Determination of Crystal Structures

Crystals diffract X-rays because of their periodic atomic arrangement. Max von Laue proposed that X-rays, with wavelengths around 100 picometers similar to internuclear distances, interact with electrons in the ordered lattice planes. This interaction enables the determination of crystal structures through measurable diffracted X-rays.

Bragg's law, expressed as nλ=2d sin θ, relates X-ray wavelength, crystal plane spacing, and incidence angle. When X-rays hit lattice planes at specific angles, constructive interference occurs when the path difference equals a multiple of the wavelength. This produces measurable diffracted X-rays, with n representing the diffraction order.

Single-crystal samples provide specific unit-cell orientations, simplifying X-ray diffraction analysis. Powdered or polycrystalline samples introduce complexity because each tiny crystal imposes its unique orientation on diffracted X-rays. This variation makes analysis more challenging but enables study of materials in different physical forms.

An X-ray diffractometer comprises an X-ray source emitting monochromatic radiation, a crystal mount, orientation-adjusting turntables, and an X-ray detector. Modern detectors include imaging plate detectors, charged-coupled device (CCD) detectors for quick data collection, and emerging pixel detectors that directly record radiation without light conversion.

In molecular crystals like water, complexity increases because each atom in the molecule acts as a refracting plane. Unlike cubic lattices with one atom type contributing to diffraction, molecular crystals have multiple atoms per unit cell, each scattering X-rays differently and requiring more sophisticated analysis.

The integer n in Bragg's law represents the diffraction order, indicating the number of wavelengths existing within the path difference between X-rays scattered from two atomic planes. Higher diffraction orders correspond to larger integers but produce lower intensity peaks, limiting practical analysis to lower orders.

Contemporary diffractometers use imaging plate detectors or charged-coupled device (CCD) detectors for faster data collection than older methods. Emerging pixel detectors directly record radiation, eliminating the need for conversion to light. This advancement speeds up crystal structure determination and improves data quality.