Crystallography- What is a Crystal? Flashcards
What is a crystal?
Periodically ordered arrangement of atoms. Has a periodic lattice of repeat coordinates and a unit cell as a repeat block. It is not amorphous with disordered atomic arrangement.
Complications with definition of crystal
Crystal with point defects (vacancies, inclusions) isn’t strictly periodic but can pragmatically be treated as a crystal. Multiple mis-oriented crystallites are multiple crystals called one poly-crystal. Alloys with sub-lattice chemical disorder but positional order can fit into crystallography nomenclature.
What information is needed to describe a crystal structure?
The lattice, unit cell, unit cell content.
What is the lattice?
A set of geometrical points to define the infinite repeat sequence of the crystal. The lattice points could be the location of atoms but doesn’t have to be. It has translation symmetry.
What is the unit cell?
A geometrical box which defines the preferentially smallest repeat unit within the lattice (size, shape, angles). There is unit cell symmetry.
What is the unit cell content?
Location of atoms inside unit cell (coordinates, fill factors, packing principles). Elemental identification and bonding/electronic structure. Local symmetry and chemistry.
If one type of atom is in a cube of another type of atoms, is it bcc?
No because bcc needs the central atom to be the same as those at the corners. The central atom in this case is not a lattice point just a differing central atom
Conventions for defining a unit cell
Repeat unit requirement: can fill the entire crystal upon repetition, no gaps or overlap between neighbouring cells, all unit cells are identical so there is only one type.
Smallness convention: no internal replication (sub-unit cells), as small as possible or reasonable, if same volume prefer cell with shortest edges or least acute angles.
Symmetry representation convention: cell preferred if shows the basic symmetry elements of the crystal at best by direct visual appearance (often has the full crystal symmetry)
Which unit cell conventions take priority?
Repeat unit requirement is always needed. Smallness and symmetry representation conventions are flexible and there is a trade-off between them
Origin shift convention for a unit cell
Origin chosen such to enhance visibility of overall crystal symmetry so is preferred on atoms or in the middle between atoms. Can make atom counting more difficult as will involve fractions
Can unit cells be rotated to fill the shape?
No they are only allowed to be translated
What should a unit cell be?
A box with 3 edges (a, b, c) and 3 angles (α, β, γ) to make a parallelopiped. No curves are allowed
