Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A7B2_cF144_227_2ef_e-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.

Links to this page

https://aflow.org/p/WYVV
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Dy$_{5}$Pd$_{2}$ Structure: A7B2_cF144_227_2ef_e-001

Picture of Structure; Click for Big Picture
Prototype Dy$_{5}$Pd$_{2}$
AFLOW prototype label A7B2_cF144_227_2ef_e-001
ICSD 103347
Pearson symbol cF144
Space group number 227
Space group symbol $Fd\overline{3}m$
AFLOW prototype command aflow --proto=A7B2_cF144_227_2ef_e-001
--params=$a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}$

Other compounds with this structure

Er$_{5}$Pd$_{2}$,  Ho$_{5}$Pd$_{2}$,  Lu$_{5}$Pd$_{2}$,  Tb$_{5}$Pd$_{2}$,  Tm$_{5}$Pd$_{2}$,  Y$_{5}$Pd$_{2}$


  • There is considerable disorder in this structure, with all of the (32e) sites having vacancies:
    • The Dy-I site is 50% occupied.
    • The Dy-II site is 12.5% occupied
    • The Pd site is 87.5% occupied.
  • This gives a composition of Dy$_{2.43}$Pd.

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

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ = $a x_{1} \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}+a x_{1} \,\mathbf{\hat{z}}$ (32e) Dy I
$\mathbf{B_{2}}$ = $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}- \left(3 x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{1} \,\mathbf{\hat{z}}$ (32e) Dy I
$\mathbf{B_{3}}$ = $x_{1} \, \mathbf{a}_{1}- \left(3 x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ = $- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (32e) Dy I
$\mathbf{B_{4}}$ = $- \left(3 x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ = $a x_{1} \,\mathbf{\hat{x}}- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (32e) Dy I
$\mathbf{B_{5}}$ = $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}+\left(3 x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{1} \,\mathbf{\hat{z}}$ (32e) Dy I
$\mathbf{B_{6}}$ = $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ = $- a x_{1} \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}- a x_{1} \,\mathbf{\hat{z}}$ (32e) Dy I
$\mathbf{B_{7}}$ = $- x_{1} \, \mathbf{a}_{1}+\left(3 x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ = $a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}+a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (32e) Dy I
$\mathbf{B_{8}}$ = $\left(3 x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ = $- a x_{1} \,\mathbf{\hat{x}}+a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (32e) Dy I
$\mathbf{B_{9}}$ = $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ = $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ (32e) Dy II
$\mathbf{B_{10}}$ = $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}- \left(3 x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ (32e) Dy II
$\mathbf{B_{11}}$ = $x_{2} \, \mathbf{a}_{1}- \left(3 x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ = $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (32e) Dy II
$\mathbf{B_{12}}$ = $- \left(3 x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ = $a x_{2} \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (32e) Dy II
$\mathbf{B_{13}}$ = $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\left(3 x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ (32e) Dy II
$\mathbf{B_{14}}$ = $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ = $- a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ (32e) Dy II
$\mathbf{B_{15}}$ = $- x_{2} \, \mathbf{a}_{1}+\left(3 x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ = $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (32e) Dy II
$\mathbf{B_{16}}$ = $\left(3 x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ = $- a x_{2} \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (32e) Dy II
$\mathbf{B_{17}}$ = $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ = $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ (32e) Pd I
$\mathbf{B_{18}}$ = $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- \left(3 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ (32e) Pd I
$\mathbf{B_{19}}$ = $x_{3} \, \mathbf{a}_{1}- \left(3 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ = $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (32e) Pd I
$\mathbf{B_{20}}$ = $- \left(3 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ = $a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (32e) Pd I
$\mathbf{B_{21}}$ = $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\left(3 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ (32e) Pd I
$\mathbf{B_{22}}$ = $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ = $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ (32e) Pd I
$\mathbf{B_{23}}$ = $- x_{3} \, \mathbf{a}_{1}+\left(3 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ = $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (32e) Pd I
$\mathbf{B_{24}}$ = $\left(3 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ = $- a x_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (32e) Pd I
$\mathbf{B_{25}}$ = $- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ = $a x_{4} \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ (48f) Dy III
$\mathbf{B_{26}}$ = $x_{4} \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ (48f) Dy III
$\mathbf{B_{27}}$ = $x_{4} \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ = $\frac{1}{8}a \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ (48f) Dy III
$\mathbf{B_{28}}$ = $- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $\frac{1}{8}a \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ (48f) Dy III
$\mathbf{B_{29}}$ = $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ (48f) Dy III
$\mathbf{B_{30}}$ = $- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ = $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (48f) Dy III
$\mathbf{B_{31}}$ = $\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $\frac{3}{8}a \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ (48f) Dy III
$\mathbf{B_{32}}$ = $- x_{4} \, \mathbf{a}_{1}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ = $\frac{3}{8}a \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ (48f) Dy III
$\mathbf{B_{33}}$ = $- x_{4} \, \mathbf{a}_{1}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{4} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ (48f) Dy III
$\mathbf{B_{34}}$ = $\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ = $- a x_{4} \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ (48f) Dy III
$\mathbf{B_{35}}$ = $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ (48f) Dy III
$\mathbf{B_{36}}$ = $\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ = $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (48f) Dy III

References

  • M. L. Fornasini and Palenzona, Crystal structure of the so-called R.E.$_{5}$Pd$_{2}$ compounds, J. Less-Common Met. 38, 77–82 (1974), doi:10.1016/0022-5088(74)90205-7.

Prototype Generator

aflow --proto=A7B2_cF144_227_2ef_e --params=$a,x_{1},x_{2},x_{3},x_{4}$

Species:

Running:

Output: