Question

Need some help in memorizing Crystal systems, can any body help? :(

Answer 1

Warning! Long Answer. Here's what I get.

Explanation:

Disclaimer: I am neither a crystallographer nor a geologist. I invite others to improve this answer.

It's not hard to devise a mnemonic for the names, but you must still memorize the structures corresponding to the names.

The best mnemonics are ones you make up yourself. The sillier they are, the better.

The seven crystal systems are:

`color(red)("Cu")"bic "color(red)("Te")"tragonal "color(red)("Or")"thorhombic "color(red)("H")"exagonal "color(red)("Mon")"oclinic "color(red)("Tr")"iclinic"`
`color (red)("T")"rigonal"`

Here's a senseless mnemonic I just devised.

`color(red)("CuTe") or color(red)("H")"ip, "color(red)("Mon")"ey "color(red)("Tr")"uly " color(red)("T")"alks"`

I'm sure you can come up with a much better one.

Bravais Lattices

There are fourteen Bravais lattices within the seven crystal classes.

The unit cell is defined by the lengths of the three edges `a, b` and `c"` and by the angles between the edges `αcolor(white)(l) (∠bcolor(red)(a)c), βcolor(white)(l) (∠acolor(red)(b)c)`, and `γcolor(white)(l) (∠acolor(red)(c)b)`.

(Fromcommons.wikimedia.org)

A. `color(red)("Cu")`bic (`a = b = c; α = β = γ = 90°`)

Three axes of equal length; three 90° angles; three unit cells

`bbcolor(blue)(1.)` Simple cubic (sc)

`bbcolor(blue)(2.)` Body-centred cubic (bcc)

`bbcolor(blue)(3.)` Face centred cubic (fcc)

Here's a cubic crystal in nature.

(From Chemistry Stack Exchange)

B. `color(red)("Te")`tragonal (`a = b ≠ c; α = β = γ = 90°`)

Two equal axes and a third of different length; three 90° angles; two unit cells

Similar to cubic crystals, but longer along one axis than the other.

`bbcolor(blue)(4.)` Simple tetragonal

`bbcolor(blue)(5.)` Body-centred tetragonal

The tetragonal prism and the tetragonal bipyramid belong to this system.

You also find the tetragonal prism capped by a square pyramid.

An example is the crystal of apophyllite shown below.

(From Inspiring Things from around the World - WordPress.com)

C. `color(red)("Or")`thorhombic(`a ≠ b ≠ c; α = β = γ = 90°`)

Three axes of unequal length; 90° angles; four unit cells

Like tetragonal crystals except not square in cross-section

`bbcolor(blue)(6.)` Simple orthorhombic

`bbcolor(blue)(7.)` Body-centred orthorhombic

`bbcolor(blue)(8.)` Face-centred orthorhombic

`bbcolor(blue)(9.)` Base-centred orthorhombic

Other variations are a bipyramid and a prism.

D. `color(red)("H")`exagonal (`a = b ≠ c; α = β = 90°; γ = 120°`)

`bbcolor(blue)(10.)` Hexagonal

Two equal axes and a third of different length; two 90° angles and a 120° angle; one unit cell

Hexagonal in cross-section

(From Croatian-English Chemistry Dictionary & Glossary)

You also find the hexagonal bipyramid and the hexagonal capped prism.

An example is the crystal of quartz shown below.

E. `color(red)("Mon")`oclinic (`a ≠ b ≠ c; α = γ = 90° ≠ β`)
Axes of unequal length; two 90° angles.

`bbcolor(blue)(11.)` Simple monoclinic
`bbcolor(blue)(12.)` Base-centred monoclinic

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

E. Triclinic (`a ≠ b ≠ c; α ≠ β ≠ γ`)

Three axes of unequal length; three different angles; one unit cell.

`bbcolor(blue)(13.)` Triclinic

F. Trigonal (`a = b = c; α = β = γ < 120° ≠ 90°`)

A single 3-fold axis of rotation instead of the 6-fold axis of the hexagonal division.

`bbcolor(blue)(14.)` Trigonal

Here's a summary of the 14 Bravais lattices.