🔎 Crystallography – Definition and Explanations

an introduction

The Crystallography It is the science devoted to the study of crystalline materials at the atomic level. The physical and chemical properties of a crystal are closely related to the spatial arrangement of atoms (atom (from Greek ατομος, atom, “one cannot…) In the issue (Matter is the substance that makes up any body that has a tangible reality. …). The crystalline state is determined by a periodic character and is arranged at the atomic or molecular level. The Crystal (Crystal is a common term for a solid with a regular shape, though…) It is obtained by translating in all directions of a basic unit called the elementary network.

related to various disciplines such as physical (Physics (from Greek φυσις, nature) is etymologically…)The chemistry (Chemistry is a natural science divided into several disciplines, to …)they Maths (Mathematics is the field of abstract knowledge created with…)The Biophysics (Biophysics is a discipline at the interface of physics and biology where the tools…)The biology (Biology, commonly known as “vitality”, is the science of life….)The medicine (Medicine (from the Latin medicine, “that which heals”) is the science and…)The Materials science (Materials science is based on the relationship between properties, morphology…)The blacksmithing (Mineralogy is the science of materials that studies minerals, …) So are sciences Earth (Earth is the third planet in the solar system in order of distance…).

Historical

Crystal, at first simple subject (In general, the word object (from the Latin objectum, 1361) designates a specific entity in …) Out of curiosity, the collectors were amazed at the scientists who, intrigued by their curiosity, by studying their structure, drew the first theories about the intimate formation of matter. Abe defined the law of rational pointers or simple deductions Renee just hi (Father Rene Just Hay, born February 28, 1743 in …) In 1774. By Observation (Observation is the act of vigilant following of phenomena, without wanting to see them…) of phenomenon division (Criticism is the ability of some minerals to crack along flat surfaces…) affiliate calcite (Calcite is a chemical or biochemical (bio-mineralizing) mineral composed of …)define “integral particles”, that is, symmetric parallel lines form crystals, and then conclude that each face of a crystal can be located in space by integers.

The perfect crystal

An “ideal crystal” is a model used to represent the crystalline structure of a substance. This model considers the crystal to be an ordered packing f No final (The word for “infinity” (-e, -s; from the Latin finitus, …) atoms, ions, or molecules.

A crystal is a solid that has a structure made up of atoms arranged in an arrangement network (A computer network is a group of equipment linked together to exchange information…) Periodic, even triangular and symmetrical. It has properties symmetry (The term symmetry generally refers to being, in …) With direct and reverse axes of rotation, mirrors, planes and centers of symmetry.

The crystal can be isotropic (even refractive index (It measures the refractive index of a medium at a given wavelength factor…) affiliate light (Light is the set of electromagnetic waves visible to the eye…) in all directions) or anisotropic (Anisotropy (isotropic) is the property of being direction dependent….) (two different indicators in two orthogonal directions).

The unit cell is the smallest the sound (Volume, in the physical or mathematical sciences, is the quantity that measures extension…) Crystalline that retains all the physical, chemical, and engineering properties of a crystal. It is defined by three vectors that thus generate six mesh parameters: the three lengths of vectors a, b, and c and three angles α, , .

crystal network

Grid is a file together (In set theory, a set axiomatically defines a set…) stitches or “knots” in three Dimensions (In a general sense, the concept of dimension refers to volume; dimensions of a room…) Which introduces the following property: when we translate in space according to given vectors, we find exactly the same thing environment (Environment is everything that surrounds us. It is all natural elements and…). So there is a spatial periodicity. This makes it possible to identify seven basic lattice systems: cubic, hexagonal, rhombic, quadratic (or quadrangular), orthogonal, monoclinic and triclinic.

The Bravais lattice (In crystallography, a Bravais lattice is a uniform distribution of points…)

French August Braves (Auguste Bravais (August 23, 1811, Annonay – March 30, 1863, Le Chesnay, France) was a physicist…) He defines, in 1848, from various groups of elements of crystal symmetry, 32 classes of symmetry, which themselves are subdivided into 14 kinds of lattices (there is no other way of arranging points in space, in order to make a lattice or lattice, so as not to leave free space between networks). 14 Bravais Lattices are expansions of the Seven Primal Forms of Crystals.

Here are two examples of primitive Bravais networks:

We own None of the angles are equal to 90 degrees.

The second Bravais lattice is a monoclinic lattice. This consists of 2 rectangular bases and 4 parallelogram-shaped sides. The three lengths a, b and c are not equal: but two of the three angles are equal to 90 degrees.

can be found in the primitive lattice (s ), or in a centralized base network (against ) (a knot in the middle of the face defined by the axes to me And the B).

Miller indicators

Haüy specific indications (sAnd the sAnd the s) which makes it possible to identify crystal faces in space. Miller, for simplicity, said no one should use sAnd the s And the s But their reflections (1 /s1 /s1 /s) that will be observed hAnd the KAnd the I. They must be integers, relatively prime, with simple values.

Symmetry point groups and space groups

The set point of symmetry (In chemistry, a group of points of symmetry is a subset of an orthogonal group: it is…) from one crystal system (The crystal system is a classification of crystals based on…) is the group (in the meaning (SENS (Neglected Engineering Aging Strategies) is a science project that aims to…) mathematical) compilation of the set of symmetry operations that leave the network node stationary. So this node is located at the intersection of all symmetry operations, of which translation is not a part. There are 32 distinct symmetry point groups.

The space group of a crystal system includes all symmetry operations of the point group, to which translation operations are added. Around 1890 Fedorov and Schoenflies showed – independently of each other – that there are 230 groups, which represent all possible combinations of lattices and symmetry operations.

For more information, see the articles:

• crystal system
• set point of symmetry
• space group.