Slide 1

32 Crystal FormsDisclaimer:The information contained in this presentation is intended for educational purposes only. It also can be used in other Mineralogy classes.Six Crystal SystemsIsometricTetragonalHexagonalOrthorhombicTriclinicMonoclinicIsometricThree equal length axes that intersecting at right-angles to one another.

The axes are indistinguishable, as are the intersecting angles. As such all are interchangable.

TetragonalThree mutually perpendicular axes, two are equal, the third (vertical) is shorter.

The two horizontal axis in a tetragronal mineral are oriented in of horizontal the plane the horizontal. Therefore, if a = b, c must be inthe vertical.HexagonalThree equal horizontal axes (a1, a2, a3) and a 4th perpendicular vertical axis of different length.

The three horizontal axis of a hexagonal mineral are oriented the plane of the horizontal, with c in the vertical.OthorhombicThree mutually perpendicular axes of different lengths.

Convention has it that a crystal is oriented such that c > b > a.

Crystals are oriented so that c is parallel to crystal elongation.TriclinicThree unequal axes with oblique angles.

To orientate a triclinic crystal the most pronounced zone should be vertical.

The b axis should be longer than the a axis.MonoclinicThree unequal axes, two are inclined with oblique angles, the third is perpendicular.

Orientation of a crystal has few constraints b is the only axis fixed by symmetry.A crystal's form may be completely described by use of the Miller's indices and the Hermann-Mauguin notation of its POINT GROUP SYMMETRY. The latter notation tells us how to orient the crystal, in each specific crystal class, to recognize which axis (a, b, or c) is designated as having the highest symmetry. It also tells us what other symmetry elements may be present and where they are in orientation to the other elements.

Crystal SymmetryWhen listing the symmetry of each crystal class an axis of rotational symmetry is represented by the capital letter A. Whether this axis is a 2-fold, 3-fold, or 4-fold axis is indicated by a subscript following the letter A. The number of such axes present is indicated by a numeral preceding the capital A. 1A2, 2A3, and 3A4 thus represent one 2-fold axis of rotation, two 3-fold axes, and three 4-fold axes respectivelyA center of inversion is noted by the lowercase letter 'i' while a mirror plane is denoted by 'm'. The numeral preceding the m indicates how many mirror planes are present. Axes of rotary inversion are usually replaced by the equivalent rotations and reflections. For example, a 2-fold rotoinversion axis is equivalent to reflection through a mirror plane perpendicular to the rotoinversion axis.

A crystal which possesses a 3-fold rotoinversion axis is equivalent to one which possesses both 3-fold rotational symmetry and inversion symmetry.

A 6-fold rotoinversion is equivalent to 3-fold rotation and reflection across a mirror plane at right angles to the rotation axis. The only rotoinversion operation which cannot be thus replaced is 4-fold rotoinversion, which is indicated by R4.

The class which possesses the highest possible symmetry within each crystal system is termed the holomorphic class of that system.

The holomorphic class of each crystal system is indicated in the table by bold type. For example, the triclinic parallelohedron is the holomorphic class of the triclinic crystal system while the isometric hexoctahedron is the holomorphic class of the isomorphic or cubic crystal system.

The characteristic symmetry element of each crystal system is listed in bold type. It is thus apparent that the characteristic symmetry element of the isometric crystal system is the possession of four 3-fold axes of rotational symmetry, while the characteristic symmetry element of the rhombohedral division of the hexagonal crystal system is the possession of a single 3-fold axis of rotational symmetry. 32 Crystal FormsThe 32 crystal classes represent the 32 possible combinations of symmetry operations. Each crystal class will have crystal faces that uniquely define the symmetry of the class. These faces, or groups of faces are called crystal forms.

The table below shows the 32 crystal classes, their symmetry, Hermann-Mauguin symbol, and class nameCrystal SystemCrystal ClassSymmetryName of ClassTriclinic1nonePedialiPinacoidalMonoclinic21A2Sphenoidalm1mDomatic2/mi, 1A2, 1mPrismaticOrthorhombic2223A2Rhombic-disphenoidalmm2 (2mm)1A2, 2mRhombic-pyramidal2/m2/m2/mi, 3A2, 3mRhombic-dipyramidal

Isometric233A2, 4A3Tetaroidal2/m3A2, 3m, 43Diploidal4323A4, 4A3, 6A2Gyroidal3m34, 4A3, 6mHextetrahedral4/m2/m3A4, 43, 6A2, 9mHexoctahedral

Tetragonal41A4Tetragonal- Pyramidal4Tetragonal-disphenoidal4/mi, 1A4, 1mTetragonal-dipyramidal4221A4, 4A2Tetragonal-trapezohedral4mm1A4, 4mDitetragonal-pyramidal2m14, 2A2, 2mTetragonal-scalenohedral4/m2/m2/mi, 1A4, 4A2, 5mDitetragonal-dipyramidalHexagonal31A3Trigonal-pyramidal13Rhombohedral321A3, 3A2Trigonal-trapezohedral3m1A3, 3mDitrigonal-pyramidal2/m13, 3A2, 3mHexagonal-scalenohedral61A6Hexagonal-pyramidal16Trigonal-dipyramidal6/mi, 1A6, 1mHexagonal-dipyramidal6221A6, 6A2Hexagonal-trapezohedral6mm1A6, 6mDihexagonal-pyramidalm216, 3A2, 3mDitrigonal-dipyramidal6/m2/m2/mi, 1A6, 6A2, 7mDihexagonal-dipyramidal

Note that the 32 crystal classes are divided into 6 crystal systems.

The Triclinic System has only 1-fold or 1-fold rotoinversion axes.The Monoclinic System has only mirror plane(s) or a single 2-fold axis.The Orthorhombic System has only two fold axes or a 2-fold axis and 2 mirror planes.The Tetragonal System has either a single 4-fold or 4-fold rotoinversion axis.The Hexagonal System has no 4-fold axes, but has at least 1 6-fold or 3-fold axis.The Isometric System has either 4 3-fold axes or 4 3-fold rotoinversion axes.

References:http://www.geo.umass.edu/courses/geo311/Lecture8.pdfhttp://www.tulane.edu/~sanelson/eens211/32crystalclass.htmhttp://www.ce.berkeley.edu/~paulmont/CE60New/crystal_structure.pdfhttp://www.ece.utah.edu/~angelar/FinalReportExample.pdfLectures from Past Mineralogy Class