Title: ETH_Sem4 / ACII / Basics of Crystal Structure

Q: There are only [...] distinct space-filling volume elements meaning [...] lattice systems.
A: seven; seven

Header: 14 Bravais Lattices in 3D

Unit Cell:
1. The smallest volume that can generate the entire crystal structure in void-free manner by means of translation
2. Contains the macroscopic stoichiometry of the compound
3. Contains full symmetry of the crystal
4. Has symmetry axes parallel to the unit cell a/b/c vectors and mirror planes normal to them

Q: [...] + [...] = Crystal Structure
A: Bravais Lattice; Basis or Motif

A Bravais lattice describes only the geometry of the unit cell (7 types) and location of the lattice sites within the unit cell
A crystal structure describes both the geometry of a unit cell and the atomic arrangements within the unit cell
Back Extra: Example: Location of the trees (Bravais lattice) + location of the fruits (atoms/molecules/...) make for a garden (Crystal structure)

Cubic Close-Packed Structure (CCP = FCC)

Hexagonal Close-Packed Structure (HCP)

Tetrahedral hole

Octahedral hole

Q: The atomic positions are given in terms of fractional coordinates x, y, z (separated by commas, round brackets), which describe fractions of [...] (along x, y, z coordinates)
A: the lattice constants a, b and c

Q: 3 types of cubic systems
A: - Simple cubic (P)
- Body centered cubic (BCC)
- Face centered cubic (FCC)

.) Corner atom shared by 8 cells -> 1/8 atom per cell
.) Edge atom shared by 4 cells -> 1/4 atom per cell
.) Face atom shared by 2 cells -> 1/2 atom per cell
.) Body atom shared by 1 cells -> 1 atom per cell

Q: Packing density of...
...simple cubic = [...]
...body centered cubic = [...]
...face centered cubic = [...]
A: 0.52; 0.68; 0.74

Q: Volumetric density of a crystal
A: \[\rho=\frac{\text{atoms per unit cell} * FW}{\text{volume of formula unit} * N_A}\]

Header: Hermann-Mauguin symbols

Q: A space group defines both the [...] and the [...] of the structure.
A: translational symmetry (type of the Bravais lattice); rotational symmetry (point group)

Herman-Mauguin symbols for space groups

Space group symbol rules (meaning of four positions):
1. First letter: P, A, B, C, I or R -> translation symmetry + type of centering
2. The orientation of the symmetry elements
3. A possible inversion center
4. A possible reflection plane orthogonal to a symmetry axis

Q: Point symmetry leads to [...] crystallographic point groups
A: 32

Q: Point and translational symmetry elements define [...] unique atomic arrangements (space groups). All crystals can be described by one of these groups.
A: 230