Crystal Lattice#

Record a sample’s crystalline lattice parameters: \(a, b, c, \alpha, \beta, \gamma\). Information for a crystal lattice is stored in an instance of hklpy2.blocks.lattice.Lattice(). This class will examine the lattice parameters and report the crystal system. If the parameters do not match any of these crystal systems, an exception will be raised.

A lattice is stored as part of the sample.

Examples of the Seven 3-D Crystal Systems (highest to lowest symmetry)

system

command

a

b

c

alpha

beta

gamma

cubic

Lattice(5.)

5

5

5

90

90

90

hexagonal

Lattice(4., c=3., gamma=120)

4

4

3

90

90

120

rhombohedral

Lattice(4., alpha=80.2)

4

4

4

80.2

80.2

80.2

tetragonal

Lattice(4, c=3)

4

4

3

90

90

90

orthorhombic

Lattice(4, 5, 3)

4

5

3

90

90

90

monoclinic

Lattice(4, 5, 3, beta=75)

4

5

3

90

75

90

triclinic

Lattice(4, 5, 3, 75., 85., 95.)

4

5

3

75

85

95

Default values are italicized. It is not necessary to supply the default parameters.

see:

https://dictionary.iucr.org/Crystal_system

see:

https://en.wikipedia.org/wiki/Crystal_system

EXAMPLES

It is not necessary to enter any of the default information for any lattice (such as the 90 degree angles for an orthorhombic crystals).

 1>>> from hklpy2 import Lattice
 2>>> Lattice(5.)
 3Lattice(a=5.0, b=5.0, c=5.0, alpha=90.0, beta=90.0, gamma=90.0)
 4
 5>>> Lattice(4., c=3., gamma=120)
 6Lattice(a=4.0, b=4.0, c=3.0, alpha=90.0, beta=90.0, gamma=120)
 7
 8>>> Lattice(4., alpha=80.2)
 9Lattice(a=4.0, b=4.0, c=4.0, alpha=80.2, beta=80.2, gamma=80.2)
10
11>>> Lattice(4, c=3)
12Lattice(a=4, b=4, c=3, alpha=90.0, beta=90.0, gamma=90.0)
13
14>>> Lattice(4, 5, 3)
15Lattice(a=4, b=5, c=3, alpha=90.0, beta=90.0, gamma=90.0)
16
17>>> Lattice(4, 5, 3, beta=75)
18Lattice(a=4, b=5, c=3, alpha=90.0, beta=75, gamma=90.0)
19
20>>> Lattice(4, 5, 3, 75., 85., 95.)
21Lattice(a=4, b=5, c=3, alpha=75.0, beta=85.0, gamma=95.0)

See also

Glossary