1.4 Zones, Forms, Habits

1.4 Zones, Forms, Habits - Zones, Forms, Habits Zones,...

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Unformatted text preview: Zones, Forms, Habits Zones, Forms, Habits Quantitative description of orientation in minerals – use Miller indices: Zone ­ Lines, or linear directions within minerals Form ­ Shapes of three dimensional objects Qualitative description of mineral shapes: Habit Crystal Habit Crystal Habit Qualitative terminology to describe individual minerals and aggregates of minerals Shape of individual minerals Intergrowths of several mineral grains Shape of masses of grains Colloform finely crystalline, concentric mineral layer Globular – (spherulitic) radiating, concentrically arranged acicular minerals Reniform kidney shaped Botryoidal like a bunch of grapes Mammillary similar, but larger than botryoidal, breast­like or portions of spheres Drusy Surface covered with layer of small crystals Drusy quartz Globular hematite Terminology useful for describing general shapes of minerals (asbestos: amphiboles and pyroxenes) (table­like) (knife like – kyanite) (Mica) Fig. 2­47 Fig. 2­47 Fibrous tremolite Bladed kyanite Zones Zones Collection of common faces Parallel to some common line Line called the zone axis Identified by index [hkl] Zone axis parallels intersection of edges of faces c Faces = (110), (110), (110), (110) Zone axis intesects (001) lattice nodes = [001] a b Intersection of faces Note typo Fig 2­28 Fig 2­28 Lattice node Other linear crystallographic directions Referenced to intersection of lattice nodes For example: location of rotation axes or other linear features Fig 2­27 Fig 2­27 Form Form Formal crystallographic nomenclature of the shape of minerals Description Collection of crystal faces Related to each other by symmetry Identified by index: {hkl} Values for h, k and l are determined by one of the faces Example Example There are six faces in a cube: (100), (010), (001), (100), (010), (001) Form is written with brackets Uses miller index of one face Generally positive face E.g., {001} a c b Possible to determine the shape of a form with: 1) Miller index of one face in form 2) Point symmetry of the crystal class The form is created by operating point symmetry on the initial face Number of faces in a form depends on crystal class Face parallel to a axis Mirror parallel to (010) Mirror parallel to (001) {011} form in crystal class with point symmetry 2/m 2/m 2/m (Orthorhombic) – called a rhombic prism Rhombus – an equilateral parallelogram Prism – a crystal form whose faces are parallel to one axis Fig. 2­29 Fig. 2­29 Triclinic system: Point group (i.e. crystal class) = 1 Symmetry content = (1A1) {111} has only 2 faces Isometric system: Point group (crystal class) = 4/m 3 2/m Symmetry content = 3A4, 4A3, 6A2, 9m {111} has 8 faces Form is an octahedron Isometric system Point group (crystal class) = 4 Symmetry content = 1A4 {111} has 4 faces Form is a tetrahedron Two types of forms: Open form – does not enclose a volume Closed form – encloses a volume Minerals must have more than one form if they have an open form Minerals may have only one closed form (could have more than 1) Example of multiple forms Example of multiple forms Cube {001}, octahedron {111}, and prisms{110}, {101}, {011} Both forms have 4/m 3 2/m symmetry Prisms {110} {101} {001} Two combined closed forms, plus additional open forms {111} = octahedron {001} = cube Isometric forms Isometric forms 15 possible forms 4 common ones Cube {001} – 4/m 3 2/m symmetry Octahedron {111} – 4/m 3 2/m symmetry Tetrahedron {111} – 4 symmetry Dodecahedron {110} Both isometric forms: c c b a b Octahedron {111} Crystal class = 4/m 3 2/m a Tetrahedron {111} Crystal class = 4 Non­isometric form Non­isometric form 10 types of forms Pedion (open) Pinacoid (open) Single face No symmetrically identical face Two parallel faces Related by mirror plane or inversion Dihedron (open ­ 2 types) Two non­parallel face Related by mirror (dome) or 2­fold rotation (sphenoid) Note: dome switches handedness Sphenoid retains handedness Fig. 2­31 Fig. 2­31 Prism (open) Pyramid (open) 3, 4, 6, 8, or 12 faces Intersect at a point Dipyramid (closed) 3, 4, 6, 8 or 12 faces Intersect with mutually parallel edges forming a tube 6, 8, 12, 16, or 24 faces Two pyramids at each end of crystal All of these forms are named on the basis of the shape of the cross section Pyramids Prisms Three types – seven modifiers – total of 21 forms Open Dipyramids Open Closed Cross section Rhombic Tetragonal Trigonal Ditetragonal Hexagonal Ditrigonal Dihexagonal Fig. 2­32 Fig. 2­32 Trapezohedrons (closed) 6, 8, 12 faces each a trapezoid (plane shape with 4 unequal sides) Named according to number of faces Scalenohedron (closed) 8 or 12 faces Each a scalene triangle (no two angles are equal) Rhombohedrons (closed) 6 faces, each rhomb shaped (4 equal sides, no 90 angles) Looks like a stretched or shortened cube Tetrahedron (closed) 4 triangular faces Fig. 2­33 Fig. 2­33 Combining forms Combining forms Restrictions on types of forms within a crystal All forms must be in the same crystal system All forms must have symmetry of one crystal class Tetragonal prism has a single 4­fold rotation, only found in tetragonal crystal class with single 4­fold rotation axis Pedions never occur in mineral with center of symmetry Multi­faced forms are not composed of several simpler forms A cube is not 6 pedions or 3 pinacoids Relationship between forms Relationship between forms Entantiomorphous forms Two forms related to each other by mirror planes Mirror planes missing within the form itself Positive and negative forms Two forms related to each other by rotation axis Rotation axis missing within the forms Enantiomorphous Forms Enantiomorphous Forms Lack center of symmetry and mirrors Since they are mirror images, they are right and left handed forms Individual crystal of enantiomorphic mineral may be right or left handed, but not both Originate from a type of symmetry called screw axis (may spiral right or left) Quartz is common example 3­fold screw axis Enantiomorphous forms result from either right or left spiral May be 2­fold, 4­fold, or 6­fold Fig. 2.20 Fig. 2.20 Crystal are mirror images of each other, but there are no mirror images in the crystals Right and left handed quartz Fig. 2­34 Fig. 2­34 Positive and Negative Forms Positive and Negative Forms Two forms related by rotation Two possible rotations: 60º on 3­fold rotation axis 90º on 4­ or 2­fold rotation axis Positive and negative faces in quartz crystal Quartz lacks center of symmetry Fig. 2­35 Fig. 2­35 Forms in the Six Crystal System Forms in the Six Crystal System Forms control orientation of crystallographic axes of the 6 crystal system Systematic relationship between form, symmetry present, and Hermann­Maugin symbols Following slides show these relationships Triclinic Triclinic Common symmetry: 1­fold rotation c­axis parallels prominent zone axis b and a axes parallel crystal edges α and β typically > 90º Single Hermann­Maugain symbol Common minerals: plagioclase and microcline Triclinic c = zone axis Pedions Pinacoid b a 1 1 Fig. 2­36 Fig. 2­36 Monoclinic Monoclinic Common symmetry: 2­fold rotation and/or single mirror plane b axis commonly parallel the 2­fold rotation or perpendicular to mirror plane c axis parallel to prominent zone a axis down and to front so β > 90 Single H­M symbol (2, m, or 2/m) Common minerals: amphiboles, pyroxenes, micas Monoclinic 2­fold rotation axis Fig. 2­37 Fig. 2­37 Orthorhombic Orthorhombic Common symmetry: 3 2­fold rotations and/ or 3 mirror planes Crystal axes are parallel to 2­fold rotations or perpendicular to mirror planes, or both Any axis could have any symmetry Reported in H­M notation: 1st = a axis, 2nd = b axis, 3rd = c axis E.g. mm2 – a ⊥ mirror, b ⊥ mirror, c parallel 2­fold rotation Orthorhombic c c c b b a mm2 b 222 a a 2/m2/m2/m Fig. 2­38 Fig. 2­38 Tetragonal Tetragonal Common symmetry: single 4­fold rotation, or 4­fold rotoinversion c axis always the single 4­fold rotation axis a and b coincide with 2­fold rotation or ⊥ mirror (if present) mirror (if present) H­M symbol: 1st = c axis 2nd = b and a axes 3rd = symmetry on [110] and [110] axis at 45º to a and b axes Example Example 42m C = 4­fold rotoinversion a and b axes [100] and [010] are 2­fold rotation There are mirrors ⊥ to [110] and [110] to [110] and [110] c 42m Positive and negative tetragonal tetrahedron b a Note – tetragonal so a = b ≠ c, this is not an isometric form Fig. 2­39 Fig. 2­39 Hexagonal Hexagonal Common symmetry: 1 3­fold axis (trigonal division) or 1 6­fold axis (hexagonal division) c axis parallel to 6­fold or 3­fold rotation A axes parallel to 2­fold rotation or perpendicular to mirror H­M symbols written with 1st = c axis, 2nd parallel a axes, 3rd perpendicular to a c a2 A prism and multiple dipyramids ­a3 a1 6/m2/m2/m Figure 2­41 Figure 2­41 Isometric Isometric Common symmetry 4 3­fold axes 3 equivalent symmetry axes coincide with crystallographic axes (e.g. for cube, it’s the 4 fold rotations) Symmetry either 2­fold or 2­fold H­M symbols; 1st crystallographic axes 2nd diagonal axes [111] 3rd center of one edge to center of another edge [110] 4/m32/m ­ Isometric 3 c a b 4/m 2/m Fig. 2­44 Fig. 2­44 ...
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This note was uploaded on 09/19/2011 for the course GLY 3200 taught by Professor Staff during the Fall '10 term at University of Florida.

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