Scanning electron microscopeA scanning electron microscope (SEM) is a type of electron microscope that produces images of a sample by scanning the surface with a focused beam of electrons. The electrons interact with atoms in the sample, producing various signals that contain information about the surface topography and composition of the sample. The electron beam is scanned in a raster scan pattern, and the position of the beam is combined with the intensity of the detected signal to produce an image.
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.
Electron microscopeAn electron microscope is a microscope that uses a beam of electrons as a source of illumination. They use electron optics that are analogous to the glass lenses of an optical light microscope. As the wavelength of an electron can be up to 100,000 times shorter than that of visible light, electron microscopes have a higher resolution of about 0.1 nm, which compares to about 200 nm for light microscopes.
Ionization energyIn physics and chemistry, ionization energy (IE) (American English spelling), ionisation energy (British English spelling) is the minimum energy required to remove the most loosely bound electron of an isolated gaseous atom, positive ion, or molecule. The first ionization energy is quantitatively expressed as X(g) + energy ⟶ X+(g) + e− where X is any atom or molecule, X+ is the resultant ion when the original atom was stripped of a single electron, and e− is the removed electron.
Scheme (mathematics)In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x = 0 and x2 = 0 define the same algebraic variety but different schemes) and allowing "varieties" defined over any commutative ring (for example, Fermat curves are defined over the integers). Scheme theory was introduced by Alexander Grothendieck in 1960 in his treatise "Éléments de géométrie algébrique"; one of its aims was developing the formalism needed to solve deep problems of algebraic geometry, such as the Weil conjectures (the last of which was proved by Pierre Deligne).
Electronic band structureIn solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called band gaps or forbidden bands). Band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron in a large, periodic lattice of atoms or molecules.
Dynamical mean-field theoryDynamical mean-field theory (DMFT) is a method to determine the electronic structure of strongly correlated materials. In such materials, the approximation of independent electrons, which is used in density functional theory and usual band structure calculations, breaks down. Dynamical mean-field theory, a non-perturbative treatment of local interactions between electrons, bridges the gap between the nearly free electron gas limit and the atomic limit of condensed-matter physics.
Hilbert schemeIn algebraic geometry, a branch of mathematics, a Hilbert scheme is a scheme that is the parameter space for the closed subschemes of some projective space (or a more general projective scheme), refining the Chow variety. The Hilbert scheme is a disjoint union of projective subschemes corresponding to Hilbert polynomials. The basic theory of Hilbert schemes was developed by . Hironaka's example shows that non-projective varieties need not have Hilbert schemes.
Inert-pair effectThe inert-pair effect is the tendency of the two electrons in the outermost atomic s-orbital to remain unshared in compounds of post-transition metals. The term inert-pair effect is often used in relation to the increasing stability of oxidation states that are two less than the group valency for the heavier elements of groups 13, 14, 15 and 16. The term "inert pair" was first proposed by Nevil Sidgwick in 1927. The name suggests that the outermost s electron pairs are more tightly bound to the nucleus in these atoms, and therefore more difficult to ionize or share.
Sinusoidal plane waveIn physics, a sinusoidal plane wave is a special case of plane wave: a field whose value varies as a sinusoidal function of time and of the distance from some fixed plane. It is also called a monochromatic plane wave, with constant frequency (as in monochromatic radiation). For any position in space and any time , the value of such a field can be written as where is a unit-length vector, the direction of propagation of the wave, and "" denotes the dot product of two vectors.
18-electron ruleThe 18-electron rule is a chemical rule of thumb used primarily for predicting and rationalizing formulas for stable transition metal complexes, especially organometallic compounds. The rule is based on the fact that the valence orbitals in the electron configuration of transition metals consist of five (n−1)d orbitals, one ns orbital, and three np orbitals, where n is the principal quantum number. These orbitals can collectively accommodate 18 electrons as either bonding or non-bonding electron pairs.
Structural functionalismStructural functionalism, or simply functionalism, is "a framework for building theory that sees society as a complex system whose parts work together to promote solidarity and stability". This approach looks at society through a macro-level orientation, which is a broad focus on the social structures that shape society as a whole, and believes that society has evolved like organisms. This approach looks at both social structure and social functions.
