Nearly free electron modelIn solid-state physics, the nearly free electron model (or NFE model and quasi-free electron model) is a quantum mechanical model of physical properties of electrons that can move almost freely through the crystal lattice of a solid. The model is closely related to the more conceptual empty lattice approximation. The model enables understanding and calculation of the electronic band structures, especially of metals. This model is an immediate improvement of the free electron model, in which the metal was considered as a non-interacting electron gas and the ions were neglected completely.
Cubic crystal systemIn crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals. There are three main varieties of these crystals: Primitive cubic (abbreviated cP and alternatively called simple cubic) Body-centered cubic (abbreviated cI or bcc) Face-centered cubic (abbreviated cF or fcc) Note: the term fcc is often used in synonym for the cubic close-packed or ccp structure occurring in metals.
MineralogyMineralogy is a subject of geology specializing in the scientific study of the chemistry, crystal structure, and physical (including optical) properties of minerals and mineralized artifacts. Specific studies within mineralogy include the processes of mineral origin and formation, classification of minerals, their geographical distribution, as well as their utilization. History of mineralogy Early writing on mineralogy, especially on gemstones, comes from ancient Babylonia, the ancient Greco-Roman world, ancient and medieval China, and Sanskrit texts from ancient India and the ancient Islamic world.
Zone axisZone axis, a term sometimes used to refer to "high-symmetry" orientations in a crystal, most generally refers to any direction referenced to the direct lattice (as distinct from the reciprocal lattice) of a crystal in three dimensions. It is therefore indexed with direct lattice indices, instead of with Miller indices. High-symmetry zone axes through a crystal lattice, in particular, often lie in the direction of tunnels through the crystal between planes of atoms.
DiffractionDiffraction is the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating wave. Italian scientist Francesco Maria Grimaldi coined the word diffraction and was the first to record accurate observations of the phenomenon in 1660.
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.
Lattice graphIn graph theory, a lattice graph, mesh graph, or grid graph is a graph whose drawing, embedded in some Euclidean space \mathbb{R}^n, forms a regular tiling. This implies that the group of bijective transformations that send the graph to itself is a lattice in the group-theoretical sense. Typically, no clear distinction is made between such a graph in the more abstract sense of graph theory, and its drawing in space (often the plane or 3D space). This type of graph may more shortly be called just a lattice, mesh, or grid.
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.
Brillouin scatteringBrillouin scattering (also known as Brillouin light scattering or BLS), named after Léon Brillouin, refers to the interaction of light with the material waves in a medium (e.g. electrostriction and magnetostriction). It is mediated by the refractive index dependence on the material properties of the medium; as described in optics, the index of refraction of a transparent material changes under deformation (compression-distension or shear-skewing).
Nearest neighbor searchNearest neighbor search (NNS), as a form of proximity search, is the optimization problem of finding the point in a given set that is closest (or most similar) to a given point. Closeness is typically expressed in terms of a dissimilarity function: the less similar the objects, the larger the function values. Formally, the nearest-neighbor (NN) search problem is defined as follows: given a set S of points in a space M and a query point q ∈ M, find the closest point in S to q. Donald Knuth in vol.
Tight bindingIn solid-state physics, the tight-binding model (or TB model) is an approach to the calculation of electronic band structure using an approximate set of wave functions based upon superposition of wave functions for isolated atoms located at each atomic site. The method is closely related to the LCAO method (linear combination of atomic orbitals method) used in chemistry. Tight-binding models are applied to a wide variety of solids.
K-nearest neighbors algorithmIn statistics, the k-nearest neighbors algorithm (k-NN) is a non-parametric supervised learning method first developed by Evelyn Fix and Joseph Hodges in 1951, and later expanded by Thomas Cover. It is used for classification and regression. In both cases, the input consists of the k closest training examples in a data set. The output depends on whether k-NN is used for classification or regression: In k-NN classification, the output is a class membership.
