La2O3 ($D5_{2}$) Structure: A2B3_hP5_164_d_ad

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Prototype : La2O3
AFLOW prototype label : A2B3_hP5_164_d_ad
Strukturbericht designation : $D5_{2}$
Pearson symbol : hP5
Space group number : 164
Space group symbol : $P\bar{3}m1$
AFLOW prototype command : aflow --proto=A2B3_hP5_164_d_ad
--params=
$a$,$c/a$,$z_{2}$,$z_{3}$


Other compounds with this structure

  • $\alpha$-Bi2Mg3, $\alpha$-Sb2Mg3, Ac2O3, As2Mg3, Ce2O3, Gd2O3, Nd2O3, Pr2O3, Pu2O3, Th2N3, and U2N3

  • This structure has proved rather controversial. (Zachariasen 1926, 1929) originally proposed that the crystal structure of La2O3 and other lanthanide series oxides belong to trigonal space group $P321$ #150. This was immediately criticized by (Pauling, 1929), who suggested the trigonal space group ($P\bar{3}m1$ #164). This was confirmed by (Koehler, 1953). Much later, (Aldebert, 1979) stated that the structure was hexagonal, space group $P6_3/mmc$ #194. This would represent a doubling of the $P\bar{3}m1$ unit cell in the $z$-direction. However, they give structural parameters, used by us and by (Villars, 1991, 2016), which have a density consistent with the $P\bar{3}m1$ structure, and are in reasonable agreement with lattice parameters given in (Pearson, 1958) and (Koehler, 1953). We agree with (Villars, 1991, 2016) that these are close to the correct values for the structure. This structure is very similar to Al$_{3}$Ni$_{2}$ ($D5_{13}$, A3B2_hP5_164_ad_d). We follow (Pearson, 1958) and assign the intermetallics as $D5_{13}$, keeping $D5_{2}$ for oxides and related compounds. The ternary Ce2O2S structure, aka CaAl2Si2, is related to this structure, the sulfur atom replacing the oxygen on the (1a) site.

Trigonal Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{O I} \\ \mathbf{B}_{2} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(2d\right) & \mbox{La} \\ \mathbf{B}_{3} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2}-z_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(2d\right) & \mbox{La} \\ \mathbf{B}_{4} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(2d\right) & \mbox{O II} \\ \mathbf{B}_{5} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(2d\right) & \mbox{O II} \\ \end{array} \]

References

  • P. Aldebert and J. P. Traverse, Etude par diffraction neutronique des structures de haute temperature de La2O3 et Nd2O3, Mater. Res. Bull. 14, 303–323 (1979), doi:10.1016/0025-5408(79)90095-3.
  • W. Zachariasen, Die Kristallstruktur der A–Modifikation von den Sesquioxyden der seltenen Erdmetalle. (La2O3, Ce2O3, Pr2O3, Nd2O3), Z. Phys. Chem. 123U, 134–150 (1926), doi:10.1515/zpch-1926-12309.
  • W. Zachariasen, Kürzere Originalmitteilungen und Notizen, Zeitschrift für Kristallographie – Crystalline Materials 70, 187–189 (1929), doi:10.1524/zkri.1929.70.1.187.
  • L. Pauling, The Crystal Structure of the A–Modification of the Rare Earth Sesquioxides, Zeitschrift für Kristallographie – Crystalline Materials 69, 415–421 (1929), doi:10.1524/zkri.1929.69.1.415.
  • W. C. Koehler and E. O. Wollan, Neutron–diffraction study of the structure of the A–form of the rare earth sesquioxides, Acta Cryst. 6, 741–742 (1953), doi:10.1107/S0365110X53002076.
  • P. Villars, ed., PAULING FILE in: Inorganic Solid Phases (SpringerMaterials (online database), Heidelberg, 2016).
  • W. B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys, no. N.R.C. No. 4303 in International Series of Monographs on Metal Physics and Physical Metallurgy (Pergamon Press, Oxford, London, Edinburgh, New York, Paris, Frankfort, 1958), 1964 reprint with corrections edn.

Geometry files


Prototype Generator

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