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.

Mirror plane (symmetry 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 Symbol or for Inversion axis 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 faces-trigonal; 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