\(\textrm{La}_{2}\textrm{CoMnO}_{6}\), RT \(+\) HT¶

Target

Another compound, from another family: the same parent phase
Another High Temperature Distorted Phase:
- Finding the Transformation Matrix

Steps

AMPLIMODES for FullProf with the standard: previous parent phase, as usual
Use STRUCTURE RELATIONS: Transformation Matrix
AMPLIMODES with standard: parent phase from the paper

Take the structure from the paper¶

# P 1 21/n 1
014
5.5251   5.4875   7.7786   90.000   89.940   90.000
6
Mn  1    2a     0.00000     0.00000     0.00000
Co  1    2b     0.00000     0.00000     0.50000
La  1    4e    -0.00660     0.46450     0.74990
O   1    4e    -0.27710     0.21680    -0.03620
O   2    4e    -0.79820     0.29420     0.04000
O   3    4e     0.07530     0.01280     0.75800

# P 1 21/c 1
014
7.7786 5.4875 9.5459 90.00 144.63 90.00
6
Mn	1	2a	0.000000	0.000000	 0.000000
Co	1	2b	0.500000	0.000000	 0.000000
La	1	4e	0.756500	0.464500	 0.006600
O	1	4e	0.240900	0.216800	 0.277100
O	2	4e	0.838200	0.294200	 0.798200
O	3	4e	0.682700	0.012800	-0.075300

…go through \(I\frac{2}{m}\)

# C 1 2/m 1
012
9.8516 5.6861 5.7021 90.00 125.41 90.00
5
Sb	1	2d	-0.500000	0.000000	-0.500000
Sc	1	2a	 0.000000	0.000000	 0.000000
Sr	1	4i	-0.249400	0.000000	 0.249910
O	1	4i	-0.255990	0.000000	-0.304570
O	2	8j	-0.023630	0.255510	 0.232860

Find the Transformation Matrix with STRUCTURE RELATIONS¶

Lattice Pseudosymmetry

[ Data obtained via CCTBX library ]

Please, select one the possible metrics:

No. #	Latt.	Idealized/Transformed cell	Transformation matrix P	Strain	Tol.
1	cF	8.0449 8.0449 8.0449 90.00 90.00 90.00 8.0527 8.0293 8.0527 89.97 89.84 89.97	[ 1/2 1/2 -1/2 ] [ 1 0 0 ] [ 1/2 -1/2 -1/2 ]	0.00104	0.215
2	tI	5.6859 5.6859 8.0527 90.00 90.00 90.00 5.6874 5.6843 8.0527 90.09 89.86 90.17	[ 3/2 1/2 -1/2 ] [ 1/2 -1/2 1/2 ] [ 1/2 -1/2 -1/2 ]	0.00099	0.215
3	tI	5.6859 5.6859 8.0527 90.00 90.00 90.00 5.6843 5.6874 8.0527 90.14 90.09 89.83	[ -1/2 -1/2 -1/2 ] [ 3/2 -1/2 -1/2 ] [ -1/2 -1/2 1/2 ]	0.00099	0.215
4	tI	5.6941 5.6941 8.0293 90.00 90.00 90.00 5.6861 5.7021 8.0293 89.96 90.00 90.00	[ 0 -1 0 ] [ 1 0 -1 ] [ 1 0 0 ]	0.00068	0.164
5	hR	5.6913 5.6913 13.9211 90.00 90.00 120.00 5.6843 5.6874 13.9211 89.94 90.08 119.81	[ -1/3 1/3 1 ] [ -5/3 -1/3 1 ] [ 1/3 -1/3 0 ]	0.00098	0.215
6	hR	5.6849 5.6849 13.9523 90.00 90.00 120.00 5.6843 5.6843 13.9523 89.81 90.19 119.98	[ 1/3 -1 1/3 ] [ -1/3 -1 -1/3 ] [ 2/3 0 -1/3 ]	0.00091	0.190
7	hR	5.6913 5.6913 13.9211 90.00 90.00 120.00 5.7021 5.6843 13.9211 90.08 89.97 120.07	[ -5/3 1/3 1 ] [ -4/3 2/3 0 ] [ -1/3 -1/3 0 ]	0.00097	0.215
8	hR	5.6870 5.6870 13.9422 90.00 90.00 120.00 5.6874 5.6861 13.9422 90.00 89.79 119.99	[ 2 0 -2/3 ] [ 1 -1 -1/3 ] [ 0 0 -1/3 ]	0.00100	0.215
9	oI	5.6861 5.7021 8.0293 90.00 90.00 90.00 5.6861 5.7021 8.0293 89.96 90.00 90.00	[ 0 -1 0 ] [ 1 0 -1 ] [ 1 0 0 ]	0.00016	0.044
10	oI	5.6843 5.6874 8.0527 90.00 90.00 90.00 5.6843 5.6874 8.0527 89.86 90.09 90.17	[ 1/2 1/2 1/2 ] [ 3/2 -1/2 -1/2 ] [ 1/2 1/2 -1/2 ]	0.00098	0.215
11	oI	5.6843 5.6874 8.0527 90.00 90.00 90.00 5.6843 5.6874 8.0527 89.86 89.91 89.83	[ -1/2 1/2 -1/2 ] [ 3/2 1/2 -1/2 ] [ 1/2 -1/2 -1/2 ]	0.00098	0.215
12	oF	8.0293 8.0527 8.0527 90.00 90.00 90.00 8.0293 8.0527 8.0527 89.84 90.03 90.03	[ -1 0 0 ] [ 1/2 1/2 -1/2 ] [ 1/2 -1/2 -1/2 ]	0.00068	0.164

Select minimal supergroup

Possible lattices: cF,tI,hR,oI,oF

No. #	HM Symb.	IT Numb.	Latt.	Index
1	P2/m	10	mP	2
2	Cmcm	63	oC	2
3	Cmce	64	oC	2
4	Cmmm	65	oC	2
5	Cmme	67	oC	2
6	Fmmm	69	oF	2
7	Immm	71	oI	2
8	Ibam	72	oI	2
9	Imma	74	oI	2
10	I4/m	87	tI	2
11	C2/m	12	mC	2
12	C2/m	12	mC	3
13	C2/m	12	mC	5
14	C2/m	12	mC	7
15	P-31m	162	hP	3
16	P-3m1	164	hP	3
17	R-3m	166	hR	3

Result for pseudosymmetry search

Formulae

Input of the program

Initial structure:

12
9.8516 5.6861 5.7021 90.00 125.41 90.00
5
Sb	1	2d	-0.500000	0.000000	-0.500000
Sc	1	2a	0.000000	0.000000	0.000000
Sr	1	4i	-0.249400	0.000000	0.249910
O	1	4i	-0.255990	0.000000	-0.304570
O	2	8j	-0.023630	0.255510	0.232860

Maximum tolerance: 2

Summary search results

Pseudosymmetry search among minimal supergroups within the specialized normalizer and compatible with possible high symmetry lattices.

Case #	Supergroup G	Index i	Index i_k	(P,p)	Tr. Matrix	Δ_max	u_max
1	R-3m (166)	3	1	2a+b,-b,-2/3a-1/3b-1/3c ; 0,0,0	[ 2 0 -2/3 ] [ 0] [ 1 -1 -1/3 ] [ 0] [ 0 0 -1/3 ] [ 0]	0.4313	0.2726
2	R-3m (166)	3	1	2a+b,-b,-2/3a-1/3b-1/3c ; 1,1/2,0	[ 2 0 -2/3 ] [ 1] [ 1 -1 -1/3 ] [ 1/2] [ 0 0 -1/3 ] [ 0]	>tol	-

Idealized structures

1# Supergroup R-3m (166): 2a+b,-b,-2/3a-1/3b-1/3c ; 0,0,0 and index 3

Displacements:

Atom	Idealized Coordinates	u_x	u_y	u_z	\|u\|
Sb1	(0.5000, 0.0000, 0.5000)	0.000000	0.000000	0.000000	0.0000
Sc1	(0.0000, 0.0000, 0.0000)	0.000000	0.000000	0.000000	0.0000
Sr1	(0.7500, 0.0000, 0.2499)	0.000630	0.000000	0.000000	0.0062
O1	(0.7440, 0.0000, 0.7432)	0.000007	0.000000	-0.047807	0.2726
O2	(0.0004, 0.2556, 0.2568)	-0.024013	-0.000103	-0.023903	0.1928

NOTE: u_x, u_y and u_z are given in relative units. |u| is the absolute displacement given in Å

Idealized structure (subgroup setting):

12
9.8516 5.6861 5.7021 90.00 125.41 90.00
5
Sb	1	2d	0.500000	0.000000	0.500000
Sc	1	2a	0.000000	0.000000	0.000000
Sr	1	4i	0.749970	0.000000	0.249910
O	1	4i	0.744003	0.000000	0.743237
O	2	8j	0.000383	0.255613	0.256763

Idealized structure (supergroup setting):

166
5.6874 5.6861 13.9422 90.00 89.79 119.99
4
Sb	1	3b	0.666667	0.333333	0.833333
Sc	1	3a	0.000000	0.000000	0.000000
Sr	1	6c	0.333333	0.666667	0.916697
O	1	18h	0.992515	0.496257	0.752254

Notes:

Idealized structure with space group 166 related with the given by the transformation 2a+b,-b,-2/3a-1/3b-1/3c ; 0,0,0 and index 3
Cell parameters have not been symmetrized. They may include in general some symmetry breaking strain, to be removed by hand.
Some problems might be present in the assignment of Wyckoff positions of the idealized orbits due to the decimal point errors.

AMPLIMODES for FullProf with standard, previous parent¶

225
8.087481 8.087481 8.087481 90.00000 90.00000 90.00000
4
Mn	1	4a	0.000000	0.000000	0.000000
Co	1	4b	0.500000	0.500000	0.500000
La	1	8c	0.250000	0.250000	0.250000
O	1	24e	0.254100	0.000000	0.000000

# R -3 m
166
5.6874 5.6861 13.9422 90.00 89.79 119.99
4
Mn	1	3b	0.666667	0.333333	0.833333
Co	1	3a	0.000000	0.000000	0.000000
La	1	6c	0.333333	0.666667	0.916697
O	1	18h	0.992515	0.496257	0.752254

2a+b,-b,-2/3a-1/3b-1/3c; 0 0 0

Structural refinement with modes using FullProf and AMPLIMODES

\textrm{La}_{2}\textrm{CoMnO}_{6}, RT + HT

Contents

\(\textrm{La}_{2}\textrm{CoMnO}_{6}\), RT \(+\) HT¶

Take the structure from the paper¶

Find the Transformation Matrix with STRUCTURE RELATIONS¶

Lattice Pseudosymmetry

Select minimal supergroup

Result for pseudosymmetry search

Formulae

Input of the program

Summary search results

Idealized structures

1# Supergroup R-3m (166): 2a+b,-b,-2/3a-1/3b-1/3c ; 0,0,0 and index 3

AMPLIMODES for FullProf with standard, previous parent¶

Structural refinement with modes using FullProf and AMPLIMODES

\textrm{La}_{2}\textrm{CoMnO}_{6}, RT + HT

Contents

\(\textrm{La}_{2}\textrm{CoMnO}_{6}\), RT \(+\) HT¶

Take the structure from the paper¶

Find the Transformation Matrix with STRUCTURE RELATIONS¶

Lattice Pseudosymmetry

Select minimal supergroup

Result for pseudosymmetry search

Formulae

Input of the program

Summary search results

Idealized structures

1# Supergroup R-3m (166): 2a+b,-b,-2/3a-1/3b-1/3c ; 0,0,0 and index 3

AMPLIMODES for FullProf with standard, previous parent¶

Refinements¶