-    TSCHERMAKITE     -    []Ca2Mg3Al2Si6Al2O22(OH)2

 

Crystal Structure 


Because of the translational symmetry all the calculations are performed in the primitive unit cell and not in the conventional unit cell. The following information regarding the structure is given with respect to this primitive unit cell, which sometimes can take an unintuitive shape.

Symmetry (experimental): 

Space group:  P1 
Lattice parameters (Å):       
Angles (°):       

Symmetry (theoretical): 

Space group:  P1 
Lattice parameters (Å):  0.5292  0.5292  0.5292 
Angles (°):  82.76  97.10  57.16 

Cell contents: 

Number of atoms:  41 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Mg:  0.0872  0.0872  0.5000 
Al:  0.0969  0.0832  0.5021 
Mg:  0.1788  0.1689  0.9995 
Ca:  0.0114  0.9933  0.0068 
Al:  0.2838  0.2734  0.5090 
Al:  0.3746  0.7981  0.3141 
O:  0.4694  0.8801  0.8330 
O:  0.1952  0.9937  0.2050 
O:  0.2782  0.0681  0.7488 
O:  0.1117  0.8853  0.7119 
O:  0.6276  0.8983  0.7891 
O:  0.5134  0.7812  0.1464 
O:  0.4660  0.7644  0.6268 
H:  0.3199  0.6656  0.2748 
Si:  0.2240  0.7903  0.7639 
Si:  0.8077  0.3655  0.6967 
O:  0.8823  0.4662  0.1800 
O:  0.9825  0.1972  0.7909 
O:  0.0574  0.2929  0.2498 
O:  0.8906  0.1096  0.2874 
O:  0.8768  0.6276  0.1911 
O:  0.7870  0.4874  0.8871 
O:  0.7858  0.4569  0.4042 
H:  0.6681  0.3333  0.6957 
Mg:  0.7872  0.2150  0.2283 
Al:  0.9136  0.9108  0.5002 
Ca:  0.8169  0.8271  0.9937 
Si:  0.7043  0.7267  0.5004 
Si:  0.6373  0.1922  0.6976 
O:  0.5360  0.1187  0.1793 
O:  0.8071  0.0166  0.7933 
O:  0.7118  0.9462  0.2515 
O:  0.3736  0.1289  0.1851 
O:  0.5136  0.2198  0.8881 
Si:  0.5410  0.2184  0.4053 
Si:  0.1876  0.6319  0.2953 
O:  0.1100  0.5350  0.8151 
O:  0.0070  0.7993  0.2041 
O:  0.9396  0.7129  0.7438 
O:  0.1085  0.3781  0.7991 
O:  0.2050  0.5046  0.1136 
Atom type 

We have listed here the reduced coordinates of all the atoms in the primitive unit cell.
It is enough to know only the position of the atoms from the assymetrical unit cell and then use the symmetry to build the whole crystal structure.

Visualization of the crystal structure: 

Size:

Nx:  Ny:  Nz: 
You can define the size of the supercell to be displayed in the jmol panel as integer translations along the three crys­tallo­gra­phic axis.
Please note that the structure is represented using the pri­mi­tive cell, and not the conventional one.
 

Dielectric Properties 


We define:

  • The Born effective charges, also called dynamical charges, are tensors that correspond to the energy derivative with respect to atomic displacements and electric fields or, equivalently, to the change in atomic force due to an electric field: The sum of the Born effective charges of all nuclei in one cell must vanish, element by element, along each of the three directions of the space.
  • The dielectric tensors are the energy derivative with respect to two electric fields. They also relate the induced polarization to the external electric field.

Born effective charges (Z): 

Mg: 1.9175 -0.0272 -0.0377 
0.0199 1.9955 0.0236 
-0.0410 -0.0007 2.0318 
Eig. Value: 1.9052 1.9927 2.0468 
Al: 3.1633 0.0827 0.0733 
0.0358 3.0261 -0.0267 
0.0635 0.0365 2.8600 
Eig. Value: 3.1982 3.0062 2.8450 
Mg: 1.8515 -0.0445 0.0424 
-0.0116 2.1799 -0.0185 
-0.0087 -0.0133 1.9737 
Eig. Value: 1.8472 2.1837 1.9742 
Ca: 2.4701 0.0342 -0.0006 
0.0054 2.0439 -0.0398 
0.0228 -0.0424 2.3078 
Eig. Value: 2.4716 2.0366 2.3136 
Al: 2.2589 0.2257 0.0154 
0.0451 2.8907 0.0881 
0.0598 0.0181 2.3904 
Eig. Value: 2.2268 2.9251 2.3881 
Al: 2.4472 0.2362 -0.0888 
0.0427 2.2443 0.0932 
-0.1108 0.1509 2.5872 
Eig. Value: 2.5106 2.1220 2.6462 
O: -1.8898 0.0687 -0.1620 
0.0800 -1.7904 0.1484 
-0.1655 0.1591 -1.7002 
Eig. Value: -2.0632 -1.7607 -1.5565 
O: -2.1179 -0.0451 0.0315 
0.0036 -1.5642 -0.0213 
0.0443 -0.0225 -1.7890 
Eig. Value: -2.1228 -1.5610 -1.7873 
O: -1.2293 -0.0102 0.1069 
-0.0465 -1.5861 0.0003 
0.1056 0.0081 -1.4735 
Eig. Value: -1.1879 -1.5901 -1.5108 
O: -1.7748 -0.3075 0.0087 
-0.2136 -1.9714 -0.1485 
0.0345 -0.1764 -1.7080 
Eig. Value: -1.5206 -2.1839 -1.7497 
O: -1.5740 -0.3385 0.0224 
-0.2463 -1.5674 0.2176 
-0.0193 0.1879 -2.0707 
Eig. Value: -1.7972 -1.2522 -2.1627 
O: -1.5919 -0.1568 0.1730 
-0.0660 -1.6480 -0.3599 
0.1583 -0.3555 -1.9322 
Eig. Value: -1.6976 -1.2895 -2.1851 
O: -1.1978 -0.0461 -0.0431 
-0.0607 -2.6932 -0.0160 
-0.0245 -0.0414 -1.1815 
Eig. Value: -1.2220 -2.6957 -1.1548 
H: 0.3483 0.0694 -0.0683 
0.0849 0.5744 -0.0276 
-0.0726 -0.0264 0.5026 
Eig. Value: 0.3059 0.6190 0.5005 
Si: 2.8873 -0.2343 -0.0677 
0.0121 3.7556 -0.0774 
-0.0876 0.0347 3.3259 
Eig. Value: 2.8596 3.7699 3.3393 
Si: 3.2128 -0.4020 -0.2372 
-0.0802 2.9151 -0.0324 
-0.2381 -0.2697 3.5292 
Eig. Value: 3.2963 2.7037 3.6571 
O: -1.9404 -0.0670 -0.1825 
-0.0935 -1.7149 -0.1109 
-0.1930 -0.1309 -1.6041 
Eig. Value: -2.0682 -1.7015 -1.4896 
O: -2.2318 0.0869 0.0104 
-0.0299 -1.4157 0.0383 
0.0352 0.0575 -1.6707 
Eig. Value: -2.2336 -1.4058 -1.6789 
O: -1.1233 -0.0009 0.1333 
-0.0129 -1.5594 0.0019 
0.1358 -0.0010 -1.4419 
Eig. Value: -1.0741 -1.5596 -1.4910 
O: -1.8144 0.5070 -0.0129 
0.4902 -1.9967 0.2049 
-0.0408 0.2645 -1.5459 
Eig. Value: -1.3134 -2.4560 -1.5876 
O: -1.4285 0.4023 0.2119 
0.2964 -1.5394 -0.5836 
0.2129 -0.5954 -2.2845 
Eig. Value: -1.0668 -1.4760 -2.7096 
O: -1.4065 0.0590 0.2301 
-0.0485 -1.5932 0.7233 
0.2770 0.7727 -2.3929 
Eig. Value: -1.4361 -1.0836 -2.8729 
O: -1.1277 0.0272 -0.0429 
-0.0011 -3.0732 -0.0053 
-0.0150 0.0041 -1.0931 
Eig. Value: -1.1440 -3.0733 -1.0767 
H: 0.2079 -0.0090 -0.0905 
-0.0149 0.5262 -0.0031 
-0.0994 0.0008 0.4713 
Eig. Value: 0.1768 0.5268 0.5017 
Mg: 1.9258 -0.0030 -0.0456 
0.0112 2.0330 0.0096 
-0.0441 -0.0020 2.0485 
Eig. Value: 1.9110 2.0330 2.0633 
Al: 3.1963 -0.0402 0.0240 
-0.0453 2.9156 -0.0643 
0.0750 -0.0066 2.8539 
Eig. Value: 3.2110 2.9194 2.8355 
Ca: 2.3372 0.0621 -0.0144 
0.0158 2.0443 0.0634 
-0.0242 0.0640 2.3092 
Eig. Value: 2.3472 2.0241 2.3195 
Si: 2.8324 0.1265 -0.0726 
-0.0367 3.8548 0.0744 
-0.0881 -0.0355 3.2921 
Eig. Value: 2.8166 3.8572 3.3055 
Si: 3.1405 0.4567 -0.2778 
0.1029 2.9074 0.0501 
-0.2970 0.2256 3.5929 
Eig. Value: 3.2696 2.6388 3.7325 
O: -1.9035 0.0713 -0.1669 
0.0475 -1.7771 0.1107 
-0.1770 0.1270 -1.5854 
Eig. Value: -2.0236 -1.7589 -1.4836 
O: -2.1562 -0.0997 0.0748 
0.0052 -1.4181 -0.0715 
0.0881 -0.1048 -1.7139 
Eig. Value: -2.1720 -1.3879 -1.7283 
O: -1.8347 -0.5956 0.0218 
-0.5019 -1.9715 -0.1854 
0.0053 -0.2907 -1.5726 
Eig. Value: -1.2545 -2.4883 -1.6360 
O: -1.4522 -0.3785 0.2500 
-0.2885 -1.5657 0.5464 
0.2275 0.5717 -2.2505 
Eig. Value: -1.1227 -1.4676 -2.6781 
O: -1.3955 -0.0530 0.2084 
0.0264 -1.6264 -0.6968 
0.2484 -0.7304 -2.3866 
Eig. Value: -1.4386 -1.1300 -2.8400 
Si: 2.8015 -0.1652 -0.0877 
-0.0444 3.5508 -0.1516 
-0.0802 0.0353 3.2675 
Eig. Value: 2.7704 3.5724 3.2770 
Si: 3.0768 -0.4243 -0.2439 
-0.1447 2.8608 -0.0516 
-0.2706 -0.2515 3.5268 
Eig. Value: 3.2355 2.5847 3.6442 
O: -1.9975 -0.0992 -0.1812 
-0.0874 -1.7056 -0.1198 
-0.2126 -0.1587 -1.5950 
Eig. Value: -2.1255 -1.7014 -1.4713 
O: -2.2457 0.0918 0.0304 
0.0062 -1.4167 0.0704 
0.0613 0.0821 -1.6522 
Eig. Value: -2.2515 -1.3899 -1.6732 
O: -1.7861 0.4925 0.0159 
0.4557 -1.9641 0.1490 
0.0091 0.2417 -1.5542 
Eig. Value: -1.3118 -2.3825 -1.6101 
O: -1.4348 0.4081 0.2015 
0.3145 -1.5574 -0.5337 
0.1788 -0.5700 -2.2782 
Eig. Value: -1.0758 -1.5219 -2.6727 
O: -1.4210 0.0395 0.2384 
-0.0269 -1.6026 0.7321 
0.2670 0.7835 -2.3940 
Eig. Value: -1.4495 -1.0838 -2.8844 
Atom type 

Dielectric tensors: 

 
Ɛ2.7462 0.0000 0.0000 
0.0000 2.7730 0.0000 
0.0000 0.0000 2.7909 
Eig. Value: 2.7461 2.7731 2.7909 
Refractive index (N): 1.6572 0.0000 0.0000 
0.0000 1.6652 0.0000 
0.0000 0.0000 1.6706 
Eig. Value: 1.6571 1.6652 1.6706 
Ɛ00.0000 0.0000 0.0000 
0.0000 0.0000 0.0000 
0.0000 0.0000 0.0000 
Eig. Value: 0.0000 0.0000 0.0000