Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics. The word crystallography is derived from the Ancient Greek word κρύσταλλος, with its meaning extending to all solids with some degree of transparency, and γράφειν. In July 2012, the United Nations recognised the importance of the science of crystallography by proclaiming that 2014 would be the International Year of Crystallography.
X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles and intensities of these diffracted beams, a crystallographer can produce a three-dimensional picture of the density of electrons within the crystal. From this electron density, the mean positions of the atoms in the crystal can be determined, as well as their chemical bonds, their crystallographic disorder, and various other information.
Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of reflected radiation from the angle predicted by the law of reflection. Reflections of radiation that undergo scattering are often called diffuse reflections and unscattered reflections are called specular (mirror-like) reflections. Originally, the term was confined to light scattering. As more "ray"-like phenomena were discovered, the idea of scattering was extended to them, so that William Herschel could refer to the scattering of "heat rays" in 1800. John Tyndall, a pioneer in light scattering research, noted the connection between light scattering and acoustic scattering in the 1870s. Near the end of the 19th century, the scattering of cathode rays and X-rays was observed and discussed. With the discovery of subatomic particles and the development of quantum theory in the 20th century, the sense of the term became broader as it was recognized that the same mathematical frameworks used in light scattering could be applied to many other phenomena.
Electron diffraction refers to changes in the direction of electron beams due to interactions with atoms. Close to the atoms the changes are described as Fresnel diffraction; far away they are called Fraunhofer diffraction. The resulting map of the directions of the electrons far from the sample is called a diffraction pattern. These are similar to x-ray and neutron diffraction patterns.
Neutron diffraction or elastic neutron scattering is the application of neutron scattering to the determination of the atomic and/or magnetic structure of a material. A sample to be examined is placed in a beam of thermal or cold neutrons to obtain a diffraction pattern that provides information of the structure of the material. The technique is similar to X-ray diffraction but due to their different scattering properties, neutrons and X-rays provide complementary information: X-Rays are suited for superficial analysis, strong x-rays from synchrotron radiation are suited for shallow depths or thin specimens, while neutrons having high penetration depth are suited for bulk samples.
A synchrotron light source is a source of electromagnetic radiation (EM) usually produced by a storage ring, for scientific and technical purposes. First observed in synchrotrons, synchrotron light is now produced by storage rings and other specialized particle accelerators, typically accelerating electrons. Once the high-energy electron beam has been generated, it is directed into auxiliary components such as bending magnets and insertion devices in storage rings and free electron lasers. These supply the strong magnetic fields perpendicular to the beam which are needed to convert high energy electrons into photons.
In physics and chemistry, Bragg's law, Wulff–Bragg's condition or Laue–Bragg interference, a special case of Laue diffraction, gives the angles for coherent scattering of waves from a large crystal lattice. It encompasses the superposition of wave fronts scattered by lattice planes, leading to a strict relation between wavelength and scattering angle, or else to the wavevector transfer with respect to the crystal lattice. Such law had initially been formulated for X-rays upon crystals. However, It applies to all sorts of quantum beams, including neutron and electron waves at atomic distances if there are a large number of atoms, as well as visible light with artificial periodic microscale lattices.
Reflection high-energy electron diffraction (RHEED) is a technique used to characterize the surface of crystalline materials. RHEED systems gather information only from the surface layer of the sample, which distinguishes RHEED from other materials characterization methods that also rely on diffraction of high-energy electrons. Transmission electron microscopy, another common electron diffraction method samples mainly the bulk of the sample due to the geometry of the system, although in special cases it can provide surface information. Low-energy electron diffraction (LEED) is also surface sensitive, but LEED achieves surface sensitivity through the use of low energy electrons.
Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected.
The Ewald sphere is a geometric construction used in electron, neutron, and x-ray diffraction which shows the relationship between:
In physics, the phase problem is the problem of loss of information concerning the phase that can occur when making a physical measurement. The name comes from the field of X-ray crystallography, where the phase problem has to be solved for the determination of a structure from diffraction data. The phase problem is also met in the fields of imaging and signal processing. Various approaches of phase retrieval have been developed over the years.
The Davisson–Germer experiment was a 1923-27 experiment by Clinton Davisson and Lester Germer at Western Electric, in which electrons, scattered by the surface of a crystal of nickel metal, displayed a diffraction pattern. This confirmed the hypothesis, advanced by Louis de Broglie in 1924, of wave-particle duality, and also the wave mechanics approach of the Schrödinger equation. It was an experimental milestone in the creation of quantum mechanics.
Powder diffraction is a scientific technique using X-ray, neutron, or electron diffraction on powder or microcrystalline samples for structural characterization of materials. An instrument dedicated to performing such powder measurements is called a powder diffractometer.
X-ray optics is the branch of optics that manipulates X-rays instead of visible light. It deals with focusing and other ways of manipulating the X-ray beams for research techniques such as X-ray crystallography, X-ray fluorescence, small-angle X-ray scattering, X-ray microscopy, X-ray phase-contrast imaging, and X-ray astronomy.
The dynamical theory of diffraction describes the interaction of waves with a regular lattice. The wave fields traditionally described are X-rays, neutrons or electrons and the regular lattice are atomic crystal structures or nanometer-scale multi-layers or self-arranged systems. In a wider sense, similar treatment is related to the interaction of light with optical band-gap materials or related wave problems in acoustics. The sections below deal with dynamical diffraction of X-rays.
The X-ray standing wave (XSW) technique can be used to study the structure of surfaces and interfaces with high spatial resolution and chemical selectivity. Pioneered by B.W. Batterman in the 1960s, the availability of synchrotron light has stimulated the application of this interferometric technique to a wide range of problems in surface science.
Helium atom scattering (HAS) is a surface analysis technique used in materials science. HAS provides information about the surface structure and lattice dynamics of a material by measuring the diffracted atoms from a monochromatic helium beam incident on the sample.
Grazing-incidence small-angle scattering (GISAS) is a scattering technique used to study nanostructured surfaces and thin films. The scattered probe is either photons or neutrons. GISAS combines the accessible length scales of small-angle scattering and the surface sensitivity of grazing incidence diffraction (GID).
The angle of incidence, in geometric optics, is the angle between a ray incident on a surface and the line perpendicular to the surface at the point of incidence, called the normal. The ray can be formed by any waves, such as optical, acoustic, microwave, and X-ray. In the figure below, the line representing a ray makes an angle θ with the normal. The angle of incidence at which light is first totally internally reflected is known as the critical angle. The angle of reflection and angle of refraction are other angles related to beams.
