorbances that are readily identifiable and these occur in places that are generally not too valuable for an analysis (2950 - 2800 cm^-1, 1465 - 1450 cm^-1, 1380 - 1300 cm^-1). IR absorbance can also be used to determine the concentration of a substance in a solution as the absorbance, A, is proportional to the concentration, C, the pathlength, ℓ, and molar absorptivity, ε, of compound by the equation A = ε × C × ℓ. Transmittance can also be used as A = - log₁₀[T/T₀], where T₀ = 100%, but most infrared spectrophotometers will readily switch between giving the data in either asorbance and transmittance modes.

There are usually a number of infrared bands in a particular compound and, in principle, these could all be individually attributed to particular bonds in the molecule. To do a full analysis of every bond in a molecule, however, is very time connsuming and often not particularly interesting. In practice the technique is more often used to identify particular types of bonds that lie in characteristic regions of the IR region or are used as simple fingerprints, meaning that the compound is identified by comparison to a database of infrared spectra of known materials.

The Mona Lisa (left), Leonardo da Vinci, Public domain, via Wikimedia Commons, and its Infrared reflectance image (right), Tangopaso, Public domain, via Wikimedia Commons.

Infrared reflectography looks at an object from the total infrared radiation absorbed rather than looking at the absorbance as a function of wavelength. This technique is most often used to identify underdrawings in paintings that were done with charcoal, as carbon-based materials absorb infrared radiation strongly.

Cuvette for measuring UV-vis spectra, taken from Ittarusp, CC BY-SA 4.0 , via Wikimedia Commons.

Visible light is the radiation source by which we normally interact with Art, as this is the radiation that activates our detection system, the human eye. It is understandable that our eyes would develop to see visible light as it is the major component of solar radiation (see below). Other animals and insects have eyes that detect different regions of the electromagnetic spectrum. Bees like many insects, for example, see ultraviolet light. Dogs see only limited color as they only have red and green cones, unlike humans who have red, green and blue. Visible light lies in the range of 400 nm to 750 nm and it causes electrons to move from one orbital to another on the molecule in a process known as an electronic transition. Ultraviolet light may also cause electronic transitions, and often spectrometers designed to measure visible spectra will also measure UV absorptions. Consequently, these instruments are generally called UV-vis spectrophotometers, and together these constitute the field of electronic spectroscopy. Sometimes the transitions that take place in the UV region are so intense that the absorption bands tail into the visible spectrum causing the compounds to have color. Normally visible spectra are obtained by placing solutions of the sample in glass or plastic cuvettes. These are small, test tube-like glass containers that have a square cross section providing a 1 cm^-1 pathlength.

X-ray absorption is one of the simplest techniques using X-rays. When X-ray radiation is focused on an object much of the radiation passes through but some will be absorbed. If a photographic film or an X-ray-sensitive detector is place on the opposite site of the object from the X-ray source, an image of those areas of the object that absorb X-ray will be produced. This is well-known in medicince to detect broken bones, but in Art it can be used to detect the wooden frame that supports a canvas painting or areas of pigments that contain heavy metals such as lead or mercury, which asbsorb X-rays strongly. As seen in the images of the Syndics of the Drapers' Guild by Rembrandt and its X-ray absorption study, Rembrandt had earlier versions of the composition before settling on the final image.

A simulated single crystal X-ray diffraction pattern for Dravite (Tourmaline). Diffraction image simulated using the program Single Crystal v.4.1.4, © 1995 -2021, Crystal Maker Software.

In addition to absorption and fluorescence, X-rays are diffracted by crystalline materials. This process is analogous to that of passign light through a set of slits. In the case of crystalline materials, the "slits" are the regular repeating arrangements of the electrons surrounding the atoms in a crystal. According to our understanding of quantum mechanics, electrons have wave properties just as electromagnetic radiation does and these waves interact to form an interference pattern that can be analyzed to provide the size and shape of the crystal unit cell as well as the locations of the atoms of different types within that cell. These data can be measured either on single crystals or on powdered samples of crystals (powder X-ray diffraction or PXRD).

The regular patterns of diffraction peaks seen in the single crystal pattern is the related to the unit cell parameters (edge lengths and angles), while the intensities of the spots can be analyzed to determine the locations of the atoms in the crystal. Each of those spots represents diffraction from a particular set of equivalent lattice planes, and the more intense spots correspond to planes that have larger atoms with more electrons. A database of powder XRD spectra are now available for a large variety of minerals, gems and other solid materials and the composition of an unknown sample can be readily determined by matching in the database. This process is made easier if a rough idea of the composition of material is known, such as the elemental composition provided by XRF spectra.

The diffraction peaks obey a mathematical relationship known as Bragg's Law, where d is the distance between the parallel planes of an equivalent set, n is an integer, and θ is the angle at which the X-rays strike the set of planes. This is illustrated in the diagram below. If the diffraction condition is not met, the X-ray components of the X-ray beam will be out of phase as they exit the crystal, resulting in destructive interference between the X-ray waves. As a result, no intensity is seen in those regions. When a beam of X-rays encounters a single crystal, diffraction spots are created in many different directions. Often, a large set of diffraction spots are measured by rotating the crystal in the X-ray beam.

A diagram illustrating the origin of the Bragg diffraction relationship. Figure is a modification of the image Bragg diffraction by Hydrargyrum, CC BY-SA 3.0 , via Wikimedia Commons. Constructive interference of the X-rays, which results in the observation of a diffraction spot, only occurs if the difference in the distance that the component X-ray waves travel when striking the different planes (i.e., the distance from A-B plus the distance B-C) is equal to some integral number of wavelengths.

Radioisotope dating is a method of determining the age of an object by looking at the ratio of isotopes present in an object. One of the most well-known isotopes studied and perhaps the most useful for determing the age of art objects is Carbon-14. Naturally-abundant carbon is composed mainly of three isoopes Carbon-12, Carbon-13 and Carbon-14. Of these only Carbon-14 has an unstable nucleus with half life of 5730±40 years. Carbon-14 is created in a steady state abundance by high energy radiation that creates neutrons in the upper atmosphere according to the equation: