In the late 1800s, the revelation that light extended beyond visible wavelengths led to the discovery of X-rays by Wilhelm Roentgen. Recognized as high-energy electromagnetic radiation with short wavelengths, X-rays prompted exploration into their interaction with crystals. Max von Laue proposed in 1912 that the periodic arrangement of atoms, ions, or molecules in crystals would cause them to diffract X-rays, a hypothesis confirmed through experiments with copper sulfate and zinc sulfide crystals.
This result was furthered through the work of von Laue and the father-and-son duo William Henry Bragg and William Lawrence Bragg. The Braggs formulated Bragg's law of diffraction in 1915, expressing the relationship between the wavelength of X-rays, the spacing of crystal planes, and the angle of incidence, nλ=2dsinθ.
This equation became fundamental in crystallography, enabling the determination of crystal structures. Here, n is an integer (0, 1, 2, 3, …), λ is the wavelength of X-rays, d is the distance between crystal planes, and θ is the angle between the crystal planes and the incident X-rays. The integer n of a diffraction order represents the number of wavelengths that can exist within the path difference between x-rays scattered from two atomic planes. The larger the integer, the lower the intensity of the diffraction peak.
The simplicity of Bragg's law can be deceptive. For cubic lattices, the process is straightforward, with only one type of atom contributing to X-ray diffraction. However, in molecular crystals like water (H2O), the complexity increases as each atom in the molecule can act as a refracting plane.
The determination of crystal structures is also influenced by the sample's form and orientation. Single-crystal samples provide specific unit-cell orientations, simplifying X-ray diffraction analysis. In contrast, powdered or polycrystalline samples introduce complexity, as each tiny crystal imposes its unique orientation on the diffracted X-rays.
An X-ray diffractometer comprises an X-ray source, a crystal mount, orientation-adjusting turntables, and an X-ray detector. The source emits monochromatic radiation, which the detector records after it's scattered by the crystal. Contemporary diffractometers utilize imaging plate detectors or charged-coupled device (CCD) detectors for quicker data collection. These detectors require radiation to be converted to light before recording. However, emerging pixel detectors can directly record radiation, eliminating the need for conversion to light.
Max von Laue proposed that crystals could diffract X-rays due to their periodic atomic arrangement.
X-rays, having about 100-picometer wavelength similar to internuclear distances in molecules, interact with electrons, enabling structure determination using an X-ray diffractometer.
Later, it was furthered by William and Lawrence Bragg, considering an ordered array of atoms in lattice planes separated by a distance d. If two waves of monochromatic X-rays hit the crystal, one wave is reflected from an atom in the first lattice plane and the second from an atom in the second lattice plane.
When hit at a random angle, it results in destructive interference, producing no detectable diffracted X-rays. On the other hand, when hit at a specific angle, constructive interference leads to measurable diffracted X-rays.
This constructive interference happens if the additional distance traveled by the second wave equals a multiple of the wavelength, expressed as 2d sin θB.
This equation is known as Bragg's law of diffraction, which relates X-ray wavelength, crystal lattice spacing, and incidence angle.
Bragg's law allows for different diffraction orders, each corresponding to integral values of n.
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