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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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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

Art, glass and ducks

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lattice, crystals and ducks

comes from: The lattice

Maurits Escher (1898-1972), MC Escher , was a Dutch artist, whose works more famous buildings include stairs and impossible. Some of his works also deal with how to fill the space, through the repetition of patterns, as occurs in a crystalline solid. It is easy to identify in his works the same kind of structures that occur in a solid, albeit restricted to two dimensions.

From a base of two ducks, including a parallelogram structure, Escher can fill an entire plane to repeat the parallelogram. Ducks are coupled with each other to keep free holes, and fill the plane to infinity.

Related links Official website MC Escher

Negative Effects Of Selling Stock

The development of quantum mechanics makes possible the discovery of new effects, impossible from a classical viewpoint. Perhaps the most popular is the tunnel, where making a quick comparison and bad, it's like throwing a ball at a wall to cross it without touching it. This is how it appears from an analysis of a similar situation, through the Schrödinger equation .

quantum Wall

Consider first what is meant by " wall" and what happens to an electron when it arrives. The energy of a particle is always the sum of its kinetic energy and potential energy. Thus, energy will always be equal to or greater than the potential. The cases in which the energy is lower than potential from classical physics, states represent unattainable by a particle. Thus, the point at which the total energy equals the potential represents a "turning point , the particle can not move forward, but must go back. Is the equivalent of a "wall ."

In the figure, the electron energy above is greater than the step, and both are superior, losing a bit of kinetic energy. Below the electron instead he should go back after reaching the point where its energy is equal to the potential energy, and therefore its kinetic energy is zero at that point.

Consider the situation of the second electron from the quantum point of view, with the Schrödinger equation.

The equation to solve is:

whose solution we saw in the previous entry , is a combination of sine and cosine. The combination of sine and cosine, by Euler's formula is equivalent to an exponential function imaginary and more useful for the analysis that follows. Thus, the wave function can be expressed generally as:

As we saw earlier, k (the wave vector ) is related to the angular momentum and therefore the sense that the particle moves. A + means that moves in the direction of x increasing (going from left to right). The sign - describes a movement in the opposite direction. As the picture has been raised, we are in the first case, ie, the electron moves from left to right, whereas in the wave function describes the first term ( k positive). Therefore, in our case, you should choose B = 0 to cancel the second term.

Let's see the two regions of space that defines the step. On the left, (EV) is a positive quantity (total energy greater than the potential), and the wave equation represents a free electron (an imaginary exponential, or a combination of sine and cosine). In contrast, in the right area, (EV) is negative (energy less than the potential energy), the wave vector is imaginary , and the wave function represents a real exponentially decreasing. That is, although it is a forbidden zone as classical physics, in quantum mechanics a particle can exist in that area, but with a diminishing likelihood as deeply into the wall.

The distance that an electron can penetrate into the forbidden zone before your chance is almost nil, depends on the difference between energy and the value of the potential. The greater the difference EV, the probability falls more rapidly. In the extreme case in which V tends to infinity, the penetration depth tends to zero, ie, the electron does not enter into the wall (as we assumed when we spoke of quantum well).

The tunnel effect

Therefore, a particle can penetrate a wall of potential, something impossible according to classical physics. A particle can penetrate a distance (small), although the probability of finding the particle at that location decreases as depth. What if the potential wall finishes before this probability is terminated, or reduced too?. In this case, the "other side " from the wall of the wave function again described by a free electron. It is therefore possible that an electron reaches a barrier, the cross, and appears on the other side of it, with a certain probability, although less than it did before crossing the barrier.

The probability of crossing the barrier depends on the mass of the particle, the barrier height, but above all, of its width. The typical distances that probability is sufficient to tunnel is in the order of angstroms and nanometers. Alpha decay



The emission of alpha particles is related to the tunnel effect. An alpha particle is an atom composed of 2 protons and 2 neutrons, not electrons. Corresponds to a nucleus of helium 4 (4 ^I 2 +). An atom with a large number of protons and neutrons keeps these particles stuck together by the strong interaction. An outline of the potential energy inside an atom is as follows:

There is an area of \u200b\u200bpotential barrier at the transition between the strong interaction domain and the electrostatics. Overcoming this barrier would require making a lot of energy. However, an alpha particle is able to cross the barrier by tunnel effect, breaking up the nucleus to which it belonged.

The scanning tunneling microscope

The tunnel is now the basis of some devices such as diodes, lasers and detectors. But one of the most important is related to the surface microscopy.

View STM: Scanning tunneling microscope