CRYSTALLOGRAPHY INTRODUCTION crystallography is the study of crystal

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: • A 2= 2 -fold--a reproduction of face(s) twice • A 3= 3 -fold--the same 3 times • A 4= 4 -fold--the same 4 times • A 6= 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 4 m • 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 y. Ax 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 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 A 3 axis, the symmetry is designated as an A 3 with a bar above • there can be a bar. A 3, bar. A 4 or bar. A 6 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 bar. A 3 is equivalent to an A 3 + an i; a bar. A 4, to an A 2 ; a bar. A 6 to an A 3+ 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 A 6 cannot be present with an A 4 and vice versa • an A 6 cannot be present with an A 3 and vice versa • the number or kind of symmetry function(s) can lend important information • the presence of a 1 A 4 signifies a tetragonal class crystal and if more A 4 there must be 3 A 4, then belonging to the isomeric class

• presence of 1 A 3 signifies a hexagonal class, if more, there must be 4 A 3 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 A 2 --located at top of crystal • sphenoid--two nonparallel faces related to an A 2 --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 A 2 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 A 2 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