See also: Crystal (homonymy)

The structure of a Cristal (or crystalline structure ) is completely described by the parameters of network of one of its elementary meshs, its Groupe of space and the position of the atoms which when all the operations of Symétrie of the group of space are applied to them, will generate all the contents of the mesh. The structure of a crystal is a fundamental concept for many fields of the Science and Technologie.

Crystal lattice

A crystalline solid is consisted the periodic repetition in 3 dimensions of the space of an atomic reason or molecular, called mesh ; in the same way that a wallpaper is consisted of the repetition of the same reason. The periodicity of the structure of a crystal is thus represented by a whole of points regularly laid out. This unit is called crystal lattice and the points the components are called nodes network.

Because of the periodicity of the network, any pair of nodes ( O , M ) defines a Vecteur:

$\backslash \; vec\; OM\; =\; m\_1\; \backslash \; vec\; a\_1\; +\; m\_2\; \backslash \; vec\; a\_2\; +\; m\_3\; \backslash \; vec\; a\_3$

$m\_1,\; m\_2,\; m\_3$ being relative whole .

Elementary mesh

A elementary mesh is a minimal mesh of the crystal lattice; i.e. the repetition of this mesh in 3 dimensions is enough to reproduce the entirety of the network. Larger meshs, for example the juxtaposition of two elementary meshs, also make it possible to reproduce the network, but are not minimal.

An elementary mesh is defined by the 3 Vecteur S a₁ , a₂ , a₃ , linearly independent. The choice of these 3 vectors is not single, one can thus define several elementary meshs which will be able not to have same symmetry.

Often, for reasons of convenience or to emphasize symmetry, one uses to describe the crystal a multiple mesh , containing several nodes and which is thus not elementary.

Network of Faced

A Réseau of Faced is a network of nodes obtained by translation following of the Vecteur S basic starting from a single node. There are 14 networks of Faced different in three dimensions, having groups of space and specific groups of different symmetry. All the crystalline materials have a symmetry corresponding to the one of these networks (but not the quasi-crystals). The 14 networks of Faced in three dimensions are listed in the table below.

Relation between family and systems

According to Massimo Nespolo, professor of mineralogy, there exists an historical error of correspondence between the reticular system and the crystalline system, more particularly dependant in the middle of French-speaking mineralogy:

For five of the seven systems, classification led finally to the same result. But in the case of the groups with ternary axis the things are more complicated. A crystal which has its specific group among 3 32 3m -3 and -3m belong to the trigonal crystalline system. But its network can be either hexagonal or rhomboedric, from where its possibility of belonging to two different reticular systems. On the other hand, a crystal which belongs to the reticular system rhomboedric is trigonal forcing.

It summarizes the problem of correspondence thus in the case of a space with three dimensions:

Such a problem would more specifically affect the classification of the quartz and the Calcite.

Thus, quartz α would crystallize in the trigonal system, with hexagonal network, rather than in the trigonal system with network rhomboedric:

From which comes then the error from description of symmetry of quartz? Friedel (1926, page 432) defines quartz-α as “senary, holoaxial tetartohedron”: it thus places well correctly quartz α in the reticular system (at the time known as “crystalline system”) hexagonal and not in the reticular system rhomboedric. Nevertheless, in almost all the books of French mineralogy, including in “Mineralogy of France” of François-Antoine-Alfred Lacroix (Volume III) and in several books of French crystallography, quartz-α is described like “rhomboedric”, which is quite simply false.

On the other hand, calcite is in fact trigonal with network rhomboedric.

These modifications of classification, to date, are used still little in the medium of French mineralogy.

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