Dr Helen Lang Dept of Geology Geography West Virginia University FALL 2013 GEOLOGY 284 MINERALOGY External Shape of Crystals reflects Internal Structure External Shape is best described by Symmetry Symmetry Repetitive arrangement of features faces corners and edges of a crystal around imaginary lines points or planes Reflects internal ordering of atoms in the mineral structure Mirror Symmetry reflection across a mirror plane Exists if two halves of an image or figure are identical Mammals have Bi lateral Symmetry a mirror plane Rotational Symmetry Rotation of x degrees with respect to a line called a rotation axis leaves the image or shape unchanged 60o Rotational Symmetry If an object looks the same after rotation of 360o n that object is said to have n fold rotational symmetry or an n fold axis Called n fold because it takes n rotations to return to its original position Only certain angles folds of rotational symmetry are possible in minerals Rotational Symmetry in Minerals Name Short hand Angle 1 fold 1 360o 2 fold 2 180o 3 fold 3 120o 4 fold 4 90o 6 fold 6 60o Symbol Only these five are possible 5 fold 7 fold and other symmetries are not possible in crystals because you can t fill space with 5 sided objects Rotational Symmetry of 3 D Objects 4 fold 90o rotation 90o Prism Dipyramid Rotational Symmetry of 3 D Objects 6 fold 60o rotation 60o Prism To test for rotational symmetry Hold a wooden block or crystal with your index finger and thumb on two opposite corners opposite faces or opposite edges Rotate the block or crystal 60o 90o 120o 180o and check to see if it looks the same Grasp it in other orientations to check for additional rotation axes All symmetry elements must intersect at the center of the crystal Most Crystal shapes have several Rotation Axes that cross at the center Cube Octahedron Inversion or a Center of Symmetry symbol is 1 For every point or face on one side of the center of symmetry there is similar point or face at an equal distance on the opposite side of the center Inversion Centers in Crystals Inversion Center Only No other symmetry Inversion Center with other symmetry Prism Dipyramid Some Crystals or blocks have no Center of Symmetry Trigonal pyramid pedion Rotoinversion combined rotation and inversion 4 4 bar 90o rotation plus inversion Note 2 faces or pairs of faces on top and 2 faces on the bottom off set by 90o Rotoinversion combined rotation and inversion 3 3 bar 120o rotation plus inversion Note 3 faces or pairs of faces on top and 3 faces on the bottom off set by 60o rhombohedron Dogtooth Spar also has 3 symmetry 3 axis in Rhodochrosite Rhombohedron Types of symmetry possible in Minerals 1 2 3 4 6 m 1 4 3 proper rotations mirror planes center of symmetry rotoinversion rotoinversion These can be combined in 32 ways to make crystal shapes Minerals are Grouped into Six Crystal Systems based on Symmetry System Isometric Cubic System Hexagonal System Tetragonal System Orthorhombic System Monoclinic System Triclinic System Characteristic Symmetry four 3 or 3 one 6 6 3 or 3 one 4 or 4 three 2 and or m one 2 and or m 1 or 1 Isometric System Must have four 3 or 3 corner tocorner of reference cube axes All isometric shapes also have three perpendicular 4 4 or 2 axes These are the crystallographic axes a1 a2 a3 all equal length All isometric forms are equidimensional Highest symmetry system cube octahedron Crystallographic Axes Reference axes Conventional ways to hold and refer to faces on crystals Different convention for each system Crystallographic Axes Isometric System Three perpendicular axes Coincide with three 4 fold or 2 fold axes All equal length Called a1 a2 a3 Garnet halite pyrite and fluorite are isometric a3 a2 a1 Isometric Minerals Garnet Ca Fe Mg Mn 3Al2Si3O12 All isometric minerals are isotropic which means Name of Garnet Growth Form Isometric Minerals Fluorite CaF2 Other Isometric Minerals Name of growth form Name of cleavage form Halite Galena Magnetite Pyrite Crystallographic Axes Tetragonal System Must have one 4 or 4 bar axis Three perpendicular axes Vertical axis c coincides with 4 or 4 bar axis One axis c is longer or shorter than other two a1 and a2 which are equal 4 fold axis c a2 a1 Tetragonal Examples Tetragonal Examples Wulfenite PbMoO4 Tetragonal Examples Zircon ZrSiO4 Jay VonderhayBancroft Ontario John H Betts Brazil Crystallographic Axes Orthorhombic System c Has three 2 fold axes and or one mirror plane Three perpendicular axes coincide with 2 fold axes or are perpendicular to mirror planes All different lengths called a b c b a Orthorhombic Examples c Two Rhombic Dipyramids a b b a Sulfur c Crystallographic Axes Monoclinic System c Has one 2 fold axis or mirror All axes different lengths Called a b c o 90 b axis coincides with 2 fold axis or is mirror plane c is parallel to long edges a a slants down to the front a b b c angle between a and c 90o b Monoclinic Example c a b b a c Orthoclase KAlSi3O8 Crystallographic Axes Triclinic System c No perpendicular axes All different lengths Called a b c b a Crystallographic Axes Hexagonal System Four axes Vertical axis c is longer or shorter and coincides with 6 fold or 3 fold axis Three horizontal axes coincide with 2 fold axes are to c and 120o to each other Three horizontal axes are equal lengths a1 a2 a3 c or 3 a3 120o a1 or 3 a2 Some Hexagonal Forms Hexagonal prism Rhombohedron Hexagonal scalenohedron Hexagonal Examples Emerald beryl names of forms 3 fold or 6 fold Calcite Hexagonal Examples Mineral Shape form Six Crystal Systems System Isometric System Hexagonal System Tetragonal System Orthorhombic System Monoclinic System Triclinic System Char Symmetry Axial Relations SUMMARY OF THE SYSTEMS CRYSTAL SYSTEM CHARACTERISTIC SYMMETRY AXIAL RELATIONSHIPS Isometric four 3 or 3 a1 a2 a3 90o Tetragonal one 4 or 4 a1 a2 c 90o Orthorhombic three 2 and or m a b c c b a 90o Hexagonal one 6 6 3 or 3 a1 a2 a3 c a1 a2 120o a c 90o Monoclinic one 2 and or one m a b c 90o 90o Triclinic 1 or 1 a b c or 90o 90o b c a c a b