BPO4 ($H0_{7}$) Structure: AB4C_tI12_82_c_g_a

Picture of Structure; Click for Big Picture
Prototype : BPO4
AFLOW prototype label : AB4C_tI12_82_c_g_a
Strukturbericht designation : $H0_{7}$
Pearson symbol : tI12
Space group number : 82
Space group symbol : $\mbox{I}\bar{4}$
AFLOW prototype command : aflow --proto=AB4C_tI12_82_c_g_a
--params=
$a$,$c/a$,$x_{3}$,$y_{3}$,$z_{3}$


Body-centered Tetragonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & - \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, c \, \mathbf{\hat{z}}\\ \mathbf{a}_2 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, c \, \mathbf{\hat{z}}\\ \mathbf{a}_3 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} - \frac12 \, c \, \mathbf{\hat{z}}\\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B_1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(2a\right) & \mbox{P} \\ \mathbf{B_2} & =& \frac34 \, \mathbf{a}_{1} + \frac14 \, \mathbf{a}_{2} + \frac12 \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{y}} + \frac14 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{B} \\ \mathbf{B_3} & =& \left(y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(z_{3}+x_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}+y_{3}\right) \, \mathbf{a}_{3}& =& x_{3} \, a \, \mathbf{\hat{x}} + y_{3} \, a \, \mathbf{\hat{y}} + z_{3} \, c \, \mathbf{\hat{z}}& \left(8g\right) & \mbox{O} \\ \mathbf{B_4} & =& \left(z_{3}-y_{3}\right) \, \mathbf{a}_{1} + \left(z_{3}-x_{3}\right) \, \mathbf{a}_{2} - \left(x_{3}+y_{3}\right) \, \mathbf{a}_{3}& =& - x_{3} \, a \, \mathbf{\hat{x}} - y_{3} \, a \, \mathbf{\hat{y}} + z_{3} \, c \, \mathbf{\hat{z}}& \left(8g\right) & \mbox{O} \\ \mathbf{B_5} & =& - \left(z_{3}+x_{3}\right) \, \mathbf{a}_{1} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(y_{3}-x_{3}\right) \, \mathbf{a}_{3}& =& y_{3} \, a \, \mathbf{\hat{x}} -x_{3} \, a \, \mathbf{\hat{y}} - z_{3} \, c \, \mathbf{\hat{z}}& \left(8g\right) & \mbox{O} \\ \mathbf{B_6} & =& \left(x_{3}-z_{3}\right) \, \mathbf{a}_{1} - \left(y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}-y_{3}\right) \, \mathbf{a}_{3}& =& - y_{3} \, a \, \mathbf{\hat{x}} + x_{3} \, a \, \mathbf{\hat{y}} - z_{3} \, c \, \mathbf{\hat{z}}& \left(8g\right) & \mbox{O} \\ \end{array} \]

References

  • M. Schmidt, B. Ewald, Y. Prots, R. Cardoso–Gil, M. Armbrüster, I. Loa, L. Zhang, Y.–X. Huang, U. Schwarz, and R. Kniep, Growth and Characterization of BPO4 Single Crystals, Z. Anorg. Allg. Chem. 630, 655–662 (2004), doi:10.1002/zaac.200400002.

Geometry files


Prototype Generator

aflow --proto=AB4C_tI12_82_c_g_a --params=

Species:

Running:

Output: