# Crystal

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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 that are distinct from one another in the translational symmetry they contain. All known crystalline materials (not including quasicrystals) fit into one of these arrangements. The 14 three-dimensional lattices, classified by crystal system, are shown on 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 the particular Bravais lattices. The characteristic rotation and mirror symmetries of the group of atoms, or unit cell, is described by its "crystallographic point group."

### Point groups and space groups

The crystallographic point group or crystal class is the set of non-translational symmetry operations that leave the appearance of the crystal structure unchanged. These symmetry operations can include (a) mirror planes, which reflect the structure across a central plane; (b) rotation axes, which rotate the structure a specified number of degrees; and (c) a center of symmetry or inversion point, which inverts the structure through a central point. There are 32 possible crystal classes, each of which can be placed in one of the seven crystal systems.

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

## Crystal symmetry and physical properties

Twenty of the 32 crystal classes are described as piezoelectric, which means that they can generate a voltage in response to applied mechanical stress. All 20 piezoelectric classes lack a center of symmetry.

Any material develops a dielectric polarization (charge separation) when an electric field is applied, but a substance that has natural charge separation even in the absence of an electric 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.

A few crystal structures, notably the perovskite structure, exhibit ferroelectric behavior. This property is analogous to ferromagnetism. In the absence of an electric field during production, the crystal does not exhibit polarization, but upon application of an electric field of sufficient magnitude, the ferroelectric crystal becomes permanently polarized. This polarization can be reversed by a sufficiently large counter-charge, in the same way that a ferromagnet can be reversed. It should be noted that although these materials are called ferroelectrics, the effect is due to their crystal structure, not the presence of a ferrous metal.

### Defects in crystals

Real crystals feature defects or irregularities in the ideal arrangements described above. These defects critically determine many of the electrical and mechanical properties of real materials. For example, dislocations in the crystal lattice allow shear at much lower stress than that needed for a perfect crystal structure.

## Crystal habit

A mineralogist often describes a mineral in terms associated with the apparent shape and size of its crystals. For example, a branching structure is described as dendritic; a star-like, radiating form is called stellate; a structure with needle-shaped crystals is called acicular. Such a description is known as the crystal habit of the mineral. A list of crystal habits is given below.

Pyrite sun (or dollar) in laminated shale matrix. Between tightly spaced layers of shale, the aggregate was forced to grow in a laterally compressed, radiating manner. Under normal conditions, pyrite would form cubes or pyritohedrons.

The various terms used for crystal habits are useful in communicating the appearance of mineral specimens. Recognizing numerous habits helps a mineralogist identify a large number of minerals. Some habits are distinctive of certain minerals, but most minerals exhibit differing habits that are influenced by certain factors. Crystal habit may mislead the inexperienced person, as a mineral's crystal system can be hidden or disguised.

Factors influencing a crystal's habit include: a combination of two or more forms; trace impurities present during growth; and growth conditions, such as heat, pressure, and space available for growth. Minerals belonging to the same crystal system do not necessarily exhibit the same habit.

Some habits of a mineral are unique to its variety and locality. For example, while most sapphires form elongate, barrel-shaped crystals, those found in Montana form stout, tabular crystals. Ordinarily, the latter habit is seen only in ruby. Sapphire and ruby are both varieties of the same mineral, corundum.

Sometimes, one mineral may replace another, while preserving the original mineral's habit. This process is called pseudomorphous replacement. A classic example is tiger's eye quartz, in which silica replaces crocidolite asbestos. Quartz typically forms euhedral (well-formed), prismatic (elongate, prism-like) crystals, but in the case of tiger's eye, the original, fibrous habit of crocidolite is preserved.

### List of crystal habits

Habit:Description:Example:AcicularNeedle-like, slender and/or taperedRutile in quartzAmygdaloidalAlmond-shapedHeulanditeAnhedralPoorly formed, external crystal faces not developedOlivineBladedBlade-like, slender and flattenedKyaniteBotryoidal or globularGrape-like, hemispherical massesSmithsoniteColumnarSimilar to fibrous: Long, slender prisms often with parallel growthCalciteCoxcombAggregated flaky or tabular crystals closely spaced.BariteDendritic or arborescentTree-like, branching in one or more directions from central pointMagnesite in opalDodecahedralDodecahedron, 12-sidedGarnetDrusy or encrustationAggregate of minute crystals coating a surfaceUvaroviteEnantiomorphicMirror-image habit and optical characteristics; right- and left-handed crystalsQuartzEquant, stout, stubby or blockySquashed, pinnacoids dominant over prismsZirconEuhedralWell-formed, external crystal faces developedSpinelFibrous or columnarExtremely slender prismsTremoliteFiliform or capillaryHair-like or thread-like, extremely fineNatroliteFoliated or micaceousLayered structure, parting into thin sheetsMicaGranularAggregates of anhedral crystals in matrixScheeliteHemimorphicDoubly terminated crystal with two differently shaped ends.HemimorphiteMamillaryBreast-like: intersecting large rounded contoursMalachiteMassive or compactShapeless, no distinctive external crystal shapeSerpentineNodular or tuberoseDeposit of roughly spherical form with irregular protuberancesGeodesOctahedralOctahedron, eight-sided (two pyramids base to base)DiamondPlumoseFine, feather-like scalesMottramitePrismaticElongate, prism-like: all crystal faces parallel to c-axisTourmalinePseudo-hexagonalOstensibly hexagonal due to cyclic twinningAragonitePseudomorphousOccurring in the shape of another mineral through pseudomorphous replacementTiger's eyeRadiating or divergentRadiating outward from a central pointPyrite sunsReniform or colloformSimilar to mamillary: intersecting kidney-shaped massesHematiteReticulatedAcicular crystals forming net-like intergrowthsCerussiteRosettePlaty, radiating rose-like aggregateGypsumSphenoidWedge-shapedSpheneStalactiticForming as stalactites or stalagmites; cylindrical or cone-shapedRhodochrositeStellateStar-like, radiatingPyrophylliteStriated/striationsSurface growth lines parallel or perpendicular to c-axisChrysoberylSubhedralExternal crystal faces only partially developedTabular or lamellarFlat, tablet-shaped, prominent pinnacoidRubyWheat sheafAggregates resembling hand-reaped wheat sheavesZeolites

## Uses of crystals

Historically, gemstones, which are natural crystals, have been sought after for their aesthetic appeal. In addition, they have been said to possess healing properties. Crystals (both natural and synthetic) also have a variety of practical applications, some of which are noted below.

• Solid-state laser materials are often made by doping a crystalline solid with appropriate ions. For example, the first working laser was made from a synthetic ruby crystal (chromium-doped corundum). Also, titanium-doped sapphire (corundum) produces a highly tunable infrared laser.
• Mica crystals, which are excellent as electrical insulators, are used in the manufacture of capacitors and insulation for high-voltage electrical equipment.
• Based on their extreme hardness, diamonds are ideal for cutting, grinding, and engraving tools. They can be used to cut, polish, or wear away practically any material, including other diamonds.
• Quartz crystals, which have piezoelectric properties, are commonly used to make "oscillators" that keep track of time in wristwatches, provide a stable clock signal for digital integrated circuits, and stabilize radio transmitter frequencies.

## Notes

1. ↑ The process of forming a glass does not release latent heat of fusion. For this reason, many scientists consider glassy materials to be viscous liquids rather than solids, but this is a controversial topic.