WavenumberIn the physical sciences, the wavenumber (or wave number), also known as repetency, is the spatial frequency of a wave, measured in cycles per unit distance (ordinary wavenumber) or radians per unit distance (angular wavenumber). It is analogous to temporal frequency, which is defined as the number of wave cycles per unit time (ordinary frequency) or radians per unit time (angular frequency). In multidimensional systems, the wavenumber is the magnitude of the wave vector. The space of wave vectors is called reciprocal space.
Transmission electron microscopyTransmission electron microscopy (TEM) is a microscopy technique in which a beam of electrons is transmitted through a specimen to form an image. The specimen is most often an ultrathin section less than 100 nm thick or a suspension on a grid. An image is formed from the interaction of the electrons with the sample as the beam is transmitted through the specimen. The image is then magnified and focused onto an imaging device, such as a fluorescent screen, a layer of photographic film, or a sensor such as a scintillator attached to a charge-coupled device.
Wave–particle dualityWave–particle duality is the concept in quantum mechanics that quantum entities exhibit both particle and a wave properties according to the experimental circumstances. It expresses the inability of the classical concepts "particle" or "wave" to fully describe the behaviour of quantum-scale objects. As Albert Einstein wrote: It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty.
Wave packetIn physics, a wave packet (also known as a wave train or wave group) is a short burst of localized wave action that travels as a unit, outlined by an envelope. A wave packet can be analyzed into, or can be synthesized from, a potentially-infinite set of component sinusoidal waves of different wavenumbers, with phases and amplitudes such that they interfere constructively only over a small region of space, and destructively elsewhere.
Electron diffractionElectron 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 (Fraunhofer diffraction) is called a diffraction pattern, see for instance Figure 1. These patterns are similar to x-ray and neutron diffraction patterns, and are used to study the atomic structure of gases, liquids, surfaces and bulk solids.
Electron energy loss spectroscopyElectron energy loss spectroscopy (EELS) is a form of electron microscopy in which a material is exposed to a beam of electrons with a known, narrow range of kinetic energies. Some of the electrons will undergo inelastic scattering, which means that they lose energy and have their paths slightly and randomly deflected. The amount of energy loss can be measured via an electron spectrometer and interpreted in terms of what caused the energy loss.
X-ray crystallographyX-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.
PhononIn physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phonon is an excited state in the quantum mechanical quantization of the modes of vibrations for elastic structures of interacting particles. Phonons can be thought of as quantized sound waves, similar to photons as quantized light waves. However, photons are fundamental particles that can be individually detected, whereas phonons, being quasiparticles, are an emergent phenomenon.
Planck constantThe Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalence, the relationship between mass and frequency. Specifically, a photon's energy is equal to its frequency multiplied by the Planck constant. The constant is generally denoted by . The reduced Planck constant, or Dirac constant, equal to divided by , is denoted by .
Dispersion relationIn the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the dispersion relation, one can calculate the frequency-dependent phase velocity and group velocity of each sinusoidal component of a wave in the medium, as a function of frequency.
