Bilbao Crystallographic Server arrow Structure Relations Help

Structure Relations
special implementation for Serpil Albay's MS Thesis

Structure IDs: [91]→[77]

1st structure

164
5.622 5.622 7.259 90. 90. 120.
6
Mg    1   1a    0.000000 0.000000 0.000000              
Ca    1   1b    0.000000 0.000000 0.500000              
Na    2   2d    0.333333 0.666666 0.766000              
P     1   2d    0.333333 0.666666 0.249000              
O     1   2d    0.333333 0.666666 0.029000              
O     2   6i    0.176000 0.824000 0.310000

2nd structure

164
5.971 5.971 7.722 90. 90. 120.
6
Gd 1 1a 0.000000 0.000000 0.000000
Rb 1 1b 0.000000 0.000000 0.500000
V 1 2d 0.333333 0.666667 0.749700
K 1 2d 0.333333 0.666667 0.201300
O 1 2d 0.333333 0.666667 0.540000
O 2 6i 0.176500 0.823500 0.826000
Index: 1

Transformation MatrixMatrix FormSdmax (Å)davg (Å)ΔTotal Distortion
Amplitude (Å)
a,b,c ; 0,0,1/2
(
   1   0   0    0
   0   1   0    0
   0   0   1   1/2
)
 0.0330 0.4996 0.1373 0.027 0.7781
Details of the the transformation with: a,b,c ; 0,0,1/2

Group-Subgroup Transformation Matrix: a,b,c ; 0,0,0   [1]
Element of the Affine Normalizers: x,y,z   [2]
Lattice Compatible Transformation Matrix: a,b,c ; 0,0,0   [3] ( = [1] x [2] )
Element of the Euclidean Normalizers: x,y,z+1/2   [4]
Overall Transformation Matrix: a,b,c ; 0,0,1/2   [5] ( = [1] x [2] x [4])

Description of the 1st Structure in the most similar configuration to the 2nd Structure

164
5.622000 5.622000 7.259000 90.000000 90.000000 120.000000
6
Mg 1 0.000000 0.000000 0.500000
Ca 1 0.000000 0.000000 0.000000
Na 2 0.333333 0.666666 0.266000
P 2 0.333333 0.666666 0.749000
O 1 2d 0.333333 0.666666 0.529000
O 2 6i 0.176000 0.824000 0.810000

Atom pairings and distances

Atom Mappings
WPAtomCoordinates in S1AtomCoordinates in S2
1a(0,0,0)Ca1(0.000000,0.000000,0.000000)Gd1(0.000000,0.000000,0.000000)
1b(0,0,1/2)Mg1(0.000000,0.000000,0.500000)Rb1(0.000000,0.000000,0.500000)
2d(1/3,2/3,z)P1(0.333333,0.666666,0.749000)V1(0.333333,0.666667,0.749700)
2d(1/3,2/3,z)Na2(0.333333,0.666666,0.266000)K1(0.333333,0.666667,0.201300)
2d(1/3,2/3,z)O1(0.333333,0.666666,0.529000)O1(0.333333,0.666667,0.540000)
6i(x,-x,z)O2(0.176000,0.824000,0.810000)O2(0.176500,0.823500,0.826000)


WPAtomAtomic Displacements
uxuyuz|u|
1a(0,0,0)Ca1 0.0000 0.0000 0.0000 0.0000
1b(0,0,1/2)Mg1 0.0000 0.0000 0.0000 0.0000
2d(1/3,2/3,z)P1 0.0000 -0.0000 -0.0007 0.0054
2d(1/3,2/3,z)Na2 0.0000 -0.0000 0.0647 0.4996
2d(1/3,2/3,z)O1 0.0000 -0.0000 -0.0110 0.0849
6i(x,-x,z)O2 -0.0005 0.0005 -0.0160 0.1237

NOTE: ux, uy and uz are given in relative units. |u| is the absolute distance given in Å


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