# Get fractional coordinates from special Wyckoff positions

I'm trying to get the fractional coordinates for Mo and S, for MoS$$_2$$-2H, where 2H means the phase. MoS$$_2$$-2H is a bilayer, in which each layer is separated from each other by Van der Waals forces. The MoS$$_2$$-2H belongs to the space group 194 and is hexagonal.

As in the unit cell are the two layers of MoS$$_2$$, I believe that to find the fractional coordinates of each element, I need Mo to be in a Wyckoff position with multiplicity 2 and the S to be in a Wyckoff position with multiplicity 4. The problem is that there are several positions with this type of multiplicity (2a, 2b, 2c and 2d for Mo and 4e and 4f for S), but the crystal tends to acquire the most stable Wyckoff positions. How can I know which Wyckoff positions for Mo and S make the crystal stable?

I just found a book on the Internet (page, book) that says it is necessary to calculate the bond length for each of the combinations. Once the bond length is calculated, how do I know which combination for Mo and S is most stable?

(Images taken from International Tables of Crystallography pages 600 and 601)

From that reference, what we got is the bond length from the atomic positions.

One easy way is to look for a CIF file with the crystal information.

From the CIF49801 bellow, we get the following info:

(label type_symbol symmetry_multiplicity Wyckoff_symbol fract_x fract_y fract_z B_iso_or_equiv occupancy)

    Mo1 Mo4+ 2 c 0.3333 0.6667 0.25     . 1.
S1  S2-  4 f 0.3333 0.6667 0.621(3) . 1.


Whereas from the CIF84180, we get the following info:

    Mo1 Mo4+ 2 d 0.6667 0.3333 0.25     . 1.
S1  S2-  4 f 0.3333 0.6667 0.120(1) . 1.


The full CIFs were obtained from the ICSD - Inorganic Crystal Structure Database.

CIF49801:

#(C) 2020 by FIZ Karlsruhe - Leibniz Institute for Information Infrastructure.  All rights reserved.
data_49801-ICSD
_database_code_ICSD 49801
_audit_creation_date 1987-01-31
_audit_update_record 2015-02-01
_chemical_name_common 'Molybdenum disulfide'
_chemical_formula_structural 'Mo S2'
_chemical_formula_sum 'Mo1 S2'
_chemical_name_structure_type MoS2(4H)
_chemical_name_mineral ''Molybdenite 2H''
_exptl_crystal_density_diffrn 5.
_citation_title 'On the Structure of Molybdenum Diselenide and Disulfide'
loop_
_citation_id
_citation_journal_full
_citation_year
_citation_journal_volume
_citation_page_first
_citation_page_last
_citation_journal_id_ASTM
primary 'Zeitschrift fuer Anorganische und Allgemeine Chemie (1950) (DE)' 1986
540 15 17 ZAACAB
loop_
_citation_author_citation_id
_citation_author_name
primary 'Bronsema, K.D.'
primary 'de Boer, J.L.'
primary 'Jellinek, F.'
_cell_length_a 3.16021
_cell_length_b 3.16021
_cell_length_c 12.294(4)
_cell_angle_alpha 90.
_cell_angle_beta 90.
_cell_angle_gamma 120.
_cell_volume 106.33
_cell_formula_units_Z 2
_space_group_name_H-M_alt 'P 63/m m c'
_space_group_IT_number 194
loop_
_space_group_symop_id
_space_group_symop_operation_xyz
1 'x, x-y, -z+1/2'
2 '-x+y, y, -z+1/2'
3 '-y, -x, -z+1/2'
4 '-x+y, -x, -z+1/2'
5 '-y, x-y, -z+1/2'
6 'x, y, -z+1/2'
7 '-x, -x+y, z+1/2'
8 'x-y, -y, z+1/2'
9 'y, x, z+1/2'
10 'x-y, x, z+1/2'
11 'y, -x+y, z+1/2'
12 '-x, -y, z+1/2'
13 '-x, -x+y, -z'
14 'x-y, -y, -z'
15 'y, x, -z'
16 'x-y, x, -z'
17 'y, -x+y, -z'
18 '-x, -y, -z'
19 'x, x-y, z'
20 '-x+y, y, z'
21 '-y, -x, z'
22 '-x+y, -x, z'
23 '-y, x-y, z'
24 'x, y, z'
loop_
_atom_type_symbol
_atom_type_oxidation_number
Mo4+ 4
S2- -2
loop_
_atom_site_label
_atom_site_type_symbol
_atom_site_symmetry_multiplicity
_atom_site_Wyckoff_symbol
_atom_site_fract_x
_atom_site_fract_y
_atom_site_fract_z
_atom_site_B_iso_or_equiv
_atom_site_occupancy
Mo1 Mo4+ 2 c 0.3333 0.6667 0.25 . 1.
S1 S2- 4 f 0.3333 0.6667 0.621(3) . 1.
#End of TTdata_49801-ICSD


and

CIF84180:

#(C) 2020 by FIZ Karlsruhe - Leibniz Institute for Information Infrastructure.  All rights reserved.
data_84180-ICSD
_database_code_ICSD 84180
_audit_creation_date 1999-01-19
_audit_update_record 2013-02-01
_chemical_name_common 'Molybdenum(IV) sulfide - 2H'
_chemical_formula_structural 'Mo S2'
_chemical_formula_sum 'Mo1 S2'
_chemical_name_structure_type MoS2(4H)
_chemical_name_mineral ''Molybdenite 2H''
_exptl_crystal_density_diffrn 5.
_citation_title

;
Characteristics of the crystal structure, electrophysical properties, and
model of the valence band spectrum of laminar compounds of molybdenum
disulfide type
;
loop_
_citation_id
_citation_journal_full
_citation_year
_citation_journal_volume
_citation_page_first
_citation_page_last
_citation_journal_id_ASTM
primary 'Izvestiya Akademii Nauk SSSR, Neorganicheskie Materialy' 1983 19 1060
1065 IVNMAW
loop_
_citation_author_citation_id
_citation_author_name
primary 'Kalikhman, V.L.'
_cell_length_a 3.16
_cell_length_b 3.16
_cell_length_c 12.29
_cell_angle_alpha 90.
_cell_angle_beta 90.
_cell_angle_gamma 120.
_cell_volume 106.28
_cell_formula_units_Z 2
_space_group_name_H-M_alt 'P 63/m m c'
_space_group_IT_number 194
loop_
_space_group_symop_id
_space_group_symop_operation_xyz
1 'x, x-y, -z+1/2'
2 '-x+y, y, -z+1/2'
3 '-y, -x, -z+1/2'
4 '-x+y, -x, -z+1/2'
5 '-y, x-y, -z+1/2'
6 'x, y, -z+1/2'
7 '-x, -x+y, z+1/2'
8 'x-y, -y, z+1/2'
9 'y, x, z+1/2'
10 'x-y, x, z+1/2'
11 'y, -x+y, z+1/2'
12 '-x, -y, z+1/2'
13 '-x, -x+y, -z'
14 'x-y, -y, -z'
15 'y, x, -z'
16 'x-y, x, -z'
17 'y, -x+y, -z'
18 '-x, -y, -z'
19 'x, x-y, z'
20 '-x+y, y, z'
21 '-y, -x, z'
22 '-x+y, -x, z'
23 '-y, x-y, z'
24 'x, y, z'
loop_
_atom_type_symbol
_atom_type_oxidation_number
Mo4+ 4
S2- -2
loop_
_atom_site_label
_atom_site_type_symbol
_atom_site_symmetry_multiplicity
_atom_site_Wyckoff_symbol
_atom_site_fract_x
_atom_site_fract_y
_atom_site_fract_z
_atom_site_B_iso_or_equiv
_atom_site_occupancy
Mo1 Mo4+ 2 d 0.6667 0.3333 0.25 . 1.
S1 S2- 4 f 0.3333 0.6667 0.120(1) . 1.
#End of TTdata_84180-ICSD

• For the uninitiated, is there a good graphical tool for viewing these CIF files? – taciteloquence Jul 28 '20 at 7:17
• If you are on linux it is very easy to install ASE using pip, then "ase-gui file.cif" will show it. On windows I find the GUI does not always install correctly. – Tristan Maxson Jul 28 '20 at 19:46