GY 302: Crystallography & MineralogyGY 302: Crystallography & MineralogyUNIVERSITY OF SOUTH ALABAMALecture 4: Stereo ProjectionsLecture 4: Stereo ProjectionsLast Time1. Miller Indices2. Point Groups (32 of them)3. Hermann-Mauguin Class SymbolsMiller IndicesThe Point Groups•There are 32 possible combinations of symmetry operations (the Point Groups)•Each crystal class will have crystal faces that define the symmetry of the class (the crystal forms)Example 1: Orthorhombic crystal Hermann-Mauguin Class SymbolsStep 3: Mirror planes perpendicular to rotational axes are put in a denominator position relative to the rotational axes2/m 2/m 2/mToday’s Agenda1. Stereo Projections and the Wulff Net2. Stereo projections of the Point GroupsStereo projectionsConsider an cubic form (100)Stereo projectionsEnvision the cube suspended in a sphereStereo projectionsNow pass a line that is perpendicular to each crystal face (poles) outward to intersect the sphere001001010010001Stereo projectionsNow envision the equatorial cross section of the spherical projection.There are 2 possible stereonet configurations:1) Wulff Net (equal angles)2) Smith Net (equal area)Projection:Equal AngleRadius:3.50 inchesWulff NetNSWE10170350190201603402003015033021040140320220501303102306012030024070110290250801002802600 DATASource: D. AllisonStereo projectionsNow envision the equatorial cross section of the spherical projection.There are 2 possible stereonet configurations:1) Wulff Net (equal angles)2) Smith Net (equal area)Projection:Equal AreaRadius:3.50 inchesSchmidt NetNSWE10170350190201603402003015033021040140320220501303102306012030024070110290250801002802600 DATASource: D. AllisonStereonet comparisonsProjection:Equal AngleRadius:3.50 inchesWulff NetNSWE10170350190201603402003015033021040140320220501303102306012030024070110290250801002802600 DATAProjection:Equal AreaRadius:3.50 inchesSchmidt NetNSWE10170350190201603402003015033021040140320220501303102306012030024070110290250801002802600 DATAStereonets courtesy of D. AllisonPreferred for crystallographyStereo projectionsLines of “longitude” and “latitude” correspond to intersections of planes with the spherical shape;Great Circles: intersections the same diameter as the sphereSmall Circles: intersections smaller than the diameter as the sphereModel/Chalk BoardStereo projectionsPoles of planes intersect the Wulff net as points010001Stereo projections100 Face010001100100Viewing Viewing DirectionDirectionStereo projections010001100100010010010 FaceStereo projections010001100100010010001/001001 FaceStereo projectionsOctahedron (111 Form)Stereo projections001111/111111/111111/111111/111Octahedron (111 Form)Stereo projectionsAnd so on….Klein VideoStereo projections001111/111111/111111/111111/111The stereonet allows for precise measurements of angular relationships between crystal facesStereo projections001All faces are orientated 45° from the poles of the steronet-45°45°0°Stereo projections001All faces are 90° apart from one another…-45°45°90°0°Stereo projections001All faces are 90° apart from one another…90°90°90°Stereo projections010001…and rotated 45° from the faces of a cubic form45°45°Stereo Net Projections of Point Groups MSA Video (cubic 12.19; hexagonal 12.24) Quick Time videos of stereoprojectionsSource: Interactive Mineralogy DVD(Dyar, Gunter and Tasa, 2008)The Point Groups•Orthorhombic Point Groups; 2-fold rotational axes or 2 fold-rotational axes and mirror planesThe Point Groups•Tetragonal Point Groups; a single 4-fold rotational axis or a 4 fold-rotoinversion axisThe Point Groups•Hexagonal; at least one 6-fold rotational axis, Trigonal,at least one 3-fold rotational axisThe Point Groups•Isometric Point Groups either have 4 3-fold rotational axes or 4 fold-rotoinversionaxesThe Point Groups•Monoclinic Point Groups; a single 2-fold rotational axis or a single mirror planeStereo Net Projections of Point Groups Triclinic Point Groups: 1-fold rotational axes or 1 fold-rotoinversion axesToday’s Homework1.1.Finish assignment 1 models (due next Tuesday)Finish assignment 1 models (due next Tuesday)2.2.Assignment Two issued (due next Thursday)Assignment Two issued (due next Thursday)Next Week1.1.Space GroupsSpace Groups2.2.First lab quiz (Isometric and Hexagonal models) First lab quiz (Isometric and Hexagonal models) 3.3.Tetragonal and Orthorhombic modelsTetragonal and Orthorhombic