monoclinic

Information about monoclinic

In crystallography, the monoclinic crystal system is one of the 7 lattice point groups. A crystal system is described by three vectors. In the monoclinic system, the crystal is described by vectors of unequal length, as in the orthorhombic system. They form a rectangular prism with a parallelogram as base. Hence two pairs of vectors are perpendicular, while the third pair make an angle other than 90°.

There exist two monoclinic Bravais lattices: the simple monoclinic and the centered monoclinic lattices, with layers with a rectangular and rhombic lattice, respectively.




Simple monoclinic

Centered monoclinic




The crystal classes that fall under this crystal system are listed below, followed by their representations in international notation and Schoenflies notation, and mineral examples.

Name International Schoenflies Example
monoclinic normalC2hgypsum, orthoclase, mica
monoclinic hemimorphicC2halotrichite
monoclinic hemihedralC1hhilgardite


The number of space groups for each crystal class is 6, 3, and 4, respectively.

The three monoclinic hemimorphic space groups are as follows:
  • a prism with as cross-section wallpaper group p2
  • ditto with screw axes instead of axes
  • ditto with screw axes as well as axes, parallel, in between; in this case an additional translation vector is one half of a translation vector in the base plane plus one half of a perpendicular vector between the base planes
The four monoclinic hemihedral space groups include
  • those with pure reflection at the base of the prism and halfway
  • those with glide planes instead of pure reflection planes; the glide is one half of a translation vector in the base plane
  • those with both in between each other; in this case an additional translation vector is this glide plus one half of a perpendicular vector between the base planes.

See also

References

  • Hurlbut, Cornelius S.; Klein, Cornelis, 1985, Manual of Mineralogy, 20th ed., pp. 65 - 69, ISBN 0-471-80580-7
For the book of poetry, see Crystallography (book).

Crystallography (from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and graphein
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A crystal system is a category of space groups, which characterize symmetry of structures in three dimensions with translational symmetry in three directions, having a discrete class of point groups.
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In mathematics, a point group is a group of geometric symmetries (isometries) leaving a point fixed.

Overview

Point groups can exist in a Euclidean space of any dimension.
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spatial vector, or simply vector, is a concept characterized by a magnitude and a direction. A vector can be thought of as an arrow in Euclidean space, drawn from an initial point A pointing to a terminal point B.
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CRYSTAL is a quantum chemistry ab initio program, designed primarily for calculations on crystals (3 dimensions), slabs (2 dimensions) and polymers (1 dimension) using translational symmetry, but it can be used for single molecules.[1] It is written by V.R. Saunders, R.
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orthorhombic crystal system is one of the 7 lattice point groups. Orthorhombic lattices result from stretching a cubic lattice along two of its lattice vectors by two different factors, resulting in a rectangular prism with a rectangular base (a by b
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prism is a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides. Thus these joining faces are parallelograms. All cross-sections parallel to the base faces are the same. A prism is a subclass of the prismatoids.
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In geometry, a parallelogram is a quadrilateral with two sets of parallel sides. The opposite sides of a parallelogram are of equal length, and the opposite angles of a parallelogram are congruent. The three-dimensional counterpart of a parallelogram is a parallelepiped.
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In geometry and crystallography, a Bravais lattice, named after Auguste Bravais, is an infinite set of points generated by a set of discrete translation operations. A crystal is made up of one or more atoms (the basis) which is repeated at each lattice point.
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In crystallography, a crystallographic point group is a set of symmetry operations, like rotations or reflections, that leave a point fixed while moving each atom of the crystal to the position of an atom of the same kind.
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The Schoenflies notation is one of two conventions commonly used to describe crystallographic point groups. This notation is used in spectroscopy. The other convention is the Hermann-Mauguin notation, also known as the International notation.
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A mineral is a naturally occurring substance formed through geological processes that has a characteristic chemical composition, a highly ordered atomic structure and specific physical properties.
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Gypsum is a very soft mineral composed of calcium sulfate dihydrate, with the chemical formula CaSO4·2H2O.

Crystal varieties

Gypsum occurs in nature as flattened and often twinned crystals and transparent cleavable masses called selenite.
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Orthoclase (endmember formula KAlSi3O8) is an important tectosilicate mineral, which forms igneous rock. It is also known as alkali feldspar and is common in granite and related rocks.
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Mica may refer to:
  • Mica, a silicate mineral group
  • The biblical prophet Micah
  • The book of Micah in the Tanakh
  • Mica is a song by Danish indie rock band Mew.

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Halotrichite, also known as feather alum, is a highly hydrated sulfate of aluminium and iron. It is formed by the weathering and decomposition of pyrite commonly near or in volcanic vents.
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Hilgardite is a mineral with the chemical formula Ca2B5O9Cl·H2O. It is named after Eugene W. Hilgard. It is found in Germany and Louisiana. It is transparent and has vitreous luster. It is colorless, but leaves a white streak.
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The space group of a crystal is a mathematical description of the symmetry inherent in the structure. The word 'group' in the name comes from the mathematical notion of a group, which is used to build the set of space groups.
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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
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