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[½»Á÷] The Bravais Lattices Song ÒÑÓÐ3È˲ÎÓë

The Bravais Lattices Song
Walter F. Smith 1-22-02

If you have to fill a volume with a structure that¡¯s repetitive,
Just keep your wits about you, you don¡¯t need to take a sedative!
Don¡¯t freeze with indecision, there¡¯s no need for you to bust a seam!
Although the options may seem endless, really there are just fourteen!
There¡¯s cubic, orthorhombic, monoclinic, and tetragonal,
There¡¯s trigonal, triclinic, and then finally hexagonal!
There¡¯s only seven families, but kindly set your mind at ease¡ª
¡®Cause four have sub-varieties, so there¡¯s no improprieties!
(Chorus:
¡®Cause four have sub-varieties, so there¡¯s no improprieties.
¡®Cause four have sub-varieties, so there¡¯s no improprieties.
¡®Cause four have sub-varieties, so there¡¯s no impropri-e, prieties!)
These seven crystal systems form the fourteen Bravais lattices.
They¡¯ve hardly anything to do with artichokes or radishes ¨C
They¡¯re great for metals, minerals, conductors of the semi-kind ¨C
The Bravais lattices describe all objects that are crystalline!

The cubic is the most important one in my ¡°exparience¡±,
It comes in simple and in face- and body-centered variants.
And next in line¡¯s tetragonal, it¡¯s not at all diagonal,
Just squished in one dimension, so it¡¯s really quite rectagonal!
The orthorhombic system has one less degree of symmetry
Because an extra squish ensures that a not equals b or c.
If angle gamma isn¡¯t square, the side lengths give the ¡°sig-o-nal¡±
For monoclinic if they¡¯re different, or, if equal, trigonal!
(Chorus (reprovingly):
Of course for trigonal, recall that alpha, beta, gamma all
Are angles that are equal but don¡¯t equal ninety, tut, tut, tut!
Are angles that are equal but don¡¯t equal ninety, tut, tut, tut, tut tut!)
If you squish the lattice up in every way that is conceivable,
You¡¯ll get the least amount of symmetry that is achievable ¨C
It¡¯s called triclinic, then remains the one that really self explains ¨C
Hexagonal gives us no pains, and so we now may rest our brains!

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