_/_/_/ _/_/_/ _/_/_/_/ _/_/_/ _/ _/ _/_/_/_/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/_/_/ _/ _/_/_/ _/_/_/_/ _/ _/ _/ _/ _/_/_/_/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/_/_/ _/_/_/ _/ _/ _/_/_/ _/_/_/ _/ =========================================================================== | | | -------------------------------------- | | SGROUP version 3.0.06 22 Sep. 2009 | | -------------------------------------- | | | | A program to perform symmetry analysis and identify the 1/2/3D group. | | | =========================================================================== ------------------------ Keywords Read from Input ------------------------- $lattice group Dimension of the system : IDIMN = 2 I.T. number of the system : ITNO = 0 Centring mode : CENTRING = P Lattice parameters : AA = 2.97692000 : BB = 2.97692000 : CC = 297.69200000 : ALPHA(Deg.) = 90.00000000 : BETA(Deg.) = 90.00000000 : GAMMA(Deg.) = 90.00000000 Whether use Bohr unit for distances : IFBOHR = T Whether use fractional coordinates : IFFRAC = T Threshold : IZERO = 4 Print level : LPRINT = -1 Whether use the primitive cell : IFPRIM = F --------------------------------------------------------------------------- (full output) ************************************************************************** * NOTE : all coordinates and operations are given in CONVENTIONAL basis! * ************************************************************************** Parameters of cell: a b 2.97692000 2.97692000 (in Bohr) 1.57531821 1.57531821 (in Angstrom) gamma 90.00000000 (in degree) Real Space Lattice Vector Components (Bohr) Length ----------------------------------------------------------- ------ X Y Z 1) 2.97692000 0.00000000 0.00000000 2.9769 2) 0.00000000 2.97692000 0.00000000 2.9769 3) 0.00000000 0.00000000 297.69200000 297.6920 K-Space Lattice Vector Components (1/Bohr) Length ----------------------------------------------------------- ------ X Y Z 1) 2.11063290 0.00000000 0.00000000 2.1106 2) 0.00000000 2.11063290 0.00000000 2.1106 3) 0.00000000 0.00000000 0.02110633 0.0211 =========== Decomposition of new basis vectors over input basis =========== 1.000000 0.000000 0.000000 <--- 1 0.000000 1.000000 0.000000 <--- 2 0.000000 0.000000 1.000000 <--- 3 ============================ Wigner-Seitz Cell ============================ NOTE: in this section, unit is in a.u. (Real Space) --------------------------------------------------------------------------- Number of coplanar vertices: 4 Edge No. 1) ( -1.4885, -1.4885, 0.0000) ( 1.4885, -1.4885, 0.0000) Direction (X-Y-Z): ( 0.0000, -1.0000, 0.0000) * 1.4885 Edge No. 2) ( 1.4885, -1.4885, 0.0000) ( 1.4885, 1.4885, 0.0000) Direction (X-Y-Z): ( 1.0000, 0.0000, 0.0000) * 1.4885 Edge No. 3) ( 1.4885, 1.4885, 0.0000) ( -1.4885, 1.4885, 0.0000) Direction (X-Y-Z): ( 0.0000, 1.0000, 0.0000) * 1.4885 Edge No. 4) ( -1.4885, 1.4885, 0.0000) ( -1.4885, -1.4885, 0.0000) Direction (X-Y-Z): ( -1.0000, 0.0000, 0.0000) * 1.4885 --------------------------------------------------------------------------- Total number of planes: 1 (K-Space) --------------------------------------------------------------------------- Number of coplanar vertices: 4 Edge No. 1) ( -1.0553, -1.0553, 0.0000) ( 1.0553, -1.0553, 0.0000) Direction (X-Y-Z): ( 0.0000, -1.0000, 0.0000) * 1.0553 Edge No. 2) ( 1.0553, -1.0553, 0.0000) ( 1.0553, 1.0553, 0.0000) Direction (X-Y-Z): ( 1.0000, 0.0000, 0.0000) * 1.0553 Edge No. 3) ( 1.0553, 1.0553, 0.0000) ( -1.0553, 1.0553, 0.0000) Direction (X-Y-Z): ( 0.0000, 1.0000, 0.0000) * 1.0553 Edge No. 4) ( -1.0553, 1.0553, 0.0000) ( -1.0553, -1.0553, 0.0000) Direction (X-Y-Z): ( -1.0000, 0.0000, 0.0000) * 1.0553 --------------------------------------------------------------------------- Total number of planes: 1 ======================= Wigner-Seitz Cell generated ======================= No. of atoms in the cell: 6 Positions in the conventional cell: (a and b directions in Fractionary Units, and Z in Bohr) Atom Charge [a] [b] Z --------------------------------------------------------------------------- O 8 0.00000000 0.00000000 1.15000000 O 8 0.50000000 0.50000000 -2.36000000 O 8 0.50000000 0.50000000 -4.46500000 C 6 0.00000000 0.00000000 0.00000000 Mg 12 0.00000000 0.00000000 -4.46500000 Mg 12 0.00000000 0.00000000 -2.36000000 (X, Y, and Z in Bohr) Atom Charge X Y Z --------------------------------------------------------------------------- O 8 0.00000000 0.00000000 1.15000000 O 8 1.48846000 1.48846000 -2.36000000 O 8 1.48846000 1.48846000 -4.46500000 C 6 0.00000000 0.00000000 0.00000000 Mg 12 0.00000000 0.00000000 -4.46500000 Mg 12 0.00000000 0.00000000 -2.36000000 (X, Y, and Z in Angstrom) Atom Charge X Y Z --------------------------------------------------------------------------- O 8 0.00000000 0.00000000 0.60855379 O 8 0.78765911 0.78765911 -1.24885821 O 8 0.78765911 0.78765911 -2.36277624 C 6 0.00000000 0.00000000 0.00000000 Mg 12 0.00000000 0.00000000 -2.36277624 Mg 12 0.00000000 0.00000000 -1.24885821 Positions in the Wigner-Seitz cell: (X, Y, and Z in Bohr) Atom Charge X Y Z --------------------------------------------------------------------------- O 8 0.00000000 0.00000000 1.15000000 O 8 1.48846000 1.48846000 -2.36000000 O 8 1.48846000 1.48846000 -4.46500000 C 6 0.00000000 0.00000000 0.00000000 Mg 12 0.00000000 0.00000000 -4.46500000 Mg 12 0.00000000 0.00000000 -2.36000000 Number of nonequivalent sorts: 6 ============= Nonequivalent atoms, point group for each sort ============== Sort number: 1 Names of point group: 4mm 4mm C4v New basis vectors for this point group: 1.000000 0.000000 0.000000 <--- 1 0.000000 1.000000 0.000000 <--- 2 0.000000 0.000000 1.000000 <--- 3 Atom positions ([a], [b] in frac., and Z in Bohr): 1 O ( 1 ) 8 0.00000000 0.00000000 1.15000000 Sort number: 2 Names of point group: 4mm 4mm C4v New basis vectors for this point group: 1.000000 0.000000 0.000000 <--- 1 0.000000 1.000000 0.000000 <--- 2 0.000000 0.000000 1.000000 <--- 3 Atom positions ([a], [b] in frac., and Z in Bohr): 1 O ( 2 ) 8 0.50000000 0.50000000 -2.36000000 Sort number: 3 Names of point group: 4mm 4mm C4v New basis vectors for this point group: 1.000000 0.000000 0.000000 <--- 1 0.000000 1.000000 0.000000 <--- 2 0.000000 0.000000 1.000000 <--- 3 Atom positions ([a], [b] in frac., and Z in Bohr): 1 O ( 3 ) 8 0.50000000 0.50000000 -4.46500000 Sort number: 4 Names of point group: 4mm 4mm C4v New basis vectors for this point group: 1.000000 0.000000 0.000000 <--- 1 0.000000 1.000000 0.000000 <--- 2 0.000000 0.000000 1.000000 <--- 3 Atom positions ([a], [b] in frac., and Z in Bohr): 1 C 6 0.00000000 0.00000000 0.00000000 Sort number: 5 Names of point group: 4mm 4mm C4v New basis vectors for this point group: 1.000000 0.000000 0.000000 <--- 1 0.000000 1.000000 0.000000 <--- 2 0.000000 0.000000 1.000000 <--- 3 Atom positions ([a], [b] in frac., and Z in Bohr): 1 Mg ( 1 ) 12 0.00000000 0.00000000 -4.46500000 Sort number: 6 Names of point group: 4mm 4mm C4v New basis vectors for this point group: 1.000000 0.000000 0.000000 <--- 1 0.000000 1.000000 0.000000 <--- 2 0.000000 0.000000 1.000000 <--- 3 Atom positions ([a], [b] in frac., and Z in Bohr): 1 Mg ( 2 ) 12 0.00000000 0.00000000 -2.36000000 *************************************************************************** Number of symmetry operations in real space: 8 --------------------------------------------------------------------------- No. Symbol Matrix Transl. Euler Ang. Axis Determ. --------------------------------------------------------------------------- 1) E 1.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 2) C2z -1.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 180.0 1.0 3) C+4z 0.0 -1.0 0.0 0.0 0.0 0.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 90.0 1.0 4) C-4z 0.0 1.0 0.0 0.0 0.0 0.0 1.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 270.0 1.0 5) sy 1.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 -1.0 0.0 0.0 180.0 1.0 0.0 0.0 1.0 0.0 0.0 0.0 6) sx -1.0 0.0 0.0 0.0 0.0 1.0 -1.0 0.0 1.0 0.0 0.0 180.0 0.0 0.0 0.0 1.0 0.0 180.0 0.0 7) sda 0.0 -1.0 0.0 0.0 0.0 1.0 -1.0 -1.0 0.0 0.0 0.0 180.0 1.0 0.0 0.0 1.0 0.0 90.0 0.0 8) sdb 0.0 1.0 0.0 0.0 0.0 1.0 -1.0 1.0 0.0 0.0 0.0 180.0 -1.0 0.0 0.0 1.0 0.0 270.0 0.0 *************************************************************************** Number of symmetry operations in k-space: 8 >>>>>>>>>>>> NOTE: the highest point group (C4v) of BZ is used <<<<<<<<<<<< --------------------------------------------------------------------------- No. Symbol Matrix Euler Ang. Axis Determ. --------------------------------------------------------------------------- 1) E 1.0 0.0 0.0 0.0 0.0 1.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 2) C2z -1.0 0.0 0.0 0.0 0.0 1.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 1.0 180.0 1.0 3) C+4z 0.0 -1.0 0.0 0.0 0.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 90.0 1.0 4) C-4z 0.0 1.0 0.0 0.0 0.0 1.0 -1.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 270.0 1.0 5) sx -1.0 0.0 0.0 0.0 1.0 -1.0 0.0 1.0 0.0 180.0 0.0 0.0 0.0 1.0 180.0 0.0 6) sy 1.0 0.0 0.0 0.0 0.0 -1.0 0.0 -1.0 0.0 180.0 1.0 0.0 0.0 1.0 0.0 0.0 7) sdb 0.0 1.0 0.0 0.0 1.0 -1.0 1.0 0.0 0.0 180.0 -1.0 0.0 0.0 1.0 270.0 0.0 8) sda 0.0 -1.0 0.0 0.0 1.0 -1.0 -1.0 0.0 0.0 180.0 1.0 0.0 0.0 1.0 90.0 0.0 *************************************************************************** ==================== Irreducible Brillouin Zone (IBZ) ===================== Coplanar vertices: =========================================================================== No. Carthesian Coordinates (a.u.) Fractionary Coordinates --------------------------------------------------------------------------- [x] [y] [z] [b1*] [b2*] [b3*] 1) 1.05532 0.00000 0.00000 0.50000 0.00000 0.00000 2) 1.05532 1.05532 0.00000 0.50000 0.50000 0.00000 3) 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 --------------------------------------------------------------------------- Edges: =========================================================================== Edge No. 1) 2 vertices: -- 1 -- 2 -- Direction (X-Y-Z): ( 1.0000, 0.0000, 0.0000) * 1.0553 Edge No. 2) 2 vertices: -- 2 -- 3 -- Direction (X-Y-Z): ( -0.7071, 0.7071, 0.0000) * 0.0000 Edge No. 3) 2 vertices: -- 3 -- 1 -- Direction (X-Y-Z): ( 0.0000, -1.0000, 0.0000) * 0.0000 --------------------------------------------------------------------------- High-Symmetry K-Points and Their Equivalent Sites (in Frac. Coordinates) =========================================================================== No. 1, Gamma ( 0 0 0) No. 2, M ( 1/2 1/2 0) ( -1/2 -1/2 0) ( 1/2 -1/2 0) ( -1/2 1/2 0) No. 3, X ( 0 1/2 0) ( 0 -1/2 0) ( 1/2 0 0) ( -1/2 0 0) --------------------------------------------------------------------------- =========================================================================== Number of neighbour lattice points in real space: 8 --------------------------------------------------------------------------- Carthesian Coordinates (a.u.): ( -2.9769, -2.9769, 0.0000) ( -2.9769, 0.0000, 0.0000) ( -2.9769, 2.9769, 0.0000) ( 0.0000, -2.9769, 0.0000) ( 0.0000, 2.9769, 0.0000) ( 2.9769, -2.9769, 0.0000) ( 2.9769, 0.0000, 0.0000) ( 2.9769, 2.9769, 0.0000) --------------------------------------------------------------------------- Note that shift vectors for this space group are defined only up to the vector ( 0, 0, Z ). Here Z can take any value. Number of possible shift vectors: 2 List of shift vectors: 0.0000 0.0000 0.0000 0.5000 0.5000 0.0000 List of shifted cells: Shifted Cell #1 Shift vector: 0.5000 0.5000 0.0000 Nonequivalent atoms ([a], [b] in frac., and Z in Bohr): O ( 1 ) 8 0.50000000 0.50000000 1.15000000 O ( 2 ) 8 0.00000000 0.00000000 -2.36000000 O ( 3 ) 8 0.00000000 0.00000000 -4.46500000 C 6 0.50000000 0.50000000 0.00000000 Mg ( 1 ) 12 0.50000000 0.50000000 -4.46500000 Mg ( 2 ) 12 0.50000000 0.50000000 -2.36000000 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SYMMETRY ANALYSIS IS FINISHIED ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ **************************** Slab Calculation *************************** * * * Crystal Family : Tetragonal * * Bravais Lattice : Square * * The Layer Group Number : 55 * * Corresponding Space Group No. : 99 * * * * Shoenflies Hermann-Mauguin * * symbol symbol * * __ _ * * | 1 |_| * * |_/ 4v | 4 m m * * * *************************************************************************** References: [1] T. Hahn, International Tables for Crystallography, Volume A: Space- Group Symmetry, 5th ed., Kluwer Academic Publishers, London, 2002. [2] V. Kopsky and D.B. Litvin, International Tables for Crystallography, Volume E: Subperiodic Groups, Kluwer Academic Publishers, London, 2002. [3] B. Z. Yanchitsky and A. N. Timoshevskii, Determination of the Space Group and Unit Cell for a Periodic Solid, Comput. Phys. Commun., 139(2), 235-242, 2001. [4] C. J. Bradley and A. P. Cracknell, The Mathematical Theory of Symmetry in Solids; Representation Theory for Point Groups and Space Groups, Clarendon Press, Oxford, 1972. Time: Mon Nov 09 16:13:06 2009 (Test run finished.) ===========================================================================