M3, pt. 2: Crystals - Space Lattice & Unit Cell

Lattice

A collection of points that divide space into smaller equally sized segments

Basis

A group of atoms associated with a lattice point

Unit Cell

A subdivision of the lattice that still retains the overall characteristics of the entire lattice

Atomic Radius

The apparent radius of an atom, typically calculated from the dimension of the unit cell, using close-packed directions (depends upon coordination number)

Packing Factor

The fraction of space in a unit cell occupied by atoms

1. Lattice

2. Basis (Motif)

two parts of a crystal

Lattice

• A 3-D array of points in space

• Each point must have identical surroundings

Basis (Motif)

The identical group of atoms which surround each point in the lattice (repeated by symmetry) to construct the crystals

COORDINATION NUMBER

Indication of how tight and efficient atoms are packed together

COORDINATION NUMBER

Number of atoms touching a particular atom

PACKING FACTOR

Fraction of space occupied by atoms, assuming that the atoms are hard spheres

PACKING FACTOR

Independent of the radius of atoms, as long as we assume that all atoms have a fixed radius

𝜋/√18!

Kepler’s conjecture

𝜋/√18!

Maximum achievable packing factor

CRYSTAL STRUCTURE

is a solid where the atoms form a periodic arrangement (Quasicrystals are an exception)

Amorphous solids

These have no periodic order, even microscopically

Amorphous solids

also called glassy, vitreous, or noncrystalline

Amorphous solids

Solids that are neither crystalline nor polycrystalline, such as glass

Crystal Structure

The unit cells are stacked in three-dimensional space to form the crystal

Crystal Structure

is characterized by its unit cell, a small imaginary box containing one or more atoms in a specific spatial arrangement

Crystal Structure

an arrangement of atoms in a crystal

219 possible crystal symmetries

called crystallographic space groups

Euhedral Crystals

are those with obvious, well-formed flat faces

Euhedral Crystals

The flat faces/facets of a euhedral crystal are oriented in a specific way relative to the underlying atomic arrangement of the crystal: they are planes of relatively low Miller index

low Miller index

This occurs because some surface orientations are more stable than others (lower surface energy)

Anhedral Crystals

the crystal is one grain in a polycrystalline solid

Anhedral Crystals

do not have well-formed flat faces

Crystal’s Habit

This is determined by the crystal structure (which restricts the possible facet orientations), the specific crystal chemistry and bonding

Crystal’s Habit

is its visible external shape

Cubic or Isometric

These are not always cube-shaped. You'll also find octahedrons (eight faces) and dodecahedrons (10 faces)

Tetragonal

Similar to cubic crystals, but longer along one axis than the other, these crystals forming double pyramids and prisms

Orthorhombic

Like tetragonal crystals except not square in cross-section (when viewing the crystal on end), these crystals form rhombic prisms or dipyramids (two pyramids stuck together)

Hexagonal

When you look at the crystal on end, the cross-section is a sixsided prism or hexagon

Trigonal

These crystals possess a single 3-fold axis of rotation instead of the 6-fold axis of the hexagonal division

Triclinic

These crystals are not usually symmetrical from one side to the other, which can lead to some fairly strange shapes

Monoclinic

Like skewed tetragonal crystals, these crystals often form prisms and double pyramids

Solar Cells

One of the largest uses for crystals

Solar Cells

it power various instruments from calculators to space vehicles

Solar Cells

produces energy, called photovoltaic energy, by using silicon (which is based on a tetragonal crystal)

Transistors

Made out of semi-conductors, which are based on the same types of materials and crystals as hence acting like digital "switches." Transistor radios, for example, make this use out of crystals

Liquid Crystals

For example, wristwatches and some types of clocks use liquid crystals, as do some pocket calculators.

Liquid Crystals

This precise substance made out of crystals can be used for a variety of different means, from heat and electricity to magnetism and mechanics.

Spiritual Crystals

Different kinds of crystals have long been thought to bestow certain traits or qualities on those using them, helping them access certain emotions. 

amethyst crystals

are thought to reduce feelings of anger and impatience

aquamarine

used to release fear

carnelian

used to produce confidence

coral

used to intensify emotions

diamonds

used to increase prosperity

emeralds

used to relieve depression and insomnia

sapphire

used to restore calm and a sense of balance

Medicinal Crystals

some new age medical practitioners claim that the presence and other uses of certain crystals promote different kinds of medical benefits

amethyst

used to treat headaches or unbalanced blood sugar

aquamarine

used to regulate the immune system, heart and lymph nodes

carnelian

used to help with energy, the reproductive system and menstrual cramps

Cetrine

used to cleanse the spleen, kidneys and liver

coral

used to help the metabolism, spine and tissue regeneration

emeralds

used to help with the thymus and childbirth

jade

used to help cleanse the blood and the nervous system

rubies

used to help with cholesterol and blood clots

sapphire

used to help with inflammation, fever and nosebleeds as well as tuberculosis