The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...

Crystal symmetry operations are isometric transformations that map objects onto indistinguishable copies while preserving distances, angles, and volumes. The simplest symmetry operation is translation, which shifts the entire infinite crystal lattice parallelly by a translation vector.Crystallographic rotations involve rotations by an angle of 2π/n around an axis without changing the positions of points on the axis. It is called the rotational axis of the symmetry, denoted by n. The combination...

Crystallographic point groups represent the various symmetry operations that can occur within crystals. They are unique in that at least one point will always remain unchanged during these actions. For instance, consider the triclinic system. This system, devoid of any axis or plane of symmetry, aligns with the C1 and Ci point groups.where Cᵢ is characterized solely by a center of inversion.Contrastingly, the monoclinic system introduces an element of symmetry. This system with one plane and...

The spin state of an NMR-active nucleus can have a slight effect on its immediate electronic environment. This effect propagates through the intervening bonds and affects the electronic environments of NMR-active nuclei up to three bonds away; occasionally, even farther. This phenomenon is called spin–spin coupling or J-coupling. Coupling interactions are mutual and result in small changes in the absorption frequencies of both nuclei involved. While nuclei of the same element are involved in...

The underlying principle of Raman spectroscopy is based on the interaction between light and matter, specifically molecules' inelastic scattering of photons. When a monochromatic beam of light, typically from a laser source, interacts with a sample, most scattered light has the same frequency as the incident light. This is known as Rayleigh scattering.
However, a small fraction of the scattered light exhibits a frequency shift due to the exchange of energy between the incident photons and the...

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...