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A solid body is described as crystalline if its components are arranged in a regular manner and characterized by fixed intervals in the three dimensions, and if this regular repetition of the atoms appears in one or two directions, the substance is semi-crystalline. In the event that the repetition is not regular and the atoms are arranged randomly, the solid body is described as amorphous “amorphous” like glass.

Thus, a crystal can be defined as a homogeneous solid body, having a chemical composition, They are caused by geological factors under suitable conditions of pressure and temperature in nature, bounded externally by flat surfaces called crystal faces, these flat surfaces are a reflection of the regular internal atomic arrangement. They are arranged during formation in a geometric system of their own, and this system does not necessarily reflect flat surfaces to form the crystal, as ** the appearance of crystal faces is related to various factors, the most important of which are: **

- That the atoms or ions are free Movement during melting in order to approach each other based on the correct proportions of the metal.

- The prevailing conditions must also be appropriate in terms of pressure and temperature and concentration in order to allow the crystal to grow and form slowly and continuously.

It may result in the formation of crystalline materials that are not It has any crystalline faces, and in the current one it is called “Anhedral” or some facets appear on it and others disappear so it is called “Subhedral”, or all the crystal faces appear and it is called “Euhedral”

Properties of Crystals

** Crystal Faces: ** The crystal is characterized by the presence of flat outer surfaces that determine the shape of the crystal, and it is in fact a reflection of the regular internal atomic arrangement that characterizes crystallized materials. ** Characters: ** Characters occur as a result of the meeting of two adjacent crystal faces.

** Stereoscopic Angles: ** It is formed as a result of the meeting of more than two crystal faces.

** Crystal form: ** It is a group of crystalline faces that are equal and similar in shape Each, position and area, for example, a cube or hexagon consists of six square crystal faces, and a quadrilateral prism is a crystal form consisting of four main faces, each of which is in the form of a rectangle. A crystal may consist of a single crystal form such as a cube or hexagonal, and in this case it is called a closed crystal form because it alone occupies a certain space of space, or it may consist of several complex forms such as a prism and a flat, and each of them is called an open crystal form because neither of them has been individually defined.

Closed and Open Crystal Shapes

### crystal symmetry

The essence of the symmetry process is repetition, so we find that a face of the crystal is repeated several times and in identical places and in the same position during the full cycle, i.e. all

Therefore, symmetry is defined as the process that results in a group of similar faces taking the same place that one of them occupies. The crystal was rotated a full cycle and repetition also occurs for any phenomenon on the crystal such as letters and solid angles.

** Symmetry level: ** It is that plane that passes through the center of the crystal and divides it into two equal and similar halves, so that one of them is an identical image of the other half and is denoted by the symbol (m). ** The axis of symmetry: It is that line around which if the crystal is rotated a full revolution 360° Without displacement, the crystal returns to its original position “meaning the repetition of a face, a letter, or a stereoscopic angle” for a number of times, taking each time The same place and situation, and the number of repetitions of the phenomenon on the crystal determines the degree of the axis, so the axis is bilateral symmetry if the phenomenon “letter – face – stereoscopic angle” is repeated twice during the full cycle, i.e. during 360 A degree and it is triple if the repetition occurs three times, i.e. all **

a degree and it is a quadrilateral if the repetition occurs four times during

the degree of any each

degree and it is hexagonal if the repetition occurs six times during the full cycle, i.e. each 380 degree and so on.

### The binary axis is symbolized by the symbol (⬬), the triple by the symbol (▲), and the quadrilateral with the symbol (■), and the hexagon with the symbol (⬢).

^{ or referred to by the numbers (2, 3, 4, 6) respectively. It is worth noting that there is no pentagonal, heptagonal, or octagonal axis of symmetry, because the structural unit capable of repetition in the space without the back of the interspaces is the binary, triple, quaternary, and hexagonal units. While the repetition of the five, seven, and eight units leads to the emergence of interstitial spaces, which contradicts the solid crystal material, and the nature of its regular internal atomic structure, therefore, the geometric shape of the repeated structural unit must occupy the space occupied by the crystal completely without leaving any interspaces.}

** The center of symmetry: ** is a point inside the crystal, characterized as If we move from it in two opposite directions of equal “dimension” we will find the same phenomenon, in other words, every crystal face, letter or stereo angle on one side of the crystal must have another crystal face, letter or stereo angle similar to it on the opposite side of the crystal, and for each Both of them are of equal distance from the center of symmetry “the center of the crystal” and symbolizes the center of symmetry by the symbol (n).

Law of Symmetry in Crystals

It is a law that includes all the elements of symmetry in the crystal written in the form of the symbol of these elements, and arranged in a special system according to the gradation in the degree of the axis, the numbers (2, 3, 4, 6) refer to the symmetrical hexagonal, quadrilateral, triple and bilateral axes on the order and the letter (m) for the symmetry plane (n) for the center of symmetry. :

There are three quadrilateral axes of symmetry, each perpendicular to The level of symmetry, represented by

while the four axes of tripartite symmetry are represented in (3)^{4}).

Just as the axes are bi-symmetric, they are Perpendicular to each level axis (2 ^{6/M).}

Symmetry Center (n).

Accordingly, the symmetry formula for that crystal is: (4 ** ^{3}**

/ M

3 ^{4} 2 ^{6} / M 2119n

).