Crystal

A crystal is a solid whose building blocks - atoms, ions or molecules - are not random, but regularly arranged in a crystal structure. Known crystalline materials are salt, sugar, minerals and snow - but also the metals.

The science that studies the properties and shapes of crystals, the crystallography.

• 6.1 single crystal and polycrystal
• 6.2 Minerals
• 6.3 Technical Applications
• 6.4 Organic Crystals

More precise definition, distinctions

A crystal is a homogeneous body, for he is both materially and physically uniform. However, many physical properties are dependent on the spatial direction, that is, a crystal is anisotropic.

Crystals were defined prior to 1992 built as three-dimensional periodically consistent structural units. This structural unit is called unit cell or unit cell.

Since 1992, a crystal according to the International Union IUCr Crystallographic by its discrete diffraction orders ( when illuminated with X-rays) defined. So he has a long-range order, but is not necessarily periodic. This definition was in 1984 discovered quasicrystals enforced that form a subgroup of aperiodic crystals. However, the periodic crystals form by far the largest sub-group of the crystals.

Depending on the severity of the outer shape, a distinction is

• Unaffected educated, so-called idiomorphic ( ancient Greek ἲδιος own and μορφἠ shape) crystals and
• Anhedral ( ancient Greek ξένος strange and μορφἠ shape) crystals whose external shape is determined by external interfaces.

The euhedral crystal has in its outer form back to the respective crystal structure. Therefore, for example, undisturbed grown crystals of sodium chloride (common salt, mineral halite ) are cube- shaped. Even with euhedral crystals is in the nature usually some distortion before, ie, the edge lengths (but not the angle) to differ from the ideal shape ( cf. law of constant angles ).

The external shape of a crystal is determined by the independent features Crystal habit and crystal habit. The crystal surfaces as well as lattice planes described by Miller indices.

Since the characteristic of crystals is the regular arrangement in all three spatial directions, even body are conceivable, the blocks are repeated only in one or two directions. Then we can speak of one-dimensional and two-dimensional crystals. In nature, membrane proteins occur that arrange as two-dimensional crystals in the biomembrane. One example is Bacteriorhodopsin. In structural biology 2D crystals are grown to determine the atomic positions of the crystallized macromolecules using electron cryomicroscopy.

Besides crystals, there is also the body that have no inherent long-range order and are called amorphous. An example is glass (also called lead crystal and other crystal glass).

When a liquid is anisotropic and thereby having some properties of a crystal, is a liquid crystal.

Word origin

The term crystal comes from the Greek word κρύσταλλος ( krystallos to κρύος kryos " icy cold, frost, ice "). It means, first, in Homer, " ice " - later also all the ice like, Light and Transparent. In particular, the rock crystal as well as colored gemstones and glass are so called (eg in Strabo and Claudius Aelianus ).

In the operated already in ancient Greece mining quartz crystals were probably discovered. They were kept on ice, which must have originated at such low temperatures that it could no longer melt. This view was prevalent until the early Middle Ages. About the Latin Crystallus the Old High German name has crystallographic formed, which has evolved over time to crystal. In the 19th century crystal was common.

Structure and classification of periodic crystals

The direction and length of the vectors by which a crystal structure can be moved so that a repeat of the atomic positions, describe the axes of the crystal lattice ( or shortly crystal axes ). Therefore, the structure of each crystal is shown with its own specific coordinate system, the axis system. In addition to the displacement of a crystal structure can also theoretically be rotated around these axes, and the twisted structure covered with the original structure. Because the translational symmetry must be preserved, only rotational symmetries can occur that describe one, two, three, four, or six repetitions in a complete rotation (360 °). It is thereby zähligen 1 of 2 -, 3 -, 4 - or 6 -fold axes spoken. There are crystals that have more symmetry elements except axes of rotation and translations, namely mirror planes and inversion centers, as well as couplings between these symmetries to axes of rotation with inversion [Note 1], and glide reflections [Note 2] and screw axes. [Note 3]

The classification of the symmetry properties of crystals can be used. The number of possible combinations and coupling possibilities of symmetry elements is limited (see also group theory). There is in the two-dimensional plane crystallographic groups crystals 17 and three-dimensional crystals 230 crystallographic space groups which are completely A volume listed in the International Tables for Crystallography.

If a new crystal studied, the space group is initially unknown. In the description of the external shape of the crystal, it can be just one of the 32 point groups or crystal classes assign. These point groups describe the macroscopic symmetry properties of the crystals and summarize those space groups that differ only in the translational symmetry. Plays no role in the translation of the external view of crystals. Because the angle between the crystal faces of each crystal are equal and often are compatible with rotational symmetry ( for example, 90 ° with halite quadruple rotational symmetry ), the seven crystal systems are used to describe the crystal morphology is used in which the location and relative length of the cell axes differ. A crystal is triclinic, depending on the membership of the corresponding crystal system, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal or cubic.

Auguste Bravais classified the different possible translation lattice. These grids consist of identical parallelepipeds represent the corners of the grid points. In order to describe the symmetry of certain lattices, he had next to primitive unit cells ( with a lattice point per cell), larger elementary cells, which are flat or centered inside. An example of a face-centered unit cell is shown in Figure 5. There are 14 Bravais lattices in three-dimensional space.

In the crystal structure analysis, the scattering pattern of the X-ray diffraction Laue groups or Laue classes can be divided into eleven centrosymmetric point groups are called. Even in non- centrosymmetric crystal structures arise centrosymmetric diffraction pattern because the reflexes occur as Friedel pairs with normally the same intensity. The Laue groups can be derived accordingly by a center of symmetry is added to the point group of the crystal.

The crystal structure is not material specific, which is a substance having a certain chemical composition, depending on the external conditions (pressure, temperature ) have different thermodynamically stable structures. The different crystal structures of the same substance are called modifications; the existence of different modifications is called polymorphism. The modifications represent different stages in the sense of physical chemistry, the stability ranges can be shown in phase diagrams. The individual modification or phases of a substance, in addition to any existing proper names, usually with small Greek letters numbered ( in iron eg α ( ferrite), γ ( austenite ), δ -, ε - iron: see iron -carbon diagram).

Crystallization

A crystal may arise when the temperature of a melt falls slowly enough below the melting point and then the thermal motion of the individual atoms takes such a small value that the mutual bonds can not be broken by vibration - in the formation of a uniform lattice, which is characterized by long-range order. The uniform grid has a lower free energy than the amorphous glass, which has only short-range order. We call this process as crystallization.

The formation of a crystal is an exergonic process: While increases the entropy within the system from ( for increase in the long-range order ), this is conducted at temperatures up to the melting point, however, by an enthalpy due to attraction between the particles ( = heat of crystallization ) overcompensated.

Starting point for crystal formation is a crystallization germ, which grows with decreasing temperature. If there are many such nuclei or sets the crystallization at several points a the same time, the result is a polycrystal. If the temperature of the melt so fast that the atoms can not be arranged periodically, the result is an amorphous material, a glass. In many cases it is in the course of crystallization to an intergrowth of two crystals of the same structure and composition, which is referred to in sequence as a twin crystal.

Under a recrystallization is defined as the change in a crystal structure due to the change of external factors such as pressure and temperature conditions. In this case, the crystalline solid changes its modification.

The artificial production of crystals are called crystal growth.

Properties

Non-metallic inorganic crystals are harder but also more brittle. All metals solidify usually crystalline.

The behavior of light in the crystal is defined by the crystal optical system. Important properties and phenomena associated therewith are the optical type, polarization, birefringence, and the pleochroism. Periodic dielectric structures, so-called photonic crystals novel optical properties show.

Some crystals, such as quartz crystals have piezoelectric properties. They build an electric voltage when they are deformed and deform when an electric voltage is applied. This effect is used in piezo lighters to generate spark. In electronics, piezoelectric quartz crystals are used as a clock (eg quartz watches). Some piezoelectric crystals, but not all, convert a temperature difference into a charge separation. This property is called pyroelectricity. Such crystals are used in motion sensors and temperature sensors. A particular case of the pyroelectricity is ferroelectricity: In the ferroelectric crystals, the electrical polarization can be reversed by the application of a voltage.

Lattice defects

Contains a real crystal lattice defects, that is, the three-dimensional periodic arrangement of the atoms is disturbed. There are point defects, line error, error surface and volume error. Point error is the only lattice defects, which are also present in thermodynamic equilibrium.

Embodiments and examples

Single crystal and polycrystal

Normally there is a crystalline solid as a polycrystal rather than single crystal, i.e., it consists of many small crystals ( crystallites ) that are separated by grain boundaries. For example, metal objects, wires, etc. are usually polycrystals. Is there a body of different crystal types, so the interfaces between them are called phase boundaries.

Minerals

Many minerals are able to form a variety of crystal shapes and colors. The best known examples are the one of quartz whose forms of training covers the whole range of macro - crystalline colorless ( rock crystal) to microcrystalline - colored colored ( red agate ), and secondly, the calcite with a similar wealth of varieties.

The world's largest crystals were discovered in the mine of Naica. They consist of the type of gypsum selenite, are 14 m long and weigh up to 50 tons.

The diamond, a crystalline form of carbon, is the hardest naturally occurring mineral. Also silicon crystallizes in the diamond lattice.

Technical Applications

Silicon is currently the material which is most commonly used in large quantities as a single crystal ( monocrystal ), namely, in the semiconductor technology. The gallium arsenide there also used (GaAs ), however, points to the so-called zinc blende structure. Nanotechnology deals among other things with nanocrystals.

Organic Crystals

Also, organic substances, such as proteins form crystals - but only in exceptional cases. For example, are located in the peroxisomes of plant catalase crystals, which can be visualized by electron microscopy. Protein crystallography deals with the crystal growth of proteins for structural analysis.