γ-SrZrO$_{3}$ Tetragonal Perovskite Structure: A3BC_tI20_140_ah_b_c-002
Other compounds with this structure
AsNCr$_{3}$, BaIrO$_{3}$, BaPbO$_{3}$, BaTbO$_{3}$, CaTiO$_{3}$, CeAlO$_{3}$, EuNbO$_{3}$, EuTiO$_{3}$, GeCMn$_{3}$, KMnF$_{3}$, RbCaF$_{3}$, RuZrO$_{3}$, SrHfO$_{3}$, SrMoO$_{3}$, SrRuO$_{3}$, SrSnO$_{3}$, SrTcO$_{3}$, SrTiO$_{3}$, Ba(Bi, In)O$_{3}$, Ba(Er, Mo)O$_{3}$, Ba(Ho, Mn)O$_{3}$, Sr(Mn, Nb)O$_{3}$, Sr(Mn, Ru)O$_{3}$, Sr(Mn, Sb)O$_{3}$, Sr(Ru, Ti)O$_{3}$, Sr(Ti, Zr)O$_{3}$, (Ba, Ca)SrO$_{3}$, (Ba, Sr)HfO$_{3}$, (Ca, Sr)TiO$_{3}$, (K, Sr)BiO$_{3}$, (La, Sr)MnO$_{3}$, (Pr, Sr)MnO$_{3}$
- As with most perovskites, SrZrO$_{3}$ undergoes a number of phase transitions. The temperature-driven phase transitions are summarized by (Kumar, 2017).
- We have arbitrarily labeled the phases from low- to high-temperature by Greek letters.
- Below 970K $\alpha$–SrZrO$_{3}$ is in the orthorhombic CaTiO$_{3}$ ($Pnma$) structure.
- In the range 970-1100K, the system is in either the
- Base-centered orthorhombic $\beta$–SrZrO$_{3}$ phase in the $Cmcm$ lueshite structure, or
- The body-centered orthorhombic $\beta$'-SrZrO$_{3}$ phase in the orthorhombic BaPbO$_{3}$ structure.
- Between 1100-1440K the system is in the tetragonal $\gamma$–SrZrO$_{3}$ phase. (this structure)
- Above 1440K the system is in the cubic perovskite phase ($E2_{1}$).
- Here we use the data taken by (Kennedy, 1999) at 1023K.
- The current structure can be a high-temperature ( e.g. SrZrO$_{3}$) or high-pressure (BaIrO$_{3}$) phase, depending on the compound.
- We attempted to list the chemical formulas for the similar structures in the form ABC$_{3}$, where
A
is the (4b) Wyckoff position, (corresponding to the Ca site in cubic perovskite),B
(4c) (Ti site) andC
is (4a)\&(8h) (the oxygen site). - In addition, both the
A
(4b) andB
(4c) sites are often alloyed, and even the (4a) and (8h) sites can be a mixture of oxygen and nitrogen.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4a) | O I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}$ | = | $\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4a) | O I |
| $\mathbf{B_{3}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4b) | Sr I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4b) | Sr I |
| $\mathbf{B_{5}}$ | = | $0$ | = | $0$ | (4c) | Zr I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4c) | Zr I |
| $\mathbf{B_{7}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+\left(2 x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (8h) | O II |
| $\mathbf{B_{8}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- \left(2 x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (8h) | O II |
| $\mathbf{B_{9}}$ | = | $x_{4} \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}$ | (8h) | O II |
| $\mathbf{B_{10}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}$ | (8h) | O II |
References
- B. J. Kennedy, C. J. Howard, and B. C. Chakoumakos, High-temperature phase transitions in SrZrO$_{3}$, Phys. Rev. B 56, 4023–4027 (1999), doi:10.1103/PhysRevB.59.4023.
- A. Kumar, S. Kumari, H. Borkar, R. S. Katiyar, and J. F. Scott, Experimental verification of the {\em ab initio} phase transition sequence in SrZrO$_{3}$ and comparisons with SrHfO$_{3}$ and SrSnO$_{3}$, npj Comput. Mater. 3, 2 (2017), doi:10.1038/s41524-016-0002-y.
- Q.-J. Liu, Z.-T. Liu, L.-P. Feng, and H. Tian, Study of structural, elastic, electronic and optical properties of seven SrZrO$_{3}$ phases: First-principles calculations, J. Solid State Chem. 196, 425–434 (2012), doi:10.1016/j.jssc.2012.07.005.
- H. Fujimori, M. Kakihana, K. Ioku, S. Goto, and M. Yoshimura, Structural Phase Transitions between 700 and 850$^\\circ$C in SrZrO$_{3}$ Studied by Raman Spectroscopy, J. Ceramic Soc. Japan 112, 189–192 (2004), doi:10.2109/jcersj.112.189.
Found in
- A. Kumar, S. Kumari, H. Borkar, R. S. K., and J. F. Scott, Experimental verification of the {\em ab initio} phase transition sequence in SrZrO$_{3}$ and comparisons with SrHfO$_{3}$ and SrSnO$_{3}$, npj Comput. Mater. 3, 2 (2017), doi:10.1038/s41524-016-0002-y.
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=A3BC_tI20_140_ah_b_c --params=$a,c/a,x_{4}$