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“Bravais lattice”. A Bravais lattice is an infinite arrangement of points (or atoms) in space that has the following property: The lattice looks exactly the same when viewed from any lattice point A 1D Bravais lattice: b A 2D Bravais lattice: b c
In summary, there are five distinct 2-d Bravais lattices: (1) primitive oblique; (2) primitive rectangular; (3) centered rectangular; (4) primitive tetragonal; and (5) primitive trigonal and hexagonal (same lattice due to inversion).
The Bravais lattice concept is used to formally define a crystalline arrangement and its (finite) frontiers. A crystal is made up of one or more atoms, called the basis or motif, at each lattice point. The basis may consist of atoms, molecules, or polymer strings of solid matter, and the lattice provides the locations of the basis.
Crystallographers utilize a set of patters called Bravais lattices to describe the ways atoms can be arranged to form crystalline solids. In \(3.091\), we will focus on the subset of the Bravais lattices that are cubic: the scale in all three dimensions is the same.
Bravais lattices are point lattices that are classified topologically according to the symmetry properties under rotation and reflection, without regard to the absolute length of the unit vectors. A more intuitive definition: At every point in a Bravais lattice the “world” looks the same.
Bravais lattices. In geometry and crystallography, a Bravais lattice is an infinite array of discrete points generated by a set of discrete translation operations described by: R = n1a1 + n2a2 + n3a3. This discrete set of vectors must be closed under vector addition and subtraction.
Crystallographers utilize a set of patters called Bravais lattices to describe the ways atoms can be arranged to form crystalline solids. In 3.091, we will focus on the subset of the Bravais lattices that are cubic: the scale in all three dimensions is the same.
