Crystalline structures
1) Definition of crystalline reticulum:
Two distinguished definitions of crystalline reticulum can be given :
to) It is a tidy distribution of points in the such plan that every reticular point is equivalent to the others.
b) linear combination of the carriers of translation of the crystalline reticulum Is one.
2) Aces of symmetry :
The spins respect to an axis are of the simmetrie on condition that they bring back the reticulum in if same, this only happens for 6 types of spin for which as an example if the reticulum returns in if same after a spin of 2p , the axis around to which it has ruotato is said unitary and indicated with n° the 1.
3) unitary Cell:
It is the smallest portion than such reticulum that for its translation is possible to cover all the space.
4) primitiva Cell:
It is the unitary cell of the minimal volume, has one density of a reticular point for every cell.
5) specular Plan:
It is an axis that is behaved from mirror in the sense that that that is had to its right is had also to its left. Everyone of these plans is characterized in the short description of reticulum with one m.
6) conventional unitary Cell:
It is a cell that is adopted in the case that the unitary cell has shape not simple to deal for which rifà us to a cell a larger Pò but that introduces one simpler geometry.
7) Base:
The points of the reticulum can accommodate a single atom or a structure, in particular the structure accommodated in every point is said base.
8) Cell of Wigner - Seitz:
to) all the segments are designed that connect a sure reticular point with all the near reticular points
b) to half and perpendicular to these segments to new segments or plans are designed
c) the comprised smaller volume in this way is the primitiva cell of Wigner - Seitz
9) Types of bidimensional reticula:
The 5 types are possible following :
to) quadrato b) rettangolare c) rectangular to faces centrate d) obliquo e) hexagonal
10) square Reticulum:
It is a reticulum for which 
is had and the angle between the two carriers is j = 90°
One spin of 90° filler the reticulum in if same (quaternario axis of symmetry )
Two are individualistic distinguished not riproducibili specular aces not even for spin of the reticulum.
The structure comes therefore identified 4mm where milimeter indicates that there are 2 not riproducibili independent specular plans that is not even for spin.
11) rectangular Reticulum:
It is a reticulum for which 
is had and the angle between the two carriers is j = 90°
One spin of 180° filler the reticulum in if same.
Two are individualistic distinguished not riproducibili specular aces not even for spin of the reticulum.
The structure comes therefore identified 2mm.
12) rectangular Reticulum to centered body:
To the center of the rectangle a point is present, the
included angle between the two carriers of translation is
characterized from the relation 
. The structure
equally is identified with 2mm.
13) oblique Reticulum:
It is a reticulum for which
is had and the angle between the two carriers is j ¹ 90° is characterized
from a binary axis of symmetry and its structure is identified with
2.
For j = 60° spin of 60° filler is reduced to a hexagonal reticulum for which one the reticulum in if same.
14) Types of three-dimensional reticula:
The 7 conventional unitary cells are possible following :
to) cubica b) tetragonale c) ortorombico d) trigonale and) monoclino f) triclino g) esagonale
in practical leaving from cubical that it has the modules and the equal angles I render the modules before various one to the time until arriving to the triclino, the hexagonal one is a case to part.
15) Describe the cubical reticulum:
The 3 carriers of translation have the same module and the angles between comprised they are all of 90°. The cubical reticula to centered body and faces centrate. are possible also
16) Describe the tetragonal reticulum:
Two of the 3 carriers of translation have the same module and the angles between comprised they are all of 90°. Possible E' also the tetragonal reticulum to centered body.
17) Describe the ortorombico reticulum:
The 3 carriers of translation have modules between various they and the angles between comprised they are all of 90°. The ortorombici reticula to centered bases, centered body and faces are possible also centrate.
18) Describe the trigonale reticulum:
The 3 carriers of translation have the same module and the angles between comprised they are all equal, smaller ones of 120° and various from 90°.
19) Describe the reticulum monoclino:
The 3 carriers of translation have modules between various they and single two of the angles between comprised they are of 90°. The reticulum monoclino to bases centrate. is possible also
20) Describe the reticulum triclino:
The 3 carriers of translation have modules between various they and the angles between comprised they are various between they and nobody of 90°. The cubical reticula to centered body and centered faces are possible also.
21) Describe the hexagonal reticulum:
Two carriers of translation have the same module and 2 of the angles are of 90° while the third party is of 120°.
22) Indices of Miller in order to characterize a plan:
The intercette must be characterized of the plan with the three cartesian aces, if the mutual ones write some and it is multiplied for smallest entire such rendering entire all and the three fractions. If the encounter with a data axis then happens to the infinite the correspondent index of Miller it is a zero while if the encounter with a data axis happens in then occore the negative zone to put one barretta over to the correspondent index of Miller.
The numbers therefore characterize to you go enclosed between round parentheses.
23) Indices of Miller in order to characterize one direction:
They are the coordinates that combine the origin to the reticular point more neighbor. Quadrants are enclosed between parenthesis.
24) atomic Coordinates:
They characterize a point to the inside of the unitary cell in terms of fraction of the intersection of its projection with the corresponding axis.