section_path: Physical properties/Crystal structure and habit
section_name: Crystal structure and habit
paragraph_text: Crystal structure and habit
  
  Crystal structure results from the orderly geometric spatial arrangement of atoms in the internal structure of a mineral. This crystal structure is based on regular internal atomic or ionic arrangement that is often expressed in the geometric form that the crystal takes. Even when the mineral grains are too small to see or are irregularly shaped, the underlying crystal structure is always periodic and can be determined by X-ray diffraction. Minerals are typically described by their symmetry content. Crystals are restricted to 32 point groups, which differ by their symmetry. These groups are classified in turn into more broad categories, the most encompassing of these being the six crystal families.
  
  These families can be described by the relative lengths of the three crystallographic axes, and the angles between them; these relationships correspond to the symmetry operations that define the narrower point groups. They are summarized below; a, b, and c represent the axes, and α, β, γ represent the angle opposite the respective crystallographic axis (e.g. α is the angle opposite the a-axis, viz. the angle between the b and c axes):
  
  The hexagonal crystal family is also split into two crystal systems – the trigonal, which has a three-fold axis of symmetry, and the hexagonal, which has a six-fold axis of symmetry.
  
  Chemistry and crystal structure together define a mineral. With a restriction to 32 point groups, minerals of different chemistry may have identical crystal structure. For example, halite (NaCl), galena (PbS), and periclase (MgO) all belong to the hexaoctahedral point group (isometric family), as they have a similar stoichiometry between their different constituent elements. In contrast, polymorphs are groupings of minerals that share a chemical formula but have a different structure. For example, pyrite and marcasite, both iron sulfides, have the formula FeS; however, the former is isometric while the latter is orthorhombic. This polymorphism extends to other sulfides with the generic AX formula; these two groups are collectively known as the pyrite and marcasite groups.
  
  Polymorphism can extend beyond pure symmetry content. The aluminosilicates are a group of three minerals – kyanite, andalusite, and sillimanite – which share the chemical formula Al SiO. Kyanite is triclinic, while andalusite and sillimanite are both orthorhombic and belong to the dipyramidal point group. These differences arise corresponding to how aluminium is coordinated within the crystal structure. In all minerals, one aluminium ion is always in six-fold coordination with oxygen. Silicon, as a general rule, is in four-fold coordination in all minerals; an exception is a case like stishovite (SiO, an ultra-high pressure quartz polymorph with rutile structure). In kyanite, the second aluminium is in six-fold coordination; its chemical formula can be expressed as Al Al SiO, to reflect its crystal structure. Andalusite has the second aluminium in five-fold coordination (Al Al SiO) and sillimanite has it in four-fold coordination (Al Al SiO).
  
  Differences in crystal structure and chemistry greatly influence other physical properties of the mineral. The carbon allotropes diamond and graphite have vastly different properties; diamond is the hardest natural substance, has an adamantine lustre, and belongs to the isometric crystal family, whereas graphite is very soft, has a greasy lustre, and crystallises in the hexagonal family. This difference is accounted for by differences in bonding. In diamond, the carbons are in sp hybrid orbitals, which means they form a framework where each carbon is covalently bonded to four neighbours in a tetrahedral fashion; on the other hand, graphite is composed of sheets of carbons in sp hybrid orbitals, where each carbon is bonded covalently to only three others. These sheets are held together by much weaker van der Waals forces, and this discrepancy translates to large macroscopic differences.
  
  Twinning is the intergrowth of two or more crystals of a single mineral species. The geometry of the twinning is controlled by the mineral's symmetry. As a result, there are several types of twins, including contact twins, reticulated twins, geniculated twins, penetration twins, cyclic twins, and polysynthetic twins. Contact, or simple twins, consist of two crystals joined at a plane; this type of twinning is common in spinel. Reticulated twins, common in rutile, are interlocking crystals resembling netting. Geniculated twins have a bend in the middle that is caused by start of the twin. Penetration twins consist of two single crystals that have grown into each other; examples of this twinning include cross-shaped staurolite twins and Carlsbad twinning in orthoclase. Cyclic twins are caused by repeated twinning around a rotation axis. This type of twinning occurs around three, four, five, six, or eight-fold axes, and the corresponding patterns are called threelings, fourlings, fivelings, sixlings, and eightlings. Sixlings are common in aragonite. Polysynthetic twins are similar to cyclic twins through the presence of repetitive twinning; however, instead of occurring around a rotational axis, polysynthetic twinning occurs along parallel planes, usually on a microscopic scale.
  
  Crystal habit refers to the overall shape of crystal. Several terms are used to describe this property. Common habits include acicular, which describes needlelike crystals as in natrolite, bladed, dendritic (tree-pattern, common in native copper), equant, which is typical of garnet, prismatic (elongated in one direction), and tabular, which differs from bladed habit in that the former is platy whereas the latter has a defined elongation. Related to crystal form, the quality of crystal faces is diagnostic of some minerals, especially with a petrographic microscope. Euhedral crystals have a defined external shape, while anhedral crystals do not; those intermediate forms are termed subhedral.