La$_{3}$TiSb$_{5}$: A3B5C_hP18_193_g_dg_b-001
| Prototype | La$_{3}$Sb$_{5}$Ti |
| AFLOW prototype label | A3B5C_hP18_193_g_dg_b-001 |
| ICSD | 80907 |
| CCDC | 1641084 |
| Pearson symbol | hP18 |
| Space group number | 193 |
| Space group symbol | $P6_3/mcm$ |
| AFLOW prototype command |
aflow --proto=A3B5C_hP18_193_g_dg_b-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak x_{4}$ |
Other compounds with this structure
Al$_{3}$NHf$_{5}$, Ba$_{3}$ScTe$_{5}$, Bi$_{3}$BrBa$_{5}$, Bi$_{3}$BrCa$_{5}$, Bi$_{3}$BrLa$_{5}$, Bi$_{3}$ClBa$_{5}$, Bi$_{3}$ClCa$_{5}$, Bi$_{3}$CuCe$_{5}$, Bi$_{3}$CuGd$_{5}$, Bi$_{3}$CuLa$_{5}$, Bi$_{3}$CuNd$_{5}$, Bi$_{3}$CuPr$_{5}$, Bi$_{3}$CuTb$_{5}$, Bi$_{3}$CuZr$_{5}$, Ce$_{3}$HfSb$_{5}$, Ce$_{3}$MnBi$_{5}$, Ce$_{3}$NbSb$_{5}$, Ce$_{3}$TiBi$_{5}$, Ce$_{3}$TiSb$_{5}$, Ce$_{3}$ZrSb$_{5}$, Ge$_{3}$CrLa$_{5}$, In$_{3}$AgZr$_{5}$, In$_{3}$BrLa$_{5}$, In$_{3}$CuSc$_{5}$, In$_{3}$CuZr$_{5}$, La$_{3}$CrAs$_{5}$, La$_{3}$HfBi$_{5}$, La$_{3}$HfSb$_{5}$, La$_{3}$MgBi$_{5}$, La$_{3}$MnBi$_{5}$, La$_{3}$NbSb$_{5}$, La$_{3}$ScBi$_{5}$, La$_{3}$TiAs$_{5}$, La$_{3}$TiBi$_{5}$, La$_{3}$TiP$_{5}$, La$_{3}$TiSb$_{5}$, La$_{3}$ZrBi$_{5}$, La$_{3}$ZrSb$_{5}$, Nd$_{3}$HfSb$_{5}$, Nd$_{3}$MnBi$_{5}$, Nd$_{3}$NbSb$_{5}$, Nd$_{3}$TiSb$_{5}$, Nd$_{3}$ZrSb$_{5}$, P$_{3}$NV$_{5}$, Pb$_{3}$AgCe$_{5}$, Pb$_{3}$AgLa$_{5}$, Pb$_{3}$AgZr$_{5}$, Pb$_{3}$AlZr$_{5}$, Pb$_{3}$AsLa$_{5}$, Pb$_{3}$AsZr$_{5}$, Pb$_{3}$CdZr$_{5}$, Pb$_{3}$CeLa$_{5}$, Pb$_{3}$CoLa$_{5}$, Pb$_{3}$CoZr$_{5}$, Pb$_{3}$CrLa$_{5}$, Pb$_{3}$CuCe$_{5}$, Pb$_{3}$CuHf$_{5}$, Pb$_{3}$CuLa$_{5}$, Pb$_{3}$CuY$_{5}$, Pb$_{3}$CuZr$_{5}$, Pb$_{3}$FeCa$_{5}$, Pb$_{3}$FeLa$_{5}$, Pb$_{3}$FeZr$_{5}$, Pb$_{3}$GaZr$_{5}$, Pb$_{3}$GeZr$_{5}$, Pb$_{3}$ILa$_{5}$, Pb$_{3}$InZr$_{5}$, Pb$_{3}$MnLa$_{5}$, Pb$_{3}$NiDy$_{5}$, Pb$_{3}$NiEr$_{5}$, Pb$_{3}$NiHo$_{5}$, Pb$_{3}$NiLa$_{5}$, Pb$_{3}$NiLu$_{5}$, Pb$_{3}$NiPr$_{5}$, Pb$_{3}$NiTb$_{5}$, Pb$_{3}$NiTm$_{5}$, Pb$_{3}$NiZr$_{5}$, Pb$_{3}$PLa$_{5}$, Pb$_{3}$PZr$_{5}$, Pb$_{3}$RuLa$_{5}$, Pb$_{3}$SLa$_{5}$, Pb$_{3}$SZr$_{5}$, Pb$_{3}$SbLa$_{5}$, Pb$_{3}$SbZr$_{5}$, Pb$_{3}$SeLa$_{5}$, Pb$_{3}$SeZr$_{5}$, Pb$_{3}$SiZr$_{5}$, Pb$_{3}$SnZr$_{5}$, Pb$_{3}$TeZr$_{5}$, Pb$_{3}$ZnLa$_{5}$, Pb$_{3}$ZnZr$_{5}$, Pr$_{3}$HfSb$_{5}$, Pr$_{3}$MnBi$_{5}$, Pr$_{3}$NbSb$_{5}$, Pr$_{3}$TiSb$_{5}$, Pr$_{3}$ZrSb$_{5}$, Sb$_{3}$AgZr$_{5}$, Sb$_{3}$AlZr$_{5}$, Sb$_{3}$AsZr$_{5}$, Sb$_{3}$BrBa$_{5}$, Sb$_{3}$BrLa$_{5}$, Sb$_{3}$ClBa$_{5}$, Sb$_{3}$ClCa$_{5}$, Sb$_{3}$ClSr$_{5}$, Sb$_{3}$CoZr$_{5}$, Sb$_{3}$CuHf$_{5}$, Sb$_{3}$CuTi$_{5}$, Sb$_{3}$CuZr$_{5}$, Sb$_{3}$FeZr$_{5}$, Sb$_{3}$GeZr$_{5}$, Sb$_{3}$NiHf$_{5}$, Sb$_{3}$NiZr$_{5}$, Sb$_{3}$PZr$_{5}$, Sb$_{3}$RuZr$_{5}$, Sb$_{3}$SZr$_{5}$, Sb$_{3}$SeZr$_{5}$, Sb$_{3}$SiZr$_{5}$, Sb$_{3}$ZnHf$_{5}$, Sb$_{3}$ZnZr$_{5}$, Si$_{3}$DTi$_{5}$, Si$_{3}$PNb$_{5}$, Sm$_{3}$HfSb$_{5}$, Sm$_{3}$NbSb$_{5}$, Sm$_{3}$TiSb$_{5}$, Sm$_{3}$ZrBi$_{5}$, Sm$_{3}$ZrSb$_{5}$, Sn$_{3}$AgCe$_{5}$, Sn$_{3}$AlZr$_{5}$, Sn$_{3}$AsZr$_{5}$, Sn$_{3}$BrLa$_{5}$, Sn$_{3}$ClLa$_{5}$, Sn$_{3}$CuCe$_{5}$, Sn$_{3}$CuYb$_{5}$, Sn$_{3}$CuZr$_{5}$, Sn$_{3}$GaZr$_{5}$, Sn$_{3}$GeZr$_{5}$, Sn$_{3}$HfGa$_{5}$, Sn$_{3}$ILa$_{5}$, Sn$_{3}$LiTb$_{5}$, Sn$_{3}$NZr$_{5}$, Sn$_{3}$NiHf$_{5}$, Sn$_{3}$PZr$_{5}$, Sn$_{3}$SZr$_{5}$, Sn$_{3}$SeZr$_{5}$, Sn$_{3}$SiZr$_{5}$, Sn$_{3}$ZnZr$_{5}$, U$_{3}$CrSb$_{5}$, U$_{3}$HfSb$_{5}$, U$_{3}$MnSb$_{5}$, U$_{3}$NbSb$_{5}$, U$_{3}$ScSb$_{5}$, U$_{3}$TiGe$_{5}$, U$_{3}$TiSb$_{5}$, U$_{3}$VSb$_{5}$, U$_{3}$ZrSb$_{5}$
- This is a ternary form of the Ti$_{5}$Ga$_{4}$ structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2b) | Ti I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2b) | Ti I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}$ | (4d) | Sb I |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4d) | Sb I |
| $\mathbf{B_{5}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}$ | (4d) | Sb I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4d) | Sb I |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{3} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6g) | La I |
| $\mathbf{B_{8}}$ | = | $x_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6g) | La I |
| $\mathbf{B_{9}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6g) | La I |
| $\mathbf{B_{10}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6g) | La I |
| $\mathbf{B_{11}}$ | = | $- x_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{3} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6g) | La I |
| $\mathbf{B_{12}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6g) | La I |
| $\mathbf{B_{13}}$ | = | $x_{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{4} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6g) | Sb II |
| $\mathbf{B_{14}}$ | = | $x_{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{4} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6g) | Sb II |
| $\mathbf{B_{15}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6g) | Sb II |
| $\mathbf{B_{16}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{4} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6g) | Sb II |
| $\mathbf{B_{17}}$ | = | $- x_{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{4} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6g) | Sb II |
| $\mathbf{B_{18}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6g) | Sb II |
References
- G. Bolloré, M. J. Ferguson, R. W. Hushagen, and A. Mar, New Ternary Rare-Earth Transition-Metal Antimonides RE$_{3}$MSb$_{5}$ (RE = La, Ce, Pr, Nd, Sm; M = Ti, Zr, Hf, Nb), Chem. Mater. 7, 2229–2231 (1995), doi:10.1021/cm00060a005.
Found in
- M. Matin, R. Kulkarni, A. Thamizhavel, S. K. Dhar, A. Provino, and P. Manfrinetti, Probing the magnetic ground state of single crystalline Ce$_{3}$TiSb$_{5}$, J. Phys.: Condens. Matter 29, 145601 (2017), doi:10.1088/1361-648X/aa57c0.
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=A3B5C_hP18_193_g_dg_b --params=$a,c/a,x_{3},x_{4}$