Bravais lattices

Question 1

What crystal families are there in 3D?

Answer 1

1. Triclinic
2. Monoclinic
3. Orthorhombic
4. Tetragonal
5. Hexagonal
6. Cubic

Question 2

What crystal systems are there in 3D?

Answer 2

1. Triclinic
2. Monoclinic
3. Orthorhombic
4. Tetragonal
5. Trigonal
6. Hexagonal
7. Cubic

Question 3

What Bravais lattices exist for the triclinic crystal system?

Answer 3

aP

Question 4

Why is the symbol for triclinic ‘a’?

Answer 4

From the word anorthic.

Question 5

What Bravais lattices exist for the monoclinic crystal system?

Answer 5

mP, mS

Question 6

What Bravais lattices exist for the orthorhombic crystal system?

Answer 6

oP, oF, oI, oA, oB, oC

Question 7

What kind of centering exists for the orthorhombic crystal system?

Answer 7

Primitive, face-centering, body-centering, side-centering (A, B and C).

Question 8

What restrictions are there on the lattice parameters in the triclinic crystal system?

Answer 8

None.

Question 9

What restrictions are there on the lattice parameters in the monoclinic crystal system?

Answer 9

Two angles are 90°.
In b-unique setting: α = γ = 90°
In the c-unique setting: α = β = 90°.

Question 10

What restrictions are there on the lattice parameters in the orthorhombic crystal system?

Answer 10

All angles are 90°.

Question 11

What restrictions are there on the lattice parameters in the tetragonal crystal system?

Answer 11

All angles are 90° and a = b.

Question 12

What restrictions are there on the lattice parameters in the cubic crystal system?

Answer 12

a = b = c, and all angles are 90°.

Question 13

What restrictions are there on the lattice parameters in the trigonal crystal system (with rhombohedral axes)?

Answer 13

a = b = c, α = β = γ.

Question 14

Why isn’t there a face-centered tetragonal Bravais lattice?

Answer 14

For a face-centered tetragonal lattice, a smaller body-centered lattice can always be chosen.

Question 15

What is the standard setting for monoclinic cells?

Answer 15

Choosing b as the unique axis. The angle is usually taken to be acute (> 90°)

Question 16

Which direction does the 3-fold axis run in the rhombohedral lattice cell?

Answer 16

Along the body diagonal.

Question 17

How are directions denoted in a crystal structure?

Answer 17

[uvw]

Question 18

How are sets of symmetrically equivalent lattice directions denoted in a crystal structure?

Answer 18

. E.g.:

[100], [010], [001], [-100], [0-10], [00-1] in a cubic lattice is denoted as <100>

Question 19

How are sets of parallel equidistant planes in a lattice denoted?

Answer 19

hkl

Question 20

How are single planes in a lattice denoted?

Answer 20

(hkl)

Question 21

Why can’t there be a B-centered monoclinic cell (with unique b-axis setting)?

Answer 21

In such a cell, you could always draw a smaller primitive cell (mP).

Question 22

Why can’t there be a F-centered monoclinic cell?

Answer 22

In such a cell, you could always draw a smaller C-centered cell.

Question 23

Why can’t there be an I-centered monoclinic cell?

Answer 23

In such a cell, you could always draw a smaller C-centered cell (via A-centered rotated around b-axis).

Question 24

Why can’t there be a C-centered tetragonal cell?

Answer 24

In such a cell, you could draw a smaller primitive cell.