What type of crystal lattice is characteristic of copper?

Native copper measuring about 4 cm

Copper

- a mineral from the class of native elements. Fe, Ag, Au, As and other elements are found in natural minerals as impurities or forming solid solutions with Cu. The simple substance copper is a ductile transition metal of golden-pink color (pink in the absence of an oxide film). One of the first metals widely mastered by man due to its relative availability for extraction from ore and low melting point. It is one of the seven metals known to man since very ancient times. Copper is an essential element for all higher plants and animals.

1. Structure
2. Properties
3. Reserves and production
4. Origin
5. Application
6. Classification
7. Physical properties
8. Optical properties
9. Crystallographic properties

See also:

Gold

— structure and physical properties

Aluminum

— structure and physical properties

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Lesson summary “Types of crystal lattices”

To determine the type of crystal lattice proceed as follows. If the bond in a compound is ionic, then the crystal lattice is always of the ionic type

: potassium chloride, potassium nitrate, calcium nitride, calcium carbide, aluminum oxide.

If the bond is metallic, then the crystal lattice is always metallic

: brass, iron, copper, sodium.

If the bond is covalent, then the lattice can be like an atomic one

, and
molecular
. Substances with an atomic crystal lattice are: carborundum, silicon oxide four, boron, silicon, diamond, graphite, black and red phosphorus.

For substances with a molecular crystal lattice

molecules are located at the nodes of the crystal lattice;
the strength of this bond is weak
.

For substances with a molecular crystal lattice

characterized by low
melting points
, that is, they are fusible and volatile, significant compressibility, sometimes odor, as well as the phenomenon of sublimation, or sublimation, as for iodine and solid carbon dioxide.

For substances with a molecular crystal lattice

characterized by
low hardness
, most of these substances are highly soluble in water. Gases and liquids in a solid state of aggregation have a molecular crystal lattice. For example, crystalline iodine, sulfur, white phosphorus, carbon dioxide, most organic compounds.

For substances with an atomic crystal lattice

atoms are located at nodes.
The bond between atoms in crystal lattices
is
covalent
and very strong. These substances are characterized by high boiling and melting points, that is, they are refractory and non-volatile, very hard, practically insoluble in water and odorless.

Examples of substances with this type of crystal lattices are diamond and graphite.

As is known, the hardness of diamond

It is estimated at the highest value on the Mohs scale - 10. Due to its high hardness, diamond is used for the manufacture of drills, drills, grinding tools, and glass cutters. Diamond is the stone of jewelers; they use polished diamonds - brilliants.

Graphite

It is also a substance with an atomic crystal lattice, but despite this, it is soft, since it has a layered structure.
In the crystal lattice of graphite, carbon atoms lying in the same plane are bound into regular hexagons. The bonds between the layers are fragile
, due to this the graphite is soft. Graphite, like diamond, is refractory. It is used to make electrodes, solid lubricants, pencil leads, and neutron moderators in nuclear reactors.

Atomic crystal lattices contain not only simple but also complex substances. For example, all varieties of aluminum oxide. Such as emery, corundum, ruby, sapphire.

The most common silicon compound

is silicon oxide four, which also has an atomic crystal lattice. Almost pure silicon oxide four is the mineral quartz.

For substances with ionic type

bonds at the nodes of the crystal lattice there are ions, the bond between particles is ionic, it is strong.

Substances with an ionic bond type are characterized by the following properties

:
high melting and boiling points
, they are refractory and nonvolatile, they are hard, brittle, many are soluble in water. Their fragility is explained by the fact that if you try to deform such a crystal lattice, then one of its layers will move relative to the other layer until the equally charged ions are against each other. These ions will begin to repel each other, and the crystal lattice will collapse.

Substances with ionic bonds do not conduct electricity and heat well. But their solutions and melts conduct electric current. Substances with ionic bonds are odorless

.

An ionic compound is a giant association of ions located in space due to the balance of attractive and repulsive forces.

For example, a sodium chloride crystal consists of sodium cations and chlorine anions. Each sodium cation is surrounded by six chlorine anions, and each chlorine anion is surrounded by six sodium cations. The smallest structural unit of a crystal is the unit cell. The structure of the unit cell depends on the ratio of the sizes of the cation and anion.

For substances with a metallic type

bonds at the nodes of the crystal lattice are atom-ions, the bond between them is metallic. The bond may vary in strength.

Metal crystal lattice

determines the properties of metals: malleability, plasticity, electrical and thermal conductivity, metallic luster, ability to form alloys.

Plastic

is expressed in the ability of metals to deform under mechanical load. This property underlies the forging, rolling of metals, and their ability to be drawn into wire. Plasticity is explained by the fact that under the influence of force, the layers move relative to each other without breaking the bond between them.

For example, if you place a few drops of water on two flat glass plates, the plates will slide freely relative to each other, but it will be quite difficult to separate them. Thus, in this experiment, water played the role of free electrons that are located in the metal crystal lattice.

The most ductile metals are gold, silver and copper. It is from gold that the thinnest foil, three thousandths of a millimeter thick, can be made. I use this thin foil for gilding. An example is the Amber Room in the Great Catherine Palace.

The high electrical conductivity of metals is due to the presence of free electrons, which, under the influence of electric current, acquire directional movement.

The best conductors
of the electrical eye
are
silver
and
copper
, a little worse is aluminum. However, in most cases, aluminum rather than copper is used as electrical wires.

Thermal conductivity of metals

also explained
by the movement of free electrons
, which collide with atom ions at the nodes of the crystal lattice and exchange energy with them. Thanks to this property, metal cookware heats up evenly.

Substances with a metallic crystal lattice have a metallic luster due to the reflection of light rays.

Mercury, silver, palladium and aluminum have high reflective properties. Mirrors, spotlights and headlights are made from silver, palladium and aluminum. In a powdered state, metals lose their shine; only magnesium and aluminum retain it.

Most metals are silvery-white in color. Only gold is colored yellow, and copper is red.

The metal crystal lattice is characteristic not only of metals, but also of alloys

. This distinguishes metal alloys from other alloys: glass, porcelain, ceramics, basalts, granites, gneisses.

PROPERTIES

Native copper crystals, Lake Superior, Kinawee County, Michigan, USA. Size 12 x 8.5 cm

Copper is a golden-pink ductile metal; in air it quickly becomes covered with an oxide film, which gives it a characteristic intense yellowish-red hue. Thin films of copper have a greenish-blue color when exposed to light.

Along with osmium, cesium and gold, copper is one of the four metals that have a distinct coloration that is different from the gray or silver of other metals. This color tint is explained by the presence of electronic transitions between the filled third and half-empty fourth atomic orbitals: the energy difference between them corresponds to the wavelength of orange light. The same mechanism is responsible for the characteristic color of gold.

Copper has high thermal and electrical conductivity (it ranks second in electrical conductivity among metals after silver). Specific electrical conductivity at 20 °C: 55.5-58 MS/m. Copper has a relatively large temperature coefficient of resistance: 0.4%/°C and is weakly dependent on temperature over a wide temperature range. Copper is diamagnetic.

There are a number of copper alloys: brass - with zinc, bronze - with tin and other elements, cupronickel - with nickel and others.

General structure

Metals are solid substances with a crystalline structure. The exception is mercury, a liquid metal. Crystal lattices are metal atoms ordered in a certain way. Each atom consists of a positively charged nucleus and several negatively charged electrons. Metal atoms don't have enough electrons, so they are ions.

A unit of a crystal lattice is an elementary crystal cell, in the conventional nodes and on the faces of which there are positively charged ions. They are held together by metallic bonds that arise due to the random movement of electrons separated from the atoms (due to which the atoms turned into ions).

Rice. 1. Metal connection diagram.

The free movement of electrons determines the electrical and thermal conductivity of metals.

Types of crystal lattices

In fact, all substances in a solid state have a clear structure. Atoms and molecules move, but the forces of attraction and repulsion between particles are balanced, so atoms and molecules are located at a certain point in space (but continue to make small fluctuations depending on temperature). Such structures are called crystal lattices . The places where the molecules, ions or atoms themselves are located are called nodes . And the distances between nodes are called periods of identity . Depending on the position of particles in space, there are several types:

1. atomic;
2. ionic;
3. molecular;
4. metal.

In liquid and gaseous states, substances do not have a clear lattice; their molecules move chaotically, which is why they have no shape. For example, oxygen, when in a gaseous state, is a colorless, odorless gas; in a liquid state (at -194 degrees) it is a bluish solution. When the temperature drops to -219 degrees, oxygen turns into a solid state and becomes red. lattice, while it turns into a snow-like mass of blue color.

Interestingly, amorphous substances do not have a clear structure, which is why they do not have strict melting and boiling points. When heated, resin and plasticine gradually soften and become liquid; they do not have a clear transition phase.

General information:

Atomic crystal lattice

The nodes contain atoms, as the name suggests. These substances are very strong and durable , since a covalent bond is formed between the particles. Neighboring atoms share a pair of electrons with each other (or rather, their electron clouds are layered on top of each other), and therefore they are very well connected to each other. The most obvious example is diamond, which has the greatest hardness on the Mohs scale. Interestingly, diamond, like graphite, consists of carbohydrates. Graphite is a very brittle substance (Mohs hardness 1), which is a clear example of how much depends on the type.

Atomic region lattice is poorly distributed in nature, it includes: quartz, boron, sand, silicon, silicon (IV) oxide, germanium, rock crystal. These substances are characterized by a high melting point, strength, and these compounds are very hard and insoluble in water. Due to the very strong bonds between atoms, these chemical compounds hardly interact with others and conduct current very poorly.

Methods for obtaining copper

In nature, copper exists in compounds and in the form of nuggets. The compounds are represented by oxides, bicarbonates, sulfur and carbon dioxide complexes, as well as sulfide ores. The most common ores are copper pyrite and copper luster. The copper content in them is 1-2%. 90% of primary copper is mined using the pyrometallurgical method and 10% using the hydrometallurgical method.

1. The pyrometallurgical method includes the following processes: enrichment and roasting, smelting for matte, purging in a converter, electrolytic refining. Copper ores are enriched by flotation and oxidative roasting. The essence of the flotation method is as follows: copper particles suspended in an aqueous medium adhere to the surface of air bubbles and rise to the surface. The method allows you to obtain copper powder concentrate, which contains 10-35% copper.

Copper ores and concentrates with a significant sulfur content are subject to oxidative roasting. When heated in the presence of oxygen, sulfides are oxidized, and the amount of sulfur is reduced by almost half. Poor concentrates containing 8-25% copper are roasted. Rich concentrates containing 25-35% copper are melted without resorting to roasting.

The next stage of the pyrometallurgical method for producing copper is smelting for matte. If lump copper ore with a large amount of sulfur is used as a raw material, then smelting is carried out in shaft furnaces. And for powdered flotation concentrate, reverberatory furnaces are used. Melting occurs at a temperature of 1450 °C.

In horizontal converters with side blowing, the copper matte is blown with compressed air in order for the oxidation of sulfides and ferrum to occur. Next, the resulting oxides are converted into slag, and sulfur into oxide. The converter produces blister copper, which contains 98.4-99.4% copper, iron, sulfur, as well as small amounts of nickel, tin, silver and gold.

Blister copper is subject to fire and then electrolytic refining. Impurities are removed with gases and converted into slag. As a result of fire refining, copper is formed with a purity of up to 99.5%. And after electrolytic refining, the purity is 99.95%.

2. The hydrometallurgical method involves leaching copper with a weak solution of sulfuric acid, and then separating copper metal directly from the solution. This method is used for processing low-grade ores and does not allow for the associated extraction of precious metals along with copper.

Ionic crystal lattice

In this type, ions are located at each node. Accordingly, this type is characteristic of substances with an ionic bond, for example: potassium chloride, calcium sulfate, copper chloride, silver phosphate, copper hydroxide, and so on. Substances with such a particle connection scheme include ;

• salt;
• metal hydroxides;
• metal oxides.

Sodium chloride has alternating positive (Na + ) and negative (Cl - ) ions. One chlorine ion located in a node attracts two sodium ions (due to the electromagnetic field) that are located in neighboring nodes. Thus, a cube is formed in which the particles are interconnected.

The ionic lattice is characterized by strength, refractoriness, stability, hardness and non-volatility. Some substances can conduct electricity.

ORIGIN

Small nugget of copper

Typically, native copper is formed in the oxidation zone of some copper sulfide deposits in association with calcite, native silver, cuprite, malachite, azurite, brochantite and other minerals. The masses of individual clusters of native copper reach 400 tons. Large industrial deposits of native copper, along with other copper-containing minerals, are formed when volcanic rocks (diabases, melaphyres) are exposed to hydrothermal solutions, volcanic vapors and gases enriched in volatile copper compounds (for example, the Lake Superior deposit, USA). Native copper is also found in sedimentary rocks, mainly in cuprous sandstones and shales. The most famous deposits of native copper are the Turin mines (Urals), Dzhezkazgan (Kazakhstan), in the USA (on the Keweenaw Peninsula, in the states of Arizona and Utah).

Molecular crystal lattice

The nodes of this structure contain molecules that are tightly packed together. Such substances are characterized by covalent polar and nonpolar bonds. It is interesting that, regardless of the covalent bond, there is a very weak attraction between the particles (due to weak van der Waals forces). That is why such substances are very fragile, have low boiling and melting points, and are also volatile. These substances include: water, organic substances (sugar, naphthalene), carbon monoxide (IV), hydrogen sulfide, noble gases, two- (hydrogen, oxygen, chlorine, nitrogen, iodine), three- (ozone), four- (phosphorus ), eight-atomic (sulfur) substances, and so on.

Metal crystal lattice

Due to the presence of ions at the nodes, the metal lattice may appear to be similar to an ionic lattice. In fact, these are two completely different models, with different properties.

Metal is much more flexible and ductile than ionic, it is characterized by strength, high electrical and thermal conductivity, these substances melt well and conduct electric current well. This is explained by the fact that the nodes contain positively charged metal ions (cations), which can move throughout the structure, thereby ensuring the flow of electrons. The particles move chaotically around their node (they do not have enough energy to go beyond), but as soon as an electric field appears, electrons form a stream and rush from the positive to the negative region.

The metal crystal lattice is characteristic of metals, for example: lead, sodium, potassium, calcium, silver, iron, zinc, platinum and so on. Among other things, it is divided into several types of packaging: hexagonal, body-centered (least dense) and face-centered. The first package is typical for zinc, cobalt, magnesium, the second for barium, iron, sodium, the third for copper, aluminum and calcium.

Thus, on the type of lattice . Knowing the type, you can predict, for example, what the refractoriness or strength of an object will be.

APPLICATION

Copper bracelets

Due to its low resistivity, copper is widely used in electrical engineering for the manufacture of power cables, wires or other conductors, for example, in printed circuit wiring. Copper wires, in turn, are also used in the windings of energy-saving electric drives and power transformers. Another useful quality of copper is its high thermal conductivity. This allows it to be used in various heat removal devices and heat exchangers, which include well-known radiators for cooling, air conditioning and heating. Alloys using copper are widely used in various fields of technology, the most widespread of which are the above-mentioned bronze and brass. Both alloys are general names for a whole family of materials, which in addition to tin and zinc may include nickel, bismuth and other metals. In jewelry, alloys of copper and gold are often used to increase the resistance of products to deformation and abrasion, since pure gold is a very soft metal and is not resistant to these mechanical influences. The predicted new mass use of copper promises to be its use as bactericidal surfaces in medical institutions to reduce intra-hospital bacterial transfer: doors, handles, water stop valves, railings, bed rails, table tops - all surfaces touched by the human hand.

Copper - Cu

Chemical bond. Part 2. Types of crystal lattices

We continue our topic on chemical bonding and today we are studying the crystalline state of a substance, the concepts of ionic bonding, metallic bonding from the 4th exam assignment in chemistry .

So, to understand the material, let’s take you a glass with a flat bottom and pour beads into it (let them be round) in one layer. We have a monoatomic layer. By the way, let one bead be different in color from the others. Let's call it central.

Let's look at our construction and draw the first conclusions:

1. Any bead is surrounded by six others (let them be under numbers 1-6)
2. The surface of the layer has irregularities, elevations and depressions. Each bead is a hill, between any three touching beads there is a depression.
3. The arrangement of beads in a layer can be represented as a grid of cross lines, and beads are located at the points of intersection of the lines. These points are called grid nodes. Since all the cells of our grid are identical to each other, we can specify the parameters of one cell to describe the geometric arrangement of particles in a layer. In this case, the cell is a rhombus with an acute angle equal to sixty degrees, and a side length equal to twice the radius of the bead.

We begin to build the second monolayer. We place it on the first monolayer, while we place one bead on the first layer so that it is in contact with our central one. This means that it will be located in our depression. We have six depressions around the central bead, and the distance between them is slightly greater than the radius of the bead. This means that in the second layer of beads, three beads will touch the central bead, instead of six (let’s denote them as 7-9). It can be clearly seen that the three beads of the second layer can be arranged in several ways:

1. we place them in the depressions between C, 1, 2; C 3.4; C,5,6;
2. place in recesses C, 2, 3; C, 4, 5; C, 1, 6;

In relation to the central bead, all options are absolutely the same. Let's take the first bead placement layer for the second monolayer. Since the centers of the particles of the first and second layers do not coincide, the mesh of the second layer is shifted relative to the first.

We begin to fill the third layer after the second. There are also two location options here. They are absolutely not identical to each other. In the first case, the bead is placed in depression A and then the grid is shifted by a third. We mentally outline a circle around point A and understand that in this case the grid of the fourth layer coincides with the first layer.

Another case is the location of the beads of the third layer in the depressions B. In this case, the grid of the third layer coincides with the grid of the first, and the grid of the second with the stack of the fourth.

That is, we have several types of bead packaging in the form of alternating layers. These are 1, 2,1,2,1,2 and 1,2,3,1,2,3,1,2,3.

In the first case, we are talking about the so-called hexagonal packing, and in the second, about cubic packing.

A large number of metals crystallize in one of these types of close packing.

At the same time, no matter how hard you try to fill the voids with beads, part of the space will still be empty. Now let's look at the beads through the side walls of the vessel. It can be seen that three beads of one layer and one of the other form a system behind which a void is hidden. The centers of these four beads are located at the vertices of the tetrahedron, which means the void is called tetrahedral.

The octahedral type is the formation of a void between three beads of one layer and three of another.

The role of such voids is extremely important in the formation of a crystal by particles of different sizes. In this case, we have particles with a large radius arranged so as to form a dense packing, and smaller ones are located in the voids formed by these particles.

The set of grids that advise all layers of crystal particles represents a spatial system called a crystal lattice. Among the characteristics of the grid, we can highlight the parameters of the cell: its dimensions, sides and angles. There are a huge variety of forms of crystal lattices. Crystallography is the study of crystal lattices.

Now let's look at a crystal not from the point of view of its “device”, but from the point of view of the chemical forces that provide communication in these crystals.

Types of chemical bond

Based on the nature of the connection between particles, crystals are divided into four types: molecular, atomic, ionic and metallic. Of course, you remember that there cannot be one hundred percent bond (only ionic or only metallic, it is important which type predominates). Let's look at each type in detail.

Molecular crystal lattice

A molecular lattice has molecules at its nodes. The connection between molecules is ensured by Van der Waals interaction. These are rather weak interactions, so the intramolecular and intermolecular distances between atoms are completely different. Due to the low energy of van der Waals interaction compared to covalent bonds in molecules, crystals with a molecular type of crystal lattice easily transform into a gaseous state at sufficiently low temperatures. Most organic compounds have a molecular type of lattice made of inorganics - hydrogen, sulfur, water, nitrogen, iodine.

Atomic crystal lattice

Atomic type of crystal lattice. Such crystals include diamond, the carbon atom in which is surrounded by four other atoms equidistant from it. All bonds between atoms have the same length and equal energy. An atomic crystal is characterized by a unified system of chemical bonds. Atoms are connected by directed, localized covalent bonds. They determine the energy characteristics of the crystal and groupings of atoms. Covalent bonds in atomic lattices have high strength; therefore, destroying such a crystal is very problematic, especially compared to a molecular one. Substances with atomic lattices have high strength and high melting and boiling points.

Methods for obtaining copper

In nature, copper exists in compounds and in the form of nuggets. The compounds are represented by oxides, bicarbonates, sulfur and carbon dioxide complexes, as well as sulfide ores. The most common ores are copper pyrite and copper luster. The copper content in them is 1-2%. 90% of primary copper is mined using the pyrometallurgical method and 10% using the hydrometallurgical method.

1. The pyrometallurgical method includes the following processes: enrichment and roasting, smelting for matte, purging in a converter, electrolytic refining. Copper ores are enriched by flotation and oxidative roasting. The essence of the flotation method is as follows: copper particles suspended in an aqueous medium adhere to the surface of air bubbles and rise to the surface. The method allows you to obtain copper powder concentrate, which contains 10-35% copper.

Copper ores and concentrates with a significant sulfur content are subject to oxidative roasting. When heated in the presence of oxygen, sulfides are oxidized, and the amount of sulfur is reduced by almost half. Poor concentrates containing 8-25% copper are roasted. Rich concentrates containing 25-35% copper are melted without resorting to roasting.

The next stage of the pyrometallurgical method for producing copper is smelting for matte. If lump copper ore with a large amount of sulfur is used as a raw material, then smelting is carried out in shaft furnaces. And for powdered flotation concentrate, reverberatory furnaces are used. Melting occurs at a temperature of 1450 °C.

In horizontal converters with side blowing, the copper matte is blown with compressed air in order for the oxidation of sulfides and ferrum to occur. Next, the resulting oxides are converted into slag, and sulfur into oxide. The converter produces blister copper, which contains 98.4-99.4% copper, iron, sulfur, as well as small amounts of nickel, tin, silver and gold.

Blister copper is subject to fire and then electrolytic refining. Impurities are removed with gases and converted into slag. As a result of fire refining, copper is formed with a purity of up to 99.5%. And after electrolytic refining, the purity is 99.95%.

2. The hydrometallurgical method involves leaching copper with a weak solution of sulfuric acid, and then separating copper metal directly from the solution. This method is used for processing low-grade ores and does not allow for the associated extraction of precious metals along with copper.

Crystal lattice and types of crystal lattices

Most substances, depending on conditions (temperature, pressure), can be in three states of aggregation. All solids can be divided into amorphous and crystalline. Each substance has a clear structure of atoms that form a specific geometric structure called a crystal lattice. But at the same time, each such substance will have different types of crystal lattices.

1. Crystalline and amorphous substance
2. Ionic crystals
3. Atomic crystals
4. Molecular crystals
5. Seven types of crystal lattices
6. Cubic (or isometric) lattice
7. Quadratic (or tetragonal) lattice
8. Orthorhombic crystal lattice
9. Monoclinic lattice
10. Triclinic lattice
11. Rhombohedral lattice
12. Hexagonal crystal lattice

Crystalline and amorphous substance

Crystalline substance: a solid whose atoms or molecules form a regular, ordered lattice. Most solids exist in a crystalline state, which is characterized by increased stability, but this does not mean that they are crystals in the true sense of the word; for example, pure copper is crystalline only because its atoms are arranged in a regular pattern.

Amorphous: A solid that has no crystalline structure. Its atoms and molecules are arranged without regularity. Supercooled liquids such as glass, rubber and some plastics are amorphous.

Crystalline structure Amorphous structure

Now we will consider only crystalline substances.

Depending on what particles the crystal lattice is made of and what the nature of the chemical bond between them is, different types of crystals are distinguished. There are 4 types of crystal lattices (CL): Molecular, ionic, metallic and atomic.

Types of crystal lattices

Halogens: F2, Cl2

Hydrogen halides: HF, HCl…

Simple substances non-metals:

O2, H2, N2, P(white)

CaC2, SiC (carborundum),

Ionic crystals

Ionic crystals are formed by cations and anions (for example, salts and hydroxides of most metals). In them there is an ionic bond between the particles. Ionic crystals can be composed of monoatomic ions. This is how crystals of sodium chloride, potassium iodide, and calcium fluoride are built.

It is impossible to isolate single molecules in an ionic crystal. Each cation is attracted to each anion and repelled by other cations.

Atomic crystals

Atomic crystals consist of individual atoms held together by covalent bonds. Of the simple substances, only boron and group IVA elements have such crystal lattices. Often, compounds of non-metals with each other (for example, silicon dioxide) also form atomic crystals. They are very durable and hard, and do not conduct heat and electricity well.

Molecular crystals

Molecular crystals are built from individual molecules, within which the atoms are connected by covalent bonds. Weaker intermolecular forces act between molecules. They are easily destroyed, so molecular crystals have low melting points, low hardness, and high volatility.

Metals are characterized by a metallic crystal lattice. It contains a metallic bond between atoms. In metal crystals, the nuclei of atoms are arranged in such a way that their packing is as dense as possible. The bonding in such crystals is delocalized and extends throughout the entire crystal.

Seven types of crystal lattices

There are seven different crystal systems. They were discovered in 1781 by Father Rene Just Howie. He accidentally noticed that some stones had an ideal shape. After many years of research, he developed his theory about the structure of crystals. In 1848, Auguste Bravais shows that there can only be seven types of elementary crystalline networks.

Systems characterize the different geometric shapes that a crystalline network can have.

Each of these systems is defined by its axes: three dimensional parameters (the length of the axes) and three angular parameters (the angles formed by the two axes). Conventionally, we call abc the lengths of the axes and α β and γ the angles formed by the axes. They are placed in space as follows:

Each cell representing a system also has a certain number of symmetries. These symmetries are of three types:

• central (marked C): the point is the center of symmetry of the mesh;
• plane (marked P): the plane is the plane of symmetry of the mesh;
• axial (O): rotation by a certain angle around the axis of symmetry returns the mesh to a position identical to the original one.

These symmetries have four orders:

• binary (labeled L2): 180° rotation (π rad)
• ternary (labeled L3): 120° rotation (2π/3 rad)
• quaternary (marked L 4): Rotation by 90° (π/2 rad.)
• hexagonal (marked L 6): 60° rotation (π/3 rad.)

Cubic (or isometric) lattice

Quadratic (or tetragonal) lattice

Orthorhombic crystal lattice

Monoclinic lattice

Triclinic lattice

Rhombohedral lattice

Hexagonal crystal lattice

Thus, we have examined in detail the concept of a crystal lattice and what the main crystal lattices are.