Crystallographic Concepts GLY 4200 Fall, 2017

Atomic Arrangement Minerals must have a highly ordered atomic arrangement The crystal structure of quartz is an example Images: http://www.infotech.ns.utexas.edu/crystal/quartz.htm

Quartz Crystals The external appearance of the crystal may reflect its internal symmetry External appearance is called the Habit Photos: http://www.msm.cam.ac.uk/doitpoms/tlplib/atomic-scale-structure/single1.php

Quartz Blob Or the external appearance may show little or nothing of the internal structure

Building Blocks A cube may be used to build a number of forms Images: http://www.gly.uga.edu/schroeder/geol3010/externalforms1.gif and http://www.gly.uga.edu/schroeder/geol3010/externalforms2.gif

Fluorite Fluorite may appear as octahedron (upper photo) Fluorite may appear as a cube (lower photo), in this case modified by dodecahedral crystal faces Photos: http://www.gc.maricopa.edu/earthsci/imagearchive/fluorite.htm

Crystal Growth Ways in which a crystal can grow: Dehydration of a solution Growth from the molten state (magma or lava) Direct growth from the vapor state

Unit Cell Simplest (smallest) parallel piped outlined by a lattice Lattice: a two or three (space lattice) dimensional array of points

Lattice Requirements Environment about all lattice points must be identical Unit cell must fill all space, with no “holes”

Auguste Bravais Found fourteen unique lattices which satisfy the requirements Published Études Crystallographiques in 1849 Photo: http://euromin.w3sites.net//textesensmp/Repere/pic_hist/bravais0.jpg

Isometric Lattices P = primitive I = body-centered (I for German innenzentriate) F = face centered a = b = c, α = β = γ = 90 ̊

Tetragonal Lattices a = b ≠c α = β = γ = 90 ̊

Tetragonal Axes The tetragonal unit cell vectors differ from the isometric by either stretching the vertical axis, so that c > a (upper image) or compressing the vertical axis, so that c < a (lower image)

Orthorhombic Lattice a ≠ b ≠c α = β = γ = 90 ̊ C - Centered: additional point in the center of each end of two parallel faces

Orthorhombic Axes The axes system is orthogonal Common practice is to assign the axes so the the magnitude of the vectors is c > a > b

Monoclinic Lattice a ≠ b ≠c α = γ = 90 ̊ (β ≠ 90 ̊)

Monoclinic Axes The monoclinic axes system is not orthogonal

Triclinic Lattice a ≠ b ≠c α ≠ β ≠ γ ≠ 90 ̊

Triclinic Axes None of the axes are at right angles to the others Relationship of angles and axes is as shown

Hexagonal Some crystallographers call the hexagonal group a single crystal system, with two divisions Rhombohedral division Hexagonal division Others divide it into two systems, but this practice is discouraged

Hexagonal Lattice a = b ≠ c α = γ = 90 ̊ β = 120 ̊

Rhombohedral Lattice a = b = c α = β = γ ≠ 90 ̊

Hexagonal Axes The hexagonal system uses an ordered quadruplicate of numbers to designate the axes a1, a2, a3, c

Arrangement of Ions Ions can be arranged around the lattice point only in certain ways These are known as point groups

Crystal Systems The six different groups of Bravais lattices are used to define the Crystal Systems The thirty-two possible point groups define the Crystal Classes

Point Group Point indicates that, at a minimum, one particular point in a pattern remains unmoved Group refers to a collection of mathematical operations which, taken together, define all possible, nonidentical, symmetry combinations