Why X-rays?:

When measuring distance, it is important to select a unit of measure that is on the scale of the object being measured. For example, to measure the length of a pencil, one would not want to use a yard stick that only has feet gradations. Similarly, if one wanted to measure the length of a car, it would be inappropriate to use a 12-inch ruler with cm marks. Therefore, in order to study bonds in molecules, it is important to use a wavelength of light that matches the length of those bonds. X-rays have wavelengths in the Å range, which matches perfectly with typical bond distances (1-3 Å).

The Unit Cell:

Imagine trying to describe all of the molecules on the tip of a pen. If one approximates that it's comprised of 6.02 × 1023 molecules (or 1 mole), it would seem nearly impossible to describe that object on the molecular level. The complexity of an object is simplified when it exists as a crystal, where the contents of a unit cell can be used to describe the entire structure. The unit cell of a crystal is the least volume containing a repeating unit of a solid. It is defined as a 3D "box" with lengths a, b, and c, and angles α, β, and γ (Figure 1). The unit cell allows chemists to describe the contents of a crystal using a fraction of or a small number of atoms or molecule(s). By repeating the unit cell in space, one can generate a 3D representation of the solid.

Figure 1. Unit cell parameters.

Experimental Setup:

Single-crystal and powder XRD have similar instrumentation setups. For single-crystal XRD, a crystal is mounted and centered within the X-ray beam. For powder XRD, a polycrystalline sample is ground into a fine powder and mounted on a plate. The sample (single- or polycrystalline) is irradiated with X-rays and the diffracted X-rays hit a detector. During data collection, the sample is rotated with respect to the X-ray source and detector.

Double-slit Experiment:

Recall that light has both wave- and particle-like properties. When monochromatic light enters two slits, the wave-like property of light results in light emanating in a spherical fashion from each slit. When the waves interact, they can add together (if the waves have the same wavelength and phase) or cancel each other out (if the waves have the same wavelength, but have different phases), which is called constructive and destructive interference, respectively. The resulting light pattern is made of a series of lines, where the light areas represent constructive interference while the dark areas are a result of destructive interference.

Typical Diffraction Patterns: Single-crystal Versus Powder:

Upon irradiation of a crystal by X-rays, the radiation is diffracted upon interaction with electron density within the crystal. Just like water waves in the classic double-slit experiment from physics, the diffracted X-rays interact, resulting in constructive and destructive interference. In XRD, the diffraction pattern represents the electron density due to atoms and bonds within the crystal. A typical diffraction pattern for a single crystal is shown in (Figure 2). Notice that the diffraction pattern is comprised of spots instead of lines like in the double slit experiment. In fact, these “spots” are 2D slices of 3-dimensional spheres. Crystallographers use a computer program to integrate the resulting spots in order to determine the shape and intensity of the diffracted X-rays. In a powder sample, the X-rays interact with many tiny crystals in random orientations. Therefore, instead of seeing spots, a circular diffraction pattern is observed (Figure 3). The intensities of the diffracted circles are then plotted against the angles between the ring the beam axis (denoted 2θ) to give a 2 dimensional plot known as a powder pattern.

Here, we will collect single crystal and powder XRD data on Mo2(ArNC(H)NAr)4 where Ar = p-MeOC6H5, which was synthesized in the module “Preparation and Characterization of a Quadruply Metal–Metal Bonded Compound.”

Figure 2. Single Crystal Diffraction Pattern.

Figure 3. Powder XRD: Circular Diffraction Pattern.