Definitions

# 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 Rock crystal formerly was used extensively as a gemstone, but it has been replaced by glass and plastic; rhinestones originally were quartz pebbles found in the Rhine River.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.

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.

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.

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.

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.

Any rock composed entirely of crystallized minerals without glassy matter (matter without visible crystals). Intrusive igneous rocks (see intrusive rock) are nearly always crystalline; extrusive igneous rocks (see extrusive rock) may be partly to entirely glassy. Metamorphic rocks are also always completely crystalline and are termed crystalline schists or gneisses. Sedimentary rocks can also be crystalline, such as crystalline limestones that precipitate directly from solution; the term is not generally applied to clastic sediments (made of fragments of preexisting rock), even though they are formed largely from the accumulation of crystalline materials.

In materials science, texture is the distribution of crystallographic orientations of a sample. A sample in which these orientations are fully random is said to have no texture. If the crystallographic orientations are not random, but have some preferred orientation, then the sample has a weak, strong, or moderate texture. The degree is dependent on the percentage of crystals that have the preferred orientation. Texture is seen in almost all engineered materials, and it can have a great influence on material properties. Also geologic rocks show texture due to their thermo-mechanic history of formation processes.

One extreme case is a complete lack of texture: a solid with perfectly random crystallite orientation, which will have isotropic properties at length scales sufficiently larger than the size of the crystallites. The opposite extreme is a perfect single crystal, which has anisotropic properties by geometric necessity.

## Characterization and representation

Texture can be determined by different method. Some of them allow a quantitative analysis of the texture others are only qualitative. Among the quantitative techniques the most widely used is X-ray diffraction using texture goniometers, followed by EBSD-method (electron backscatter diffraction) in Scanning Electron Microscopes. For qualitative analysis it can be done by Laue photography, simple X-ray diffraction or with the polarized microscope. neutron and synchrotron high-energy X-ray diffraction allow to access textures of bulk material and in-situ whereas laboratory x-ray diffraction instrument are more appropriate for thin film textures.

Texture is often represented using a pole figure, in which a specified crystallographic axis (or pole) from each of a representative number of crystallites is plotted in a stereographic projection, along with directions relevant to the material's processing history such as the rolling direction and transverse direction or the fiber axis (see below).

## Orientation distribution function

The full 3D representation of crystallographic texture is given by the orientation distribution function ($ODF$) which can be achieved through evaluation of a set of pole figures or diffraction spectra. Subsequently, all pole figures can be derived from the $ODF$.

The $ODF$ is defined as the volume fraction of grain oriented along a certain direction $boldsymbol\left\{g\right\}$.

$ODF\left(boldsymbol\left\{g\right\}\right)=frac\left\{1\right\}\left\{V\right\} frac\left\{dV\left(boldsymbol\left\{g\right\}\right)\right\}\left\{d g\right\}.$

the direction $boldsymbol\left\{g\right\}$ is normally identified using three Euler angles. The orientation distribution function, $ODF$, cannot be measured directly by any technique. Traditionally both X-ray diffraction and EBSD may collect pole figures. Different methodologies exist to obtain the ODF from the pole figures or data in general. They can be classify at first based on how they represent the $ODF$. Some use to represent the $ODF$ as a function, sum of functions or expand it in series of harmonic functions. Others, known as discrete methods, divide the $ODF$ space in cells and focus on determine the value of the $ODF$ in each cell.

## Origins

In wire and fiber, all crystals tend to have nearly identical orientation in the axial direction, but nearly random radial orientation. The most familiar exceptions to this rule are fiberglass, which has no crystal structure, and carbon fiber, in which the crystalline anisotropy is so great that a good-quality filament will be a distorted single crystal with approximately cylindrical symmetry (often compared to a jelly roll). Single-crystal fibers are also not uncommon.

The making of metal sheet often involves compression in one direction and, in efficient rolling operations, tension in another, which can orient crystallites in both axes by a process known as grain flow. However, cold work destroys much of the crystalline order, and the new crystallites that arise with annealing usually have a different texture. Control of texture is extremely important in the making of silicon steel sheet for transformer cores (to reduce magnetic hysteresis) and of aluminium cans (since deep drawing requires extreme and relatively uniform plasticity).

Texture in ceramics usually arises because the crystallites in a slurry have shapes that depend on crystalline orientation, often needle- or plate-shaped. These particles align themselves as water leaves the slurry, or as clay is formed.

Casting or other fluid-to-solid transitions (i.e., thin-film deposition) produce textured solids when there is enough time and activation energy for atoms to find places in existing crystals, rather than condensing as an amorphous solid or starting new crystals of random orientation. Some facets of a crystal (often the close-packed planes) grow more rapidly than others, and the crystallites for which one of these planes faces in the direction of growth will usually out-compete crystals in other orientations. In the extreme, only one crystal will survive after a certain length: this is exploited in the Czochralski process (unless a seed crystal is used) and in the casting of turbine blades and other creep-sensitive parts.