Unit Cell¶
The variables in the UNIT_CELL section of the parameter file specify the Bravais lattice of the crystal. The variables required in this section, in the required order, are:
Variable Meaning dim number of periodic directions (1,2, or 3) crystal_system lattice system string identifier N_cell_param the number of required unit cell parameters cell_param an array of unit cell parameter values
The “crystal_system” for a three dimensional crystal string could, for example, be “cubic”, “tetragonal”, “orthorhombic” or several other possibilities. All allowed values of the “crystal_system” string are given below 1, 2 and 3 dimensionally periodic systems. The number N_cell_param of parameters required to specify the unit cell is also listed for each crystal_system, along with the meaning and order of appearance of different parameters. The value of N_cell_param, is, for example, 1 for a 1D lamellar phase, a 2D hexagonal phase or a 3D cubic phase, 3 for an orthorhombic 3D phase or 6 for a triclinic 3D phase.
Below, we discuss all possible crystal systems of 1, 2, and 3 dimensional crystals separately. Lists of the names of all possible space groups for each crystal system are given on the following page.
1D Crystal Systems
The only allowed crystal system name for a one-dimensional crystal is s “lamellar”. Only one unit cell parameter is required to specify a lamellar unit cell (i.e., N_cell_param = 1). The value of that parameter is equal to the layer spacing.
2D Crystal Systems
For two dimensional crystals (dim=2), let the parameters a and b denote the lengths of two independent Bravais lattice basis vectors. For oblique crystals, gamma denotes the angle between these two basis vectors, in radians.
| systems | N_cell_param | cell_param |
|---|---|---|
| square | 1 | a |
| hexagonal | 1 | a |
| rectangular | 2 | a, b |
| oblique | 3 | a, b, gamma |
3D Crystal Systems
For three dimensional crystals (dim=3), the parameters a, b, and c are the lengths of the three Bravais lattice vectors, alpha is the angle between b and c, beta is the angle between c and a, and gamma is the angle between a and b.
| 3D systems | N_cell_param | cell_param |
|---|---|---|
| cubic | 1 | a |
| tetragonal | 2 | a, c |
| orthorhombic | 3 | a, b, c |
| monoclinic | 4 | a, b, c, beta |
| hexagonal | 2 | a, c |
| trigonal | 2 | a, alpha |
| triclinic | 6 | a, b, c alpha, beta, gamma |