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

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Unformatted text preview: Zones, Forms, Habits Quantitative description of orientation in minerals use Miller indices: Qualitative description of mineral shapes Habit Lines, or linear directions within minerals Zone Shapes of three dimensional objects Form 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 Fibrous tremolite Bladed kyanite 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 = [001] a b Note typo Fig 228 Lattice node Other linear crystallographic directions For example: location of rotation axes or other linear features Referenced to unit cell dimensions of lattice nodes Fig 227 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 There are six faces in a cube: (100), (010), (001), (100), (010), (001) c Form is written with brackets Uses miller index of one face Generally positive face E.g., {001} b a Possible to determine the shape of a form with: The form is created by operating point symmetry on the initial face Point symmetry Miller index of one face in form Number of faces in a form depends on crystal class: Triclinic system: Point group (i.e. crystal class) = 1 Symmetry content = (1A1) {111} has only 2 faces Isometric system: 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 Point group (crystal class) = 4 Symmetry content = 1A4 {111} has 4 faces Form is a tetrahedron 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 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 Cube {001} and octahedron {111} Both forms have 4/m 3 2/m symmetry Two combined closed forms, plus additional open forms {111} = octahedron {001} = cube 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} c c a b b a Octahedron Tetrahedron {111} {111} 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 Two nonparallel face Related by mirror (dome) or 2fold rotation (sphenoid) Dihedron (open 2 types) Note: dome switches handedness Sphenoid retains handedness Fig. 231 Prism (open) Pyramid (open) 3, 4, 6, 8 or 12 faces Intersect with mutually parallel edges forming a tube 3, 4, 6, 8, or 12 faces Intersect at a point 6, 8, 12, 16, or 24 faces Two pyramids at each end of crystal Dipyramid (closed) All of these forms are named on the basis of the shape of the cross section Rhombic Pyramids Prisms Tetragonal Trigonal Ditetragonal Hexagonal Dihexagonal Ditrigonal Open Open Dipyramids Closed Cross section Fig. 232 Trapezohedrons (closed) Scalenohedron (closed) 6, 8, 12 faces each a trapezoid (plane shape with 4 unequal sides) Named according to number of faces 8 or 12 faces Each a scalene triangle (no two angles are equal) Rhombohedrons (closed) Tetrahedron (closed) 6 faces, each rhomb shaped (4 equal sides, no 90 angles) Looks like a stretched or shortened cube 4 triangular faces Fig. 233 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 Entantiomorphous forms Positive and negative forms Two forms related to each other by mirror planes Mirror planes missing within the form itself Two forms related to each other by rotation axis Rotation axis missing within the 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 Glide symmetry 3fold screw axis Silica tetrahedron, e.g. pyroxenes May be 2fold, 4fold, or 6fold Fig. 2.19 & 2.20 Enantiomorphous forms result from either right or left spiral Crystal are mirror images of each other, but there are no mirror images in the crystals Right and left handed quartz Fig. 234 Positive and Negative Forms Two forms related by rotation Two possible rotations: 60 on 3fold rotation axis 90 on 4 or 2fold rotation axis Positive and negative faces in quartz crystal Quartz lacks center of symmetry Fig. 235 Forms in the Six Crystal System Forms control orientation of crystallographic axes of the 6 crystal system Systematic relationship between form, symmetry present, and HM symbols Following slides show these relationships Triclinic Common symmetry: 1fold rotation caxis parallels prominent zone axis b and a axes parallel crystal edges and typically > 90 Single HermannMaugain symbol Common minerals: plagioclase and microcline Triclinic c = zone axis Pedions Pinacoids b a 1 1 Fig. 236 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 > 90 Single HM symbol (2, m, or 2/m) Common minerals: amphiboles, pyroxenes, micas Monoclinic 2fold rotation axis Fig. 237 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: E.g. mm2 a mirror, b mirror, c parallel 2fold rotation 1st = a axis, 2nd = b axis, 3rd = c axis Orthorhombic c c b a mm2 b 222 a a 2/m2/m2/m c b Fig. 238 Tetragonal Common symmetry: single 4fold rotation, or 4fold rotoinversion a and b coincide with 2fold rotation or mirror (if present) HM symbol: c axis always the single 4fold rotation axis 1st = c axis 2nd = b and a axes 3rd = symmetry on [110] and [110] axis at 45 to a and b axes Example 42m C = 4fold rotoinversion a and b axes [100] and [010] are 2fold rotation There are mirrors to [110] and [110] c 42m Positive and negative tetragonal tetrahedron b Note tetragonal so a = b c, this is not an isometric form a Fig. 239 Hexagonal Common symmetry: 1 3fold axis (trigonal division) or 1 6fold axis (hexagonal division) c axis parallel to 6fold or 3fold rotation a and b axes parallel to 2fold rotation or perpendicular to mirror HM symbols written with 1st = c axis, 2nd b and a axes, 3rd parallel to a and b c a2 A prism and multiple dipyramids a1 a3 Figure 241 Isometric Common symmetry 4 3fold axes 3 equivalent symmetry axes coincide with crystallographic axes Symmetry either 2fold or 2fold HM symbols; (e.g. for cube, it's the 4 fold rotations) 1st crystallographic axes 2nd diagonal axes [111] 3rd center of one edge to center of another edge [110] 4/m32/m Isometric 3 c b a 4/m 2/m Fig. 244 ...
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