Bravais lattices Flashcards
What crystal families are there in 3D?
- Triclinic
- Monoclinic
- Orthorhombic
- Tetragonal
- Hexagonal
- Cubic
What crystal systems are there in 3D?
- Triclinic
- Monoclinic
- Orthorhombic
- Tetragonal
- Trigonal
- Hexagonal
- Cubic
What Bravais lattices exist for the triclinic crystal system?
aP
Why is the symbol for triclinic ‘a’?
From the word anorthic.
What Bravais lattices exist for the monoclinic crystal system?
mP, mS
What Bravais lattices exist for the orthorhombic crystal system?
oP, oF, oI, oA, oB, oC
What kind of centering exists for the orthorhombic crystal system?
Primitive, face-centering, body-centering, side-centering (A, B and C).
What restrictions are there on the lattice parameters in the triclinic crystal system?
None.
What restrictions are there on the lattice parameters in the monoclinic crystal system?
Two angles are 90°.
In b-unique setting: α = γ = 90°
In the c-unique setting: α = β = 90°.
What restrictions are there on the lattice parameters in the orthorhombic crystal system?
All angles are 90°.
What restrictions are there on the lattice parameters in the tetragonal crystal system?
All angles are 90° and a = b.
What restrictions are there on the lattice parameters in the cubic crystal system?
a = b = c, and all angles are 90°.
What restrictions are there on the lattice parameters in the trigonal crystal system (with rhombohedral axes)?
a = b = c, α = β = γ.
Why isn’t there a face-centered tetragonal Bravais lattice?
For a face-centered tetragonal lattice, a smaller body-centered lattice can always be chosen.
What is the standard setting for monoclinic cells?
Choosing b as the unique axis. The angle is usually taken to be acute (> 90°)
Which direction does the 3-fold axis run in the rhombohedral lattice cell?
Along the body diagonal.
How are directions denoted in a crystal structure?
[uvw]
How are sets of symmetrically equivalent lattice directions denoted in a crystal structure?
. E.g.:
[100], [010], [001], [-100], [0-10], [00-1] in a cubic lattice is denoted as <100>
How are sets of parallel equidistant planes in a lattice denoted?
hkl
How are single planes in a lattice denoted?
(hkl)
Why can’t there be a B-centered monoclinic cell (with unique b-axis setting)?
In such a cell, you could always draw a smaller primitive cell (mP).
Why can’t there be a F-centered monoclinic cell?
In such a cell, you could always draw a smaller C-centered cell.
Why can’t there be an I-centered monoclinic cell?
In such a cell, you could always draw a smaller C-centered cell (via A-centered rotated around b-axis).
Why can’t there be a C-centered tetragonal cell?
In such a cell, you could draw a smaller primitive cell.
