$\alpha$–N (Pa3) Structure: A_cP8_205_c

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Prototype : $\alpha$–N
AFLOW prototype label : A_cP8_205_c
Strukturbericht designation : None
Pearson symbol : cP8
Space group number : 205
Space group symbol : $\mbox{Pa}\bar{3}$
AFLOW prototype command : aflow --proto=A_cP8_205_c
--params=
$a$,$x_{1}$


  • There is considerable controversy about the crystal structure of $\alpha$–N, as outlined in (Donohue, 1982) 280-285. This page assumes the centrosymmetric Pa3 structure. The other possibility is the P213 structure, where the N2 dimers are not centered on an inversion site. (Venables, 1974) makes a convincing case that the ground state is Pa3, but we present both structures. Density Functional Theory calculations show no appreciable difference in energy between the Pa3 and P213 structures. (Mehl, 2015)

Simple Cubic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & a \, \mathbf{\hat{x}} \\ \mathbf{a}_2 & = & a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & a \, \mathbf{\hat{z}} \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = &x_{1} \, \mathbf{a}_{1}+ x_{1} \, \mathbf{a}_{2}+ x_{1} \, \mathbf{a}_{3}& = &x_{1} \, a \, \mathbf{\hat{x}}+ x_{1} \, a \, \mathbf{\hat{y}}+ x_{1} \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{N} \\ \mathbf{B}_{2} & = &\left(\frac12 - x_{1}\right) \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}+ \left(\frac12 + x_{1}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{x}}- x_{1} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{N} \\ \mathbf{B}_{3} & = &- x_{1} \, \mathbf{a}_{1}+ \left(\frac12 + x_{1}\right) \, \mathbf{a}_{2}+ \left(\frac12 - x_{1}\right) \, \mathbf{a}_{3}& = &- x_{1} \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{N} \\ \mathbf{B}_{4} & = &\left(\frac12 + x_{1}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{1}\right) \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}& = &\left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{y}}- x_{1} \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{N} \\ \mathbf{B}_{5} & = &- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}& = &- x_{1} \, a \, \mathbf{\hat{x}}- x_{1} \, a \, \mathbf{\hat{y}}- x_{1} \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{N} \\ \mathbf{B}_{6} & = &\left(\frac12 + x_{1}\right) \, \mathbf{a}_{1}+ x_{1} \, \mathbf{a}_{2}+ \left(\frac12 - x_{1}\right) \, \mathbf{a}_{3}& = &\left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{x}}+ x_{1} \, a \, \mathbf{\hat{y}}+ \left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{N} \\ \mathbf{B}_{7} & = &x_{1} \, \mathbf{a}_{1}+ \left(\frac12 - x_{1}\right) \, \mathbf{a}_{2}+ \left(\frac12 + x_{1}\right) \, \mathbf{a}_{3}& = &x_{1} \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{N} \\ \mathbf{B}_{8} & = &\left(\frac12 - x_{1}\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{1}\right) \, \mathbf{a}_{2}+ x_{1} \, \mathbf{a}_{3}& = &\left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{y}}+ x_{1} \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{N} \\ \end{array} \]

References

  • M. Ruhemann, Röntgenographische Untersuchungen an festem Stickstoff und Sauerstoff, Z. Phys. 76, 368–385 (1932).
  • T. H. Jordan, H. Warren Smith, W. E. Streib, and W. N. Lipscomb, Single–Crystal X–Ray Diffractions Studies of alpha–N2 and beta–N2, J. Chem. Phys. 41, 756–759 (1964), doi:10.1063/1.1725956.
  • J. A. Venables and C. A. English, Electron diffraction and the structure of alpha–N2, Acta Crystallogr. Sect. B Struct. Sci. 30, 929–935 (1974), doi:10.1107/S0567740874004067.
  • M. J. Mehl, D. Finkenstadt, C. Dane, G. L. W. Hart, and S. Curtarolo, Finding the stable structures of N1–xWx with an textitab initio high–throughput approach, Phys. Rev. B 91, 184110 (2015), doi:10.1103/PhysRevB.91.184110.M. J. Mehl, D. Finkenstadt, C. Dane, G. L. W. Hart, and S. Curtarolo, Finding the stable structures of N1–xWx with an ab initio high–throughput approach, Phys. Rev. B 91, 184110 (2015),

Found in

  • J. Donohue, The Structure of the Elements (Robert E. Krieger Publishing Company, Malabar, Florida, 1982)., pp. 280-285.

Geometry files


Prototype Generator

aflow --proto=A_cP8_205_c --params=

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