Bilbao Crystallographic Server Structure Relations

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Structure Relations
special implementation for Serpil Albay's MS Thesis

High symmetry structure

15
10.117 5.843 15.024 90. 89.967 90.
8
Cr    1   8f    0.165700 0.491420 0.136780              
K     1   8f    0.168500 0.489670 0.416090              
K     2   4e    0.000000 0.970100 0.250000              
Na    1   4a    0.000000 0.000000 0.000000              
O     1   8f    0.169000 0.523200 0.243900              
O     2   8f    0.087200 0.709200 0.091200              
O     3   8f    0.087900 0.254500 0.109500              
O     4   8f    0.316900 0.482300 0.095100              

Low symmetry structure

14
9.120 5.198 13.370 90. 90.78 90.
14
Na 1 4e 0.581190 0.278600 0.398590
Na 2 4e 0.083460 0.777400 0.410060
Ca 1 4e 0.237270 0.314910 0.249430
Mg 1 4e 0.252580 0.254150 0.501790
P 1 4e 0.413660 0.772670 0.369480
P 2 4e 0.918470 0.270660 0.365450
O 1 4e 0.402400 0.672300 0.263280
O 2 4e 0.923600 0.195100 0.255780
O 3 4e 0.334810 0.034100 0.381140
O 4 4e 0.831930 0.521500 0.381240
O 5 4e 0.075800 0.305200 0.406790
O 6 4e 0.575200 0.802800 0.401370
O 7 4e 0.341000 0.574600 0.438590
O 8 4e 0.845500 0.050500 0.424200

Transformation Matrix	Matrix Form	S	dmax (Å)	davg (Å)	Δ	Total Distortion Amplitude (Å)
-a,b,-c ; -1/4,1/4,-1/2	-1 0 0 -1/4 0 1 0 1/4 0 0 -1 -1/2	0.0731	2.2357	0.9922	0.206	8.7642

• Lattice and atomic position criteria:
  
  
  • The degree of lattice distortion (S) is the spontaneous strain (sum of the squared eigenvalues of the strain tensor divided by 3).
    
    
  • The maximum distance (d_max) shows the maximal displacement between the atomic positions of the paired atoms.
    
    
• The average distance (d_avg) is defined as the average over the primitive unit cell of the distances between the atomic positions of the paired atoms.
  
  
• The measure of compatibility (Δ) (Bergerhoff et al., 1998) is a function of the differences in atomic positions (weighted by the multiplicities of the sites) and the ratios of the corresponding lattice parameters of the structures..
  
  
• The total distortion amplitude is calculated by multiplying each displacement's square with the corresponding site's multiplicity, summing them and taking square root

014
10.117000 5.843000 15.024000 90 89.967003 90
14
Cr 4 0.584300 0.241420 0.363220
Cr 1 4e 0.084300 0.741420 0.363220
K 4 0.418500 0.739670 0.416090
K 1 4e 0.918500 0.239670 0.416090
K 2 4e 0.250000 0.220100 0.250000
Na 1 4e 0.250000 0.250000 0.500000
O 1 4e 0.419000 0.773200 0.243900
O 2 4e 0.919000 0.273200 0.243900
O 3 4e 0.337200 0.540800 0.591200
O 4 4e 0.837200 0.040800 0.591200
O 5 4e 0.662100 0.004500 0.390500
O 6 4e 0.162100 0.504500 0.390500
O 7 4e 0.433100 0.232300 0.404900
O 8 4e 0.933100 0.732300 0.404900