AFLOW Prototype: A4B_tI20_88_f_a-001
This structure originally had the label A4B_tI20_88_f_a. Calls to that address will be redirected here.
If you are using this page, please cite:
D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comp. Mat. Sci. 161, S1-S1011 (2019). (doi=10.1016/j.commatsci.2018.10.043)
Links to this page
https://aflow.org/p/5VT7
or
https://aflow.org/p/A4B_tI20_88_f_a-001
or
PDF Version
Prototype | Cl$_{4}$Th |
AFLOW prototype label | A4B_tI20_88_f_a-001 |
ICSD | 6055 |
Pearson symbol | tI20 |
Space group number | 88 |
Space group symbol | $I4_1/a$ |
AFLOW prototype command |
aflow --proto=A4B_tI20_88_f_a-001
--params=$a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}$ |
ThBr$_{4}$
Basis vectors
Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
---|---|---|---|---|---|---|
$\mathbf{B_{1}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (4a) | Th I |
$\mathbf{B_{2}}$ | = | $\frac{5}{8} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (4a) | Th I |
$\mathbf{B_{3}}$ | = | $\left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (16f) | Cl I |
$\mathbf{B_{4}}$ | = | $\left(- y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (16f) | Cl I |
$\mathbf{B_{5}}$ | = | $\left(x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16f) | Cl I |
$\mathbf{B_{6}}$ | = | $\left(- x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16f) | Cl I |
$\mathbf{B_{7}}$ | = | $- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (16f) | Cl I |
$\mathbf{B_{8}}$ | = | $\left(y_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a \left(y_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (16f) | Cl I |
$\mathbf{B_{9}}$ | = | $- \left(x_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16f) | Cl I |
$\mathbf{B_{10}}$ | = | $\left(x_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16f) | Cl I |