Ca3PI3 Structure: A3B3C_cI56_214_g_h_a

Picture of Structure; Click for Big Picture
Prototype : Ca3PI3
AFLOW prototype label : A3B3C_cI56_214_g_h_a
Strukturbericht designation : None
Pearson symbol : cI56
Space group number : 214
Space group symbol : $I4_{1}32$
AFLOW prototype command : aflow --proto=A3B3C_cI56_214_g_h_a
--params=
$a$,$y_{2}$,$y_{3}$


Body-centered Cubic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(8a\right) & \mbox{P} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{3} & = & - \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(8a\right) & \mbox{P} \\ \mathbf{B}_{3} & = & \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}}- \frac{1}{8}a \, \mathbf{\hat{z}} & \left(8a\right) & \mbox{P} \\ \mathbf{B}_{4} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{8}a \, \mathbf{\hat{x}}- \frac{1}{8}a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(8a\right) & \mbox{P} \\ \mathbf{B}_{5} & = & \left(\frac{1}{4} +2y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{3}{8} +y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{8} +y_{2}\right) \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + y_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +y_{2}\right)a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Ca} \\ \mathbf{B}_{6} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(\frac{1}{8} +y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{3}{8} - y_{2}\right) \, \mathbf{a}_{3} & = & - \frac{1}{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +y_{2}\right)a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Ca} \\ \mathbf{B}_{7} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(\frac{1}{8} - y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{3}{8} +y_{2}\right) \, \mathbf{a}_{3} & = & \frac{7}{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - y_{2}\right)a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Ca} \\ \mathbf{B}_{8} & = & \left(\frac{1}{4} - 2y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{3}{8} - y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{8} - y_{2}\right) \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}}-y_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - y_{2}\right)a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Ca} \\ \mathbf{B}_{9} & = & \left(\frac{1}{8} +y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +2y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{3}{8} +y_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +y_{2}\right)a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + y_{2}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Ca} \\ \mathbf{B}_{10} & = & \left(\frac{3}{8} - y_{2}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{8} +y_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +y_{2}\right)a \, \mathbf{\hat{x}}- \frac{1}{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - y_{2}\right)a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Ca} \\ \mathbf{B}_{11} & = & \left(\frac{3}{8} +y_{2}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{8} - y_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - y_{2}\right)a \, \mathbf{\hat{x}} + \frac{7}{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{2}\right)a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Ca} \\ \mathbf{B}_{12} & = & \left(\frac{1}{8} - y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - 2y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{3}{8} - y_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - y_{2}\right)a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}}-y_{2}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Ca} \\ \mathbf{B}_{13} & = & \left(\frac{3}{8} +y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{8} +y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +2y_{2}\right) \, \mathbf{a}_{3} & = & y_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{2}\right)a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Ca} \\ \mathbf{B}_{14} & = & \left(\frac{1}{8} +y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{3}{8} - y_{2}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{2}\right)a \, \mathbf{\hat{y}}- \frac{1}{8}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Ca} \\ \mathbf{B}_{15} & = & \left(\frac{1}{8} - y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{3}{8} +y_{2}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - y_{2}\right)a \, \mathbf{\hat{y}} + \frac{7}{8}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Ca} \\ \mathbf{B}_{16} & = & \left(\frac{3}{8} - y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{8} - y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - 2y_{2}\right) \, \mathbf{a}_{3} & = & -y_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - y_{2}\right)a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Ca} \\ \mathbf{B}_{17} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(\frac{3}{8} - y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{8} +y_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - y_{3}\right)a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{I} \\ \mathbf{B}_{18} & = & \left(\frac{3}{4} - 2y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{8} - y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{3}{8} - y_{3}\right) \, \mathbf{a}_{3} & = & - \frac{1}{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - y_{3}\right)a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{I} \\ \mathbf{B}_{19} & = & \left(\frac{3}{4} +2y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{8} +y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{3}{8} +y_{3}\right) \, \mathbf{a}_{3} & = & \frac{7}{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +y_{3}\right)a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{I} \\ \mathbf{B}_{20} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(\frac{3}{8} +y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{8} - y_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +y_{3}\right)a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{I} \\ \mathbf{B}_{21} & = & \left(\frac{1}{8} +y_{3}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{3}{8} - y_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - y_{3}\right)a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + y_{3}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{I} \\ \mathbf{B}_{22} & = & \left(\frac{3}{8} - y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} - 2y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{8} - y_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - y_{3}\right)a \, \mathbf{\hat{x}}- \frac{1}{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - y_{3}\right)a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{I} \\ \mathbf{B}_{23} & = & \left(\frac{3}{8} +y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} +2y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{8} +y_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +y_{3}\right)a \, \mathbf{\hat{x}} + \frac{7}{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{I} \\ \mathbf{B}_{24} & = & \left(\frac{1}{8} - y_{3}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{3}{8} +y_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +y_{3}\right)a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}}-y_{3}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{I} \\ \mathbf{B}_{25} & = & \left(\frac{3}{8} - y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{8} +y_{3}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - y_{3}\right)a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{I} \\ \mathbf{B}_{26} & = & \left(\frac{1}{8} - y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{3}{8} - y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} - 2y_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - y_{3}\right)a \, \mathbf{\hat{y}}- \frac{1}{8}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{I} \\ \mathbf{B}_{27} & = & \left(\frac{1}{8} +y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{3}{8} +y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} +2y_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{3}\right)a \, \mathbf{\hat{y}} + \frac{7}{8}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{I} \\ \mathbf{B}_{28} & = & \left(\frac{3}{8} +y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{8} - y_{3}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{3}\right)a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{I} \\ \end{array} \]

References

  • C. Hamon, R. Marchand, Y. Laurent, and J. Lang, Etude d'halogenopictures. m. Structures de Ca2PI et Ca3Pl3. Sur structures de type NaCl, Bull. Soc. fr. Mineral. Crystallogr. 97, 6–12 (1974).

Found in

  • P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds, ASM International (2013).

Geometry files


Prototype Generator

aflow --proto=A3B3C_cI56_214_g_h_a --params=

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