KH2PO4 ($H2_{2}$) Structure : A4BC4D_tI40_122_e_b_e_a

Picture of Structure; Click for Big Picture
Prototype : H2KO4P
AFLOW prototype label : A4BC4D_tI40_122_e_b_e_a
Strukturbericht designation : $H2_{2}$
Pearson symbol : tI40
Space group number : 122
Space group symbol : $I\bar{4}2d$
AFLOW prototype command : aflow --proto=A4BC4D_tI40_122_e_b_e_a
--params=
$a$,$c/a$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$


Other compounds with this structure

  • RbH2PO4, KH2AsO4, RbH2AsO4, CsH2AsO4, NH4H2PO4, and NH4H2AsO4

  • The hydrogen ($16e$) sites are half–occupied. Given the closeness of pairs of hydrogen positions, presumably only one site in each pair is ever occupied.
  • This partial occupancy gives a structure that differs slightly from the $H2_{2}$ structure described by (Ewald, 1928). There, the hydrogen atoms are at their averaged positions, Wyckoff position ($8d$).

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(4a\right) & \mbox{P} \\ \mathbf{B}_{2} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{P} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{K} \\ \mathbf{B}_{4} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{K} \\ \mathbf{B}_{5} & = & \left(y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}+z_{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(16e\right) & \mbox{H} \\ \mathbf{B}_{6} & = & \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}+z_{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(16e\right) & \mbox{H} \\ \mathbf{B}_{7} & = & \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(16e\right) & \mbox{H} \\ \mathbf{B}_{8} & = & \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(16e\right) & \mbox{H} \\ \mathbf{B}_{9} & = & \left(\frac{3}{4} +y_{3} - z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{3} - z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{3} + y_{3}\right) \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{3}\right)c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{H} \\ \mathbf{B}_{10} & = & \left(\frac{3}{4} - y_{3} - z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{3} - z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{3} - y_{3}\right) \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{3}\right)c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{H} \\ \mathbf{B}_{11} & = & \left(\frac{3}{4} - x_{3} + z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - y_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{3} - y_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{H} \\ \mathbf{B}_{12} & = & \left(\frac{3}{4} +x_{3} + z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +y_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{3} + y_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{H} \\ \mathbf{B}_{13} & = & \left(y_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(x_{4}+z_{4}\right) \, \mathbf{a}_{2} + \left(x_{4}+y_{4}\right) \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + y_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{O} \\ \mathbf{B}_{14} & = & \left(-y_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(-x_{4}+z_{4}\right) \, \mathbf{a}_{2} + \left(-x_{4}-y_{4}\right) \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-y_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{O} \\ \mathbf{B}_{15} & = & \left(-x_{4}-z_{4}\right) \, \mathbf{a}_{1} + \left(y_{4}-z_{4}\right) \, \mathbf{a}_{2} + \left(-x_{4}+y_{4}\right) \, \mathbf{a}_{3} & = & y_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{O} \\ \mathbf{B}_{16} & = & \left(x_{4}-z_{4}\right) \, \mathbf{a}_{1} + \left(-y_{4}-z_{4}\right) \, \mathbf{a}_{2} + \left(x_{4}-y_{4}\right) \, \mathbf{a}_{3} & = & -y_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{O} \\ \mathbf{B}_{17} & = & \left(\frac{3}{4} +y_{4} - z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{4} - z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{4} + y_{4}\right) \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{4}\right)c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{O} \\ \mathbf{B}_{18} & = & \left(\frac{3}{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{4} - z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{4} - y_{4}\right) \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{4}\right)c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{O} \\ \mathbf{B}_{19} & = & \left(\frac{3}{4} - x_{4} + z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{4} - y_{4}\right) \, \mathbf{a}_{3} & = & -y_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{O} \\ \mathbf{B}_{20} & = & \left(\frac{3}{4} +x_{4} + z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +y_{4} + z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{4} + y_{4}\right) \, \mathbf{a}_{3} & = & y_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{O} \\ \end{array} \]

References

  • R. J. Nelmes, G. M. Meyer, and J. E. Tibballs, The crystal structure of tetragonal KH2PO4 and KD2PO4 as a function of temperature, J. Phys. C:\ Solid State Phys. 15, 59–75 (1982), doi:10.1088/0022-3719/15/1/005. Corrigendum: R. J. Nelmes and G. M. Meyer and J. E. Tibballs, J. Phys. C 15, 3040 (1982).
  • R. J. Nelmes, G. M. Meyer, and J. E. Tibballs, The crystal structure of tetragonal KH2PO4 and KD2PO4 as a function of temperature, J. Phys. C:\ Solid State Phys. 15, 3040 (1982), doi:10.1088/0022-3719/15/13/531. Corrigendum to R. J. Nelmes and G. M. Meyer and J. E. Tibballs, J. Phys. C 15, 59 (1982).
  • P. P. Ewald and C. Hermann, eds., Strukturbericht 1913–1928 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1931).

Geometry files


Prototype Generator

aflow --proto=A4BC4D_tI40_122_e_b_e_a --params=

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