-    EDENITE     -    NaCa2Mg5Si7AlO22(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 (°):  82.56  97.24  57.79 

Cell contents: 

Number of atoms:  42 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Mg:  0.0902  0.0838  0.4993 
Mg:  0.1769  0.1699  0.0046 
Mg:  0.0037  0.9973  0.0049 
Ca:  0.2821  0.2748  0.5064 
Al:  0.3637  0.8025  0.3122 
Si:  0.4633  0.8825  0.8192 
O:  0.1889  0.9817  0.2188 
O:  0.2904  0.0495  0.7321 
O:  0.1061  0.8901  0.7167 
O:  0.6091  0.8958  0.7823 
O:  0.4985  0.7843  0.1220 
O:  0.4667  0.7599  0.6353 
O:  0.3404  0.6488  0.2663 
H:  0.2093  0.7900  0.7802 
Si:  0.8074  0.3610  0.6971 
Si:  0.8868  0.4585  0.1924 
O:  0.9742  0.1957  0.7754 
O:  0.0531  0.2896  0.2753 
O:  0.8883  0.1086  0.2824 
O:  0.8795  0.6160  0.2035 
O:  0.7866  0.4808  0.8931 
O:  0.7692  0.4585  0.3938 
O:  0.6607  0.3403  0.7191 
H:  0.7820  0.2052  0.2321 
Mg:  0.9140  0.9095  0.4988 
Mg:  0.8226  0.8256  0.9959 
Ca:  0.7105  0.7276  0.4922 
Si:  0.6376  0.1944  0.6980 
Si:  0.5409  0.1166  0.1892 
O:  0.8037  0.0263  0.7800 
O:  0.7112  0.9497  0.2696 
O:  0.3863  0.1188  0.2031 
O:  0.5161  0.2142  0.8875 
O:  0.5421  0.2297  0.3961 
Si:  0.1948  0.6314  0.2947 
Si:  0.1094  0.5386  0.8036 
O:  0.0255  0.7990  0.2170 
O:  0.9436  0.7108  0.7224 
O:  0.1064  0.3862  0.7850 
O:  0.2034  0.5102  0.1090 
O:  0.2244  0.5371  0.5986 
Na:  0.5308  0.5490  0.9949 
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: 2.0037 0.0083 0.0018 
0.0152 2.0002 0.0226 
-0.0015 0.0049 1.9727 
Eig. Value: 2.0159 1.9942 1.9664 
Mg: 2.1699 0.0429 0.0186 
0.0138 2.0413 -0.0050 
0.0485 0.0091 1.9281 
Eig. Value: 2.1802 2.0355 1.9235 
Mg: 1.9148 -0.0398 0.0922 
-0.0108 2.0266 -0.0137 
0.0322 -0.0062 1.9834 
Eig. Value: 1.8761 2.0460 2.0027 
Ca: 2.5762 0.0087 -0.0107 
0.0025 2.1134 -0.0158 
0.0059 -0.0153 2.2549 
Eig. Value: 2.5763 2.1116 2.2565 
Al: 2.2759 0.1472 -0.0888 
0.0394 2.8088 0.1493 
-0.1103 0.0051 2.5685 
Eig. Value: 2.2236 2.8388 2.5907 
Si: 2.8912 0.2323 -0.1112 
-0.0080 2.8244 0.0199 
-0.1199 0.0841 3.1445 
Eig. Value: 2.9592 2.7115 3.1895 
O: -1.8212 -0.0071 -0.0607 
-0.0197 -1.6820 -0.0101 
-0.0411 0.0177 -1.6424 
Eig. Value: -1.8356 -1.6820 -1.6280 
O: -2.1626 -0.0768 -0.1685 
-0.0000 -1.4911 -0.0384 
-0.1495 -0.0541 -1.5709 
Eig. Value: -2.2059 -1.4679 -1.5508 
O: -1.1591 0.0059 0.1062 
-0.0077 -1.5118 0.0138 
0.0833 0.0054 -1.4778 
Eig. Value: -1.1331 -1.5181 -1.4975 
O: -1.6844 -0.3445 0.1061 
-0.3011 -1.9449 -0.0113 
0.1169 -0.0616 -1.5308 
Eig. Value: -1.3810 -2.1644 -1.6148 
O: -1.4620 -0.2429 0.0673 
-0.1761 -1.5717 0.3623 
0.0281 0.4160 -2.2736 
Eig. Value: -1.5940 -1.2496 -2.4637 
O: -1.5413 0.0546 0.2186 
0.1297 -1.6990 -0.4630 
0.2237 -0.4826 -2.0203 
Eig. Value: -1.4989 -1.3406 -2.4211 
O: -1.3678 -0.1037 0.0249 
-0.1188 -2.5321 0.0216 
0.0487 0.0050 -1.2477 
Eig. Value: -1.3676 -2.5428 -1.2371 
H: 0.1841 0.0126 -0.0817 
0.0147 0.5269 -0.0208 
-0.0769 -0.0083 0.5203 
Eig. Value: 0.1660 0.5146 0.5507 
Si: 2.8015 -0.1615 -0.1352 
-0.0112 3.5331 -0.1552 
-0.1805 0.0267 3.2837 
Eig. Value: 2.7414 3.5521 3.3248 
Si: 2.9503 -0.3178 -0.2178 
0.0198 2.9231 0.0268 
-0.1966 -0.1420 3.3976 
Eig. Value: 2.7341 3.0581 3.4788 
O: -1.9023 0.0168 -0.1056 
0.0280 -1.5706 0.0256 
-0.0883 -0.0067 -1.5453 
Eig. Value: -1.9285 -1.5692 -1.5204 
O: -2.0584 0.0885 -0.1167 
-0.0332 -1.4825 0.0202 
-0.1140 0.0592 -1.5624 
Eig. Value: -2.0860 -1.4654 -1.5518 
O: -1.1221 0.0054 0.1214 
0.0104 -1.5077 0.0015 
0.1019 -0.0013 -1.4570 
Eig. Value: -1.0882 -1.5081 -1.4905 
O: -1.7442 0.3742 0.0856 
0.3587 -1.8407 0.0669 
0.0774 0.1355 -1.5151 
Eig. Value: -1.3328 -2.1629 -1.6044 
O: -1.4487 0.3120 0.2473 
0.2592 -1.6064 -0.5788 
0.2334 -0.6275 -2.3237 
Eig. Value: -1.1756 -1.4422 -2.7610 
O: -1.4279 -0.0425 0.1743 
-0.1096 -1.6487 0.6307 
0.1887 0.6610 -2.2960 
Eig. Value: -1.4047 -1.2440 -2.7239 
O: -1.2768 0.0417 0.0337 
0.0205 -2.8520 -0.0134 
0.0527 -0.0082 -1.1618 
Eig. Value: -1.2905 -2.8526 -1.1474 
H: 0.1300 -0.0044 -0.1022 
-0.0165 0.5225 -0.0165 
-0.1002 -0.0115 0.4850 
Eig. Value: 0.1027 0.5296 0.5052 
Mg: 2.0402 -0.0129 -0.0387 
-0.0054 1.9870 0.0061 
-0.0281 0.0030 1.9706 
Eig. Value: 2.0551 1.9855 1.9571 
Mg: 2.1736 -0.0126 0.0373 
-0.0015 2.0363 -0.0079 
0.0506 -0.0043 1.9320 
Eig. Value: 2.1818 2.0361 1.9241 
Ca: 2.5082 0.0217 -0.0451 
-0.0074 2.0968 0.0091 
-0.0349 0.0135 2.2828 
Eig. Value: 2.5151 2.0959 2.2768 
Si: 2.7812 0.1253 -0.1244 
0.0075 3.5843 0.1658 
-0.1554 -0.0326 3.2621 
Eig. Value: 2.7356 3.5994 3.2926 
Si: 2.9222 0.3569 -0.2446 
-0.0025 2.9104 -0.0043 
-0.2268 0.1690 3.4487 
Eig. Value: 3.0698 2.6724 3.5391 
O: -1.9172 -0.0032 -0.1008 
-0.0266 -1.5813 -0.0238 
-0.0848 0.0103 -1.5511 
Eig. Value: -1.9401 -1.5808 -1.5287 
O: -2.0579 -0.0877 -0.1086 
0.0322 -1.4971 -0.0270 
-0.1020 -0.0668 -1.5720 
Eig. Value: -2.0821 -1.4736 -1.5713 
O: -1.7432 -0.4040 0.1066 
-0.3581 -1.8544 -0.0655 
0.0986 -0.1427 -1.5366 
Eig. Value: -1.3170 -2.1841 -1.6331 
O: -1.3971 -0.3578 0.2298 
-0.2854 -1.6015 0.5534 
0.2149 0.5983 -2.3253 
Eig. Value: -1.1251 -1.4624 -2.7365 
O: -1.4005 0.0064 0.2337 
0.0865 -1.6662 -0.6490 
0.2324 -0.6791 -2.2741 
Eig. Value: -1.4076 -1.1960 -2.7372 
Si: 2.7945 -0.1096 -0.1290 
-0.0527 3.4153 -0.1937 
-0.1591 0.0116 3.1999 
Eig. Value: 2.7322 3.4499 3.2276 
Si: 2.9121 -0.3266 -0.2271 
-0.0343 2.8824 0.0095 
-0.2352 -0.1611 3.4442 
Eig. Value: 3.0516 2.6564 3.5307 
O: -1.9926 0.0091 -0.1034 
0.0467 -1.5743 0.0296 
-0.0929 -0.0136 -1.5326 
Eig. Value: -2.0146 -1.5724 -1.5124 
O: -2.0968 0.0956 -0.1227 
-0.0155 -1.4827 0.0269 
-0.1077 0.0589 -1.5658 
Eig. Value: -2.1243 -1.4644 -1.5566 
O: -1.7178 0.3479 0.0965 
0.3242 -1.8935 0.0458 
0.0981 0.1203 -1.5363 
Eig. Value: -1.3637 -2.1530 -1.6308 
O: -1.3809 0.3652 0.1973 
0.2945 -1.6113 -0.5600 
0.1853 -0.6163 -2.3430 
Eig. Value: -1.1026 -1.4829 -2.7496 
O: -1.4209 -0.0304 0.2459 
-0.1033 -1.6573 0.6731 
0.2584 0.7244 -2.2871 
Eig. Value: -1.4070 -1.1743 -2.7839 
Na: 1.2743 0.0066 -0.0011 
0.0018 1.1278 -0.0076 
0.0261 0.0030 1.0697 
Eig. Value: 1.2752 1.1278 1.0688 
Atom type 

Dielectric tensors: 

 
Ɛ2.7316 0.0000 0.0000 
0.0000 2.7546 0.0000 
0.0000 0.0000 2.7675 
Eig. Value: 2.7315 2.7546 2.7675 
Refractive index (N): 1.6527 0.0000 0.0000 
0.0000 1.6597 0.0000 
0.0000 0.0000 1.6636 
Eig. Value: 1.6527 1.6597 1.6636 
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