ThCr2Si2 Structure : A2B2C_tI10_139_d_e_a

Picture of Structure; Click for Big Picture
Prototype : Cr2Si2Th
AFLOW prototype label : A2B2C_tI10_139_d_e_a
Strukturbericht designation : None
Pearson symbol : tI10
Space group number : 139
Space group symbol : $I4/mmm$
AFLOW prototype command : aflow --proto=A2B2C_tI10_139_d_e_a
--params=
$a$,$c/a$,$z_{3}$


Other compounds with this structure

  • BaAl2Ge2, BaFe2As2, BaFe2P2, BaMn2Ge2, BaNi2As2, BaNi2Ge2, BaRh2B2, CaAl2Zn2, CaAu2Si2, CaFe2As2, CaMn2Ge2, CaNi2Ge2, CeAl2Ga2, CsCo2As2, CsCo2P2, CsFe2As2, CsFe2P2, CsIr2As2, CsIr2P2, CsRh2As2, CsRh2P2, CsRu2As2, CsRu2P2, DyCr2Si2, EuCo2As2, EuCo2P2, EuFe2P2, EuRh2P2, KNi2S2, KNi2Se2, LaCo2P2, LaRu2P2, LuFe2B2, LuRu2Si2, PuCr2Si2, SrCo2P2, SrFe2As2, SrFe2P2, SrNi2P2, SrRh2P2, SrRu2P2, ThCu2Si2, ThMn2Ge2, ThMn2Si2, ThNi2Si2, UCr2Si2, and YNi2Ge2

  • (Shatruk, 2019) refers to this as the perovskite of intermetallics. The list of compounds above is by no means complete.
  • This is a ternary form of the $D1_{3}$ (BaAl4) structure.
  • The structures generally identified as having prototype ThCr2Si2 actually divide into two distinct regions, based on $c/a$ ratio. We assign structures with $c/a \le 3$ to the ThCr2Si2 structure, and those with $c/a > 3$ to the TlCo2S2 structure.

Body-centered Tetragonal primitive vectors:

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

Basis vectors:

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

References

  • Z. Ban and M. Sikirica, The crystal structure of ternary silicides Th$M$2Si2 ($M$ = Cr, Mn, Fe, Co, Ni and Cu), Acta Cryst. 18, 594–599 (1965), doi:10.1107/S0365110X6500141X.

Geometry files


Prototype Generator

aflow --proto=A2B2C_tI10_139_d_e_a --params=

Species:

Running:

Output: