Contents

\textrm{Sr}_{2}\textrm{ScSbO}_{6}, RT

\(\textrm{Sr}_{2}\textrm{ScSbO}_{6}\), RT



Target

  1. Perform previous calculations, as needed

  2. Obtain the control file, .pcr, and understand it


Steps

  1. Take the structure from the paper

  2. Take the Sb to the origin

  3. Convert non-standard to standard

  4. AMPLIMODES needs the Transformation Matrix (TM)

  5. AMPLIMODES with non-standard: Transformation Matrix

  6. AMPLIMODES with standard: Transformation Matrix

  7. AMPLIMODES for FullProf with non-standard/standard

  8. Comparison of the control file (.pcr/.new) between co-ordinates and modes

  9. Comments



Take the structure from the paper



# P 1 21/n 1
014
5.6915 5.6778 8.0244 90.000000 90.03 90.000000
6
Sb	1	-	0.000000	0.500000	0.000000
Sc	1	-	0.500000	0.000000	0.000000
Sr	1	-	0.002100	0.009900	0.248700
O	1	-	0.261500	0.268000	0.028000
O	2	-	0.274000	0.262000	0.477000
O	3	-	0.949300	0.494400	0.245600


Take the Sb to the origin



  1. Copy structure

  2. Use EQUIVSTRU

Result

# P 1 21/n 1
014
5.6915 5.6778 8.0244 90.00 90.03 90.00
6
Sb	1	-	0.000000	 0.000000	0.000000
Sc	1	-	0.500000	-0.500000	0.000000
Sr	1	-	0.002100	-0.490100	0.248700
O	1	-	0.261500	-0.232000	0.028000
O	2	-	0.274000	-0.238000	0.477000
O	3	-	0.949300	-0.005600	0.245600


Convert non-standard to standard



  1. Copy structure

  2. Use SETSTRU

Result

# P 1 21/c 1
014
8.0244 5.6778 9.8355 90.00 144.64 90.00
6
Sb	1	2a	 0.000000	 0.000000	 0.000000
Sc	1	2b	-0.500000	-0.500000	-0.500000
Sr	1	4e	 0.246600	-0.490100	-0.002100
O	1	4e	-0.233500	-0.232000	-0.261500
O	2	4e	 0.203000	-0.238000	-0.274000
O	3	4e	-0.703700	-0.005600	-0.949300


AMPLIMODES needs the Transformation Matrix {TM}



Parent Phase

# F m -3 m
225
8.087481 8.087481 8.087481 90.00000 90.00000 90.00000
4
Sb	1	4a	0.000000	0.000000	0.000000
Sc	1	4b	0.500000	0.500000	0.500000
Sr	1	8c	0.250000	0.250000	0.250000
O	11	24e	0.254100	0.000000	0.000000

At least, 3 ways to obtain the Transformation Matrix:

  1. Calculate by hand: Previous Information

  2. Use PSEUDO: be careful, only admits standard settings You can obtain it also for the non-standard setting

  3. Calculate by STRUCTURE RELATIONS It is also reachable from AMPLIMODES


1. Calculate by hand: Previous Information


2. Use PSEUDO

../_images/pseudo_path_1.png

Fig. 15 irudi-oina.


../_images/pseudo_path_2.png

Fig. 16 irudi-oina.


../_images/pseudo_path_3.png

Fig. 17 irudi-oina.


Transformation Matrix (P,p): (c,1/2a+1/2b,-1/2a+1/2b-c;0,0,0)

Transformation matrix:
[     0   1/2  -1/2 ] [      0]
[     0   1/2   1/2 ] [      0]
[     1     0    -1 ] [      0]

3. Calculate by STRUCTURE RELATIONS

Transformation Matrix (P,p): (b,1/2a-1/2c,-1/2a-b-1/2c;0,0,0)

Transformation matrix:
[     0   1/2  -1/2 ] [      0]
[     1     0    -1 ] [      0]
[     0  -1/2  -1/2 ] [      0]

You can check that both matrices give the same final result…


Result, for the non-standard

Transformation Matrix (P,p): (1/2a-1/2b,1/2a+1/2b,c;0,0,0)

Result, for the standard

Transformation Matrix (P,p): (b,1/2a-1/2c,-1/2a-b-1/2c;0,0,0)

Transformation Matrix (P,p): (c,1/2a+1/2b,-1/2a+1/2b-c;0,0,0)


AMPLIMODES with non-standard: Transformation Matrix



# F m -3 m
225
8.087481 8.087481 8.087481 90.00000 90.00000 90.00000
4
Sb	1	4a	0.000000	0.000000	0.000000
Sc	1	4b	0.500000	0.500000	0.500000
Sr	1	8c	0.250000	0.250000	0.250000
O	11	24e	0.254100	0.000000	0.000000


# P 1 21/n 1
014
8.0244 5.6778 9.8355 90.00 144.64 90.00
6
Sb	1	2a	 0.000000	 0.000000	 0.000000
Sc	1	2b	-0.500000	-0.500000	-0.500000
Sr	1	4e	 0.246600	-0.490100	-0.002100
O	1	4e	-0.233500	-0.232000	-0.261500
O	2	4e	 0.203000	-0.238000	-0.274000
O	3	4e	-0.703700	-0.005600	-0.949300


Transformation matrix:

[     0   1/2  -1/2 ] [      0]
[     1     0    -1 ] [      0]
[     0  -1/2  -1/2 ] [      0]

b,1/2a-1/2c,-1/2a-b-1/2c; 0 0 0


AMPLIMODES with standard: Transformation Matrix



# F m -3 m
225
8.087481 8.087481 8.087481 90.00000 90.00000 90.00000
4
Sb	1	4a	0.000000	0.000000	0.000000
Sc	1	4b	0.500000	0.500000	0.500000
Sr	1	8c	0.250000	0.250000	0.250000
O	11	24e	0.254100	0.000000	0.000000


# P 1 21/n 1
014
5.6915 5.6778 8.0244 90.00 90.03 90.00
6
Sb	1	-	0.000000	 0.000000	0.000000
Sc	1	-	0.500000	-0.500000	0.000000
Sr	1	-	0.002100	-0.490100	0.248700
O	1	-	0.261500	-0.232000	0.028000
O	2	-	0.274000	-0.238000	0.477000
O	3	-	0.949300	-0.005600	0.245600


Transformation matrix:

[   1/2   1/2     0 ] [      0]
[  -1/2   1/2     0 ] [      0]
[     0     0     1 ] [      0]

1/2a+1/2b,1/2a-1/2b,c; 0 0 0


AMPLIMODES for FullProf with non-standard/standard



# F m -3 m
225
8.087481 8.087481 8.087481 90.00000 90.00000 90.00000
4
Sb	1	4a	0.000000	0.000000	0.000000
Sc	1	4b	0.500000	0.500000	0.500000
Sr	1	8c	0.250000	0.250000	0.250000
O	11	24e	0.254100	0.000000	0.000000


# P 1 21/n 1
014
5.6915 5.6778 8.0244 90.00 90.03 90.00
6
Sb	1	-	0.000000	 0.000000	0.000000
Sc	1	-	0.500000	-0.500000	0.000000
Sr	1	-	0.002100	-0.490100	0.248700
O	1	-	0.261500	-0.232000	0.028000
O	2	-	0.274000	-0.238000	0.477000
O	3	-	0.949300	-0.005600	0.245600


Transformation matrix:

[   1/2   1/2     0 ] [      0]
[  -1/2   1/2     0 ] [      0]
[     0     0     1 ] [      0]

1/2a-1/2b,1/2a+1/2b,c; 0 0 0


Comparison of the control file (.pcr/.new) between co-ordinates and modes



!Nat Dis Ang Pr1 Pr2 Pr3 Jbt Irf Isy Str Furth       ATZ    Nvk Npr More
   6   0   0 1.0 0.0 0.0   0   0   0   0   0        875.885   0   7   1
!
!Jvi Jdi Hel Sol Mom Ter  Brind   RMua    RMub    RMuc   Jtyp  Nsp_Ref Ph_Shift N_Domains
   0   3   0   0   0   0  1.0000  0.0000  0.0000  0.0000    1      0      0      0
!
! Max_dst(dist) (angles)  Bond-Valence Calc.
      3.2000      3.2000        BVS
!  N_cations   N_anions     Tolerance(%) / Name or cations/ and Anions
       3           1                0.00
SR+2 SC+3 SB+5
O-2
!
!
P 1 21/N 1               <--Space group symbol
!Atom   Typ       X        Y        Z     Biso       Occ     In Fin N_t Spc /Codes
Sb     SB      0.00000  0.50000  0.00000  0.14020   0.50000   0   0   0    1  
                  0.00     0.00     0.00   271.00      0.00
Sc     SC      0.50000  0.00000  0.00000  0.14020   0.50000   0   0   0    2  
                  0.00     0.00     0.00   271.00      0.00
Sr     SR      0.00023  0.00977  0.25025  0.32583   1.00000   0   0   0    3  
                131.00   141.00   151.00   261.00      0.00
O1     O       0.25933  0.27162  0.02536  0.49182   1.00000   0   0   0    4  
                161.00   171.00   181.00   251.00      0.00
O2     O       0.27538  0.26338  0.47468  0.49182   1.00000   0   0   0    4  
                191.00   201.00   211.00   251.00      0.00
O3     O       0.94813  0.49532  0.24404  0.49182   1.00000   0   0   0    4  
                221.00   231.00   241.00   251.00      0.00


!Nat Dis Ang Pr1 Pr2 Pr3 Jbt Irf Isy Str Furth       ATZ    Nvk Npr More
   6   0   0 1.0 0.0 0.0   6   0   0   0  12        875.885   0   7   1
!
!Jvi Jdi Hel Sol Mom Ter  Brind   RMua    RMub    RMuc   Jtyp  Nsp_Ref Ph_Shift N_Domains
   0   3   0   0   0   0  1.0000  0.0000  0.0000  0.0000    1      0      0      0
!
! Max_dst(dist) (angles)  Bond-Valence Calc.
      3.2000      3.2000        BVS
!  N_cations   N_anions     Tolerance(%) / Name or cations/ and Anions
       3           1                0.00
SR+2 SC+3 SB+5
O-2
!
!
P 1 21/n 1               <--Space group symbol
!Atom   Typ       X         Y         Z     Biso      Occ     In Fin N_t Spc /Codes
Sb1    SB      0.000000  0.000000  0.000000 0.500000 0.500000  0   0   0    1
                   0.00      0.00      0.00     0.00     0.00
Sc1    SC      0.500000  0.000000  0.000000 0.500000 0.500000  0   0   0    1
                   0.00      0.00      0.00     0.00     0.00
Sr1    SR      0.750000  0.000000  0.500000 0.500000 1.000000  0   0   0    1
                   0.00      0.00      0.00     0.00     0.00
O11    O       0.745900  0.254100  0.745900 0.500000 1.000000  0   0   0    1
                   0.00      0.00      0.00     0.00     0.00
O11_2  O       0.254100  0.500000  0.500000 0.500000 1.000000  0   0   0    1
                   0.00      0.00      0.00     0.00     0.00
O11_3  O       0.745900  0.754100  0.245900 0.500000 1.000000  0   0   0    1
                   0.00      0.00      0.00     0.00     0.00
! Polarisation Vectors of Symmetry Modes for each atom
V_MODES   30
! Nm Atm     Irrep      Vx        Vy        Vz         Coeff
  1 O11    GM1+   -0.035694  0.035694 -0.035694 1.00
  1 O11_2  GM1+    0.035694  0.000000  0.000000 1.00
  1 O11_3  GM1+   -0.035694  0.035694 -0.035694 1.00
  2 O11    GM3+   -0.025240  0.025240 -0.025240 1.00
  2 O11_2  GM3+   -0.050479  0.000000  0.000000 1.00
  2 O11_3  GM3+   -0.025240  0.025240 -0.025240 1.00
  3 O11    GM4+   -0.030912  0.000000  0.000000 1.00
  3 O11_2  GM4+   -0.061824  0.000000 -0.061824 1.00
  3 O11_3  GM4+   -0.030912  0.000000  0.000000 1.00
  4 Sr1    GM5+    0.061824  0.000000  0.000000 1.00
  5 Sr1    GM5+   -0.087432  0.000000 -0.087432 1.00
  6 O11    GM5+    0.030912  0.000000  0.000000 1.00
  6 O11_2  GM5+   -0.061824  0.000000 -0.061824 1.00
  6 O11_3  GM5+    0.030912  0.000000  0.000000 1.00
  7 O11    GM5+   -0.043716 -0.043716 -0.043716 1.00
  7 O11_2  GM5+    0.000000  0.000000  0.000000 1.00
  7 O11_3  GM5+   -0.043716 -0.043716 -0.043716 1.00
  8 O11    X2+    -0.043716  0.043716 -0.043716 1.00
  8 O11_2  X2+     0.000000  0.000000  0.000000 1.00
  8 O11_3  X2+     0.043716 -0.043716  0.043716 1.00
  9 O11    X3+     0.043716  0.043716  0.043716 1.00
  9 O11_2  X3+     0.000000  0.000000  0.000000 1.00
  9 O11_3  X3+    -0.043716 -0.043716 -0.043716 1.00
 10 Sr1    X5+     0.000000 -0.087432  0.000000 1.00
 11 O11    X5+    -0.043716  0.000000  0.000000 1.00
 11 O11_2  X5+     0.000000  0.000000  0.000000 1.00
 11 O11_3  X5+     0.043716  0.000000  0.000000 1.00
 12 O11    X5+     0.000000  0.000000  0.000000 1.00
 12 O11_2  X5+     0.000000  0.087432  0.000000 1.00
 12 O11_3  X5+     0.000000  0.000000  0.000000 1.00
!Amplitudes of Symmetry Modes
A_MODES    12   2
Max_Amplitude   2.0
    A1_GM1+   -0.242338     1.00
    A2_GM3+   -0.002972     1.00
    A3_GM4+   -0.822497     1.00
    A4_GM5+    0.021028     1.00
    A5_GM5+   -0.024019     1.00
    A6_GM5+    0.002426     1.00
    A7_GM5+   -0.037172     1.00
    A8_X2+    -0.031453     1.00
    A9_X3+     0.374577     1.00
    A10_X5+   -0.113230     1.00
    A11_X5+    0.057188     1.00
    A12_X5+    0.064050     1.00


Comments



  1. \(\#\) degrees of freedom

  2. The structure is fixed: you refine the amplitude values The structure is the parent phase Result form AMPLIMODES:

    Transformed high symmetry structure in the subgroup basis Reference Structure

    Symmetry mode analysis

High symmetry structure

225
8.087481 8.087481 8.087481 90.00000 90.00000 90.00000
4
Sb	1	4a	0.000000	0.000000	0.000000
Sc	1	4b	0.500000	0.500000	0.500000
Sr	1	8c	0.250000	0.250000	0.250000
O	11	24e	0.254100	0.000000	0.000000

Transformation matrix

[     0   1/2  -1/2 ] [      0]
[     1     0    -1 ] [      0]
[     0  -1/2  -1/2 ] [      0]

Transformed high symmetry structure in the subgroup basis   
Reference Structure

014
8.087481 5.718712 9.905101 90.000000 144.735611 90.000000
6
Sb	1	2a	0.000000	0.000000	0.000000
Sc	1	2b	0.500000	0.000000	0.000000
Sr	1	4e	0.750000	0.000000	0.500000
O	11	4e	0.745900	0.254100	0.745900
O	11_2	4e	0.254100	0.500000	0.500000
O	11_3	4e	0.745900	0.754100	0.245900

    From AMPLIMODES for FullProf:


    P 1 21/n 1               <--Space group symbol
!Atom   Typ       X         Y         Z     Biso      Occ     In Fin N_t Spc /Codes
Sb1    SB      0.000000  0.000000  0.000000 0.500000 0.500000  0   0   0    1
                   0.00      0.00      0.00     0.00     0.00
Sc1    SC      0.500000  0.000000  0.000000 0.500000 0.500000  0   0   0    1
                   0.00      0.00      0.00     0.00     0.00
Sr1    SR      0.750000  0.000000  0.500000 0.500000 1.000000  0   0   0    1
                   0.00      0.00      0.00     0.00     0.00
O11    O       0.745900  0.254100  0.745900 0.500000 1.000000  0   0   0    1
                   0.00      0.00      0.00     0.00     0.00
O11_2  O       0.254100  0.500000  0.500000 0.500000 1.000000  0   0   0    1
                   0.00      0.00      0.00     0.00     0.00
O11_3  O       0.745900  0.754100  0.245900 0.500000 1.000000  0   0   0    1
                   0.00      0.00      0.00     0.00     0.00

  3. Differences:

    1. Jbt=6 \(\quad\) Furth=12 (depending on the case!)

    2. vector polarization list: you could generate it by hand you have to go to the Detailed Information, and further…

Results from AMPLIMODES

Symmetry mode analysis

High symmetry structure

Setting used: FM-3M
Transformation Matrix: a,b,c 
225
8.087481 8.087481 8.087481 90.00000 90.00000 90.00000
4
Sb	1	4a	0.000000	0.000000	0.000000
Sc	1	4b	0.500000	0.500000	0.500000
Sr	1	8c	0.250000	0.250000	0.250000
O	1	24e	0.254100	0.000000	0.000000

Low symmetry structure

Setting used: P 1 21/n 1
Transformation Matrix: c,b,-a-c 
014
5.6915 5.6778 8.0244 90.00 90.03 90.00
6
Sb	1	-	0.000000	0.000000	0.000000
Sc	1	-	0.500000	-0.500000	0.000000
Sr	1	-	0.002100	-0.490100	0.248700
O	1	-	0.261500	-0.232000	0.028000
O	2	-	0.274000	-0.238000	0.477000
O	3	-	0.949300	-0.005600	0.245600

Transformation matrix

[   1/2   1/2     0 ] [      0]
[  -1/2   1/2     0 ] [      0]
[     0     0     1 ] [      0]

Transformed high symmetry structure in the subgroup basis

Reference Structure
014
8.087500 5.718726 9.905124 90.000000 144.735626 90.000000
6
Sb	1	2a	0.000000	0.000000	0.000000
Sc	1	2b	0.500000	0.000000	0.000000
Sr	1	4e	0.250000	0.500000	0.000000
O	1	4e	0.745900	0.254100	0.745900
O	1_2	4e	0.254100	0.500000	0.500000
O	1_3	4e	0.254100	0.254100	0.254100

Atom pairings and distances

Atom Mappings
WPAtomReference Struc.AtomLow Sym Struc.
2a(0,0,0)Sb1(0.000000,0.000000,0.000000)Sb1(0.000000,0.000000,0.000000)
2b(1/2,0,0)Sc1(0.000000,0.000000,0.500000)Sc1(0.000000,0.000000,0.500000)
4e(x,y,z)Sr1(0.000000,0.500000,0.250000)Sr1(-0.997900,0.509900,-0.751300)
4e(x,y,z)O1(-0.745900,0.254100,0.000000)O2(-0.774000,0.262000,0.023000)
4e(x,y,z)O1_2(-0.500000,0.500000,-0.245900)O3(-0.550700,0.505600,-0.254400)
4e(x,y,z)O1_3(-0.254100,0.254100,0.000000)O1(-0.261500,0.232000,-0.028000)


WPAtomAtomic Displacements
uxuyuz|u|
2a(0,0,0)Sb1 0.0000 0.0000 0.0000 0.0000
2b(1/2,0,0)Sc1 0.0000 0.0000 0.0000 0.0000
4e(x,y,z)Sr1 0.0021 0.0099 -0.0013 0.0588
4e(x,y,z)O1 -0.0281 0.0079 0.0230 0.2499
4e(x,y,z)O1_2 -0.0507 0.0056 -0.0085 0.2997
4e(x,y,z)O1_3 -0.0074 -0.0221 -0.0280 0.2628

NOTE: ux, uy and uz are given in relative units. |u| is the absolute distance given in Å
Maximum atomic displacement in the distortion, Δ: 0.2997 Å
Total distortion amplitude: 0.9482 Å

Symmetry Modes Summary

AtomsWPModes
O124e GM1+(1) GM3+(1) GM4+(1) GM5+(2) X2+(1) X3+(1) X5+(2)
Sr18c GM5+(2) X5+(1)

Summary of Amplitudes

Warning: Amplitudes are given for modes normalized within the primitive unit cell of the distorted structure. Under this normalization, mode amplitudes in distorted structures with different multiplication of their primitive unit cell are not directly comparable.

K-vectorIrrepDirectionIsotropy
Subgroup		DimensionAmplitude (Å)
(0,0,0)GM1+(a)Fm-3m (225)10.2423
(0,0,0)GM3+(a,0)I4/mmm (139)10.0030
(0,0,0)GM4+(a,a,0)C2/m (12)10.8225
(0,0,0)GM5+(-b,a,-a)C2/m (12)40.0491
(0,1,0)X2+(0,a,0)P4_2/mnm (136)10.0315
(0,1,0)X3+(0,a,0)P4/mnc (128)10.3746
(0,1,0)X5+(a,a,0,0,a,-a)Pnnm (58)30.1421

Global distortion: 0.9482 Å

Normalized basis symmetry modes

The modes are normalized to the reference structure unit cell and are given as relative displacements in this cell.

K-vector: GM = (0,0,0)

Irrep GM1+

GM1+ Mode O1 1
Atomδxδyδz
O1 0.035694 0.035694 0.000000
O1_2 0.000000 0.000000 0.035694
O1_3 -0.035694 0.035694 0.000000

Irrep GM3+

GM3+ Mode O1 1
Atomδxδyδz
O1 0.025239 0.025239 0.000000
O1_2 0.000000 0.000000-0.050479
O1_3 -0.025239 0.025239 0.000000

Irrep GM4+

GM4+ Mode O1 1
Atomδxδyδz
O1 0.000000 0.000000-0.030912
O1_2 0.061824 0.000000 0.000000
O1_3 0.000000 0.000000 0.030912

Irrep GM5+

GM5+ Mode Sr1 1
Atomδxδyδz
Sr1 0.087432 0.000000 0.000000

GM5+ Mode Sr1 2
Atomδxδyδz
Sr1 0.000000 0.000000-0.061824

GM5+ Mode O1 1
Atomδxδyδz
O1 0.043716-0.043716 0.000000
O1_2 0.000000 0.000000 0.000000
O1_3 -0.043716-0.043716 0.000000

GM5+ Mode O1 2
Atomδxδyδz
O1 0.000000 0.000000-0.030912
O1_2 -0.061824 0.000000 0.000000
O1_3 0.000000 0.000000 0.030912

K-vector: X = (0,1,0)

Irrep X2+

X2+ Mode O1 1
Atomδxδyδz
O1 -0.043716-0.043716 0.000000
O1_2 0.000000 0.000000 0.000000
O1_3 -0.043716 0.043716 0.000000

Irrep X3+

X3+ Mode O1 1
Atomδxδyδz
O1 -0.043716 0.043716 0.000000
O1_2 0.000000 0.000000 0.000000
O1_3 -0.043716-0.043716 0.000000

Irrep X5+

X5+ Mode Sr1 1
Atomδxδyδz
Sr1 0.000000 0.087432 0.000000

X5+ Mode O1 1
Atomδxδyδz
O1 0.000000 0.000000 0.000000
O1_2 0.000000-0.087432 0.000000
O1_3 0.000000 0.000000 0.000000

X5+ Mode O1 2
Atomδxδyδz
O1 0.000000 0.000000 0.043716
O1_2 0.000000 0.000000 0.000000
O1_3 0.000000 0.000000 0.043716

Hide Normalized Symmetry Modes Show Normalized Symmetry Modes

K-vector: GM = (0,0,0)

Irrep: GM1+

Direction: (a)

Isotropy Subgroup: 225 Fm-3m Oh-5

Transformation matrix: 
[     1     0     0 ] [      0]
[     0     1     0 ] [      0]
[     0     0     1 ] [      0]

The amplitude of this distortion is:
AGM1+= 0.2423 Å

There is one mode with this symmetry, and its amplitude in Ångströms is:
O1 1
-0.2423


Normalized polarization vector expressed as displacements (in cell relative units) of the atoms in the asymmetric unit of the structure:(normalization unit: 1 Ångström)
Atomδxδyδz
Sb1 0.00000.00000.0000
Sc1 0.00000.00000.0000
Sr1 0.00000.00000.0000
O1 -0.0357-0.03570.0000
O1_2 0.00000.0000-0.0357
O1_3 0.0357-0.03570.0000


with only this symmetry component of the distortion frozen.
##disp-par## Sb1x|x0.000000x|x0.000000x|x0.000000 ##disp-par## Sc1x|x0.000000x|x0.000000x|x0.000000 ##disp-par## Sr1x|x0.000000x|x0.000000x|x0.000000 ##disp-par## O1x|x-0.008650x|x-0.008650x|x0.000000 ##disp-par## O1_2x|x0.000000x|x0.000000x|x-0.008650 ##disp-par## O1_3x|x0.008650x|x-0.008650x|x0.000000”>

Irrep: GM3+

Direction: (a,0)

Isotropy Subgroup: 139 I4/mmm D4h-17

Transformation matrix: 
[   1/2  -1/2     0 ] [      0]
[   1/2   1/2     0 ] [      0]
[     0     0     1 ] [      0]

The amplitude of this distortion is:
AGM3+= 0.0030 Å

There is one mode with this symmetry, and its amplitude in Ångströms is:
O1 1
-0.0030


Normalized polarization vector expressed as displacements (in cell relative units) of the atoms in the asymmetric unit of the structure:(normalization unit: 1 Ångström)
Atomδxδyδz
Sb1 0.00000.00000.0000
Sc1 0.00000.00000.0000
Sr1 0.00000.00000.0000
O1 -0.0252-0.02520.0000
O1_2 0.00000.00000.0505
O1_3 0.0252-0.02520.0000


with only this symmetry component of the distortion frozen.
##disp-par## Sb1x|x0.000000x|x0.000000x|x0.000000 ##disp-par## Sc1x|x0.000000x|x0.000000x|x0.000000 ##disp-par## Sr1x|x0.000000x|x0.000000x|x0.000000 ##disp-par## O1x|x-0.000075x|x-0.000075x|x0.000000 ##disp-par## O1_2x|x0.000000x|x0.000000x|x0.000150 ##disp-par## O1_3x|x0.000075x|x-0.000075x|x0.000000”>

Irrep: GM4+

Direction: (a,a,0)

Isotropy Subgroup: 12 C2/m C2h-3

Transformation matrix: 
[  -1/2  -1/2   1/2 ] [      0]
[   1/2  -1/2  -1/2 ] [      0]
[     1     0     0 ] [      0]

The amplitude of this distortion is:
AGM4+= 0.8225 Å

There is one mode with this symmetry, and its amplitude in Ångströms is:
O1 1
-0.8225


Normalized polarization vector expressed as displacements (in cell relative units) of the atoms in the asymmetric unit of the structure:(normalization unit: 1 Ångström)
Atomδxδyδz
Sb1 0.00000.00000.0000
Sc1 0.00000.00000.0000
Sr1 0.00000.00000.0000
O1 0.00000.00000.0309
O1_2 -0.06180.00000.0000
O1_3 0.00000.0000-0.0309


with only this symmetry component of the distortion frozen.
##disp-par## Sb1x|x0.000000x|x0.000000x|x0.000000 ##disp-par## Sc1x|x0.000000x|x0.000000x|x0.000000 ##disp-par## Sr1x|x0.000000x|x0.000000x|x0.000000 ##disp-par## O1x|x0.000000x|x0.000000x|x0.025425 ##disp-par## O1_2x|x-0.050850x|x0.000000x|x0.000000 ##disp-par## O1_3x|x0.000000x|x0.000000x|x-0.025425”>

Irrep: GM5+

Direction: (-b,a,-a)

Isotropy Subgroup: 12 C2/m C2h-3

Transformation matrix: 
[  -1/2   1/2   1/2 ] [      0]
[   1/2   1/2  -1/2 ] [      0]
[    -1     0     0 ] [      0]

The amplitude of this distortion is:
AGM5+= 0.0491 Å

Normalized polarization vector: (in terms of the amplitudes of the (normalized) atomic symmetry modes)
Sr1 1Sr1 2O1 1O1 2
0.48960.4286-0.7577-0.0495
NOTE:A second number next to the label counts the different symmetry modes that may happen for that orbit.


Normalized polarization vector expressed as displacements (in cell relative units) of the atoms in the asymmetric unit of the structure:(normalization unit: 1 Ångström)
Atomδxδyδz
Sb1 0.00000.00000.0000
Sc1 0.00000.00000.0000
Sr1 0.04280.0000-0.0265
O1 -0.03310.03310.0015
O1_2 0.00310.00000.0000
O1_3 0.03310.0331-0.0015


with only this symmetry component of the distortion frozen.
##disp-par## Sb1x|x0.000000x|x0.000000x|x0.000000 ##disp-par## Sc1x|x0.000000x|x0.000000x|x0.000000 ##disp-par## Sr1x|x0.002100x|x0.000000x|x-0.001300 ##disp-par## O1x|x-0.001625x|x0.001625x|x0.000075 ##disp-par## O1_2x|x0.000150x|x0.000000x|x0.000000 ##disp-par## O1_3x|x0.001625x|x0.001625x|x-0.000075”>

K-vector: X = (0,1,0)

Irrep: X2+

Direction: (0,a,0)

Isotropy Subgroup: 136 P4_2/mnm D4h-14

Transformation matrix: 
[   1/2   1/2     0 ] [      0]
[  -1/2   1/2     0 ] [      0]
[     0     0     1 ] [      0]

The amplitude of this distortion is:
AX2+= 0.0315 Å

There is one mode with this symmetry, and its amplitude in Ångströms is:
O1 1
0.0315


Normalized polarization vector expressed as displacements (in cell relative units) of the atoms in the asymmetric unit of the structure:(normalization unit: 1 Ångström)
Atomδxδyδz
Sb1 0.00000.00000.0000
Sc1 0.00000.00000.0000
Sr1 0.00000.00000.0000
O1 -0.0437-0.04370.0000
O1_2 0.00000.00000.0000
O1_3 -0.04370.04370.0000


with only this symmetry component of the distortion frozen.
##disp-par## Sb1x|x0.000000x|x0.000000x|x0.000000 ##disp-par## Sc1x|x0.000000x|x0.000000x|x0.000000 ##disp-par## Sr1x|x0.000000x|x0.000000x|x0.000000 ##disp-par## O1x|x-0.001375x|x-0.001375x|x0.000000 ##disp-par## O1_2x|x0.000000x|x0.000000x|x0.000000 ##disp-par## O1_3x|x-0.001375x|x0.001375x|x0.000000”>

Irrep: X3+

Direction: (0,a,0)

Isotropy Subgroup: 128 P4/mnc D4h-6

Transformation matrix: 
[   1/2   1/2     0 ] [      0]
[  -1/2   1/2     0 ] [      0]
[     0     0     1 ] [      0]

The amplitude of this distortion is:
AX3+= 0.3746 Å

There is one mode with this symmetry, and its amplitude in Ångströms is:
O1 1
0.3746


Normalized polarization vector expressed as displacements (in cell relative units) of the atoms in the asymmetric unit of the structure:(normalization unit: 1 Ångström)
Atomδxδyδz
Sb1 0.00000.00000.0000
Sc1 0.00000.00000.0000
Sr1 0.00000.00000.0000
O1 -0.04370.04370.0000
O1_2 0.00000.00000.0000
O1_3 -0.0437-0.04370.0000


with only this symmetry component of the distortion frozen.
##disp-par## Sb1x|x0.000000x|x0.000000x|x0.000000 ##disp-par## Sc1x|x0.000000x|x0.000000x|x0.000000 ##disp-par## Sr1x|x0.000000x|x0.000000x|x0.000000 ##disp-par## O1x|x-0.016375x|x0.016375x|x0.000000 ##disp-par## O1_2x|x0.000000x|x0.000000x|x0.000000 ##disp-par## O1_3x|x-0.016375x|x-0.016375x|x0.000000”>

Irrep: X5+

Direction: (a,a,0,0,a,-a)

Isotropy Subgroup: 58 Pnnm D2h-12

Transformation matrix: 
[     0   1/2  -1/2 ] [      0]
[     0   1/2   1/2 ] [      0]
[     1     0     0 ] [      0]

The amplitude of this distortion is:
AX5+= 0.1421 Å

Normalized polarization vector: (in terms of the amplitudes of the (normalized) atomic symmetry modes)
Sr1 1O1 1O1 2
0.7968-0.4507-0.4024
NOTE:A second number next to the label counts the different symmetry modes that may happen for that orbit.


Normalized polarization vector expressed as displacements (in cell relative units) of the atoms in the asymmetric unit of the structure:(normalization unit: 1 Ångström)
Atomδxδyδz
Sb1 0.00000.00000.0000
Sc1 0.00000.00000.0000
Sr1 0.00000.06970.0000
O1 0.00000.0000-0.0176
O1_2 0.00000.03940.0000
O1_3 0.00000.0000-0.0176


with only this symmetry component of the distortion frozen.
##disp-par## Sb1x|x0.000000x|x0.000000x|x0.000000 ##disp-par## Sc1x|x0.000000x|x0.000000x|x0.000000 ##disp-par## Sr1x|x0.000000x|x0.009900x|x0.000000 ##disp-par## O1x|x0.000000x|x0.000000x|x-0.002500 ##disp-par## O1_2x|x0.000000x|x0.005600x|x0.000000 ##disp-par## O1_3x|x0.000000x|x0.000000x|x-0.002500”>

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\(\textrm{Sr}_{2}\textrm{CoTeO}_{6}\), RT