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A fundamental concept in the description of crystalline solids is that of a “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. 1D Bravais lattice:
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).
All the great variety of surface lattices are organized into five main types, called two-dimensional Bravais lattices (recall that there are 14 Bravais lat- Fig. 2.2.
Bravais determined that there are fourteen distinct ways of constructing lattices in three dimensions, referred to as lattice systems. These are the fourteen three-dimensional Bravais lattices, as illustrated in figure 1.4, and they are divided into seven crystal systems, as summarized in table 1.2. Note that there is a subtle difference ...
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.
The lattice is an abstract two dimensional net or three dimensional mesh, and when you attach a basis (which could be a simple atom, or more complex: a group of atoms) to every lattice point, it becomes a real crystal.
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.