Squaric Acid (H$_{2}$C$_{4}$O$_{4}$) Structure: A2BC2_mP20_11_4e_2e_4e-001
| Prototype | C$_{2}$HO$_{2}$ |
| AFLOW prototype label | A2BC2_mP20_11_4e_2e_4e-001 |
| Mineral name | squaric acid |
| CCDC | 1194137 |
| Pearson symbol | mP20 |
| Space group number | 11 |
| Space group symbol | $P2_1/m$ |
| AFLOW prototype command |
aflow --proto=A2BC2_mP20_11_4e_2e_4e-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak x_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak z_{10}$ |
- The monoclinic form of squaric acid is stable below 373K, or 516K for the fully deuterated structure. (Semmingsen, 1974) Above that temperature it transforms into a tetragonal form, where $a = c$, the carbon atoms form a perfect square, and each oxygen has a 50% probability of being associated with one of the hydrogen atoms.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\left(a x_{1} + c z_{1} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{1} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | C I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ | = | $- \left(a x_{1} + c z_{1} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{1} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | C I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\left(a x_{2} + c z_{2} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{2} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | C II |
| $\mathbf{B_{4}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $- \left(a x_{2} + c z_{2} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{2} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | C II |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | C III |
| $\mathbf{B_{6}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- \left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | C III |
| $\mathbf{B_{7}}$ | = | $x_{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | C IV |
| $\mathbf{B_{8}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- \left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | C IV |
| $\mathbf{B_{9}}$ | = | $x_{5} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | H I |
| $\mathbf{B_{10}}$ | = | $- x_{5} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- \left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | H I |
| $\mathbf{B_{11}}$ | = | $x_{6} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | H II |
| $\mathbf{B_{12}}$ | = | $- x_{6} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- \left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | H II |
| $\mathbf{B_{13}}$ | = | $x_{7} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\left(a x_{7} + c z_{7} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{7} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O I |
| $\mathbf{B_{14}}$ | = | $- x_{7} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- \left(a x_{7} + c z_{7} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{7} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O I |
| $\mathbf{B_{15}}$ | = | $x_{8} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\left(a x_{8} + c z_{8} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{8} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O II |
| $\mathbf{B_{16}}$ | = | $- x_{8} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- \left(a x_{8} + c z_{8} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{8} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O II |
| $\mathbf{B_{17}}$ | = | $x_{9} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\left(a x_{9} + c z_{9} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{9} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O III |
| $\mathbf{B_{18}}$ | = | $- x_{9} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- \left(a x_{9} + c z_{9} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{9} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O III |
| $\mathbf{B_{19}}$ | = | $x_{10} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\left(a x_{10} + c z_{10} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{10} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O IV |
| $\mathbf{B_{20}}$ | = | $- x_{10} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $- \left(a x_{10} + c z_{10} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{10} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O IV |
References
- D. Semmingsen, The Crystal Structure of Squaric Acid, Acta Chem. Scand. 27, 3961–3972 (1973), doi:10.3891/acta.chem.scand.27-3961.
Found in
- D. Semmingsen and J. Feder, A structural phase transition in squaric acid, Solid State Commun. 15, 1369–1372 (1974), doi:10.1016/0038-1098(74)91382-9.
Prototype Generator
aflow --proto=A2BC2_mP20_11_4e_2e_4e --params=$a,b/a,c/a,\beta,x_{1},z_{1},x_{2},z_{2},x_{3},z_{3},x_{4},z_{4},x_{5},z_{5},x_{6},z_{6},x_{7},z_{7},x_{8},z_{8},x_{9},z_{9},x_{10},z_{10}$