Miller index, the Glossary
Miller indices form a notation system in crystallography for lattice planes in crystal (Bravais) lattices.[1]
Table of Contents
50 relations: Ad hoc, Adsorption, Atom, Basis (linear algebra), Birefringence, Bravais lattice, Burgers vector, Cartesian coordinate system, Christian Samuel Weiss, Cleavage (crystal), Crystal habit, Crystal structure, Crystal system, Crystallite, Crystallography, Cubic crystal system, Deformation (engineering), Dislocation, Friction, Greatest common divisor, Hexagonal crystal family, Hyperplane, Integer, Ion, Irrational number, Kikuchi lines (physics), Lattice constant, Lattice plane, Laue equations, Light, Line (geometry), Lowest common denominator, Molecule, Optics, Peierls stress, Penrose tiling, Plane (mathematics), Polygon, Quasicrystal, Rational number, Rayleigh scattering, Reactivity (chemistry), Reciprocal lattice, Speed of light, Supercell (crystal), Surface tension, Transmission electron microscopy, William Hallowes Miller, X-ray crystallography, Zone axis.
Ad hoc
Ad hoc is a Latin phrase meaning literally for this.
Adsorption
Adsorption is the adhesion of atoms, ions or molecules from a gas, liquid or dissolved solid to a surface.
See Miller index and Adsorption
Atom
Atoms are the basic particles of the chemical elements.
Basis (linear algebra)
In mathematics, a set of vectors in a vector space is called a basis (bases) if every element of may be written in a unique way as a finite linear combination of elements of.
See Miller index and Basis (linear algebra)
Birefringence
Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light.
See Miller index and Birefringence
Bravais lattice
In geometry and crystallography, a Bravais lattice, named after, is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by where the ni are any integers, and ai are primitive translation vectors, or primitive vectors, which lie in different directions (not necessarily mutually perpendicular) and span the lattice. Miller index and Bravais lattice are crystallography.
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Burgers vector
In materials science, the Burgers vector, named after Dutch physicist Jan Burgers, is a vector, often denoted as, that represents the magnitude and direction of the lattice distortion resulting from a dislocation in a crystal lattice. Miller index and Burgers vector are crystallography.
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Cartesian coordinate system
In geometry, a Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines, coordinate axes or just axes (plural of axis) of the system.
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Christian Samuel Weiss
Christian Samuel Weiss (26 February 1780 – 1 October 1856) was a German mineralogist born in Leipzig.
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Cleavage (crystal)
Cleavage, in mineralogy and materials science, is the tendency of crystalline materials to split along definite crystallographic structural planes. Miller index and Cleavage (crystal) are crystallography.
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Crystal habit
In mineralogy, crystal habit is the characteristic external shape of an individual crystal or aggregate of crystals. Miller index and crystal habit are crystallography.
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Crystal structure
In crystallography, crystal structure is a description of ordered arrangement of atoms, ions, or molecules in a crystalline material. Miller index and crystal structure are crystallography.
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Crystal system
In crystallography, a crystal system is a set of point groups (a group of geometric symmetries with at least one fixed point). Miller index and crystal system are crystallography.
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Crystallite
A crystallite is a small or even microscopic crystal which forms, for example, during the cooling of many materials.
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Crystallography
Crystallography is the branch of science devoted to the study of molecular and crystalline structure and properties.
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Cubic crystal system
In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube.
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Deformation (engineering)
In engineering, deformation (the change in size or shape of an object) may be elastic or plastic.
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Dislocation
In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms.
See Miller index and Dislocation
Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other.
Greatest common divisor
In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.
See Miller index and Greatest common divisor
Hexagonal crystal family
In crystallography, the hexagonal crystal family is one of the 6 crystal families, which includes two crystal systems (hexagonal and trigonal) and two lattice systems (hexagonal and rhombohedral).
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Hyperplane
In geometry, a hyperplane is a generalization of a two-dimensional plane in three-dimensional space to mathematical spaces of arbitrary dimension.
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Integer
An integer is the number zero (0), a positive natural number (1, 2, 3,...), or the negation of a positive natural number (−1, −2, −3,...). The negations or additive inverses of the positive natural numbers are referred to as negative integers.
Ion
An ion is an atom or molecule with a net electrical charge.
Irrational number
In mathematics, the irrational numbers (in- + rational) are all the real numbers that are not rational numbers.
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Kikuchi lines (physics)
Kikuchi lines are patterns of electrons formed by scattering.
See Miller index and Kikuchi lines (physics)
Lattice constant
A lattice constant or lattice parameter is one of the physical dimensions and angles that determine the geometry of the unit cells in a crystal lattice, and is proportional to the distance between atoms in the crystal.
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Lattice plane
In crystallography, a lattice plane of a given Bravais lattice is any plane containing at least three noncollinear Bravais lattice points. Miller index and lattice plane are crystallography and geometry.
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Laue equations
In crystallography and solid state physics, the Laue equations relate incoming waves to outgoing waves in the process of elastic scattering, where the photon energy or light temporal frequency does not change upon scattering by a crystal lattice. Miller index and Laue equations are crystallography.
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Light
Light, visible light, or visible radiation is electromagnetic radiation that can be perceived by the human eye.
Line (geometry)
In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature, an idealization of such physical objects as a straightedge, a taut string, or a ray of light.
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Lowest common denominator
In mathematics, the lowest common denominator or least common denominator (abbreviated LCD) is the lowest common multiple of the denominators of a set of fractions.
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Molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion.
Optics
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it.
Peierls stress
Peierls stress (or Peierls-Nabarro stress, also known as the lattice friction stress) is the force (first described by Rudolf Peierls and modified by Frank Nabarro) needed to move a dislocation within a plane of atoms in the unit cell.
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Penrose tiling
A Penrose tiling is an example of an aperiodic tiling.
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Plane (mathematics)
In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely. Miller index and plane (mathematics) are geometry.
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Polygon
In geometry, a polygon is a plane figure made up of line segments connected to form a closed polygonal chain.
Quasicrystal
A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. Miller index and quasicrystal are crystallography.
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Rational number
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
See Miller index and Rational number
Rayleigh scattering
Rayleigh scattering, named after the 19th-century British physicist Lord Rayleigh (John William Strutt), is the predominantly elastic scattering of light, or other electromagnetic radiation, by particles with a size much smaller than the wavelength of the radiation.
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Reactivity (chemistry)
In chemistry, reactivity is the impulse for which a chemical substance undergoes a chemical reaction, either by itself or with other materials, with an overall release of energy.
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Reciprocal lattice
In physics, the reciprocal lattice emerges from the Fourier transform of another lattice. Miller index and reciprocal lattice are crystallography.
See Miller index and Reciprocal lattice
Speed of light
The speed of light in vacuum, commonly denoted, is a universal physical constant that is exactly equal to). According to the special theory of relativity, is the upper limit for the speed at which conventional matter or energy (and thus any signal carrying information) can travel through space.
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Supercell (crystal)
In solid-state physics and crystallography, a crystal structure is described by a unit cell repeating periodically over space. Miller index and Supercell (crystal) are crystallography.
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Surface tension
Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible.
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Transmission electron microscopy
Transmission electron microscopy (TEM) is a microscopy technique in which a beam of electrons is transmitted through a specimen to form an image.
See Miller index and Transmission electron microscopy
William Hallowes Miller
Prof William Hallowes Miller FRS HFRSE LLD DCL (6 April 180120 May 1880) was a Welsh mineralogist and laid the foundations of modern crystallography.
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X-ray crystallography
X-ray crystallography is the experimental science of determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract in specific directions. Miller index and x-ray crystallography are crystallography.
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Zone axis
Zone 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. Miller index and Zone axis are crystallography.
See Miller index and Zone axis
References
[1] https://en.wikipedia.org/wiki/Miller_index
Also known as 111 surface, Bravais-Miller indices, Crystallographic face, Crystallographic plane, Miller Indices, Miller index notation, Miller indexes, Miller indice, Miller indicies, Miller-Bravais indices, Miller-Bravias Indices, Millerian.