Bilbao Crystallographic Server Structure Relations

Help

Structure Relations
special implementation for Serpil Albay's MS Thesis

1st structure

14
15.952490 5.293000 13.254000 90.000000 144.238338 90.000000
14
Ca    1   4e    0.776600 0.178900 0.032900              
Ca    2   4e    0.075300 0.227100 0.156400              
Ca    3   4e    0.574600 0.733300 0.672400              
Mg    1   4e    0.746500 0.256600 0.750800              
Si    1   4e    0.399200 0.229300 0.531800              
Si    2   4e    0.906900 0.728000 0.048100              
O     1   4e    0.555000 0.212300 0.629000              
O     2   4e    0.306300 0.419300 0.369500              
O     3   4e    0.322700 0.952500 0.448000              
O     4   4e    0.406000 0.361800 0.647400              
O     5   4e    0.059100 0.706400 0.135900              
O     6   4e    0.931700 0.813000 0.186500              
O     7   4e    0.814700 0.472600 0.941300              
O     8   4e    0.824900 0.957600 0.908100              

2nd structure

14
16.790218 5.457700 13.877000 90.000000 145.740166 90.000000
14
Sr 1 4e 0.747200 0.212600 0.997200
Sr 2 4e 0.081100 0.246000 0.167300
Sr 3 4e 0.577000 0.741000 0.665900
Mg 1 4e 0.753000 0.235000 0.750000
Si 1 4e 0.426000 0.253000 0.566700
Si 2 4e 0.918000 0.739000 0.048000
O 1 4e 0.572000 0.255000 0.659000
O 2 4e 0.320000 0.459000 0.393000
O 3 4e 0.345000 0.999000 0.430000
O 4 4e 0.440000 0.287000 0.681000
O 5 4e 0.075000 0.737000 0.200000
O 6 4e 0.915000 0.764000 0.165000
O 7 4e 0.819000 0.462000 0.926000
O 8 4e 0.833000 0.936000 0.910000

Transformation Matrix	Matrix Form	S	dmax (Å)	davg (Å)	Δ	Total Distortion Amplitude (Å)
-a,b,-c ; 0,1/2,-1/2	-1 0 0 0 0 1 0 1/2 0 0 -1 -1/2	0.0196	0.7056	0.3245	0.088	2.7615

• 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
15.952490 5.293000 13.254000 90 144.238342 90
14
Ca 4 0.776600 0.178900 0.032900
Ca 1 4e 0.075300 0.227100 0.156400
Ca 2 4e 0.574600 0.733300 0.672400
Mg 1 4e 0.746500 0.256600 0.750800
Si 1 4e 0.399200 0.229300 0.531800
Si 2 4e 0.906900 0.728000 0.048100
O 1 4e 0.555000 0.212300 0.629000
O 2 4e 0.306300 0.419300 0.369500
O 3 4e 0.322700 0.952500 0.448000
O 4 4e 0.406000 0.361800 0.647400
O 5 4e 0.059100 0.706400 0.135900
O 6 4e 0.931700 0.813000 0.186500
O 7 4e 0.814700 0.472600 0.941300
O 8 4e 0.824900 0.957600 0.908100