# Single crystal X-Ray Diffraction (XRD)

Single crystal X-ray diffraction (SCXRD) is a non-destructive technique employed for determination of the atomic structure of a crystal of a certain material (compound). When a specimen is fired with the X-ray beam of incidence, the crystalline atoms cause its diffraction into many directions (Fig.1).

Figure 1. X-ray diffraction pattern of a crystallized enzyme. Figure from Wikipedia. License: CC BY-SA 3.0.

# Theory behind SCXRD

Why do we want to use X-ray, not visible light or light of any other wavelength? Visible light radiation falls in range from 400 to 700 nm. However, smaller objects require shorter wavelength. Molecules' size varies from a few to hundreds of ångströms, which is a way too small to be seen with visible light. Hence, wavelength used for crystallography is ca. 1 Å. This is the order of bonds and atomic radii. This explains why X-rays are used for structure determination.

The story of X-ray diffractometry started in 1912, when Max von Laue observed the first X-ray diffraction pattern of the CuSO4 crystal. The law enabling the identification of the atoms positions has been discovered one year later by W.L. Bragg and W.H. Bragg and named Bragg’s law (1).                                                                                                                                                                                nλ=2dhklsinθ                                                                                                                                                                                  (1)

They found out that solid crystals, at certain wavelengths and incident angles, produced intense peaks of reflected radiation. William Lawrence Bragg interpreted this result by presenting a crystal as a set of discrete parallel planes separated by a constant parameter d. It was also realized that a Bragg peak occurs only in case when the reflections from various planes undergo the constructive interference. The interference is constructive when the phase shift is a multiple of 2π. In other words, for constructive interference to occur the path difference must be a whole wavelength (nλ where n is integer) giving the Bragg equation for diffraction.

The technique is essentially very simple: a single crystal scatters a collimated, monochromatic beam of X-rays, and the scattered beams diffracted by the sample are then measured. Processing information about the position and intensity of these diffracted X-ray beams (or reflections) yields information about the atomic arrangement within the crystalline material (Fig. 2).

Figure 2. Graphical representation of the SCXRD technique (Figure: Nea Möttönen).

# Practicalities

Any X-ray diffractometer consists of three basic elements: an X-ray tube, a sample holder, and an X-ray detector.

X-rays are generated in an X-ray tube by heating a filament to produce electrons, accelerating the electrons toward a target by applying a voltage, and impact of the electrons with the target material. These electrons possess sufficient energy to knock out the inner shell electrons of a specimen giving characteristic X-ray spectra.

Originally, the beam of electrons coming out of a tube mainly consists of Kα and Kβ radiation components. In turn, Kα consists of Kα1 and Kα2. The technique requires Kα1 mainly, which has a slightly shorter wavelength and twice the intensity as Kα2, meaning that Kα2  and Kβ  radiations need to be eliminated. To achieve this, foil or crystal monochromators (e.g. Ge (111) crystal) are applied.

Molybdenum is one of the common target materials for SCXRD. Mo Kα radiation equals to 0.7107Å. These X-rays are collimated (made accurately parallel) and directed onto the sample.

A beam stop is located directly opposite the collimator to block transmitted rays and prevent burn-out of the detector. Reflected rays are not picked up by the detector due to the angles involved. Diffracted rays at the correct orientation for the configuration are then collected by the detector and converts the signal to a count rate which is then used as output information.

Modern diffractometers use CCD (charge-coupled device) system to transform the X-ray photons into an electrical signal which are then sent to a computer for further processing. Such detectors incorporate a layer of fluorescent material (e.g. Gd2O2S) that is sensitive to X-rays.

The most popular single-crystal diffractometers used nowadays are 4-circle goniometers. These four circles refer to the four angles (2θ, χ, φ, and Ω) that define the relationship between the crystal lattice, the incident ray and detector.

It is worth mentioning, the level of background noise is high most of the times when measuring at ambient temperature. This is due to the thermal motion within a sample crystal. The problem can be solved by cooling down the sample using liquid nitrogen flow.

# Procedure

Let us now have a look at the flow chart (Fig. 3) presenting the mains steps in single-crystal x-ray diffraction analysis.

Figure 3. Flow chart of single-crystal XRD analysis (Figure: Nea Möttönen).

## Checking the quality of the crystal

Do not forget the golden rule: "Garbage in - Garbage out". If you want to obtain reliable data, use a good quality crystal. Crystal quality can be checked by polarizing microscope:

• clear edges and faces
• free of inclusions
• bright
• equidimensional

## Crystal mounting

• on a thin glass fiber
• in a capillary
• in a loop

A crystal is mounted with glue, grease or oil. Crystal holder is mounted on a XY-goniometer head with height adjustment for accurate centering.

In case of air-/moisture-sensitive crystal:

• mounting in a capillary (in glovebox or Schlenk line)
• dry inert oil as an insulator
• low temperature data collection (< -80ºC)

## Determination of the unit cell

A few orientation exposures are made that give an idea about the quality/diffracting power of the crystal and a test unit cell. Further indexing of the collected reflections provides the reciprocal vectors, symmetry and crystal system can be selected.

The step is essentially the simplest in the entire analysis, nevertheless, indexing issues might occur and the correct unit cell cannot be located then. The most common reason for this is that the chosen crystal is not single. Consequently, some reflections belong to the "satellite". The best solution is to look for another crystal.

Next step is the selection of data to be measured. The scattering angle θmax defines the measured sphere in reciprocal space (Mo Kα - θ≥25º, Cu Kα - θ=25º).

The segment of the sphere in reciprocal space (to be measured) is dependent on the Laue symmetry. For example, for crystals possessing the following crystal systems:

• Triclinic: ≥ hemisphere
• Orthorhombic: ≥ octant
• Trigonal: ≥ 2/3 of hemisphere

## Data collection parameters

May vary significantly with detemined intensities and unit cell.

• Exposure time: chosen to make the strongest reflections
• Detector-to-crystal distance: the shorter, the greater is the range of θ, the smaller is the separation of the reflections
• Angle increment: small lattice constants → large separation of reciprocal lattice points → large ω-ranges may be used (up to 2º)

## Data processing

Integration of diffraction spots (diffraction spots are shown in Figure 1). Analysis of intensities provides the background, raw intensity and net intensity as well as a standard uncertainty for each intensity. A few additional calculations are performed to identify the structure factor F0 and correct the raw data using the polarization factor ρ, the Lorentz factor L and absorption correction.

As a result of experimental measurements and data processing, the following data derived:

• unit cell parameters
• space group
• intensity data

## Structure solution and refinement

The Fourier transform (Fig. 4) provides the data on location of atoms in the unit cell. Suchwise, the electron density can be identified for every point of the unit cell and correlate the electron density with atoms.

Figure 4. Fourier transform for structure identification (Figure: Nea Möttönen).

# References

 1 1 Stout G. H., Lyle H. Jensen. X-ray structure determination: a practical guide. Vol. 2. New York: Macmillan, 1968. 2 1 2 Clark, C. M.; Dutrow, B. Single-crystal X-ray Diffraction. Integration Research and Education: Geochemical Instrumentation and Analysis. Carleton College Science Education Resource Center, 2012, 10. 3 1 4 1 Goeta, A. E.; Howard, J. A. K. Low temperature single crystal X-ray diffraction: advantages, instrumentation and applications. Chemical Society Reviews, 2004, 33.8, 490-500. 5 1 Warren, B. E. X-ray Diffraction. Courier Corporation, 1969. 6 1 Hasegawa, K. Introduction to single crystal X-ray analysis. mass spectroscopy equipped with a skimmer-type interface, 2012, 14. 7 1 2 Rankin, D.W.H.; Mitzel, N.; Morrison C. Structural Methods in Molecular Inorganic Chemistry, Wiley, 2013, Chapter 10. 8 1 2 Pflugrath, J. W.; The finer things in X-ray diffraction data collection, Acta Cryst., 1999, 55, 1718-1725. 9 1 2 Protein Crystallography Course, Fourier transforms: structure factors, phases and electron density: http://www-structmed.cimr.cam.ac.uk/Course/Fourier/Fourier.html [access 16.05.2017]
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