Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A2B7C2_tP88_76_4a_14a_4a-001

If you are using this page, please cite:
H. Eckert, S. Divilov, M. J. Mehl, D. Hicks, A. C. Zettel, M. Esters. X. Campilongo and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 4. Submitted to Computational Materials Science.

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https://aflow.org/p/BAJJ
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β-Ca$_{2}$P$_{2}$O$_{7}$ Structure: A2B7C2_tP88_76_4a_14a_4a-001

Picture of Structure; Click for Big Picture
Prototype Ca$_{2}$O$_{7}$P$_{2}$
AFLOW prototype label A2B7C2_tP88_76_4a_14a_4a-001
ICSD 73712
Pearson symbol tP88
Space group number 76
Space group symbol $P4_1$
AFLOW prototype command aflow --proto=A2B7C2_tP88_76_4a_14a_4a-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak y_{16}, \allowbreak z_{16}, \allowbreak x_{17}, \allowbreak y_{17}, \allowbreak z_{17}, \allowbreak x_{18}, \allowbreak y_{18}, \allowbreak z_{18}, \allowbreak x_{19}, \allowbreak y_{19}, \allowbreak z_{19}, \allowbreak x_{20}, \allowbreak y_{20}, \allowbreak z_{20}, \allowbreak x_{21}, \allowbreak y_{21}, \allowbreak z_{21}, \allowbreak x_{22}, \allowbreak y_{22}, \allowbreak z_{22}$

Other compounds with this structure

Eu$_{2}$Si$_{2}$O$_{7}$,  La$_{2}$Si$_{2}$O$_{7}$,  Nd$_{2}$Si$_{2}$O$_{7}$,  Pr$_{2}$Si$_{2}$O$_{7}$,  Sm$_{2}$Si$_{2}$O$_{7}$


  • (Felsche, 1970) refers to this as the A-RE$_{2}$Si$_{2}$O$_{7}$ structure, where RE is a rare-earth element.
  • This is the low-temperature form of Ca$_{2}$P$_{2}$O$_{7}$. At higher temperatures it transforms into the monoclinic $\alpha$–Ca$_{2}$P$_{2}$O$_{7}$ structure.
  • The origin of the $z$-axis in space group $P4_{1}$ #76 is not specified. We fix it by setting $z_{1} = 0$.

\[ \begin{array}{ccc} \mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}} \end{array}\]

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $x_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ = $a x_{1} \,\mathbf{\hat{x}}+a y_{1} \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ (4a) Ca I
$\mathbf{B_{2}}$ = $- x_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{1} \,\mathbf{\hat{x}}- a y_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) Ca I
$\mathbf{B_{3}}$ = $- y_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a y_{1} \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (4a) Ca I
$\mathbf{B_{4}}$ = $y_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}+\left(z_{1} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a y_{1} \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (4a) Ca I
$\mathbf{B_{5}}$ = $x_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ = $a x_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ (4a) Ca II
$\mathbf{B_{6}}$ = $- x_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) Ca II
$\mathbf{B_{7}}$ = $- y_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a y_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (4a) Ca II
$\mathbf{B_{8}}$ = $y_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a y_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (4a) Ca II
$\mathbf{B_{9}}$ = $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ = $a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ (4a) Ca III
$\mathbf{B_{10}}$ = $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) Ca III
$\mathbf{B_{11}}$ = $- y_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a y_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (4a) Ca III
$\mathbf{B_{12}}$ = $y_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a y_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (4a) Ca III
$\mathbf{B_{13}}$ = $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ = $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ (4a) Ca IV
$\mathbf{B_{14}}$ = $- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) Ca IV
$\mathbf{B_{15}}$ = $- y_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a y_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (4a) Ca IV
$\mathbf{B_{16}}$ = $y_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a y_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (4a) Ca IV
$\mathbf{B_{17}}$ = $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ (4a) O I
$\mathbf{B_{18}}$ = $- x_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O I
$\mathbf{B_{19}}$ = $- y_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a y_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (4a) O I
$\mathbf{B_{20}}$ = $y_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a y_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (4a) O I
$\mathbf{B_{21}}$ = $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ (4a) O II
$\mathbf{B_{22}}$ = $- x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O II
$\mathbf{B_{23}}$ = $- y_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a y_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (4a) O II
$\mathbf{B_{24}}$ = $y_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a y_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (4a) O II
$\mathbf{B_{25}}$ = $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ = $a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ (4a) O III
$\mathbf{B_{26}}$ = $- x_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O III
$\mathbf{B_{27}}$ = $- y_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a y_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (4a) O III
$\mathbf{B_{28}}$ = $y_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a y_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (4a) O III
$\mathbf{B_{29}}$ = $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ = $a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ (4a) O IV
$\mathbf{B_{30}}$ = $- x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O IV
$\mathbf{B_{31}}$ = $- y_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a y_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (4a) O IV
$\mathbf{B_{32}}$ = $y_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a y_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (4a) O IV
$\mathbf{B_{33}}$ = $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ = $a x_{9} \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ (4a) O V
$\mathbf{B_{34}}$ = $- x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{9} \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O V
$\mathbf{B_{35}}$ = $- y_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a y_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (4a) O V
$\mathbf{B_{36}}$ = $y_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a y_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (4a) O V
$\mathbf{B_{37}}$ = $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ = $a x_{10} \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ (4a) O VI
$\mathbf{B_{38}}$ = $- x_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{10} \,\mathbf{\hat{x}}- a y_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O VI
$\mathbf{B_{39}}$ = $- y_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a y_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (4a) O VI
$\mathbf{B_{40}}$ = $y_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a y_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (4a) O VI
$\mathbf{B_{41}}$ = $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ = $a x_{11} \,\mathbf{\hat{x}}+a y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ (4a) O VII
$\mathbf{B_{42}}$ = $- x_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{11} \,\mathbf{\hat{x}}- a y_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O VII
$\mathbf{B_{43}}$ = $- y_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a y_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (4a) O VII
$\mathbf{B_{44}}$ = $y_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a y_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (4a) O VII
$\mathbf{B_{45}}$ = $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ = $a x_{12} \,\mathbf{\hat{x}}+a y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ (4a) O VIII
$\mathbf{B_{46}}$ = $- x_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{12} \,\mathbf{\hat{x}}- a y_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O VIII
$\mathbf{B_{47}}$ = $- y_{12} \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a y_{12} \,\mathbf{\hat{x}}+a x_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (4a) O VIII
$\mathbf{B_{48}}$ = $y_{12} \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a y_{12} \,\mathbf{\hat{x}}- a x_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (4a) O VIII
$\mathbf{B_{49}}$ = $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ = $a x_{13} \,\mathbf{\hat{x}}+a y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ (4a) O IX
$\mathbf{B_{50}}$ = $- x_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{13} \,\mathbf{\hat{x}}- a y_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O IX
$\mathbf{B_{51}}$ = $- y_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a y_{13} \,\mathbf{\hat{x}}+a x_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (4a) O IX
$\mathbf{B_{52}}$ = $y_{13} \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a y_{13} \,\mathbf{\hat{x}}- a x_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (4a) O IX
$\mathbf{B_{53}}$ = $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ = $a x_{14} \,\mathbf{\hat{x}}+a y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ (4a) O X
$\mathbf{B_{54}}$ = $- x_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{14} \,\mathbf{\hat{x}}- a y_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O X
$\mathbf{B_{55}}$ = $- y_{14} \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a y_{14} \,\mathbf{\hat{x}}+a x_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (4a) O X
$\mathbf{B_{56}}$ = $y_{14} \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a y_{14} \,\mathbf{\hat{x}}- a x_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (4a) O X
$\mathbf{B_{57}}$ = $x_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ = $a x_{15} \,\mathbf{\hat{x}}+a y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ (4a) O XI
$\mathbf{B_{58}}$ = $- x_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{15} \,\mathbf{\hat{x}}- a y_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O XI
$\mathbf{B_{59}}$ = $- y_{15} \, \mathbf{a}_{1}+x_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a y_{15} \,\mathbf{\hat{x}}+a x_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (4a) O XI
$\mathbf{B_{60}}$ = $y_{15} \, \mathbf{a}_{1}- x_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a y_{15} \,\mathbf{\hat{x}}- a x_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (4a) O XI
$\mathbf{B_{61}}$ = $x_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ = $a x_{16} \,\mathbf{\hat{x}}+a y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ (4a) O XII
$\mathbf{B_{62}}$ = $- x_{16} \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{16} \,\mathbf{\hat{x}}- a y_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O XII
$\mathbf{B_{63}}$ = $- y_{16} \, \mathbf{a}_{1}+x_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a y_{16} \,\mathbf{\hat{x}}+a x_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (4a) O XII
$\mathbf{B_{64}}$ = $y_{16} \, \mathbf{a}_{1}- x_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a y_{16} \,\mathbf{\hat{x}}- a x_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (4a) O XII
$\mathbf{B_{65}}$ = $x_{17} \, \mathbf{a}_{1}+y_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ = $a x_{17} \,\mathbf{\hat{x}}+a y_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ (4a) O XIII
$\mathbf{B_{66}}$ = $- x_{17} \, \mathbf{a}_{1}- y_{17} \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{17} \,\mathbf{\hat{x}}- a y_{17} \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O XIII
$\mathbf{B_{67}}$ = $- y_{17} \, \mathbf{a}_{1}+x_{17} \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a y_{17} \,\mathbf{\hat{x}}+a x_{17} \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (4a) O XIII
$\mathbf{B_{68}}$ = $y_{17} \, \mathbf{a}_{1}- x_{17} \, \mathbf{a}_{2}+\left(z_{17} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a y_{17} \,\mathbf{\hat{x}}- a x_{17} \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (4a) O XIII
$\mathbf{B_{69}}$ = $x_{18} \, \mathbf{a}_{1}+y_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ = $a x_{18} \,\mathbf{\hat{x}}+a y_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ (4a) O XIV
$\mathbf{B_{70}}$ = $- x_{18} \, \mathbf{a}_{1}- y_{18} \, \mathbf{a}_{2}+\left(z_{18} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{18} \,\mathbf{\hat{x}}- a y_{18} \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O XIV
$\mathbf{B_{71}}$ = $- y_{18} \, \mathbf{a}_{1}+x_{18} \, \mathbf{a}_{2}+\left(z_{18} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a y_{18} \,\mathbf{\hat{x}}+a x_{18} \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (4a) O XIV
$\mathbf{B_{72}}$ = $y_{18} \, \mathbf{a}_{1}- x_{18} \, \mathbf{a}_{2}+\left(z_{18} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a y_{18} \,\mathbf{\hat{x}}- a x_{18} \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (4a) O XIV
$\mathbf{B_{73}}$ = $x_{19} \, \mathbf{a}_{1}+y_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ = $a x_{19} \,\mathbf{\hat{x}}+a y_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ (4a) P I
$\mathbf{B_{74}}$ = $- x_{19} \, \mathbf{a}_{1}- y_{19} \, \mathbf{a}_{2}+\left(z_{19} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{19} \,\mathbf{\hat{x}}- a y_{19} \,\mathbf{\hat{y}}+c \left(z_{19} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) P I
$\mathbf{B_{75}}$ = $- y_{19} \, \mathbf{a}_{1}+x_{19} \, \mathbf{a}_{2}+\left(z_{19} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a y_{19} \,\mathbf{\hat{x}}+a x_{19} \,\mathbf{\hat{y}}+c \left(z_{19} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (4a) P I
$\mathbf{B_{76}}$ = $y_{19} \, \mathbf{a}_{1}- x_{19} \, \mathbf{a}_{2}+\left(z_{19} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a y_{19} \,\mathbf{\hat{x}}- a x_{19} \,\mathbf{\hat{y}}+c \left(z_{19} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (4a) P I
$\mathbf{B_{77}}$ = $x_{20} \, \mathbf{a}_{1}+y_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ = $a x_{20} \,\mathbf{\hat{x}}+a y_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ (4a) P II
$\mathbf{B_{78}}$ = $- x_{20} \, \mathbf{a}_{1}- y_{20} \, \mathbf{a}_{2}+\left(z_{20} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{20} \,\mathbf{\hat{x}}- a y_{20} \,\mathbf{\hat{y}}+c \left(z_{20} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) P II
$\mathbf{B_{79}}$ = $- y_{20} \, \mathbf{a}_{1}+x_{20} \, \mathbf{a}_{2}+\left(z_{20} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a y_{20} \,\mathbf{\hat{x}}+a x_{20} \,\mathbf{\hat{y}}+c \left(z_{20} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (4a) P II
$\mathbf{B_{80}}$ = $y_{20} \, \mathbf{a}_{1}- x_{20} \, \mathbf{a}_{2}+\left(z_{20} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a y_{20} \,\mathbf{\hat{x}}- a x_{20} \,\mathbf{\hat{y}}+c \left(z_{20} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (4a) P II
$\mathbf{B_{81}}$ = $x_{21} \, \mathbf{a}_{1}+y_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ = $a x_{21} \,\mathbf{\hat{x}}+a y_{21} \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ (4a) P III
$\mathbf{B_{82}}$ = $- x_{21} \, \mathbf{a}_{1}- y_{21} \, \mathbf{a}_{2}+\left(z_{21} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{21} \,\mathbf{\hat{x}}- a y_{21} \,\mathbf{\hat{y}}+c \left(z_{21} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) P III
$\mathbf{B_{83}}$ = $- y_{21} \, \mathbf{a}_{1}+x_{21} \, \mathbf{a}_{2}+\left(z_{21} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a y_{21} \,\mathbf{\hat{x}}+a x_{21} \,\mathbf{\hat{y}}+c \left(z_{21} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (4a) P III
$\mathbf{B_{84}}$ = $y_{21} \, \mathbf{a}_{1}- x_{21} \, \mathbf{a}_{2}+\left(z_{21} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a y_{21} \,\mathbf{\hat{x}}- a x_{21} \,\mathbf{\hat{y}}+c \left(z_{21} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (4a) P III
$\mathbf{B_{85}}$ = $x_{22} \, \mathbf{a}_{1}+y_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ = $a x_{22} \,\mathbf{\hat{x}}+a y_{22} \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ (4a) P IV
$\mathbf{B_{86}}$ = $- x_{22} \, \mathbf{a}_{1}- y_{22} \, \mathbf{a}_{2}+\left(z_{22} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{22} \,\mathbf{\hat{x}}- a y_{22} \,\mathbf{\hat{y}}+c \left(z_{22} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) P IV
$\mathbf{B_{87}}$ = $- y_{22} \, \mathbf{a}_{1}+x_{22} \, \mathbf{a}_{2}+\left(z_{22} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a y_{22} \,\mathbf{\hat{x}}+a x_{22} \,\mathbf{\hat{y}}+c \left(z_{22} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (4a) P IV
$\mathbf{B_{88}}$ = $y_{22} \, \mathbf{a}_{1}- x_{22} \, \mathbf{a}_{2}+\left(z_{22} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a y_{22} \,\mathbf{\hat{x}}- a x_{22} \,\mathbf{\hat{y}}+c \left(z_{22} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (4a) P IV

References

  • S. Boudin, A. Grandin, M. M. Borel, A. Leclaire, and B. Raveau, Redetermination of the β-Ca$_{2}$P$_{2}$O$_{7}$ structure, Acta Crystallogr. Sect. C 49, 2062–2064 (1993), doi:10.1107/S0108270193005608.
  • J. Felsche, Polymorphism and crystal data of the rare-earth disilicates of type R.E.$_{2}$Si$_{2}$O$_{7}$, J. Less-Common Met. 21, 1–14 (1970), doi:10.1016/0022-5088(70)90159-1.

Prototype Generator

aflow --proto=A2B7C2_tP88_76_4a_14a_4a --params=$a,c/a,x_{1},y_{1},z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14},x_{15},y_{15},z_{15},x_{16},y_{16},z_{16},x_{17},y_{17},z_{17},x_{18},y_{18},z_{18},x_{19},y_{19},z_{19},x_{20},y_{20},z_{20},x_{21},y_{21},z_{21},x_{22},y_{22},z_{22}$

Species:

Running:

Output: