crystal structure

rock crystal

Rock crystal from the Dauphiné region of France.

Transparent variety of the silica mineral quartz that is valued for its clarity and total lack of colour or flaws. Rock crystal formerly was used extensively as a gemstone, but it has been replaced by glass and plastic; rhinestones originally were quartz pebbles found in the Rhine River. The optical properties of rock crystal led to its use in lenses and prisms; its piezoelectric properties (see piezoelectricity) are used to control the oscillation of electrical circuits.

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Optoelectronic device used in displays for watches, calculators, notebook computers, and other electronic devices. Current passed through specific portions of the liquid crystal solution causes the crystals to align, blocking the passage of light. Doing so in a controlled and organized manner produces visual images on the display screen. The advantage of LCDs is that they are much lighter and consume less power than other display technologies (e.g., cathode-ray tubes). These characteristics make them an ideal choice for flat-panel displays, as in portable laptop and notebook computers.

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Substance that flows like a liquid but maintains some of the ordered structure characteristic of a crystal. Some organic substances do not melt directly when heated but instead turn from a crystalline solid to a liquid crystalline state. When heated further, a true liquid is formed. Liquid crystals have unique properties. The structures are easily affected by changes in mechanical stress, electromagnetic fields, temperature, and chemical environment. Seealso liquid crystal display.

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Any solid material whose atoms are arranged in a definite pattern and whose surface regularity reflects its internal symmetry. Each of a crystal's millions of individual structural units (unit cells) contains all the substance's atoms, molecules, or ions in the same proportions as in its chemical formula (see formula weight). The cells are repeated in all directions to form a geometric pattern, manifested by the number and orientation of external planes (crystal faces). Crystals are classified into seven crystallographic systems based on their symmetry: isometric, trigonal, hexagonal, tetragonal, orthorhombic, monoclinic, and triclinic. Crystals are generally formed when a liquid solidifies, a vapour becomes supersaturated (see saturation), or a liquid solution can no longer retain dissolved material, which is then precipitated. Metals, alloys, minerals, and semiconductors are all crystalline, at least microscopically. (A noncrystalline solid is called amorphous.) Under special conditions, a single crystal can grow to a substantial size; examples include gemstones and some artificial crystals. Few crystals are perfect; defects affect the material's electrical behaviour and may weaken or strengthen it. Seealso liquid crystal.

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The Crystal Palace at Sydenham Hill, London. It was designed by Sir Joseph Paxton for the Great elipsis

Giant glass-and-iron exhibition hall in Hyde Park, London, that housed the Great Exhibition of 1851. It was taken down and rebuilt (1852–54) at Sydenham Hill, where it survived until its destruction by fire in 1936. Designed by the greenhouse builder Sir Joseph Paxton (1801–1865), it was a remarkable assembly of prefabricated parts. Its intricate network of slender iron rods sustaining walls of clear glass established an architectural standard for later international exhibitions, likewise housed in glass conservatories.

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In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms in a crystal. A crystal structure is composed of a motif, a set of atoms arranged in a particular way, and a lattice. Motifs are located upon the points of a lattice, which is an array of points repeating periodically in three dimensions. The points can be thought of as forming identical tiny boxes, called unit cells, that fill the space of the lattice. The lengths of the edges of a unit cell and the angles between them are called the lattice parameters. The symmetry properties of the crystal are embodied in its space group. A crystal's structure and symmetry play a role in determining many of its properties, such as cleavage, electronic band structure, and optical properties.

Unit cell

The crystal structure of a material or the arrangement of atoms in a crystal structure can be described in terms of its unit cell. The unit cell is a tiny box containing one or more motifs, a spatial arrangement of atoms. The units cells stacked in three-dimensional space describes the bulk arrangement of atoms of the crystal. The unit cell is given by its lattice parameters, the length of the cell edges and the angles between them, while the positions of the atoms inside the unit cell are described by the set of atomic positions (x_i, y_i, z_i) measured from a lattice point.

Although there are an infinite number of ways to specify a unit cell, for each crystal structure there is a conventional unit cell, which is chosen to display the full symmetry of the crystal (see below). However, the conventional unit cell is not always the smallest possible choice. A primitive unit cell of a particular crystal structure is the smallest possible volume one can construct with the arrangement of atoms in the crystal such that, when stacked, completely fills the space. This primitive unit cell will not always display all the symmetries inherent in the crystal. A Wigner-Seitz cell is a particular kind of primitive cell which has the same symmetry as the lattice. In a unit cell each atom has an identical environment when stacked in 3 dimensional space. In a primitive cell, each atom may not have the same environment.

Classification of crystals by symmetry

The defining property of a crystal is its inherent symmetry, by which we mean that under certain operations the crystal remains unchanged. For example, rotating the crystal 180 degrees about a certain axis may result in an atomic configuration which is identical to the original configuration. The crystal is then said to have a twofold rotational symmetry about this axis. In addition to rotational symmetries like this, a crystal may have symmetries in the form of mirror planes and translational symmetries, and also the so-called compound symmetries which are a combination of translation and rotation/mirror symmetries. A full classification of a crystal is achieved when all of these inherent symmetries of the crystal are identified.

Crystal system

The 7 Crystal systems
(Defining Symmetry)
The 14 Bravais Lattices:

(1 diad)
simple base-centered

(3 perpendicular diads)
simple base-centered body-centered face-centered

(1 hexad)
(1 triad)
(1 tetrad)
simple body-centered

(4 triads)
simple body-centered face-centered

The crystal systems are a grouping of crystal structures according to the axial system used to describe their lattice. Each crystal system consists of a set of three axes in a particular geometrical arrangement. There are seven unique crystal systems. The simplest and most symmetric, the cubic (or isometric) system, has the symmetry of a cube, that is, it exhibits four threefold rotational axes oriented at 109.5 degrees (the tetrahedral angle) with respect to each other. These threefold axes lie along the body diagonals of the cube. This definition of a cubic is correct, although many textbooks incorrectly state that a cube is defined by three mutually perpendicular axes of equal length – if this were true there would be far more than 14 Bravais lattices. The other six systems, in order of decreasing symmetry, are hexagonal, tetragonal, rhombohedral (also known as trigonal), orthorhombic, monoclinic and triclinic. Some crystallographers consider the hexagonal crystal system not to be its own crystal system, but instead a part of the trigonal crystal system. The crystal system and Bravais lattice of a crystal describe the (purely) translational symmetry of the crystal.

The Bravais lattices

When the crystal systems are combined with the various possible lattice centerings, we arrive at the Bravais lattices. They describe the geometric arrangement of the lattice points, and thereby the translational symmetry of the crystal. In three dimensions, there are 14 unique Bravais lattices which are distinct from one another in the translational symmetry they contain. All crystalline materials recognized until now (not including quasicrystals) fit in one of these arrangements. The fourteen three-dimensional lattices, classified by crystal system, are shown to the right. The Bravais lattices are sometimes referred to as space lattices.

The crystal structure consists of the same group of atoms, the basis, positioned around each and every lattice point. This group of atoms therefore repeats indefinitely in three dimensions according to the arrangement of one of the 14 Bravais lattices. The characteristic rotation and mirror symmetries of the group of atoms, or unit cell, is described by its crystallographic point group.

Point and space groups

The crystallographic point group or crystal class is the mathematical group comprising the symmetry operations that leave at least one point unmoved and that leave the appearance of the crystal structure unchanged. These symmetry operations can include reflection, which reflects the structure across a reflection plane, rotation, which rotates the structure a specified portion of a circle about a rotation axis, inversion which changes the sign of the coordinate of each point with respect to a center of symmetry or inversion point and improper rotation, which consists of a rotation about an axis followed by an inversion. Rotation axes (proper and improper), reflection planes, and centers of symmetry are collectively called symmetry elements. There are 32 possible crystal classes. Each one can be classified into one of the seven crystal systems.

The space group of the crystal structure is composed of the translational symmetry operations in addition to the operations of the point group. These include pure translations which move a point along a vector, screw axes, which rotate a point around an axis while translating parallel to the axis, and glide planes, which reflect a point through a plane while translating it parallel to the plane. There are 230 distinct space groups.

Physical properties

Defects or impurities in crystals

Real crystals feature defects or irregularities in the ideal arrangements described above and it is these defects that critically determine many of the electrical and mechanical properties of real materials. When one atom substitutes for one of the principal atomic components within the crystal structure, alteration in the electrical and thermal properties of the material may ensue. Impurities may also manifest as spin impurities in certain materials. Research on magnetic impurities demonstrates that substantial alteration of certain properties such as specific heat may be affected by small concentrations of an impurity, as for example impurities in semiconducting ferromagnetic alloys may lead to different properties as first predicted in the late 1960s. Dislocations in the crystal lattice allow shear at lower stress than that needed for a perfect crystal structure.

Crystal symmetry and physical properties

Twenty of the 32 crystal classes are so-called piezoelectric, and crystals belonging to one of these classes (point groups) display piezoelectricity. All 21 piezoelectric classes lack a center of symmetry. Any material develops a dielectric polarization when an electric field is applied, but a substance which has such a natural charge separation even in the absence of a field is called a polar material. Whether or not a material is polar is determined solely by its crystal structure. Only 10 of the 32 point groups are polar. All polar crystals are pyroelectric, so the 10 polar crystal classes are sometimes referred to as the pyroelectric classes.

There are a few crystal structures, notably the perovskite structure, which exhibit ferroelectric behaviour. This is analogous to ferromagnetism, in that, in the absence of an electric field during production, the ferroelectric crystal does not exhibit a polarisation. Upon the application of an electric field of sufficient magnitude, the crystal becomes permanently polarised. This polarisation can be reversed by a sufficiently large counter-charge, in the same way that a ferromagnet can be reversed. However, it is important to note that, although they are called ferroelectrics, the effect is due to the crystal structure, not the presence of a ferrous metal. the angle between the normals to the two intersecting faces is called interfacial angle.

Incommensurate crystals have period-varying translational symmetry. The period between nodes of symmetry is constant in most crystals. The distance between nodes in an incommensurate crystal is dependent on the number of nodes between it and the base node.

See also

For more detailed information in specific technology applications see materials science, ceramic, or metallurgy.


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