Homometric structures

Last updated

In chemistry and crystallography, crystal structures that have the same set of interatomic distances are called homometric structures. [1] Homometric structures need not be congruent (that is, related by a rigid motion or reflection). Homometric crystal structures produce identical diffraction patterns; therefore, they cannot be distinguished by a diffraction experiment.

Recently, a Monte Carlo algorithm was proposed to calculate the number of homometric structures corresponding to any given set of interatomic distances. [2]

See also

Notes

  1. Patterson, A.L. (1939). "Homometric Structures". Nature. 143 (3631): 939–940. Bibcode:1939Natur.143..939P. doi:10.1038/143939b0. S2CID   4122325.
  2. Gommes C.J.; Jiao Y; Torquato S (2012). "Density of States for a Specified Correlation Function and the Energy Landscape". Phys. Rev. Lett. 108 (8): 080601. arXiv: 1201.1142 . Bibcode:2012PhRvL.108h0601G. doi:10.1103/PhysRevLett.108.080601. PMID   22463509. S2CID   166914.


Related Research Articles

<span class="mw-page-title-main">Amorphous solid</span> Non-crystalline solid

In condensed matter physics and materials science, an amorphous solid is a solid that lacks the long-range order that is characteristic of a crystal. The terms "glass" and "glassy solid" are sometimes used synonymously with amorphous solid; however, these terms refer specifically to amorphous materials that undergo a glass transition. Examples of amorphous solids include glasses, metallic glasses, and certain types of plastics and polymers.

<span class="mw-page-title-main">Crystallographic defect</span> Disruption of the periodicity of a crystal lattice

A crystallographic defect is an interruption of the regular patterns of arrangement of atoms or molecules in crystalline solids. The positions and orientations of particles, which are repeating at fixed distances determined by the unit cell parameters in crystals, exhibit a periodic crystal structure, but this is usually imperfect. Several types of defects are often characterized: point defects, line defects, planar defects, bulk defects. Topological homotopy establishes a mathematical method of characterization.

<span class="mw-page-title-main">Quasicrystal</span> Chemical structure

A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical crystallographic restriction theorem, can possess only two-, three-, four-, and six-fold rotational symmetries, the Bragg diffraction pattern of quasicrystals shows sharp peaks with other symmetry orders—for instance, five-fold.

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.

An atom interferometer is an interferometer which uses the wave character of atoms. Similar to optical interferometers, atom interferometers measure the difference in phase between atomic matter waves along different paths. Atom interferometers have many uses in fundamental physics including measurements of the gravitational constant, the fine-structure constant, the universality of free fall, and have been proposed as a method to detect gravitational waves. They also have applied uses as accelerometers, rotation sensors, and gravity gradiometers.

<span class="mw-page-title-main">Paul Steinhardt</span> American theoretical physicist (born 1952)

Paul Joseph Steinhardt is an American theoretical physicist whose principal research is in cosmology and condensed matter physics. He is currently the Albert Einstein Professor in Science at Princeton University, where he is on the faculty of both the Departments of Physics and of Astrophysical Sciences.

This is a timeline of subatomic particle discoveries, including all particles thus far discovered which appear to be elementary given the best available evidence. It also includes the discovery of composite particles and antiparticles that were of particular historical importance.

The Patterson function is used to solve the phase problem in X-ray crystallography. It was introduced in 1935 by Arthur Lindo Patterson while he was a visiting researcher in the laboratory of Bertram Eugene Warren at MIT.

<span class="mw-page-title-main">Lanthanum hexaboride</span> Chemical compound

Lanthanum hexaboride (LaB6, also called lanthanum boride and LaB) is an inorganic chemical, a boride of lanthanum. It is a refractory ceramic material that has a melting point of 2210 °C, and is insoluble in water and hydrochloric acid. It is extremely hard, with a Mohs hardness of 9.5. It has a low work function and one of the highest electron emissivities known, and is stable in vacuum. Stoichiometric samples are colored intense purple-violet, while boron-rich ones (above LaB6.07) are blue. Ion bombardment changes its color from purple to emerald green. LaB6 is a superconductor with a relatively low transition temperature of 0.45 K.

<span class="mw-page-title-main">Bond order potential</span>

Bond order potential is a class of empirical (analytical) interatomic potentials which is used in molecular dynamics and molecular statics simulations. Examples include the Tersoff potential, the EDIP potential, the Brenner potential, the Finnis–Sinclair potentials, ReaxFF, and the second-moment tight-binding potentials. They have the advantage over conventional molecular mechanics force fields in that they can, with the same parameters, describe several different bonding states of an atom, and thus to some extent may be able to describe chemical reactions correctly. The potentials were developed partly independently of each other, but share the common idea that the strength of a chemical bond depends on the bonding environment, including the number of bonds and possibly also angles and bond lengths. It is based on the Linus Pauling bond order concept and can be written in the form

<span class="mw-page-title-main">Nematicon</span>

In optics, a nematicon is a spatial soliton in nematic liquid crystals (NLC). The name was invented in 2003 by G. Assanto. and used thereafter Nematicons are generated by a special type of optical nonlinearity present in NLC: the light induced reorientation of the molecular director. This nonlinearity arises from the fact that the molecular director tends to align along the electric field of light. Nematicons are easy to generate because the NLC dielectric medium exhibits the following properties:

Interatomic Coulombic decay (ICD) is a general, fundamental property of atoms and molecules that have neighbors. Interatomic (intermolecular) Coulombic decay is a very efficient interatomic (intermolecular) relaxation process of an electronically excited atom or molecule embedded in an environment. Without the environment the process cannot take place. Until now it has been mainly demonstrated for atomic and molecular clusters, independently of whether they are of van-der-Waals or hydrogen bonded type.

<span class="mw-page-title-main">Structure of liquids and glasses</span> Atomic-scale non-crystalline structure of liquids and glasses

The structure of liquids, glasses and other non-crystalline solids is characterized by the absence of long-range order which defines crystalline materials. Liquids and amorphous solids do, however, possess a rich and varied array of short to medium range order, which originates from chemical bonding and related interactions. Metallic glasses, for example, are typically well described by the dense random packing of hard spheres, whereas covalent systems, such as silicate glasses, have sparsely packed, strongly bound, tetrahedral network structures. These very different structures result in materials with very different physical properties and applications.

<span class="mw-page-title-main">Time crystal</span> Structure that repeats in time; a novel type or phase of non-equilibrium matter

In condensed matter physics, a time crystal is a quantum system of particles whose lowest-energy state is one in which the particles are in repetitive motion. The system cannot lose energy to the environment and come to rest because it is already in its quantum ground state. Because of this, the motion of the particles does not really represent kinetic energy like other motion; it has "motion without energy". Time crystals were first proposed theoretically by Frank Wilczek in 2012 as a time-based analogue to common crystals – whereas the atoms in crystals are arranged periodically in space, the atoms in a time crystal are arranged periodically in both space and time. Several different groups have demonstrated matter with stable periodic evolution in systems that are periodically driven. In terms of practical use, time crystals may one day be used as quantum computer memory.

<span class="mw-page-title-main">Hydrodynamic quantum analogs</span> Similar behavior of quantum systems to droplets bouncing on a fluid

In physics, the hydrodynamic quantum analogs refer to experimentally-observed phenomena involving bouncing fluid droplets over a vibrating fluid bath that behave analogously to several quantum-mechanical systems.

CeCoIn5 ("Cerium-Cobalt-Indium 5") is a heavy-fermion superconductor with a layered crystal structure, with somewhat two-dimensional electronic transport properties. The critical temperature of 2.3 K is the highest among all of the Ce-based heavy-fermion superconductors.

<span class="mw-page-title-main">Interatomic potential</span> Functions for calculating potential energy

Interatomic potentials are mathematical functions to calculate the potential energy of a system of atoms with given positions in space. Interatomic potentials are widely used as the physical basis of molecular mechanics and molecular dynamics simulations in computational chemistry, computational physics and computational materials science to explain and predict materials properties. Examples of quantitative properties and qualitative phenomena that are explored with interatomic potentials include lattice parameters, surface energies, interfacial energies, adsorption, cohesion, thermal expansion, and elastic and plastic material behavior, as well as chemical reactions.

Quantum microscopy allows microscopic properties of matter and quantum particles to be measured and imaged. Various types of microscopy use quantum principles. The first microscope to do so was the scanning tunneling microscope, which paved the way for development of the photoionization microscope and the quantum entanglement microscope.

<span class="mw-page-title-main">Orbital angular momentum of free electrons</span>

Electrons in free space can carry quantized orbital angular momentum (OAM) projected along the direction of propagation. This orbital angular momentum corresponds to helical wavefronts, or, equivalently, a phase proportional to the azimuthal angle. Electron beams with quantized orbital angular momentum are also called electron vortex beams.

Dov I. Levine is an American-Israeli physicist, known for his research on quasicrystals, soft condensed matter physics, and statistical mechanics out of equilibrium.