γ-N Structure: A_tP4_136_f-001
| Prototype | N |
| AFLOW prototype label | A_tP4_136_f-001 |
| ICSD | 24891 |
| Pearson symbol | tP4 |
| Space group number | 136 |
| Space group symbol | $P4_2/mnm$ |
| AFLOW prototype command |
aflow --proto=A_tP4_136_f-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}$ |
- Solid nitrogen is found in three forms (Mills, 1969; Donohue, 1974):
- The ground state $\alpha$–N structure, stable below 35.6K, found either in a centrosymmetric or a non-centrosymmetric cubic structure.
- The hexagonal $\beta$-phase, which has freely rotating N$_{2}$ molecules and is stable up to the melting point, and
- High-pressure $\gamma$–N, stable above 355 MPa.
- We use the data from (Mills, 1969) taken at 415 MPa and 20.5K.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}$ | = | $a x_{1} \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}$ | (4f) | N I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}$ | = | $- a x_{1} \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}$ | (4f) | N I |
| $\mathbf{B_{3}}$ | = | $- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4f) | N I |
| $\mathbf{B_{4}}$ | = | $\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4f) | N I |
References
- R. L. Mills and A. F. Schuch, Crystal Structure of Gamma Nitrogen, Phys. Rev. Lett. 23, 1154–1156 (1969), doi:10.1103/PhysRevLett.23.1154.
Found in
- J. Donohue, The Structures of the Elements (Robert E. Krieger Publishing Company, New York, 1974).
Prototype Generator
aflow --proto=A_tP4_136_f --params=$a,c/a,x_{1}$