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seen above that the atoms are placed in a crystalline solid regularly and periodically. This restriction means that there are only a few possible networks.

A 3-dimensional solid there are only 14 different networks, grouped into 7 sets. The networks are described by unit vectors (a, b, c) establishing the frequency in each direction, as well as the relative direction or angles formed between them (a, b, g)



The most general is triclinic, as it is different from one another both angles, as the vectors that define the network. However, most common methods, while simple, are the cubic and hexagonal.

The cubic, as its name suggests, is a cube with equal frequency in all three directions, and angles of 90 º. Examples are common salt (sodium chloride, NaCl), silicon (Si), or diamond (carbon, C)

The hexagonal system has two vectors forming an angle of 120 degrees, and the third 90 degrees. This form is a hexagonal prism, and corresponds to materials such as graphite (carbon, C), or sapphire (also called alumina, Al2O3)

The cubic lattice

The simplest base is to place an atom in one corner a cube:



This type of network is called simple cubic lattice (SC), and has only one point in the network before it. In forming the crystal lattice, the atoms of adjacent cells round the corners of the cube. The position of the lower left corner, foreground, is usually considered the origin of coordinates of the unit cell. Thus, the coordinates of this point of network would be (0,0,0). Despite its simplicity, there are many elements that crystallize in this way.

The second type of cubic lattice is called body-centered cubic (Body-Centered Cubic, BCC). In this case, there are two occupied grid points, which are a corner and the center of the cube:



In this case, the two network points are at coordinates (0,0,0) and (a / 2, a / 2, a / 2), being to the lattice parameter or the length of the edge of the cube of the unit cell. Examples of materials that are BCC lattices is brass (CuZn, a = 2.94 å). Cu atom is placed in the corner, while Zn occupies the center of the body. That is, the unit cell contains 1 atom of copper, zinc and 1.

The final structure is cubic face-centered (Face Centered Cubic, FCC). Network has 4 points, one in the corner, and three more in the faces of the cube.



the coordinates of the grid points are (0,0,0), (0, a / 2, a / 2), (a / 2.0, a / 2) and (a / 2 , a / 2.0). A well-known network of this type is sodium chloride (common salt, NaCl), a = 5.63 å). Unlike brass, this time each lattice point is occupied by one atom of each class, but by a molecule of NaCl, so that each unit cell contains 4 atoms of Na, Cl and 4



FCC Network Other examples are the silicon (Si) or gallium arsenide (GaAs), each with its own peculiarities in its structure, widely used in microelectronics. The

hexagonal lattice

Of all the networks, there are two that offer maximum possible compaction. The first is the FCC. The other is the hexagonal close-packed.

hexagonal network is composed of three vectors a, b, c, to satisfy a = b, with an angle of 120 ° and the angle between a and b to c is 90 °. The maximum compaction is achieved when c = 1,633 • a. The base is formed by two atoms, the first located at the origin (0,0,0), and the other positions (2a / 3, / 3, a / 2)

Annex

Diamonds and pens
Structure

crystalline architecture

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Diamonds and pens

comes from: simple crystal structures

Carbon is an element that can crystallize in the solid phase in two different ways: as a network FCC or hexagonal structure. These two types of networks give radically different properties. When crystallizes in cubic lattice is a diamond. When crystallized as hexagonal lattice, is best known for graphite, which forms the lead in a pencil.

The FCC has an associated network base with 4 points, one in the corner, and three in the center of the cube. Each lattice point is associated with two atoms of carbon. The second is displaced from the first (A / 4, a / 4, a / 4). This structure is responsible for that diamond is hard, bright, and it is a good electrical insulator.




On the other hand, graphite has a hexagonal structure with a base of two points: the origin of the network, and (2 / 3, 1 / 3, 1 / 2) . This structure makes graphite is a brittle material, dark and a conductor of electricity. Quite the opposite of a diamond.

This example so far of the structures that can acquire carbon, shows that in a material, the structure is the key from which to understand their properties.

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Welcome

This blog contains some of my artistic work that part of the design and aims to strategically fill the space. Besides images, you can read the texts that accompany each production, with their data: year, technique, dimensions and manufacturing process.

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The Art

states of matter

So far we have seen the internal structure isolated atom, and how electrons are arranged in it. The research that led to understand the atom led to the development of quantum mechanics .

However, the atoms are not isolated, but interact with other atoms and molecules, or radiation. The result of these interactions a set of atoms can occur in several different states, depending on the intensity of these interactions:

can form a gas, when interactions are weak, and reduced almost to collide among them, as if they were a bunch of billiard balls completely free to move around the table. The gas is adapted to the volume that is enclosed, occupied entirely.

form a liquid when forming bonds interactions are weak enough to bind molecules or atoms in a short period of time, so that all takes a certain cohesion, but the atoms and molecules retain a high mobility within the set. A liquid is adapted to the volume that contains it, but does not have to occupy it fully, such as when pouring water into a bottle, takes shape, but does not occupy the entire volume of the bottle.

and form a solid when interactions are able to make these lasting bonds between atoms and stable, so completely lost their mobility. A solid is rigid and not adapted to the volume that contains it. A solid has its own shape and volume.

A very important factor that determines whether the interactions are strong or weak, is the kinetic energy: the movement of atoms or molecules, if it is fast or slow. An indicator directly related to this parameter is temperature. In gases, the kinetic energy is high so that the interactions are effective only when the atoms pass very close to each other, resulting in collisions, but no brakes. It makes no sense to talk of a structure.

atoms or molecules in a liquid have a kinetic energy lower than the respective gas, so that the interactions are longer range and duration than in gases. The liquid also has a structure in itself, but may have small clusters of atoms or molecules, called "clusters" with a certain order or microscopic structure.

In a solid, the kinetic energy is so small that the interactions affect both the atoms are stopped, making the interactions between them stable and durable. In this case we can speak of a macroscopic structure of a material.

The crystalline solid

gases and liquids in the interactions between atoms are not stable or lasting. Therefore, the disturbance that would suffer the atoms are not stable, and its internal structure is not affected. In a solid
however, the interaction between atoms is so intense that keeps static, making them durable and stable as well. How do these interactions to the atoms and their internal structure? And how these differences contribute to a single atom properties of the solid?

A solid is a set of static atoms occupy given position. There is a first distinction in the structure of solids, depending on the positions of atoms:

Amorphous materials are materials that have atoms occupying the space of irregular shape: it is not possible to find a repeating pattern. An example of amorphous material is glass.

In crystalline materials, or crystals, the atoms maintain a position following a regular distribution. That is, a crystalline solid is formed by a small group of atoms with a specific structure and this structure is repeated periodically at fixed distances. The vast majority of the materials are crystalline. A well-known example is common salt, which is small cubes of sodium and chlorine which are repeated throughout the material.

An ideal crystal is constructed as an infinite repetition of a structural unit, or unit cell. " This in turn may contain several atoms, arranged in any way. Thus, there are two parts in the unit cell:

Network: The "box", or structure will be repeated throughout the crystal, which is delimited by vectors, which need not be perpendicular or have equal length.

Base: The contents of the structure, which is always the same, and always placed in the same positions and guidance regarding the origin of coordinates of the network.

lattice parameter is called the size of the network, which is what determines the frequency of the crystal. In a crystal can have different periodicities in each axis of space. As an origin of coordinates, it is possible to know the position of all atoms, since all are spaced an integral number of times the lattice parameter.



fundamental Networks A network is parameterized by a vector. They may have different sizes (giving rise to different periodicities in each direction), and need not be 90 º relative to each other. (In the drawings represented a 2-dimensional network defined by two vectors. A three-dimensional network is delimited by 3 vectors).

However, any network is valid. Are valid only to meet certain symmetries. For example, the Pentagon has a symmetry that is valid for a network, since that figure is not able to fill the space without leaving voids.

The symmetry that has a hexagon does allow, however, that a network can do:

Thus, the number of possible networks is limited. In two dimensions, there are only 5 types of networks, depending on the relative length of each vector, and the angle.

Each of these networks are called Network Bravais

To 3 dimensions, there are a few more: 14 Bravais lattices in total, grouped into 7 different systems.

Annex

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