Bravais, Auguste

Bravais, Auguste (1811-1863) presented his ideas on crystallography to the French Academy of Sciences in 1849. He was interested in a number of fields including botany, astronomy, and physics. It is for his work in crystallography that he is best remembered. 

Bravais Auguste (1811-1863) Fr. phys., upon observing natural crystals he grouped them into seven crystal systems (Bravais lattice is called after him), which is an infinite array of discrete points with an arrangement and orientation that appears exactly the same viewed from any point of the array ( Etudes cristalographiques ... 

Auguste Bravais (1811-1863) first proposed the Miller-Bravais system for indices. Also, as a result of his analyses of the external forms of crystals, he proposed the 14 possible space lattices in 1848. His Etudes Cristallographiques, published in 1866, after his death, treated the geometry of molecular polyhedra. 

In order to systematize in a logical form the lattices that are compatible with a periodicity condition, the French physicist Auguste Bravais, in 1845, demonstrated that the lattice points in three dimensions, congruent with the periodicity requirement, are the roots of the following trigonometric equation [2] ... 

Auguste Bravais (1811-1863) corrects Frankenheim s number of crystal systems, noting that two were equivalent, and that the remaining 14 coalesced by pairs, thus proving that there are really seven distinct crystal systems derives the five two-dimensional and 14 three-dimensional space lattices. 

Bravais lattice Classification of fourteen three-dimensional lattices based on primitive and nonprimitive unit cells. Named after Auguste Bravais, who first used them. 

Auguste Bravais (1811-1863). French crystallographer, who was the first to derive the 14 different lattices in 1848. 

The analogy between the equations representing the edges and faces of a crystal on the one hand, with lattice lines and lattice planes on the other is the foundation of the theory of the periodic nature of crystal structures. This interpretation of the law of rational indices was formulated by the French abbe Auguste Bravais (1811-1863) as follows ... 

There are several known approaches to classification of individual crystals in accordance with their symmetry and crystallochemislry. The particles which form a crystal are distributed in certain points in space. These points are separated by certain distances (translations) equal to each other in any chosen direction in the crystal. Crystal lattice is a diagram that describes the location of particles (individual or groups) in a crystal. The lattice parameters are three non-coplanar translations that form the crystal lattice. Three basic translations form the unit cell of a crystal. August Bravais (184S) has shown that all possible crystal lattice structures belong to one or another of fourteen lattice types (Bravais lattices). The Bravais lattices, both primitive and non-primitive, are the contents of Table 3. 

Bravals lattice A lattice defined by the combination of one of the seven possible crystal systems and one of the possible lattice centrings, i.e. (1) primitive, in which only the cell corners are occupied, (2) body centred, in which there is a point at the centre, (3) face centred, in which there are points at the centres of all the faces, (4) centred at a single face, in which there is a point at the centre of one of the faces. The Bravais lattice is named after the French physicist Auguste Bravais (1811-63), who demonstrated that in three spatial dimensions there are 14 possible such lattices. 

In three dimensions, there are seven crystal systems (Table 6.2). The crystal systems are further divided according to centerings (Figure 6.3) into 14 Bravais lattices cubic (3), tetragonal (2), orthorhombic (4), hexagonal (1), trigonal (1), monoclinic (2), and triclinic (1). Auguste Bravais was a French mathematician. 

Finally, within some of the systems are subsystems that have additional atoms or ions or molecules. These subsystems differ only by having corner species in other parts of the unit cell, like the sides or the center of the unit cell. Table 21.2 lists these details, and Figure 21.9 shows examples of the additional possible cubic, tetragonal, orthorhombic, and monoclinic crystal structures. These 14 possible crystal structures are called the Bravais lattices, after the French scientist Auguste Bravais (1811-1863), who first described them in 1848. 

There are precisely 14 different topological ways of arranging equivalent points in an atomic array and this gives rise to the 14 Bravais lattices or space lattices, as it was Auguste Bravais in 1848 who first rigorously established that other suggested lattices were in fact identical to one of his own 14. These lattices are named by their crystal system followed by a symbol P, /, F, C or / always italicized) as indicated in Fig. 7 [1]. 

M.L. Frankheim in 1842 was the first to classify the possible crystal lattices including the special body-centered and face-centered nonprimitive lattices. However, he had mistakenly added a 15th structure that turned out to be redimdant. Auguste Bravais was the first in 1845 to correctly characterize the 14 unique lattices that now bear his name. 

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