-    HORNBLENDE-Mg     -    []Ca2Mg4AlSi7AlO22(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 (°):  82.71  97.29  57.14 

Cell contents: 

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

Atomic positions (theoretical):

Mg:  0.0912  0.0829  0.4986 
Al:  0.1774  0.1702  0.0042 
Mg:  0.0056  0.9956  0.0046 
Ca:  0.2841  0.2748  0.5078 
Al:  0.3702  0.7997  0.3080 
Si:  0.4647  0.8840  0.8233 
O:  0.1946  0.9926  0.2037 
O:  0.2837  0.0578  0.7510 
O:  0.1120  0.8872  0.7156 
O:  0.6036  0.9086  0.7768 
O:  0.5038  0.7900  0.1246 
O:  0.4630  0.7747  0.6240 
O:  0.3354  0.6540  0.2864 
H:  0.2193  0.7863  0.7747 
Si:  0.8071  0.3649  0.6946 
Si:  0.8846  0.4612  0.1828 
O:  0.9842  0.1985  0.7875 
O:  0.0582  0.2861  0.2543 
O:  0.8892  0.1114  0.2837 
O:  0.8852  0.6144  0.2072 
O:  0.7896  0.4873  0.8818 
O:  0.7794  0.4546  0.3953 
O:  0.6663  0.3366  0.7045 
H:  0.7852  0.2156  0.2274 
Mg:  0.9130  0.9095  0.5000 
Mg:  0.8209  0.8271  0.9971 
Ca:  0.7106  0.7271  0.4959 
Si:  0.6354  0.1962  0.6974 
Si:  0.5347  0.1211  0.1851 
O:  0.8053  0.0248  0.7802 
O:  0.7067  0.9508  0.2700 
O:  0.3730  0.1276  0.1863 
O:  0.5137  0.2189  0.8902 
O:  0.5329  0.2276  0.4040 
Si:  0.1949  0.6299  0.3006 
Si:  0.1129  0.5329  0.8124 
O:  0.0221  0.8010  0.2187 
O:  0.9434  0.7067  0.7265 
O:  0.1160  0.3724  0.8042 
O:  0.2065  0.5071  0.1127 
O:  0.2202  0.5302  0.5963 
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: 1.9023 0.0074 -0.0184 
0.0189 1.9842 0.0135 
-0.0333 0.0023 2.0438 
Eig. Value: 1.8954 1.9860 2.0488 
Al: 3.1860 0.0719 -0.0054 
0.0328 3.0671 -0.0114 
0.0565 0.0251 2.8392 
Eig. Value: 3.2076 3.0474 2.8372 
Mg: 1.8629 -0.0380 0.0669 
-0.0137 2.1190 -0.0097 
0.0092 -0.0130 1.9741 
Eig. Value: 1.8494 2.1231 1.9834 
Ca: 2.4646 0.0074 -0.0063 
-0.0025 2.0498 -0.0180 
0.0148 -0.0169 2.2921 
Eig. Value: 2.4647 2.0485 2.2933 
Al: 2.2972 0.1369 -0.0526 
-0.0177 2.9561 0.1004 
-0.0308 -0.0465 2.5966 
Eig. Value: 2.2857 2.9630 2.6014 
Si: 2.9582 0.2598 -0.1530 
0.0429 2.7335 0.0481 
-0.2256 0.1247 3.2195 
Eig. Value: 2.9813 2.6110 3.3190 
O: -1.8365 0.0856 -0.1119 
0.0802 -1.8009 0.1254 
-0.1273 0.1593 -1.6850 
Eig. Value: -2.0081 -1.7389 -1.5755 
O: -2.3233 -0.0908 0.0048 
-0.0231 -1.4355 -0.0480 
0.0352 -0.0570 -1.6555 
Eig. Value: -2.3274 -1.4196 -1.6673 
O: -1.1762 0.0155 0.1094 
-0.0082 -1.5458 0.0061 
0.0871 -0.0032 -1.4777 
Eig. Value: -1.1470 -1.5459 -1.5069 
O: -1.6713 -0.3259 0.1027 
-0.2522 -1.9130 -0.0025 
0.1266 -0.0442 -1.5361 
Eig. Value: -1.3944 -2.1089 -1.6171 
O: -1.4413 -0.3004 0.0117 
-0.2079 -1.4954 0.3458 
0.0068 0.3886 -2.2705 
Eig. Value: -1.1546 -1.6245 -2.4281 
O: -1.5077 -0.0120 0.2888 
0.0586 -1.6394 -0.5321 
0.2883 -0.5478 -2.0518 
Eig. Value: -1.5205 -1.1896 -2.4889 
O: -1.2289 -0.0232 -0.0453 
-0.0615 -2.6388 0.0100 
-0.0151 0.0069 -1.1751 
Eig. Value: -1.2416 -2.6401 -1.1612 
H: 0.2698 0.0137 -0.0687 
0.0201 0.5401 -0.0225 
-0.0654 -0.0115 0.5135 
Eig. Value: 0.2520 0.5569 0.5145 
Si: 2.8235 -0.1516 -0.0982 
0.0624 3.6763 -0.1072 
-0.0999 0.0771 3.3163 
Eig. Value: 2.8018 3.6789 3.3354 
Si: 3.0623 -0.3520 -0.2526 
-0.0237 2.8359 -0.0108 
-0.2895 -0.2041 3.4531 
Eig. Value: 3.1002 2.6591 3.5920 
O: -1.9398 -0.0943 -0.1743 
-0.0969 -1.6941 -0.1156 
-0.1909 -0.1474 -1.6160 
Eig. Value: -2.0758 -1.6803 -1.4938 
O: -2.2314 0.0886 0.0275 
-0.0355 -1.4259 0.0419 
0.0625 0.0632 -1.6451 
Eig. Value: -2.2355 -1.4124 -1.6546 
O: -1.1369 -0.0141 0.1248 
0.0016 -1.5433 -0.0001 
0.1120 0.0029 -1.4549 
Eig. Value: -1.0976 -1.5436 -1.4939 
O: -1.7435 0.3713 0.0990 
0.3297 -1.8053 0.0604 
0.0972 0.1200 -1.5171 
Eig. Value: -1.3284 -2.1263 -1.6112 
O: -1.4056 0.3886 0.2053 
0.2985 -1.5392 -0.5533 
0.2042 -0.5965 -2.3011 
Eig. Value: -1.0683 -1.4752 -2.7026 
O: -1.3829 0.0161 0.2478 
-0.0633 -1.6071 0.6950 
0.2669 0.7373 -2.3255 
Eig. Value: -1.4000 -1.1101 -2.8053 
O: -1.1306 -0.0283 -0.0332 
-0.0338 -3.0126 0.0004 
-0.0056 -0.0077 -1.0963 
Eig. Value: -1.1389 -3.0131 -1.0875 
H: 0.2126 0.0002 -0.0851 
-0.0104 0.5267 0.0058 
-0.0878 0.0077 0.4857 
Eig. Value: 0.1876 0.5300 0.5075 
Mg: 2.0149 -0.0130 -0.0376 
-0.0069 2.0377 0.0020 
-0.0196 -0.0013 1.9752 
Eig. Value: 2.0240 2.0438 1.9600 
Mg: 2.1755 -0.0081 0.0411 
-0.0029 1.9887 -0.0118 
0.0529 -0.0029 1.9188 
Eig. Value: 2.1840 1.9890 1.9099 
Ca: 2.5326 0.0300 -0.0078 
-0.0087 2.0343 0.0080 
-0.0143 0.0138 2.2774 
Eig. Value: 2.5333 2.0336 2.2774 
Si: 2.8035 0.2461 -0.0852 
0.0950 3.8136 0.1437 
-0.1316 -0.0126 3.2397 
Eig. Value: 2.7473 3.8454 3.2641 
Si: 3.0348 0.4351 -0.2606 
0.0692 2.9262 0.0243 
-0.2107 0.2149 3.5713 
Eig. Value: 3.2138 2.6575 3.6610 
O: -1.9110 -0.0379 -0.1066 
-0.0430 -1.6228 -0.0182 
-0.0926 0.0027 -1.5388 
Eig. Value: -1.9413 -1.6176 -1.5138 
O: -2.0364 -0.0956 -0.1111 
0.0090 -1.4799 -0.0382 
-0.1122 -0.0744 -1.6050 
Eig. Value: -2.0688 -1.4583 -1.5941 
O: -1.7919 -0.5743 0.0264 
-0.4985 -2.0220 -0.1807 
-0.0079 -0.2967 -1.5680 
Eig. Value: -1.2678 -2.4914 -1.6227 
O: -1.4110 -0.4040 0.2568 
-0.3126 -1.5926 0.5599 
0.2331 0.5905 -2.3020 
Eig. Value: -1.0973 -1.4694 -2.7390 
O: -1.4187 -0.0622 0.2111 
0.0297 -1.6291 -0.6937 
0.2315 -0.7198 -2.3016 
Eig. Value: -1.4573 -1.1203 -2.7717 
Si: 2.7949 -0.2341 -0.0931 
-0.1241 3.5690 -0.1782 
-0.1346 0.0083 3.1855 
Eig. Value: 2.7192 3.6168 3.2134 
Si: 3.0236 -0.4119 -0.2327 
-0.1000 2.8801 -0.0224 
-0.2042 -0.2308 3.5425 
Eig. Value: 3.1966 2.6259 3.6238 
O: -1.9791 0.0291 -0.1156 
0.0557 -1.5980 0.0230 
-0.1082 -0.0131 -1.5272 
Eig. Value: -2.0096 -1.5939 -1.5007 
O: -2.0846 0.0950 -0.1349 
-0.0041 -1.4725 0.0379 
-0.1190 0.0710 -1.5926 
Eig. Value: -2.1205 -1.4515 -1.5778 
O: -1.7851 0.5120 0.0148 
0.4640 -2.0161 0.1632 
-0.0128 0.2663 -1.5680 
Eig. Value: -1.3187 -2.4352 -1.6153 
O: -1.4072 0.4148 0.2216 
0.3228 -1.5914 -0.5592 
0.1966 -0.6039 -2.3201 
Eig. Value: -1.0736 -1.5027 -2.7424 
O: -1.4385 0.0468 0.2301 
-0.0399 -1.6178 0.7188 
0.2575 0.7684 -2.3132 
Eig. Value: -1.4633 -1.0894 -2.8168 
Atom type 

Dielectric tensors: 

 
Ɛ2.7121 0.0000 0.0000 
0.0000 2.7409 0.0000 
0.0000 0.0000 2.7623 
Eig. Value: 2.7121 2.7409 2.7623 
Refractive index (N): 1.6468 0.0000 0.0000 
0.0000 1.6556 0.0000 
0.0000 0.0000 1.6620 
Eig. Value: 1.6468 1.6556 1.6620 
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