CRYSTALLOGRAPHY
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
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.
• 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
• 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
• 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
• 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
• 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 LET’S spend time on determining
crystal symmetry on wooden blocks and to
which crystal class and system each belongs
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
Rotation axis
or
Inversion axis
Symbol
for
axis
• 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
• 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
• 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
• 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 facestrigonal; 8 faces--tetragonal or rhombic;12 faces-hexagonal or ditrigonal;16 faces--ditetragonal ;24
faces--dihexagonal)
• 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
• 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
• disphenoid--a closed form with 2 upper
faces alternating with 2 lower faces offset
by 90 degrees
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
• 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
• 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
• diploid--24 faces
• pyritohedron--12 pentagonal faces
• 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