Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A10B3C4_oP68_55_2e2fgh2i_adef_2e2f-001

This structure previously used the label(s) A10B3C4_oP68_55_2e2fgh2i_adef_2e2f. Calls to these addresses will be redirected here.

Links to this page

https://aflow.org/p/PEKW
or ../A10B3C4_oP68_55_2e2fgh2i_adef_2e2f-001
or PDF Version

Orthorhombic Sr$_{4}$Ru$_{3}$O$_{10}$ Structure: A10B3C4_oP68_55_2e2fgh2i_adef_2e2f-001

Picture of Structure; Click for Big Picture
Prototype O$_{10}$Ru$_{3}$Sr$_{4}$
AFLOW prototype label A10B3C4_oP68_55_2e2fgh2i_adef_2e2f-001
ICSD 96729
CCDC 1656068
Pearson symbol oC68
Space group number 64
Space group symbol $Cmce$
AFLOW prototype command aflow --proto=A10B3C4_oP68_55_2e2fgh2i_adef_2e2f-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}$

  • This structure consists of triple-layer ruthenate structures separated by 2.37Å from each other. In the $Pbam$ #55 space group shown here there are two inequivalent stacks in the orthorhombic cell.
  • This cell is very problematic. (Crawford, 2002) note that the x-ray scattering intensities are pseudo body-centered, but found that refining this structure in a body-centered cell with space group $Bbcm$ ($Cmca$ #64 in our standard orientation) led to non-positive definite thermal parameters. In that case there is only one triple-layer stack in the primitive cell, and the two stacks in the conventional orthorhombic cell are equivalent.
  • If we use AFLOW with its default tolerance the structure also resolves into the smaller unit cell. The current cell can be recovered by using a smaller tolerance:
  • aflow --proto=A10B3C4_oC68_64_2dfg_ad_2d:O:Ru:Sr --params=a,b/a,c/a,x$_{2}$,z$_{3}$,z$_{4}$,z$_{5}$,z$_{6}$,z$_{7}$,z$_{8}$,z$_{9}$,z$_{10}$,z$_{11}$,z$_{12}$,x$_{13}$,y$_{13}$,x$_{14}$,y$_{14}$,x$_{15}$,y$_{15}$,z$_{15}$,x$_{16}$,y$_{16}$,z$_{16}$ --tolerance=0.001 .
  • Note that the lattice constants in the CIF for ICSD 96729 do not agree with the lattice constants in (Crawford, 2002), although the atomic positions are the same.

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

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $0$ = $0$ (4a) Ru I
$\mathbf{B_{2}}$ = $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ (4a) Ru I
$\mathbf{B_{3}}$ = $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}$ = $a x_{2} \,\mathbf{\hat{x}}$ (8d) O I
$\mathbf{B_{4}}$ = $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ (8d) O I
$\mathbf{B_{5}}$ = $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}$ = $- a x_{2} \,\mathbf{\hat{x}}$ (8d) O I
$\mathbf{B_{6}}$ = $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ (8d) O I
$\mathbf{B_{7}}$ = $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}$ = $a x_{3} \,\mathbf{\hat{x}}$ (8d) O II
$\mathbf{B_{8}}$ = $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ (8d) O II
$\mathbf{B_{9}}$ = $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}$ = $- a x_{3} \,\mathbf{\hat{x}}$ (8d) O II
$\mathbf{B_{10}}$ = $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ (8d) O II
$\mathbf{B_{11}}$ = $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}$ = $a x_{4} \,\mathbf{\hat{x}}$ (8d) Ru II
$\mathbf{B_{12}}$ = $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ (8d) Ru II
$\mathbf{B_{13}}$ = $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}$ = $- a x_{4} \,\mathbf{\hat{x}}$ (8d) Ru II
$\mathbf{B_{14}}$ = $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ (8d) Ru II
$\mathbf{B_{15}}$ = $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}$ = $a x_{5} \,\mathbf{\hat{x}}$ (8d) Sr I
$\mathbf{B_{16}}$ = $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ (8d) Sr I
$\mathbf{B_{17}}$ = $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}$ = $- a x_{5} \,\mathbf{\hat{x}}$ (8d) Sr I
$\mathbf{B_{18}}$ = $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ (8d) Sr I
$\mathbf{B_{19}}$ = $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}$ = $a x_{6} \,\mathbf{\hat{x}}$ (8d) Sr II
$\mathbf{B_{20}}$ = $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ (8d) Sr II
$\mathbf{B_{21}}$ = $- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}$ = $- a x_{6} \,\mathbf{\hat{x}}$ (8d) Sr II
$\mathbf{B_{22}}$ = $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ (8d) Sr II
$\mathbf{B_{23}}$ = $- y_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ = $b y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ (8f) O III
$\mathbf{B_{24}}$ = $\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8f) O III
$\mathbf{B_{25}}$ = $- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}+b y_{7} \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8f) O III
$\mathbf{B_{26}}$ = $y_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ = $- b y_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ (8f) O III
$\mathbf{B_{27}}$ = $\left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} + y_{8}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ = $a x_{8} \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ (16g) O IV
$\mathbf{B_{28}}$ = $\left(- x_{8} + y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{8} + y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (16g) O IV
$\mathbf{B_{29}}$ = $- \left(x_{8} + y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{8} + y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (16g) O IV
$\mathbf{B_{30}}$ = $\left(x_{8} + y_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ = $a x_{8} \,\mathbf{\hat{x}}- b y_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ (16g) O IV
$\mathbf{B_{31}}$ = $- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} + y_{8}\right) \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ = $- a x_{8} \,\mathbf{\hat{x}}- b y_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ (16g) O IV
$\mathbf{B_{32}}$ = $\left(x_{8} - y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{8} + y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (16g) O IV
$\mathbf{B_{33}}$ = $\left(x_{8} + y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{8} - y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (16g) O IV
$\mathbf{B_{34}}$ = $- \left(x_{8} + y_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ = $- a x_{8} \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ (16g) O IV

References

  • M. K. Crawford, R. L. Harlow, W. Marshall, Z. Li, G. Cao, R. L. Lindstrom, Q. Huang, and J. W. Lynn, Structure and magnetism of single crystal Sr$_{4}$Ru$_{3}$O$_{10}$: A ferromagnetic triple-layer ruthenate, Phys. Rev. B 65, 214412 (2002), doi:10.1103/PhysRevB.65.214412.

First cited in

  • D. Hicks, M.J. Mehl, M. Esters, C. Oses, O. Levy, G.L.W. Hart, C. Toher, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 3, Comp. Mat. Sci. 199, 110450 (2021). (doi=10.1016/j.commatsci.2021.110450)

Geometry files


Prototype Generator

aflow --proto=A10B3C4_oC68_64_2dfg_ad_2d --params=$a,b/a,c/a,x_{2},x_{3},x_{4},x_{5},x_{6},y_{7},z_{7},x_{8},y_{8},z_{8}$

Species:

Running:

Output: