CRYSTALLOGRAPHY

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CRYSTALLOGRAPHY
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INTRODUCTION

• crystallography is the study of crystal shapes
  based on symmetry
• atoms combine to form geometric shapes on
  smallest scale-- these in turn combine to form
  seeable crystal shapes if mineral forms in a
  nonrestrictive space (quartz crystal vs massive
  quartz)
• symmetry functions present on a crystal of a
  mineral allows the crystal to be categorized or
  placed into one of 32 classes comprising the 6
  crystal systems

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SYMMETRY FUNCTIONS

• 1. Axis of rotation
• rotation of a crystal through 360 degrees on an
  axis may reveal 2,3,4, or 6 reproductions of
  original face or faces--these kinds of fold axes
  are
• A2 2-fold--a reproduction of face(s) twice
• A3 3-fold--the same 3 times
• A4 4-fold--the same 4 times
• A6 6-fold--the same 6 times
• a crystal can have more than 1 kind and multiple
  of the kind of fold axis each located in a
  perpendicular plane to another or in some
  isometric classes the same at a 45 degree plane.

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• An axis of rotation can represent only 1 YAX
• Mirror plane (symmetry plane)
• plane dividing a crystal in equal halves in which
  one is a mirror image of the other
• there may be 0-9 different mirror planes on a
  crystal
• designation of total mirror images on a crystal
  is given by the absolute number of mirror planes
  followed by a small m--four mirror images is
  designated as 4m
• mirror planes, if present, occur in the same
  plane as rotation axes and in the isometric, also
  at 45 degrees to the axes

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• in determination of rotation axes and mirror
  planes, do not count the same yAx or m more than
  once.
• Center of symmetry
• exists if the same surface feature is located on
  exact opposite sides of the crystal and are both
  equal distance from the center of crystal
• surface features include points, corners, edges,
  or faces
• a crystal has or lacks a center of symmetry and
  if it has, there are an infinite number of cases
  on the crystal
• i is the symbol which indicates the presence of a
  center of symmetry

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• Axis of rotoinversion
• is present if a reproduction of the face or faces
  on the crystal is obtained through a rotation
  axis, then inverting the crystal
• if done so on an A3 axis, the symmetry is
  designated as an A3 with a bar above
• there can be a barA3, barA4 or barA6 but only one
  of these roto inversion axes can exist on a
  crystal if present
• although an important symmetry function, it is
  not necessary to use it to categorize
  crystals---if present a combination of the other
  3 symmetry functions substitutes for it
• a barA3 is equivalent to an A3 an i a barA4,
  to an A2 a barA6 to an A3 m

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• If the total symmetry of crystal is ascertained,
  ( substitute symmetries if an axis of roto
  inversion exists) the crystal can be categorized
  in one of 32 classes---see table
• mother nature limits the combinations of symmetry
  functions which can occur with crystals--for
  example
• an A6 cannot be present with an A4 and vice versa
• an A6 cannot be present with an A3 and vice versa
• the number or kind of symmetry function(s) can
  lend important information
• the presence of a 1A4 signifies a tetragonal
  class crystal and if more A4 there must be 3A4,
  then belonging to the isomeric class

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• presence of 1A3 signifies a hexagonal class, if
  more, there must be 4A3 present and belongs in an
  isometric class
• HOLOHEDRAL refers to the respective class in each
  crystal system possessing the highest (most
  complex) symmetry
• even though crystals may not appear to look the
  same, they may have the exact same symmetry
• NOW LETS spend time on determining crystal
  symmetry on wooden blocks and to which crystal
  class and system each belongs

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CRYSTAL FORMS

• a group of faces on a crystal related to the same
  symmetry functions
• the faces of the group are usually the same size
  and shape on the crystal
• recognition of crystal forms can help determine
  the symmetry functions present on a crystal and
  vice versa
• forms related to non isometric classes are quite
  different than those related to isometric classes
• since more than one form can exist on a crystal,
  it is more difficult to ascertain each form in
  the full form--each full form will be shown
  in the following presentation--also note the
  symmetry related to the form--see page 127 for
  axes symbols

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Rotation axis Symbol or
for Inversion axis axis
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• Non-isometric forms
• pedion--a single face
• pinacoid--an open form comprised of 2 parallel
  faces--many possible locations on crystal
• dome--open form with 2 non parallel faces with
  respect to a mirror plane and A2--located at top
  of crystal
• sphenoid--two nonparallel faces related to an
  A2--located at top of crystal

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• prism-- open form of 3 (trigonal), 4 (tetragonal,
  monoclinc or orthorhombic), 6 ( hexagonal or
  ditrigonal), 8 (ditetragonal), or 12 (
  dihexagonal) faces all parallel to same axis and
  except for some in the monoclinic, that axis is
  the highest fold axis--most prism faces are
  located on side of crystal

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• pyramid--open form with 3 (trigonal), 4
  (tetragonal or orthorhombic), 6 (hexagonal or
  ditrigonal), 8 (ditetragonal) or 12 (dihexagonal)
  nonparallel faces meeting at the top of a crystal

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• dipyramid--a closed form with an equal number of
  faces intersecting at the top and bottom of
  crystal and can be thought of as a pyramid at the
  top and bottom with a mirror plane separating
  them (6 faces-trigonal 8 faces--tetragonal or
  rhombic12 faces--hexagonal or ditrigonal16
  faces--ditetragonal 24 faces--dihexagonal)

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• trapezohedron--a closed form with 6, 8, or 12
  faces with 3 (trigonal), 4 (tetragonal) or 6
  (hexagonal) upper faces offset with each of the
  same number at bottom--no mirror plane separates
  top set from bottom--note the 3 sets of A2 at the
  sides

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• scalenohedron--a closed form with 8 (tetragonal)
  or 12 (hexagonal) faces grouped in symmetrical
  pairs--note the inversion 4 fold and inversion 3
  fold and A2 axes associated with each

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• disphenoid--a closed form with 2 upper faces
  alternating with 2 lower faces offset by 90
  degrees

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ISOMETRIC FORMS

• Many of these forms are based on a triad of
  isometric forms, the cube (hexahedron),
  octahedron, and tetrahedron--the name of a form
  often includes the suffix of the triad with a
  prefix
• cube (hexahedron)--6 equal faces intersecting at
  90 degrees
• octahedron--8 equilateral triangular faces
• tetrahedron--4 equilateral triangular faces

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• dodecahedron--12 rhombed faces
• tetrahexahedron--24 isosceles triangular faces--4
  faces on each basic hexahedron face
• trapezohedron--24 trapezium shaped faces
• trisoctahedron--24 isosceles triangular faces--3
  faces on each octahedron face

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• hexoctahedron--48 triangular faces--6 faces on
  each basic octahedron face
• tristetrahedron--12 triangular faces--3 faces on
  each basic tetrahedron face
• deltoid dodecahedron--12 faces corresponding to
  1/2 of trisoctahedron faces
• hextetrahedron--24 faces--6 faces on each basic
  tetrahedron face

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• diploid--24 faces
• pyritohedron--12 pentagonal faces

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• It is possible to identify the class of the
  crystal in some cases based on the form(s)
  present--this can be done with much practice in
  identifying crystal forms
• refer to the table with all possible forms which
  can exist in a crystal class of each crystal
  system--examples of key forms present on crystals
  are
• the rhombic dipyramid can only occur in the
  rhombic dipyramidal class
• the ditrigonal dipyramid can only occur in the
  ditrigonal dipyramidal class
• the hextetrahedron can occur only in the
  hextetrahedral class
• the tetrahexahedron can occur only in the
  hextetrahedral class
• crystal class names are based on the most
  outstanding form possible--NOW, GO TO IT