ThCr$_{2}$Si$_{2}$ Structure: A2B2C_tI10_139_d_e_a-003
| Prototype | Cr$_{2}$Si$_{2}$Th |
| AFLOW prototype label | A2B2C_tI10_139_d_e_a-003 |
| ICSD | 18157 |
| Pearson symbol | tI10 |
| Space group number | 139 |
| Space group symbol | $I4/mmm$ |
| AFLOW prototype command |
aflow --proto=A2B2C_tI10_139_d_e_a-003
--params=$a, \allowbreak c/a, \allowbreak z_{3}$ |
Other compounds with this structure
BaAl$_{2}$Ge$_{2}$, BaFe$_{2}$As$_{2}$, BaFe$_{2}$P$_{2}$, BaMg$_{2}$Si$_{2}$, BaMg$_{2}$Ge$_{2}$, BaMn$_{2}$Ge$_{2}$, BaNi$_{2}$As$_{2}$, BaNi$_{2}$Ge$_{2}$, BaRh$_{2}$B$_{2}$, CaAl$_{2}$Zn$_{2}$, CaAu$_{2}$Si$_{2}$, CaFe$_{2}$As$_{2}$, CaMn$_{2}$Ge$_{2}$, CaNi$_{2}$Ge$_{2}$, CeAl$_{2}$Ga$_{2}$, CeCu$_{2}$Si$_{2}$, CeRh$_{2}$Si$_{2}$, CeRu$_{2}$Si$_{2}$, CsCo$_{2}$As$_{2}$, CsCo$_{2}$P$_{2}$, CsFe$_{2}$As$_{2}$, CsFe$_{2}$P$_{2}$, CsIr$_{2}$As$_{2}$, CsIr$_{2}$P$_{2}$, CsRh$_{2}$As$_{2}$, CsRh$_{2}$P$_{2}$, CsRu$_{2}$As$_{2}$, CsRu$_{2}$P$_{2}$, DyCr$_{2}$Si$_{2}$, EuCo$_{2}$As$_{2}$, EuCo$_{2}$P$_{2}$, EuFe$_{2}$P$_{2}$, EuRh$_{2}$P$_{2}$, KNi$_{2}$S$_{2}$, KNi$_{2}$Se$_{2}$, LaCo$_{2}$P$_{2}$, LaRu$_{2}$P$_{2}$, LuFe$_{2}$B$_{2}$, LuRu$_{2}$Si$_{2}$, PuCr$_{2}$Si$_{2}$, SrCo$_{2}$P$_{2}$, SrFe$_{2}$As$_{2}$, SrFe$_{2}$P$_{2}$, SrNi$_{2}$P$_{2}$, SrRh$_{2}$As$_{2}$, SrRh$_{2}$P$_{2}$, SrRu$_{2}$P$_{2}$, ThCr$_{2}$Si$_{2}$, ThCu$_{2}$Si$_{2}$, ThMn$_{2}$Ge$_{2}$, ThMn$_{2}$Si$_{2}$, ThNi$_{2}$Si$_{2}$, TlCu$_{2}$Se$_{2}$, UCr$_{2}$Si$_{2}$, URu$_{2}$Si$_{2}$, YFe$_{2}$Ge$_{2}$, YNi$_{2}$Ge$_{2}$
- (Shatruk, 2019) refers to this as
the perovskite of intermetallics.
The list of compounds below is by no means complete. - This is a ternary form of the $D1_{3}$ (BaAl$_{4}$) structure.
- The structures generally identified as having prototype ThCr$_{2}$Si$_{2}$ actually divide up into two distinct regions, based on $c/a$ ratio. We assign structures with $c/a \le 3$ to the ThCr$_{2}$Si$_{2}$ structure, and those with $c/a > 3$ to the TlCo$_{2}$S$_{2}$ structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Th I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | Cr I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | Cr I |
| $\mathbf{B_{4}}$ | = | $z_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Si I |
| $\mathbf{B_{5}}$ | = | $- z_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}$ | = | $- c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Si I |
References
- Z. Ban and M. Sikirica, The crystal structure of ternary silicides ThM$_{2}$Si$_{2}$ (M = Cr, Mn, Fe, Co, Ni and Cu), Acta Cryst. 18, 594–599 (1964), doi:10.1107/S0365110X6500141X.
- M. Shatruk, ThCr$_{2}$Si$_{2}$ structure type: The
perovskite
of intermetallics, J. Solid State Chem. 272, 198–209 (2019), doi:10.1016/j.jssc.2019.02.012.
Prototype Generator
aflow --proto=A2B2C_tI10_139_d_e_a --params=$a,c/a,z_{3}$