Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: AB_cP8_198_a_a.FeSi

  • M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
  • D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comp. Mat. Sci. 161, S1-S1011 (2019). (doi=10.1016/j.commatsci.2018.10.043)
  • 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)

FeSi ($B20$) Structure: AB_cP8_198_a_a

Picture of Structure; Click for Big Picture
Prototype : FeSi
AFLOW prototype label : AB_cP8_198_a_a
Strukturbericht designation : $B20$
Pearson symbol : cP8
Space group number : 198
Space group symbol : $\text{P2}_{1}\text{3}$
AFLOW prototype command : aflow --proto=AB_cP8_198_a_a
--params=
$a$,$x_{1}$,$x_{2}$


Other compounds with this structure

  • AlPt, AuBe, CoGe, CoSi, FeGe, GaPd, GeMn, GeRh, HfSb, HfSn, RhS, SbZr, SiTc

  • When $x_{1} = 0$ and $x_{2} = 1/2$, or $x_{1} = 1/4$ and $x_{2} = 3/4$, this lattice reduces to the rock salt (B1) structure. When $x_{1} = - x_{2} = 1/8 \left(\sqrt5 - 1\right)$ we have an ideal structure where every atom is seven-fold coordinated. Note that $\alpha$–CO (AB_cP8_198_a_a, $\alpha$–CO) and FeSi (AB_cP8_198_a_a, FeSi) have the same AFLOW prototype label. They are generated by the same symmetry operations with different sets of parameters (––params) specified in their corresponding CIF files.

Simple Cubic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & a \, \mathbf{\hat{x}} \\ \mathbf{a}_2 & = & a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & a \, \mathbf{\hat{z}} \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = &x_{1} \, \mathbf{a}_{1}+ x_{1} \, \mathbf{a}_{2}+ x_{1} \, \mathbf{a}_{3}& = &x_{1} \, a \, \mathbf{\hat{x}}+ x_{1} \, a \, \mathbf{\hat{y}}+ x_{1} \, a \, \mathbf{\hat{z}}& \left(4a\right) & \text{Fe} \\ \mathbf{B}_{2} & = &\left(\frac12 - x_{1}\right) \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}+ \left(\frac12 + x_{1}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{x}}- x_{1} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{z}}& \left(4a\right) & \text{Fe} \\ \mathbf{B}_{3} & = &- x_{1} \, \mathbf{a}_{1}+ \left(\frac12 + x_{1}\right) \, \mathbf{a}_{2}+ \left(\frac12 - x_{1}\right) \, \mathbf{a}_{3}& = &- x_{1} \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{z}}& \left(4a\right) & \text{Fe} \\ \mathbf{B}_{4} & = &+ \left(\frac12 + x_{1}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{1}\right) \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}& = &+ \left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{y}}- x_{1} \, a \, \mathbf{\hat{z}}& \left(4a\right) & \text{Fe} \\ \mathbf{B}_{5} & = &x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& = &x_{2} \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}+ x_{2} \, a \, \mathbf{\hat{z}}& \left(4a\right) & \text{Si} \\ \mathbf{B}_{6} & = &\left(\frac12 - x_{2}\right) \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(4a\right) & \text{Si} \\ \mathbf{B}_{7} & = &- x_{2} \, \mathbf{a}_{1}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{2}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{3}& = &- x_{2} \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(4a\right) & \text{Si} \\ \mathbf{B}_{8} & = &+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& = &+ \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{y}}- x_{2} \, a \, \mathbf{\hat{z}}& \left(4a\right) & \text{Si} \\ \end{array} \]

References

  • L. Vovcadlo, K. S. Knight, G. D. Price, and I. G. Wood, Thermal expansion and crystal structure of FeSi between 4 and 1173 K determined by time–of–flight neutron powder diffraction, Phys. Chem. Miner. 29, 132–139 (2002), doi:10.1007/s002690100202.

Geometry files


Prototype Generator

aflow --proto=AB_cP8_198_a_a --params=

Species:

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