In crystallography, a vacancy is a type of point defect in a crystal. Crystals inherently possess imperfections, often referred to as 'crystalline defects'. A defect wherein an atom, such as silicon, is missing from one of the sites is known as a 'vacancy' defect.
Vacancies occur naturally in all crystalline materials. At any given temperature, up to the melting point of the material, there is an equilibrium concentration (ratio of vacant lattice sites to those containing atoms). At the melting point of some metals the ratio can be approximately 0.1%
The creation of a vacancy can be simply modeled by considering the energy required to break the bonds between an atom inside the crystal and its nearest neighbor atoms. Once that atom is removed from the lattice site, it is put back on the surface of the crystal and some energy is retrieved because new bonds are established with other atoms on the surface. However, there is a net input of energy because there are fewer bonds between surface atoms than between atoms in the interior of the crystal.
At any given temperature, the amount of energy needed to create a vacancy is diminished because creating a vacancy disorders the interior of the crystal. The measure of this disorder is called the entropy of the system. Adding vacancies to the material increases the entropy, which tends to reduce the total energy required to create the vacancy. We call this energy the free energy and this is the energy that is required to create an equilibrium concentration of vacancies at a given temperature.
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Crystallography
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Crystallography (from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and graphein = write) is the experimental science of determining the arrangement of atoms in solids. In older usage, it is the scientific study of crystals.
Before the development of X-ray diffraction crystallography (see below), the study of crystals was based on the geometry of the crystals. This involves measuring the angles of crystal faces relative to theoretical reference axes (crystallographic axes), and establishing the symmetry of the crystal in question. The former is carried out using a goniometer. The position in 3D space of each crystal face is plotted on a stereographic net, e.g. Wulff net or Lambert net. In fact, the pole to each face is plotted on the net. Each point is labelled with its Miller index. The final plot allows the symmetry of the crystal to be established.
Crystallographic methods now depend on the analysis of the diffraction patterns that emerge from a sample that is targeted by a beam of some type. The beam is not always electromagnetic radiation, even though X-rays are the most common choice. For some purposes electrons or neutrons are used, which is possible due to the wave properties of the particles. Crystallographers often explicitly state the type of illumination used when referring to a method, as with the terms X-ray diffraction, neutron diffraction and electron diffraction.
These three types of radiation interact with the specimen in different ways. X-rays interact with the spatial distribution of the valence electrons, while electrons are charged particles and therefore feel the total charge distribution of both the atomic nuclei and the surrounding electrons. Neutrons are scattered by the atomic nuclei through the strong nuclear forces, but in addition, the magnetic moment of neutrons is non-zero. They are therefore also scattered by magnetic fields. Because of these different forms of interaction, the three types of radiation are suitable for different crystallographic studies.
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Theory
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In several cases, an image of a microscopic object is generated by focusing the rays of the visible spectrum using a lens, as in light microscopy. However, because the wavelength of visible light is long compared to atomic bond lengths and atoms themselves, it is necessary to use radiation with shorter wavelengths, such as X-rays. Employing shorter wavelengths implies abandoning microscopy and true imaging, however, because there exists no material from which a lens capable of focusing this type of radiation can be created. (That said, scientists have had some success focusing X-rays with microscopic Fresnel zone plates made from gold). Generally, in diffraction-based imaging, the only wavelengths used are those that are too short to be focused. This difficulty is the reason that crystals must be used.
Because of their highly ordered and repetitive structure, crystals are an ideal material for analyzing the structure of solids. To use X-ray diffraction as an example, a single X-ray photon diffracting off of one electron cloud will not generate a strong enough signal for the equipment to detect. However, many X-rays diffracting off many electron clouds in approximately the same relative position and orientation throughout the crystal will result in constructive interference and hence a detectable signal.
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Vacancies occur naturally in all crystalline materials. At any given temperature, up to the melting point of the material, there is an equilibrium concentration (ratio of vacant lattice sites to those containing atoms). At the melting point of some metals the ratio can be approximately 0.1%
The creation of a vacancy can be simply modeled by considering the energy required to break the bonds between an atom inside the crystal and its nearest neighbor atoms. Once that atom is removed from the lattice site, it is put back on the surface of the crystal and some energy is retrieved because new bonds are established with other atoms on the surface. However, there is a net input of energy because there are fewer bonds between surface atoms than between atoms in the interior of the crystal.
At any given temperature, the amount of energy needed to create a vacancy is diminished because creating a vacancy disorders the interior of the crystal. The measure of this disorder is called the entropy of the system. Adding vacancies to the material increases the entropy, which tends to reduce the total energy required to create the vacancy. We call this energy the free energy and this is the energy that is required to create an equilibrium concentration of vacancies at a given temperature.
==============================================================
Crystallography
---------------------
Crystallography (from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and graphein = write) is the experimental science of determining the arrangement of atoms in solids. In older usage, it is the scientific study of crystals.
Before the development of X-ray diffraction crystallography (see below), the study of crystals was based on the geometry of the crystals. This involves measuring the angles of crystal faces relative to theoretical reference axes (crystallographic axes), and establishing the symmetry of the crystal in question. The former is carried out using a goniometer. The position in 3D space of each crystal face is plotted on a stereographic net, e.g. Wulff net or Lambert net. In fact, the pole to each face is plotted on the net. Each point is labelled with its Miller index. The final plot allows the symmetry of the crystal to be established.
Crystallographic methods now depend on the analysis of the diffraction patterns that emerge from a sample that is targeted by a beam of some type. The beam is not always electromagnetic radiation, even though X-rays are the most common choice. For some purposes electrons or neutrons are used, which is possible due to the wave properties of the particles. Crystallographers often explicitly state the type of illumination used when referring to a method, as with the terms X-ray diffraction, neutron diffraction and electron diffraction.
These three types of radiation interact with the specimen in different ways. X-rays interact with the spatial distribution of the valence electrons, while electrons are charged particles and therefore feel the total charge distribution of both the atomic nuclei and the surrounding electrons. Neutrons are scattered by the atomic nuclei through the strong nuclear forces, but in addition, the magnetic moment of neutrons is non-zero. They are therefore also scattered by magnetic fields. Because of these different forms of interaction, the three types of radiation are suitable for different crystallographic studies.
===============================================================
Theory
------------
In several cases, an image of a microscopic object is generated by focusing the rays of the visible spectrum using a lens, as in light microscopy. However, because the wavelength of visible light is long compared to atomic bond lengths and atoms themselves, it is necessary to use radiation with shorter wavelengths, such as X-rays. Employing shorter wavelengths implies abandoning microscopy and true imaging, however, because there exists no material from which a lens capable of focusing this type of radiation can be created. (That said, scientists have had some success focusing X-rays with microscopic Fresnel zone plates made from gold). Generally, in diffraction-based imaging, the only wavelengths used are those that are too short to be focused. This difficulty is the reason that crystals must be used.
Because of their highly ordered and repetitive structure, crystals are an ideal material for analyzing the structure of solids. To use X-ray diffraction as an example, a single X-ray photon diffracting off of one electron cloud will not generate a strong enough signal for the equipment to detect. However, many X-rays diffracting off many electron clouds in approximately the same relative position and orientation throughout the crystal will result in constructive interference and hence a detectable signal.
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