Trigonal α-Ca$_{2}$SiO$_{4}$ Structure: A2B4C_hP14_164_abd_di_d-001
| Prototype | Ca$_{2}$O$_{4}$Si |
| AFLOW prototype label | A2B4C_hP14_164_abd_di_d-001 |
| ICSD | 182052 |
| Pearson symbol | hP14 |
| Space group number | 164 |
| Space group symbol | $P\overline{3}m1$ |
| AFLOW prototype command |
aflow --proto=A2B4C_hP14_164_abd_di_d-001
--params=$a, \allowbreak c/a, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak z_{6}$ |
- Ca$_{2}$SiO$_{4}$ exists in a variety of structures (Mumme, 1996; Yamnova, 2011):
- hexagonal $\alpha$–Ca$_{2}$SiO$_{4}$, stable above 1445°C. There is some dispute as to whether this occurs in a
- trigonal, space group $P\overline{3}m1$ #164 structure (shown here) or a
- disordered hexagonal, space group $P6_{3}/mmc$ #194 structure.
- orthorhombic $\alpha_{H}$'-Ca$_{2}$SiO$_{4}$, stable in the range $1160-1425°$C,
- orthorhombic $\alpha_{L}$'-Ca$_{2}$SiO$_{4}$, stable in the range $690-1160°$C,
- monoclinic $\beta$–Ca$_{2}$SiO$_{4}$, stable in the range $500-690°$C and found in nature as the metastable mineral larnite, and
- $\gamma$–Ca$_{2}$SiO$_{4}$, stable below 500°C, in the olivine ($S1_{2}$) structure.
- hexagonal $\alpha$–Ca$_{2}$SiO$_{4}$, stable above 1445°C. There is some dispute as to whether this occurs in a
- The ICSD entry for this structure is from (Eysel, 1970). The atomic positions are significantly different than those given in (Mumme, 1996), but we have no ICSD entry from that paper.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Ca I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1b) | Ca II |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (2d) | Ca III |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (2d) | Ca III |
| $\mathbf{B_{5}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (2d) | O I |
| $\mathbf{B_{6}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (2d) | O I |
| $\mathbf{B_{7}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (2d) | Si I |
| $\mathbf{B_{8}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (2d) | Si I |
| $\mathbf{B_{9}}$ | = | $x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (6i) | O II |
| $\mathbf{B_{10}}$ | = | $x_{6} \, \mathbf{a}_{1}+2 x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{6} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (6i) | O II |
| $\mathbf{B_{11}}$ | = | $- 2 x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{6} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (6i) | O II |
| $\mathbf{B_{12}}$ | = | $- x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (6i) | O II |
| $\mathbf{B_{13}}$ | = | $2 x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{6} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (6i) | O II |
| $\mathbf{B_{14}}$ | = | $- x_{6} \, \mathbf{a}_{1}- 2 x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{6} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (6i) | O II |
References
- W. Mumme, L. Cranswick, and B. Chakoumakos, Rietveld crystal structure refinements from high temperature neutron powder diffraction data for the polymorphs of dicalcium silicate, Neues mineral. Abhandlungen 170, 171–188 (1996), doi:10.1134/S1063774511020209.
- W. Eysel and T. Hahn, Polymorphism and solid solution of Ca$_{2}$(GeO$_{4}$) and Ca$_{2}$(SiO$_{4}$), Z. Krystallogr. 131, 322–341 (1970), doi:10.1524/zkri.1970.131.16.322.
Found in
- N. A. Yamnova, N. V. Zubkova, N. N. Eremin, A. E. Zadov, and V. M. Gazeev, Crystal structure of larnite $\beta$-Ca$_{2}$SiO$_{4}$ and specific features of polymorphic transitions in dicalcium orthosilicate, Crystallogr. Rep. 56, 210–220 (2011), doi:10.1134/S1063774511020209.
Prototype Generator
aflow --proto=A2B4C_hP14_164_abd_di_d --params=$a,c/a,z_{3},z_{4},z_{5},x_{6},z_{6}$