This preview shows page 1. Sign up to view the full content.
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 ...
View
Full
Document
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.
 Fall '10
 Staff

Click to edit the document details