Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A2B7C10D2_hP21_143_2a_2abcd_2b2c2d_bc-001

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Averievite [Cu$_{5}$O$_{2}$(VO$_{4}$)$_{2}\cdot$CuCl$_{2}$] Structure: A2B7C10D2_hP21_143_2a_2abcd_2b2c2d_bc-001

Picture of Structure; Click for Big Picture
Prototype Cl$_{2}$Cu$_{6}$O$_{10}$V$_{2}$
AFLOW prototype label A2B7C10D2_hP21_143_2a_2abcd_2b2c2d_bc-001
Mineral name averievite
ICSD 85128
CCDC 1645070
Pearson symbol hP21
Space group number 143
Space group symbol $P3$
AFLOW prototype command aflow --proto=A2B7C10D2_hP21_143_2a_2abcd_2b2c2d_bc-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak z_{6}, \allowbreak z_{7}, \allowbreak z_{8}, \allowbreak z_{9}, \allowbreak z_{10}, \allowbreak z_{11}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}$

  • Averievite is characterized by the presence of a backbone composed of Cu$_{5}$O$_{2}$ clusters and either VO$_{4}$ or PO$_{4}$ tetrahedra. The exact structure depends on the atoms added to the backbone. We have included several averievite structures in the Encyclopedia, including
  • The current sample builds on stoiberite by including (0001) lines of CuCl$_{2}$ distributed in the interstitials between the tetrahedra. Other configurations are possible, see (Botana, 2018) and (Kornyakov, 2021).
  • The published report of (Starov, 1997), as well as the ICSD entry, omit the O VI atoms and so destroy the VO$_{4}$ tetrahedra. The American Mineralogist Crystal Structure Database entry lists the Wyckoff position for these atoms, noting that this correction was made by S. V. Krivovichev in 2005.
  • The Cu I site is occupied 69% of the time and the Cu II site 32% of the time. This gives the observed stoichiometry. These two atom types are on the CuCl$_{2}$ lines.
  • (Starov, 1997) also give the occupation of the Cl I site as 102% and the Cl II site as 97%.
  • AFLOW shifts the origin of this structure, moving it from the reported Cu III site to the Cl I site.
  • Space group $P3$ #143 allows an arbitrary choice for the $z$-axis origin. We follow (Starova, 1997) and set $z_{9} = 0$ for the Cu III Wyckoff position.
  • $P3$ allows chiral structures so any reflection, e.g. $z \rightarrow -z$ will transform the structure into its enantiomorphic image.

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

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $z_{1} \, \mathbf{a}_{3}$ = $c z_{1} \,\mathbf{\hat{z}}$ (1a) Cl I
$\mathbf{B_{2}}$ = $z_{2} \, \mathbf{a}_{3}$ = $c z_{2} \,\mathbf{\hat{z}}$ (1a) Cl II
$\mathbf{B_{3}}$ = $z_{3} \, \mathbf{a}_{3}$ = $c z_{3} \,\mathbf{\hat{z}}$ (1a) Cu I
$\mathbf{B_{4}}$ = $z_{4} \, \mathbf{a}_{3}$ = $c z_{4} \,\mathbf{\hat{z}}$ (1a) Cu II
$\mathbf{B_{5}}$ = $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ (1b) Cu III
$\mathbf{B_{6}}$ = $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ (1b) O I
$\mathbf{B_{7}}$ = $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ (1b) O II
$\mathbf{B_{8}}$ = $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ (1b) V I
$\mathbf{B_{9}}$ = $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ (1c) Cu IV
$\mathbf{B_{10}}$ = $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ (1c) O III
$\mathbf{B_{11}}$ = $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ (1c) O IV
$\mathbf{B_{12}}$ = $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ (1c) V II
$\mathbf{B_{13}}$ = $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{13} + y_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{13} - y_{13}\right) \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ (3d) Cu V
$\mathbf{B_{14}}$ = $- y_{13} \, \mathbf{a}_{1}+\left(x_{13} - y_{13}\right) \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{13} - 2 y_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ (3d) Cu V
$\mathbf{B_{15}}$ = $- \left(x_{13} - y_{13}\right) \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(2 x_{13} - y_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ (3d) Cu V
$\mathbf{B_{16}}$ = $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{14} + y_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{14} - y_{14}\right) \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ (3d) O V
$\mathbf{B_{17}}$ = $- y_{14} \, \mathbf{a}_{1}+\left(x_{14} - y_{14}\right) \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{14} - 2 y_{14}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ (3d) O V
$\mathbf{B_{18}}$ = $- \left(x_{14} - y_{14}\right) \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(2 x_{14} - y_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ (3d) O V
$\mathbf{B_{19}}$ = $x_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{15} + y_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{15} - y_{15}\right) \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ (3d) O VI
$\mathbf{B_{20}}$ = $- y_{15} \, \mathbf{a}_{1}+\left(x_{15} - y_{15}\right) \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{15} - 2 y_{15}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ (3d) O VI
$\mathbf{B_{21}}$ = $- \left(x_{15} - y_{15}\right) \, \mathbf{a}_{1}- x_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(2 x_{15} - y_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ (3d) O VI

References

  • G. L. Starova, S. V. Krivovichev, V. S. Fundamensky, and S. K. Filatov, The crystal structure of averievite, Cu$_{5}$O$_{2}$(VO$_{4}$)$_{2}\cdot$nMX; comparison with related compounds, Mineral. Mag. 61, 441–446 (1997).
  • A. S. Botana, H. Zheng, S. H. Lapidus, J. F. Mitchell, and M. R. Norman, Averievite: A copper oxide kagome antiferromagnet, Phys. Rev. B 98, August (2018), doi:10.1103/PhysRevB.98.054421.
  • I. V. Kornyakov, V. A. Vladimirova, O. I. Siidra, and S. V. Krivovichev, Expanding the Averievite Family, (MX)Cu$_{5}$O$_{2}$(T$^{5+}$O$_{4}$)$_{2}$ (T$^{5+}$ = P, V; M = K, Rb, Cs, Cu; X = Cl, Br): Synthesis and Single-Crystal X-ray Diffraction Study, Molecules 26, 1833 (2021), doi:10.3390/molecules26071833.

Found in

  • R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).

First cited in

  • N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).

Geometry files


Prototype Generator

aflow --proto=A2B7C10D2_hP21_143_2a_2abcd_2b2c2d_bc --params=$a,c/a,z_{1},z_{2},z_{3},z_{4},z_{5},z_{6},z_{7},z_{8},z_{9},z_{10},z_{11},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14},x_{15},y_{15},z_{15}$

Species:

Running:

Output: