Applied biochemistry

1. CRYSTALLOGRAPHY

2. 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

5. 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.

6. • 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

7. • 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

8. 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

9. • 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

10. • 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

11. 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

12. Rotation axis Symbol
or for
Inversion axis axis

13. • 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

14. • 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

15. • 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

16. • 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 rhombic;12 faces--
hexagonal or ditrigonal;16 faces--ditetragonal ;24
faces--dihexagonal)

17. • 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

18. • 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

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

20. 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

21. • 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

22. • 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

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

24. • 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