Low Temperature Body-Centered Orthorhombic CH$_{3}$NH$_{3}$PbBr$_{3}$ Structure: A3B4C36D4E_oI192_74_ef_hi_2h8j_hi_c-001
| Prototype | Br$_{3}$CH$_{6}$NPb |
| AFLOW prototype label | A3B4C36D4E_oI192_74_ef_hi_2h8j_hi_c-001 |
| Pearson symbol | oI192 |
| Space group number | 74 |
| Space group symbol | $Imma$ |
| AFLOW prototype command |
aflow --proto=A3B4C36D4E_oI192_74_ef_hi_2h8j_hi_c-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak y_{16}, \allowbreak z_{16}, \allowbreak x_{17}, \allowbreak y_{17}, \allowbreak z_{17}$ |
- CH$_{3}$NH$_{3}$PbBr$_{3}$ can be found in a variety of distorted perovskite ($E2_{1}$) structures, depending upon the temperature and pressure (Abia, 2022; Liang, 2023):
- A low temperature orthorhombic structure, stable below 145K.
- This intermediate temperature body-centered orthorhombic structure, stable from 145-157K.
- An intermediate temperature tetragonal structure, stable from 156-229K.
- The room-temperature cubic perovskite-like structure, stable above 229K.
- A cubic high-pressure Phase II structure, stable from 0.9-1.8 GPa.
- An orthorhombic Phase III structure, stable from 1.8-4.6 GPa.
- Another orthorhombic Phase IV structure was found by (Liang, 2023), but the atomic positions have yet to be calculated.
- We report the data taken at 150.5K
- As should be obvious from the jmol display, the carbon, nitrogen and hydrogen sites are only partially filled. The filling factors used by (Abia, 2022) do not properly account for the stoichiometry, so we have assigned our own values, trying to keep the original ratios for the site occupancies of the various types of atoms. Then
- The C I and N I (8h) sites are occupied 39.3% of the time.
- The C II and N II (8i) sites are occupied 10.7% of the time.
- The H I and HII (8h) sites are occupied 32.4% of the time.
- The H III - H VIII (16j) sites are occupied 8.8% of the time.
- The H IX and H X (16j) sites are occuped 32.4% of the time.
- This occupations will be updated if we get new information about this structure.
- In any case, only one carbon, one nitrogen, and six hydrogen sites are occupied in any unit cell.
- AFLOW rotates the axes used by (Abia, 2022), taking (x y z) $\rightarrow$ (y -x z), and moves the lead atoms from the (4a) to the (4c) site. This also moves the (8g) site to the (8f) site and swaps the (8h) and (8i) Wyckoff positions.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4c) | Pb I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4c) | Pb I |
| $\mathbf{B_{3}}$ | = | $\left(z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (4e) | Br I |
| $\mathbf{B_{4}}$ | = | $- \left(z_{2} - \frac{3}{4}\right) \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (4e) | Br I |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}$ | (8f) | Br II |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}$ | (8f) | Br II |
| $\mathbf{B_{7}}$ | = | $- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}$ | (8f) | Br II |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}$ | (8f) | Br II |
| $\mathbf{B_{9}}$ | = | $\left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}+y_{4} \, \mathbf{a}_{3}$ | = | $b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8h) | C I |
| $\mathbf{B_{10}}$ | = | $\left(- y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8h) | C I |
| $\mathbf{B_{11}}$ | = | $\left(y_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (8h) | C I |
| $\mathbf{B_{12}}$ | = | $- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}$ | = | $- b y_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (8h) | C I |
| $\mathbf{B_{13}}$ | = | $\left(y_{5} + z_{5}\right) \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}+y_{5} \, \mathbf{a}_{3}$ | = | $b y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (8h) | H I |
| $\mathbf{B_{14}}$ | = | $\left(- y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (8h) | H I |
| $\mathbf{B_{15}}$ | = | $\left(y_{5} - z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (8h) | H I |
| $\mathbf{B_{16}}$ | = | $- \left(y_{5} + z_{5}\right) \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}$ | = | $- b y_{5} \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (8h) | H I |
| $\mathbf{B_{17}}$ | = | $\left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ | = | $b y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (8h) | H II |
| $\mathbf{B_{18}}$ | = | $\left(- y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (8h) | H II |
| $\mathbf{B_{19}}$ | = | $\left(y_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (8h) | H II |
| $\mathbf{B_{20}}$ | = | $- \left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ | = | $- b y_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (8h) | H II |
| $\mathbf{B_{21}}$ | = | $\left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}+y_{7} \, \mathbf{a}_{3}$ | = | $b y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (8h) | N I |
| $\mathbf{B_{22}}$ | = | $\left(- y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (8h) | N I |
| $\mathbf{B_{23}}$ | = | $\left(y_{7} - z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}+\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (8h) | N I |
| $\mathbf{B_{24}}$ | = | $- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}- y_{7} \, \mathbf{a}_{3}$ | = | $- b y_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (8h) | N I |
| $\mathbf{B_{25}}$ | = | $\left(z_{8} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (8i) | C II |
| $\mathbf{B_{26}}$ | = | $\left(z_{8} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (8i) | C II |
| $\mathbf{B_{27}}$ | = | $- \left(z_{8} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{8} + z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (8i) | C II |
| $\mathbf{B_{28}}$ | = | $- \left(z_{8} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{8} - z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (8i) | C II |
| $\mathbf{B_{29}}$ | = | $\left(z_{9} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{9} + z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (8i) | N II |
| $\mathbf{B_{30}}$ | = | $\left(z_{9} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{9} - z_{9}\right) \, \mathbf{a}_{2}- \left(x_{9} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (8i) | N II |
| $\mathbf{B_{31}}$ | = | $- \left(z_{9} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{9} + z_{9}\right) \, \mathbf{a}_{2}- \left(x_{9} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (8i) | N II |
| $\mathbf{B_{32}}$ | = | $- \left(z_{9} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{9} - z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (8i) | N II |
| $\mathbf{B_{33}}$ | = | $\left(y_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} + y_{10}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (16j) | H III |
| $\mathbf{B_{34}}$ | = | $\left(- y_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{10} - z_{10}\right) \, \mathbf{a}_{2}- \left(x_{10} + y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- b \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (16j) | H III |
| $\mathbf{B_{35}}$ | = | $\left(y_{10} - z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(- x_{10} + y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}+b \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (16j) | H III |
| $\mathbf{B_{36}}$ | = | $- \left(y_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} - z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} - y_{10}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (16j) | H III |
| $\mathbf{B_{37}}$ | = | $- \left(y_{10} + z_{10}\right) \, \mathbf{a}_{1}- \left(x_{10} + z_{10}\right) \, \mathbf{a}_{2}- \left(x_{10} + y_{10}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (16j) | H III |
| $\mathbf{B_{38}}$ | = | $\left(y_{10} - z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{10} - z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} + y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+b \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (16j) | H III |
| $\mathbf{B_{39}}$ | = | $\left(- y_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} - y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}- b \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (16j) | H III |
| $\mathbf{B_{40}}$ | = | $\left(y_{10} + z_{10}\right) \, \mathbf{a}_{1}- \left(x_{10} - z_{10}\right) \, \mathbf{a}_{2}- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (16j) | H III |
| $\mathbf{B_{41}}$ | = | $\left(y_{11} + z_{11}\right) \, \mathbf{a}_{1}+\left(x_{11} + z_{11}\right) \, \mathbf{a}_{2}+\left(x_{11} + y_{11}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+b y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16j) | H IV |
| $\mathbf{B_{42}}$ | = | $\left(- y_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{11} - z_{11}\right) \, \mathbf{a}_{2}- \left(x_{11} + y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- b \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16j) | H IV |
| $\mathbf{B_{43}}$ | = | $\left(y_{11} - z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{11} + z_{11}\right) \, \mathbf{a}_{2}+\left(- x_{11} + y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}+b \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (16j) | H IV |
| $\mathbf{B_{44}}$ | = | $- \left(y_{11} + z_{11}\right) \, \mathbf{a}_{1}+\left(x_{11} - z_{11}\right) \, \mathbf{a}_{2}+\left(x_{11} - y_{11}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}- b y_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (16j) | H IV |
| $\mathbf{B_{45}}$ | = | $- \left(y_{11} + z_{11}\right) \, \mathbf{a}_{1}- \left(x_{11} + z_{11}\right) \, \mathbf{a}_{2}- \left(x_{11} + y_{11}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- b y_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (16j) | H IV |
| $\mathbf{B_{46}}$ | = | $\left(y_{11} - z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{11} - z_{11}\right) \, \mathbf{a}_{2}+\left(x_{11} + y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+b \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (16j) | H IV |
| $\mathbf{B_{47}}$ | = | $\left(- y_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{11} + z_{11}\right) \, \mathbf{a}_{2}+\left(x_{11} - y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}- b \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16j) | H IV |
| $\mathbf{B_{48}}$ | = | $\left(y_{11} + z_{11}\right) \, \mathbf{a}_{1}- \left(x_{11} - z_{11}\right) \, \mathbf{a}_{2}- \left(x_{11} - y_{11}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}+b y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16j) | H IV |
| $\mathbf{B_{49}}$ | = | $\left(y_{12} + z_{12}\right) \, \mathbf{a}_{1}+\left(x_{12} + z_{12}\right) \, \mathbf{a}_{2}+\left(x_{12} + y_{12}\right) \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}+b y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (16j) | H V |
| $\mathbf{B_{50}}$ | = | $\left(- y_{12} + z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{12} - z_{12}\right) \, \mathbf{a}_{2}- \left(x_{12} + y_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}- b \left(y_{12} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (16j) | H V |
| $\mathbf{B_{51}}$ | = | $\left(y_{12} - z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{12} + z_{12}\right) \, \mathbf{a}_{2}+\left(- x_{12} + y_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}+b \left(y_{12} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (16j) | H V |
| $\mathbf{B_{52}}$ | = | $- \left(y_{12} + z_{12}\right) \, \mathbf{a}_{1}+\left(x_{12} - z_{12}\right) \, \mathbf{a}_{2}+\left(x_{12} - y_{12}\right) \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}- b y_{12} \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (16j) | H V |
| $\mathbf{B_{53}}$ | = | $- \left(y_{12} + z_{12}\right) \, \mathbf{a}_{1}- \left(x_{12} + z_{12}\right) \, \mathbf{a}_{2}- \left(x_{12} + y_{12}\right) \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}- b y_{12} \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (16j) | H V |
| $\mathbf{B_{54}}$ | = | $\left(y_{12} - z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{12} - z_{12}\right) \, \mathbf{a}_{2}+\left(x_{12} + y_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}+b \left(y_{12} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (16j) | H V |
| $\mathbf{B_{55}}$ | = | $\left(- y_{12} + z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{12} + z_{12}\right) \, \mathbf{a}_{2}+\left(x_{12} - y_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}- b \left(y_{12} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (16j) | H V |
| $\mathbf{B_{56}}$ | = | $\left(y_{12} + z_{12}\right) \, \mathbf{a}_{1}- \left(x_{12} - z_{12}\right) \, \mathbf{a}_{2}- \left(x_{12} - y_{12}\right) \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}+b y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (16j) | H V |
| $\mathbf{B_{57}}$ | = | $\left(y_{13} + z_{13}\right) \, \mathbf{a}_{1}+\left(x_{13} + z_{13}\right) \, \mathbf{a}_{2}+\left(x_{13} + y_{13}\right) \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}+b y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (16j) | H VI |
| $\mathbf{B_{58}}$ | = | $\left(- y_{13} + z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{13} - z_{13}\right) \, \mathbf{a}_{2}- \left(x_{13} + y_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}- b \left(y_{13} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (16j) | H VI |
| $\mathbf{B_{59}}$ | = | $\left(y_{13} - z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{13} + z_{13}\right) \, \mathbf{a}_{2}+\left(- x_{13} + y_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}+b \left(y_{13} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (16j) | H VI |
| $\mathbf{B_{60}}$ | = | $- \left(y_{13} + z_{13}\right) \, \mathbf{a}_{1}+\left(x_{13} - z_{13}\right) \, \mathbf{a}_{2}+\left(x_{13} - y_{13}\right) \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}- b y_{13} \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (16j) | H VI |
| $\mathbf{B_{61}}$ | = | $- \left(y_{13} + z_{13}\right) \, \mathbf{a}_{1}- \left(x_{13} + z_{13}\right) \, \mathbf{a}_{2}- \left(x_{13} + y_{13}\right) \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}- b y_{13} \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (16j) | H VI |
| $\mathbf{B_{62}}$ | = | $\left(y_{13} - z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{13} - z_{13}\right) \, \mathbf{a}_{2}+\left(x_{13} + y_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}+b \left(y_{13} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (16j) | H VI |
| $\mathbf{B_{63}}$ | = | $\left(- y_{13} + z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{13} + z_{13}\right) \, \mathbf{a}_{2}+\left(x_{13} - y_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}- b \left(y_{13} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (16j) | H VI |
| $\mathbf{B_{64}}$ | = | $\left(y_{13} + z_{13}\right) \, \mathbf{a}_{1}- \left(x_{13} - z_{13}\right) \, \mathbf{a}_{2}- \left(x_{13} - y_{13}\right) \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}+b y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (16j) | H VI |
| $\mathbf{B_{65}}$ | = | $\left(y_{14} + z_{14}\right) \, \mathbf{a}_{1}+\left(x_{14} + z_{14}\right) \, \mathbf{a}_{2}+\left(x_{14} + y_{14}\right) \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}+b y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (16j) | H VII |
| $\mathbf{B_{66}}$ | = | $\left(- y_{14} + z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{14} - z_{14}\right) \, \mathbf{a}_{2}- \left(x_{14} + y_{14} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}- b \left(y_{14} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (16j) | H VII |
| $\mathbf{B_{67}}$ | = | $\left(y_{14} - z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{14} + z_{14}\right) \, \mathbf{a}_{2}+\left(- x_{14} + y_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}+b \left(y_{14} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (16j) | H VII |
| $\mathbf{B_{68}}$ | = | $- \left(y_{14} + z_{14}\right) \, \mathbf{a}_{1}+\left(x_{14} - z_{14}\right) \, \mathbf{a}_{2}+\left(x_{14} - y_{14}\right) \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}- b y_{14} \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (16j) | H VII |
| $\mathbf{B_{69}}$ | = | $- \left(y_{14} + z_{14}\right) \, \mathbf{a}_{1}- \left(x_{14} + z_{14}\right) \, \mathbf{a}_{2}- \left(x_{14} + y_{14}\right) \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}- b y_{14} \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (16j) | H VII |
| $\mathbf{B_{70}}$ | = | $\left(y_{14} - z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{14} - z_{14}\right) \, \mathbf{a}_{2}+\left(x_{14} + y_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}+b \left(y_{14} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (16j) | H VII |
| $\mathbf{B_{71}}$ | = | $\left(- y_{14} + z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{14} + z_{14}\right) \, \mathbf{a}_{2}+\left(x_{14} - y_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}- b \left(y_{14} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (16j) | H VII |
| $\mathbf{B_{72}}$ | = | $\left(y_{14} + z_{14}\right) \, \mathbf{a}_{1}- \left(x_{14} - z_{14}\right) \, \mathbf{a}_{2}- \left(x_{14} - y_{14}\right) \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}+b y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (16j) | H VII |
| $\mathbf{B_{73}}$ | = | $\left(y_{15} + z_{15}\right) \, \mathbf{a}_{1}+\left(x_{15} + z_{15}\right) \, \mathbf{a}_{2}+\left(x_{15} + y_{15}\right) \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}+b y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (16j) | H VIII |
| $\mathbf{B_{74}}$ | = | $\left(- y_{15} + z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{15} - z_{15}\right) \, \mathbf{a}_{2}- \left(x_{15} + y_{15} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}- b \left(y_{15} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (16j) | H VIII |
| $\mathbf{B_{75}}$ | = | $\left(y_{15} - z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{15} + z_{15}\right) \, \mathbf{a}_{2}+\left(- x_{15} + y_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}+b \left(y_{15} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (16j) | H VIII |
| $\mathbf{B_{76}}$ | = | $- \left(y_{15} + z_{15}\right) \, \mathbf{a}_{1}+\left(x_{15} - z_{15}\right) \, \mathbf{a}_{2}+\left(x_{15} - y_{15}\right) \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}- b y_{15} \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (16j) | H VIII |
| $\mathbf{B_{77}}$ | = | $- \left(y_{15} + z_{15}\right) \, \mathbf{a}_{1}- \left(x_{15} + z_{15}\right) \, \mathbf{a}_{2}- \left(x_{15} + y_{15}\right) \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}- b y_{15} \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (16j) | H VIII |
| $\mathbf{B_{78}}$ | = | $\left(y_{15} - z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{15} - z_{15}\right) \, \mathbf{a}_{2}+\left(x_{15} + y_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}+b \left(y_{15} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (16j) | H VIII |
| $\mathbf{B_{79}}$ | = | $\left(- y_{15} + z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{15} + z_{15}\right) \, \mathbf{a}_{2}+\left(x_{15} - y_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}- b \left(y_{15} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (16j) | H VIII |
| $\mathbf{B_{80}}$ | = | $\left(y_{15} + z_{15}\right) \, \mathbf{a}_{1}- \left(x_{15} - z_{15}\right) \, \mathbf{a}_{2}- \left(x_{15} - y_{15}\right) \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}+b y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (16j) | H VIII |
| $\mathbf{B_{81}}$ | = | $\left(y_{16} + z_{16}\right) \, \mathbf{a}_{1}+\left(x_{16} + z_{16}\right) \, \mathbf{a}_{2}+\left(x_{16} + y_{16}\right) \, \mathbf{a}_{3}$ | = | $a x_{16} \,\mathbf{\hat{x}}+b y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (16j) | H IX |
| $\mathbf{B_{82}}$ | = | $\left(- y_{16} + z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{16} - z_{16}\right) \, \mathbf{a}_{2}- \left(x_{16} + y_{16} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{16} \,\mathbf{\hat{x}}- b \left(y_{16} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (16j) | H IX |
| $\mathbf{B_{83}}$ | = | $\left(y_{16} - z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{16} + z_{16}\right) \, \mathbf{a}_{2}+\left(- x_{16} + y_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{16} \,\mathbf{\hat{x}}+b \left(y_{16} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{16} \,\mathbf{\hat{z}}$ | (16j) | H IX |
| $\mathbf{B_{84}}$ | = | $- \left(y_{16} + z_{16}\right) \, \mathbf{a}_{1}+\left(x_{16} - z_{16}\right) \, \mathbf{a}_{2}+\left(x_{16} - y_{16}\right) \, \mathbf{a}_{3}$ | = | $a x_{16} \,\mathbf{\hat{x}}- b y_{16} \,\mathbf{\hat{y}}- c z_{16} \,\mathbf{\hat{z}}$ | (16j) | H IX |
| $\mathbf{B_{85}}$ | = | $- \left(y_{16} + z_{16}\right) \, \mathbf{a}_{1}- \left(x_{16} + z_{16}\right) \, \mathbf{a}_{2}- \left(x_{16} + y_{16}\right) \, \mathbf{a}_{3}$ | = | $- a x_{16} \,\mathbf{\hat{x}}- b y_{16} \,\mathbf{\hat{y}}- c z_{16} \,\mathbf{\hat{z}}$ | (16j) | H IX |
| $\mathbf{B_{86}}$ | = | $\left(y_{16} - z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{16} - z_{16}\right) \, \mathbf{a}_{2}+\left(x_{16} + y_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{16} \,\mathbf{\hat{x}}+b \left(y_{16} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{16} \,\mathbf{\hat{z}}$ | (16j) | H IX |
| $\mathbf{B_{87}}$ | = | $\left(- y_{16} + z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{16} + z_{16}\right) \, \mathbf{a}_{2}+\left(x_{16} - y_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{16} \,\mathbf{\hat{x}}- b \left(y_{16} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (16j) | H IX |
| $\mathbf{B_{88}}$ | = | $\left(y_{16} + z_{16}\right) \, \mathbf{a}_{1}- \left(x_{16} - z_{16}\right) \, \mathbf{a}_{2}- \left(x_{16} - y_{16}\right) \, \mathbf{a}_{3}$ | = | $- a x_{16} \,\mathbf{\hat{x}}+b y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (16j) | H IX |
| $\mathbf{B_{89}}$ | = | $\left(y_{17} + z_{17}\right) \, \mathbf{a}_{1}+\left(x_{17} + z_{17}\right) \, \mathbf{a}_{2}+\left(x_{17} + y_{17}\right) \, \mathbf{a}_{3}$ | = | $a x_{17} \,\mathbf{\hat{x}}+b y_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (16j) | H X |
| $\mathbf{B_{90}}$ | = | $\left(- y_{17} + z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{17} - z_{17}\right) \, \mathbf{a}_{2}- \left(x_{17} + y_{17} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{17} \,\mathbf{\hat{x}}- b \left(y_{17} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (16j) | H X |
| $\mathbf{B_{91}}$ | = | $\left(y_{17} - z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{17} + z_{17}\right) \, \mathbf{a}_{2}+\left(- x_{17} + y_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{17} \,\mathbf{\hat{x}}+b \left(y_{17} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{17} \,\mathbf{\hat{z}}$ | (16j) | H X |
| $\mathbf{B_{92}}$ | = | $- \left(y_{17} + z_{17}\right) \, \mathbf{a}_{1}+\left(x_{17} - z_{17}\right) \, \mathbf{a}_{2}+\left(x_{17} - y_{17}\right) \, \mathbf{a}_{3}$ | = | $a x_{17} \,\mathbf{\hat{x}}- b y_{17} \,\mathbf{\hat{y}}- c z_{17} \,\mathbf{\hat{z}}$ | (16j) | H X |
| $\mathbf{B_{93}}$ | = | $- \left(y_{17} + z_{17}\right) \, \mathbf{a}_{1}- \left(x_{17} + z_{17}\right) \, \mathbf{a}_{2}- \left(x_{17} + y_{17}\right) \, \mathbf{a}_{3}$ | = | $- a x_{17} \,\mathbf{\hat{x}}- b y_{17} \,\mathbf{\hat{y}}- c z_{17} \,\mathbf{\hat{z}}$ | (16j) | H X |
| $\mathbf{B_{94}}$ | = | $\left(y_{17} - z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{17} - z_{17}\right) \, \mathbf{a}_{2}+\left(x_{17} + y_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{17} \,\mathbf{\hat{x}}+b \left(y_{17} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{17} \,\mathbf{\hat{z}}$ | (16j) | H X |
| $\mathbf{B_{95}}$ | = | $\left(- y_{17} + z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{17} + z_{17}\right) \, \mathbf{a}_{2}+\left(x_{17} - y_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{17} \,\mathbf{\hat{x}}- b \left(y_{17} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (16j) | H X |
| $\mathbf{B_{96}}$ | = | $\left(y_{17} + z_{17}\right) \, \mathbf{a}_{1}- \left(x_{17} - z_{17}\right) \, \mathbf{a}_{2}- \left(x_{17} - y_{17}\right) \, \mathbf{a}_{3}$ | = | $- a x_{17} \,\mathbf{\hat{x}}+b y_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (16j) | H X |
References
- C. Abia, C. A. López, L. C. {n}adillas Delgado, M. T. Fernández-Diaz, and J. A. Alonso, Crystal structure thermal evolution and novel orthorhombic phase of methylammonium lead bromide, CH$_{3}$NH$_{3}$PbBr$_{3}$, Sci. Rep. 12, 18647 (2022), doi:10.1038/s41598-022-21544-2.
- A. Liang, R. Turnbull, C. Popescu, I. Fernandez-Guillen, R. Abargues, P. P. Boix, and D. Errandonea, Pressure-Induced Phase Transition versus Amorphization in Hybrid Methylammonium Lead Bromide Perovskite, J. Phys. Chem. C 127, 12821–12826 (2023), doi:10.1021/acs.jpcc.3c03263.
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=A3B4C36D4E_oI192_74_ef_hi_2h8j_hi_c --params=$a,b/a,c/a,z_{2},x_{3},y_{4},z_{4},y_{5},z_{5},y_{6},z_{6},y_{7},z_{7},x_{8},z_{8},x_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14},x_{15},y_{15},z_{15},x_{16},y_{16},z_{16},x_{17},y_{17},z_{17}$