Crystal polymorphism studied with Raman spectroscopy

Abstract: in this article we deepen the phenomenon of crystalline polymorphism and its experimental study through the technique of Raman spectroscopy.

Introduction

In chemistry, the term polymorphism indicates the possibility that the same substance presents itself in different crystalline forms. This behavior can occur both in simple substances (i.e. substances formed by atoms of the same chemical element), and in compounds (i.e. substances formed by atoms of different chemical elements). The different polymorphic modifications have different physical properties, for example the density or the melting point; instead they have the same chemical behavior, and therefore, by means of chemical analysis it is possible to ascertain that they are the same substance.
Examples of polymorphic substances in nature are the following:

• Sulfur: it can occur in rhombic crystals or monoclinic needle-like crystals;
• Carbon: it can occur in various polymorphic forms, including Graphite (having a hexagonal crystalline structure) and Diamond (having a cubic crystalline structure);
• Calcium Carbonate: can be in the form of Aragonite (rhombic structure) and Calcite (trigonal structure).
• silica: it can be in the form of trigonal α Quartz, hexagonal β quartz, hexagonal Tridymite and cubic Cristobalite.

Often the different polymorphic forms of the same substance show different Raman spectra, this happens because, although the atomic species are the same, the structure of the crystal lattice is different and therefore the vibration frequencies of the atomic bonds are different.

Experimental Setup

Our DIY Raman system is based on a series of optical components.

The laser is the 100mW PGL-H-532nm model from manufacturer CNI Laser. It is a source with good monochromaticity with a line width <0.2 nm and a divergence <1.5 mrad. The laser is powered by a voltage of 3 V and absorbs about 0.3 A. The laser is equipped with a bulk cylindrical aluminum heat exchanger which is kept cool by a TEC device. In any case, the laser must be “heated up” for a couple of minutes before being used as a Raman excitation source. The laser is inserted into the Thunderoptics cuvette holder cell which is used as a receptacle for the dichroic mirror / beam splitter. The microscope objective is positioned on one side of the cell and focuses the laser beam on the sample to be examined, while on the opposite side is the optics to collect the Raman scattered light and convey the light into the optical fiber. The Raman probe is shown in figure 1.

The light collected by the fiber is filtered with a sharp-edge long-pass filter that blocks wavelengths below 540 nm and transmits the greater ones. The filter is placed at the collimator input of the optical fiber that brings the signal to the spectrometer. As already mentioned above, the purpose of the filter is to make sure that the Rayleigh radiation – much more intense than the Raman scattering – does not reach the spectrometer where it could cause problems in detecting the Raman bands with the lowest Raman shift, i.e. closer to the wavelength of excitation.

The dichroic mirror was obtained from a decommissioned equipment (fluorescence cube) and is an Omega Optical 540DRLP Dichroic Mirror. In practice, at the angle of 45° it reflects λ smaller than 540 nm (the laser emits at 532 nm), while it allows λ greater than 540 nm to pass. The dichroic mirror allows, in the backscattering configuration, to easily separate the excitation source from the backscattered light at greater λ.

The microscope objective is a 20X with a numerical aperture of 0.4 and a working distance of 2.4 mm, it is an Infinity model easily available on eBay.

Fig 1 – Detail of the Raman probe made up of laser, beam splitter, lens and light collecting fiber

The Raman probe is placed on a wooden base, on which the various components are solidly fixed, in order to maintain optical alignment. The support base can be positioned vertically, as shown in figure 2, or horizontally, as shown in figure 3. To examine liquid samples contained in test tubes it is convenient to use the horizontal configuration, while to analyze solid samples, even in granular form or in dust, vertical position can be convenient.

Fig 2 – Raman probe in vertical position

Fig 3 – Raman probe in horizontal position

In figure 4 we show how the spectroscopic analysis of a solid sample such as a mineral is carried out. In this case it is a sulfur crystal. In the image it is not seen but during the analysis the objective and the sample must be covered by a screen which has the purpose of both limiting the background light captured by the instrument and avoiding dangerous laser reflections. It is important that the operator always wear protective goggles when the laser is on.

Fig 4 – Raman spectroscopic analysis of a sulfur sample

Titanium dioxide polymorphism

The first chemical compound exhibiting polymorphism that we investigated with Raman spectroscopy is titanium dioxide. It is a chemical compound that comes in the form of a colorless crystalline powder, tending towards white; has the chemical formula TiO₂.
TiO₂ in nature is present in five different crystalline forms: Rutile, Anatase, Brookite and the two very high pressure polymorphs (due to impact from meteorites) akaogiite and TiO₂ II, which can be colored due to impurities present in the crystal. Rutile is the most common form: each titanium atom is octahedronally surrounded by six oxygen atoms; Anatase has a tetragonal structure, more elongated than that of rutile, while brookite has an orthorhombic structure. In our laboratory we found powdered titanium dioxide (rutile form) and an anatase crystal and we subjected the two samples to Raman spectroscopy. The results are reported in the spectra of figures 5, 6 and 7.

Fig.5 – Raman spectrum of titanium dioxide in the crystalline form of the mineral Anatase

Fig.6 – Raman spectrum of titanium dioxide in the crystalline form of the mineral Rutile

Fig.7 – Comparison of the Raman spectra of titanium dioxide in the two crystal configurations Anatase and Rutile

From the images above you can see the difference between the spectra of Rutile and Anatase. The differences are due to the different crystal structure of the two polymorphic forms: the atomic species involved in the crystalline vibrations are the same but the equilibrium inter-atomic distances are different and therefore the vibration frequencies of the bonds are different. In figure 8 we show the crystalline structure of the polymorphic forms of titanium dioxide.

Fig.8 – Crystal structure of the polymorphic forms of titanium dioxide (from https://giuseppedonatellis.altervista.org/polimorfismo/).

Calcium Carbonate Polymorphism

Another easily available substance which presents polymorphism is calcium carbonate. Calcium carbonate is the calcium salt of carbonic acid, having the formula CaCO₃. In geology, calcium carbonate is the material that makes up, in whole or in part, a great variety of types of rocks, precisely called carbonate rocks: marble, limestone, travertine. The minerals made up of calcium carbonate are aragonite, vaterite and calcite. Calcium carbonate (CaCO₃) has a stable trigonal phase (calcite), uniaxial birefringent and a metastable rhombic pseudohexagonal phase (aragonite), biaxial birefringent. In nature they can be found next to each other without observing the transition from the metastable to the stable phase.
In our laboratory we subjected two samples of calcite and aragonite to Raman spectroscopy, whose spectra are shown in figures 9 and 10.

Fig.9 – Raman spectrum of calcium carbonate in the crystalline form of Calcite

Fig.10 – Raman spectrum of calcium carbonate in the crystalline form of Aragonite

The Raman spectra of Calcite and Aragonite differ mainly in the peak at 300 cm^-1, present in the spectrum of Calcite but absent in that of Aragonite. As for titanium dioxide, the difference is due to the different crystal structure of the two minerals, as shown in figure 11.

Fig.11 – Crystal structure of Aragonite and Calcite.
Calcite with calcium with coordination = 6, Aragonite with calcium with coordination = 9
(from https://giuseppedonatellis.altervista.org/polimorfismo/)

Carbon polymorphism

Carbon with its two forms of graphite and diamond is an important example of polymorphism.
Carbon (C) comes in two modifications, diamond and graphite with different chemical and physical properties, both present in nature under the same ordinary conditions. Graphite, which crystallizes in the rhomboidal hexagonal system, represents the stable phase, is very soft, black, opaque; diamond crystallizes in the very hard, transparent, colorless cubic system and has a very slow transformation rate into graphite. By heating the diamond out of contact with the air it is possible to transform it into graphite, but the reverse process is difficult to achieve due to the very high pressure required. With our Raman system we have easily acquired the spectrum of the diamond, while for the graphite we have obtained a very broad spectrum. From the scientific literature, graphite should have a peak around 1600 cm^-1. The spectrum we obtained could depend on the low degree of crystallinity of our (amorphous) graphite sample or also on the wavelength of the excitation laser, which is not very suitable for highly absorbent materials in the visible band. The results are shown in figure 12.

Fig.12 – Raman spectra of carbon in the form of diamond and graphite

The Raman spectra of diamond and graphite are very different due to the different crystalline structure of the two substances. The diamond spectrum, with a single, very pronounced maximum at about 1300 cm^-1, is the expression of a highly symmetrical and ordered crystal structure. The lattice structures of diamond and graphite are shown in figure 13.

Fig.13 – Crystal structure of diamond and graphite. Diamond has cubic symmetry, graphite has hexagonal symmetry. Furthermore the diamond carbon has a tetrahedral bond, while the graphite carbon has a planar bond through Van Der Waals forces
(from https://giuseppedonatellis.altervista.org/polimorfismo/)

Solid and liquid phase of water

This is not expressly a case of polymorphism but it is still interesting to compare the Raman spectra of liquid water and solid water. In the gaseous phase, the water molecule has two vibration modes: symmetrical and anti-symmetric with frequencies of 3657 cm^-1 and 3756 cm^-1 respectively, as shown in Fig. 14. However, in water in the condensed phase, the network of hydrogen bonds that are established between neighboring molecules breaks the symmetry and leads to qualitatively different vibrations. The Raman spectra of the O-H bond show more complex bands. The Raman spectrum of the stretching vibration band of the O-H bond has a bimodal structure with two peaks centered at approximately 3400 cm^-1 and 3250 cm^-1 and an FWHM width of approximately 425 cm^-1. The substantial broadening of several hundred wavelengths seen in the Raman spectrum is a direct consequence of the very high sensitivity from the molecular environment of the stretching vibration of the O-H bond.

Fig 14 – Vibration frequencies of the water molecule (from Kananenka 2018 – The Journal of chemical Physics)

The Raman spectrum obtained by our instrument, shown in Fig. 15, shows the vibration bands at approximately 3400 and 3250 cm^-1 as predicted by the reference data available in the literature. The maximum corresponding to the bending mode at a frequency of about 1650 cm^-1 is also evident. The Raman spectrum of water in the solid phase, again shown in Fig. 15, shows the intensity increase of the symmetrical vibration mode and the decrease of the anti-symmetrical vibration mode, together with a shift towards lower energies.

Fig.15 – Raman spectra of water in liquid and solid form

From the analysis made with Raman spectroscopy it can be seen that the vibrational spectra of liquid water and solid water are very similar. This fact shows us that water in the liquid phase has a structure not too dissimilar to the structure of ice, at least on small dimensional scales.

The crystalline structure of ordinary ice, shown in figure 16, was first proposed by Linus Pauling in 1935. The structure of ice is approximately made up of rippled planes composed of pieces of hexagonal rings, with an oxygen atom at each vertex and the edges of the rings formed by hydrogen bonds. The planes alternate in an ABAB pattern, with B-planes being reflections of A-planes along the same axes as the planes.
The distance between oxygen atoms along each hydrogen bond is approximately 275 pm and is the same between all pairs of oxygen atoms bonded in the lattice. The angle between bonds in the crystal lattice comes very close to the tetrahedral angle of 109.5° which is also very close to the angle between hydrogen atoms in the water molecule (in the gaseous phase), which is 105°. This tetrahedral bond angle of the water molecule is the main explanation for the unusually low density of the crystal lattice.
This property causes naturally occurring ice to have the unusual characteristic of being less dense than its liquid form.

Fig.16 – Crystal structure of ice

Conclusions

Also for the study of crystalline polymorphism and for the study of the phase change of substances, Raman spectroscopy proves to be a powerful investigative tool, useful for distinguishing the different polymorphisms and for obtaining indications on the crystalline structure and on the vibration modes of the lattice.

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