Averievite [(ClCu)$_{2}$Cu$_{5}$O$_{2}$(PO$_{4}$)$_{2}$] Structure: A18B15C10D2_hP45_164_ij_abcdei_2di_d-001

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Prototype Cl$_{2}$Cu$_{7}$O$_{2}$(PO$_{4}$)$_{2}$
AFLOW prototype label A18B15C10D2_hP45_164_ij_abcdei_2di_d-001
Mineral name averievite
ICSD 30943
CCDC 2063823
Pearson symbol hP45
Space group number 164
Space group symbol $P\overline{3}m1$
AFLOW prototype command aflow --proto=A18B15C10D2_hP45_164_ij_abcdei_2di_d-001
--params=$a, \allowbreak c/a, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak z_{6}, \allowbreak z_{7}, \allowbreak x_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}$

  • 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:
  • See (Starov, 1997), (Botana, 2018), and (Kornyakov, 2021) for more information.
  • While all averievites have considerable disorder, (ClCu)$_{2}$Cu$_{5}$O$_{2}$(VO$_{4}$)$_{2}$ has more disorder than most:
    • The Cu I (1a) site is occupied 49.3% of the time
    • The Cu II (1b) occupation is 53.6%
    • The Cu III (2c) occupation is 35.6%
    • The Cu IV (2d) occupation is 36.0%
    • The Cl I (6i) occupation is 8.0%
    • The Cu VI (6i) occupation is 21.0%
    • The Cl II (12i) occupation is 16.4%.
  • These occupations lead to the compound Cl$_{2.064}$Cu$_{6.721}$O$_{10}$V$_{2}$ which becomes (Cl$_{2.064}$Cu$_{1.721}$)Cu$_{5}$O$_{2}$(VO$_{4}$)$_{2}$ in standard averievite notation.
  • We have shifted the origin by 1/2 c $\hat{z}$, swaping the (1a) and (1b) sites and moving the experimental Cu (3f) site to Cu (3e).

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

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $0$ = $0$ (1a) Cu I
$\mathbf{B_{2}}$ = $\frac{1}{2} \, \mathbf{a}_{3}$ = $\frac{1}{2}c \,\mathbf{\hat{z}}$ (1b) Cu II
$\mathbf{B_{3}}$ = $z_{3} \, \mathbf{a}_{3}$ = $c z_{3} \,\mathbf{\hat{z}}$ (2c) Cu III
$\mathbf{B_{4}}$ = $- z_{3} \, \mathbf{a}_{3}$ = $- c z_{3} \,\mathbf{\hat{z}}$ (2c) Cu III
$\mathbf{B_{5}}$ = $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ (2d) Cu IV
$\mathbf{B_{6}}$ = $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ (2d) Cu IV
$\mathbf{B_{7}}$ = $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ (2d) O I
$\mathbf{B_{8}}$ = $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ (2d) O I
$\mathbf{B_{9}}$ = $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ (2d) O II
$\mathbf{B_{10}}$ = $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ (2d) O II
$\mathbf{B_{11}}$ = $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ (2d) V I
$\mathbf{B_{12}}$ = $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ (2d) V I
$\mathbf{B_{13}}$ = $\frac{1}{2} \, \mathbf{a}_{1}$ = $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}$ (3e) Cu V
$\mathbf{B_{14}}$ = $\frac{1}{2} \, \mathbf{a}_{2}$ = $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}$ (3e) Cu V
$\mathbf{B_{15}}$ = $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}$ (3e) Cu V
$\mathbf{B_{16}}$ = $x_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ = $- \sqrt{3}a x_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ (6i) Cl I
$\mathbf{B_{17}}$ = $x_{9} \, \mathbf{a}_{1}+2 x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ = $\frac{3}{2}a x_{9} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ (6i) Cl I
$\mathbf{B_{18}}$ = $- 2 x_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ = $- \frac{3}{2}a x_{9} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ (6i) Cl I
$\mathbf{B_{19}}$ = $- x_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ = $\sqrt{3}a x_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ (6i) Cl I
$\mathbf{B_{20}}$ = $2 x_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ = $\frac{3}{2}a x_{9} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ (6i) Cl I
$\mathbf{B_{21}}$ = $- x_{9} \, \mathbf{a}_{1}- 2 x_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ = $- \frac{3}{2}a x_{9} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ (6i) Cl I
$\mathbf{B_{22}}$ = $x_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ = $- \sqrt{3}a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ (6i) Cu VI
$\mathbf{B_{23}}$ = $x_{10} \, \mathbf{a}_{1}+2 x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ = $\frac{3}{2}a x_{10} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ (6i) Cu VI
$\mathbf{B_{24}}$ = $- 2 x_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ = $- \frac{3}{2}a x_{10} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ (6i) Cu VI
$\mathbf{B_{25}}$ = $- x_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ = $\sqrt{3}a x_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ (6i) Cu VI
$\mathbf{B_{26}}$ = $2 x_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ = $\frac{3}{2}a x_{10} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ (6i) Cu VI
$\mathbf{B_{27}}$ = $- x_{10} \, \mathbf{a}_{1}- 2 x_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ = $- \frac{3}{2}a x_{10} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ (6i) Cu VI
$\mathbf{B_{28}}$ = $x_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ = $- \sqrt{3}a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ (6i) O III
$\mathbf{B_{29}}$ = $x_{11} \, \mathbf{a}_{1}+2 x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ = $\frac{3}{2}a x_{11} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ (6i) O III
$\mathbf{B_{30}}$ = $- 2 x_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ = $- \frac{3}{2}a x_{11} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ (6i) O III
$\mathbf{B_{31}}$ = $- x_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ = $\sqrt{3}a x_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ (6i) O III
$\mathbf{B_{32}}$ = $2 x_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ = $\frac{3}{2}a x_{11} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ (6i) O III
$\mathbf{B_{33}}$ = $- x_{11} \, \mathbf{a}_{1}- 2 x_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ = $- \frac{3}{2}a x_{11} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ (6i) O III
$\mathbf{B_{34}}$ = $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{12} + y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{12} - y_{12}\right) \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ (12j) Cl II
$\mathbf{B_{35}}$ = $- y_{12} \, \mathbf{a}_{1}+\left(x_{12} - y_{12}\right) \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{12} - 2 y_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ (12j) Cl II
$\mathbf{B_{36}}$ = $- \left(x_{12} - y_{12}\right) \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(2 x_{12} - y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ (12j) Cl II
$\mathbf{B_{37}}$ = $y_{12} \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{12} + y_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{12} - y_{12}\right) \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ (12j) Cl II
$\mathbf{B_{38}}$ = $\left(x_{12} - y_{12}\right) \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{12} - 2 y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{12} \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ (12j) Cl II
$\mathbf{B_{39}}$ = $- x_{12} \, \mathbf{a}_{1}- \left(x_{12} - y_{12}\right) \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(2 x_{12} - y_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{12} \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ (12j) Cl II
$\mathbf{B_{40}}$ = $- x_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{12} + y_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{12} - y_{12}\right) \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ (12j) Cl II
$\mathbf{B_{41}}$ = $y_{12} \, \mathbf{a}_{1}- \left(x_{12} - y_{12}\right) \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(- x_{12} + 2 y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{12} \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ (12j) Cl II
$\mathbf{B_{42}}$ = $\left(x_{12} - y_{12}\right) \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(2 x_{12} - y_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{12} \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ (12j) Cl II
$\mathbf{B_{43}}$ = $- y_{12} \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{12} + y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{12} - y_{12}\right) \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ (12j) Cl II
$\mathbf{B_{44}}$ = $- \left(x_{12} - y_{12}\right) \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(- x_{12} + 2 y_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ (12j) Cl II
$\mathbf{B_{45}}$ = $x_{12} \, \mathbf{a}_{1}+\left(x_{12} - y_{12}\right) \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(2 x_{12} - y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ (12j) Cl II

References

  • 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.
  • 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.

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=A18B15C10D2_hP45_164_ij_abcdei_2di_d --params=$a,c/a,z_{3},z_{4},z_{5},z_{6},z_{7},x_{9},z_{9},x_{10},z_{10},x_{11},z_{11},x_{12},y_{12},z_{12}$

Species:

Running:

Output: