In crystallography, the monoclinic crystal system is one of the seven crystal systems. A crystal system is described by three vectors. In the monoclinic system, the crystal is described by vectors of unequal lengths, as in the orthorhombic system. They form a parallelogramprism. Hence two pairs of vectors are perpendicular (meet at right angles), while the third pair makes an angle other than 90°.
Monoclinic crystalAn example of the monoclinic crystal orthoclase
For the base-centered monoclinic lattice, the primitive cell has the shape of an oblique rhombic prism;[1] it can be constructed because the two-dimensional centered rectangular base layer can also be described with primitive rhombic axes. The length of the primitive cell below equals of the conventional cell above.
Oblique rhombic prism primitive cell
Primitive cell of the base-centered monoclinic lattice
Relationship between base layers of primitive and conventional cells
The table below organizes the space groups of the monoclinic crystal system by crystal class. It lists the International Tables for Crystallography space group numbers,[2] followed by the crystal class name, its point group in Schoenflies notation, Hermann–Mauguin (international) notation, orbifold notation, and Coxeter notation, type descriptors, mineral examples, and the notation for the space groups.
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 Hahn (2002), p. 746, row mC, column Primitive, where the cell parameters are given as a1 = a2, α = β
^Prince, E., ed. (2006). International Tables for Crystallography. International Union of Crystallography. doi:10.1107/97809553602060000001. ISBN978-1-4020-4969-9. S2CID 146060934.
Hurlbut, Cornelius S.; Klein, Cornels (1985). Manual of Mineralogy (20th ed.). pp. 69–73. ISBN0-471-80580-7.
Hahn, Theo, ed. (2002). International Tables for Crystallography, Volume A: Space Group Symmetry. Vol. A (5th ed.). Berlin, New York: Springer-Verlag. doi:10.1107/97809553602060000100. ISBN978-0-7923-6590-7.
January 01, 1970
monoclinic, crystal, system, crystallography, monoclinic, crystal, system, seven, crystal, systems, crystal, system, described, three, vectors, monoclinic, system, crystal, described, vectors, unequal, lengths, orthorhombic, system, they, form, parallelogram, . In crystallography the monoclinic crystal system is one of the seven crystal systems A crystal system is described by three vectors In the monoclinic system the crystal is described by vectors of unequal lengths as in the orthorhombic system They form a parallelogram prism Hence two pairs of vectors are perpendicular meet at right angles while the third pair makes an angle other than 90 Monoclinic crystal An example of the monoclinic crystal orthoclase Contents 1 Bravais lattices 2 Crystal classes 3 In two dimensions 4 See also 5 References 6 Further readingBravais lattices editFurther information Bravais lattice Two monoclinic Bravais lattices exist the primitive monoclinic and the base centered monoclinic Bravais lattice Primitivemonoclinic Base centeredmonoclinic Pearson symbol mP mS Unit cell nbsp nbsp For the base centered monoclinic lattice the primitive cell has the shape of an oblique rhombic prism 1 it can be constructed because the two dimensional centered rectangular base layer can also be described with primitive rhombic axes The length a displaystyle a nbsp of the primitive cell below equals 1 2 a 2 b 2 displaystyle frac 1 2 sqrt a 2 b 2 nbsp of the conventional cell above Oblique rhombic prism primitive cell nbsp Primitive cell of the base centered monoclinic lattice nbsp Relationship between base layers of primitive and conventional cellsCrystal classes editFurther information Crystallographic point group The table below organizes the space groups of the monoclinic crystal system by crystal class It lists the International Tables for Crystallography space group numbers 2 followed by the crystal class name its point group in Schoenflies notation Hermann Mauguin international notation orbifold notation and Coxeter notation type descriptors mineral examples and the notation for the space groups Point group Type Example Space groups Name 3 Schon Intl Orb Cox Primitive Base centered 3 5 Sphenoidal C2 2 22 2 enantiomorphic polar halotrichite P2 P21 C2 6 9 Domatic Cs C1h m 11 polar hilgardite Pm Pc Cm Cc 10 12 Prismatic C2h 2 m 2 2 2 centrosymmetric gypsum P2 m P21 m C2 m 13 15 P2 c P21 c C2 c Sphenoidal is also called monoclinic hemimorphic domatic is also called monoclinic hemihedral and prismatic is also called monoclinic normal The three monoclinic hemimorphic space groups are as follows a prism with a wallpaper group p2 cross section 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 In two dimensions editMain article Oblique lattice The only monoclinic Bravais lattice in two dimensions is the oblique lattice Bravais lattice Oblique Pearson symbol mp Unit cell nbsp See also editCrystal structure Crystal systemReferences edit See Hahn 2002 p 746 row mC column Primitive where the cell parameters are given as a1 a2 a b Prince E ed 2006 International Tables for Crystallography International Union of Crystallography doi 10 1107 97809553602060000001 ISBN 978 1 4020 4969 9 S2CID 146060934 The 32 crystal classes Retrieved 2018 06 19 Further reading editHurlbut Cornelius S Klein Cornels 1985 Manual of Mineralogy 20th ed pp 69 73 ISBN 0 471 80580 7 Hahn Theo ed 2002 International Tables for Crystallography Volume A Space Group Symmetry Vol A 5th ed Berlin New York Springer Verlag doi 10 1107 97809553602060000100 ISBN 978 0 7923 6590 7 Retrieved from https en wikipedia org w index php title Monoclinic crystal system amp oldid 1189547466, wikipedia, wiki, book, books, library,
