Crystals (Objectives)

Module 2 Unit 1: Crystal Structures Objective part only

Crystal Structure

Description of the ordered arrangement of atoms, ions, or molecules in a crystalline material.

Crystallography

experimental science of determining the arrangement of atoms in crystalline solids.

Atom

smallest constituent of ordinary matter

Ion

an atom or molecule that has a non-zero net electric charge

Molecule

electrically neutral group of two or more atoms held together by chemical bonds

Covalent Bond

sharing of electrons between atoms

Ionic Bond

Transfer of valence electrons

Unit Cell

The smallest group of particles in the material that constitutes the repeating pattern.

Crystalline Lattice

Regular arrangement of atoms within a crystalline solid.

Bravais Lattice

Where are the repeating patterns located?

Coordination Number

The number of atoms with each atom is in direct contact.

Packing Efficiency

Percentage of the volume of the unit cell occupied by the spheres.

1/8 atom

How many atoms are at every corner of the simple cubic lattice?

l=2r

edge length of a simple cubic lattice

1 atom

How many atoms are in the unit cell of a simple cubic lattice?

52%

Packing Efficiency of simple cubic lattice

Body-Centered Cubic Lattice

Has one atom in the center and 1/8 of an atom at each corner.

8

coordination # of BCC

2 atoms

# of atoms per each unit cell in BCC

68%

Packing efficiency of BCC

Face-Centered Cubic Lattice

Has 1/8 of an atom at each corner and 1/2 of an atom at each face.

12

coordination # of FCC

4 atoms

# of atoms in one unit cell in FCC

74%

packing efficiency of FCC

Hexagonal Closest Packing

ABAB Pattern
Third layer is aligned with the first layer
Unit Cell: Hexagonal
Coordination #: 12
Packing Efficiency: 74%

Cubic Closest Packing

ABCABC Pattern
Third layer is offset from the first layer
Identical to FCC unit cell and structure
Unit Cell: Cube

Symmetry

pertains to the repetition of structural features

Translational Symmetry

Executable shifting movements proceeding along a straight line and on a certain specified distance

Point Symmetry

Repetition of a structural feature around a single reference point, commonly the center of a unit or a crystal

Rotation, Reflection, Inversion, Rotoinversion

4 types of Point Symmetry

Reflection

The structure features on one side of a plane passing through the center of a crystal are the mirror image of the structural features on the other side.

Rotation

A structural element is rotated a fixed number of degrees about a central point and then repeated.

Inversion

Any line drawn through the origin at the center of the crystal will connect two identical features on opposite sides of the plane.

Rotoinversion

Performance of a rotation followed by an inversion

Rotation by 360 degrees followed by an inversion

1-fold

Reflection through a mirror plane perpendicular to the rotoinversion axis

2-fold

3-fold rotational symmetry and inversion symmetry

3-fold

3-fold rotation and reflection across a mirror plane which lies at right angles to the rotation axis

6-fold

32

# of possible crystal classes

6

# of crystal systems

all edges are equal, all angles are equal to 90 degrees

Cubic System

Halite, Magnetite, Garnet

Crystals produced by the cubic system

a=b≠c
α=β=γ=90°

Tetragonal System

Zircon, Cassiterite

crystals produced by the tetragonal system

Prismatic Habit

Crystals of the tetragonal system exhibit this habit

a=b≠c
α=β=90°;γ=120°

Hexagonal System

Hexagonal, Rhombohedral

2 divisions of the hexagonal system

a≠b≠c
α=β=γ=90°

Orthorhombic System

Olivine, Barite

Crystals produced by the orthorhombic system

Prismatic, Tabular, Acicular

crystals of the orthorhombic system exhibit these habits

a≠b≠c
α=γ=90°≠β

Monoclinic System

Pyroxene, Amphibole, Orthoclase, Azurite, Malachite

crystals produced by the monoclinic system

Long Prisms

Type of crystals produced by the monoclinic system

a≠b≠c
α≠β≠γ≠90°

Triclinic System

Triclinic System

Crystal system that possesses no symmetry at all

Plagioclase, Axinite

crystals produced by the triclinic system

Tabular Habit

crystals produced by the triclinic system exhibit this habit

Monohedron, Parallelohedron, Dihedron, Disphenoid, Prism, Pyramid, Dipyramid, Trapezohedron, Scalenohedron, Rhombohedron, Tetrahedron

11 Crystal Forms

Bragg's Law

X-rays are scattered from a crystal lattice; peaks of scattered intensity are observed which correspond to the following conditions. Angle of Incidence = Angle of Scattering.

Crystal Defects

Imperfection and flaws in the regular geometrical arrangement of the atoms in a crystalline solid.