Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A_mC16_12_4i

  • M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
  • D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comp. Mat. Sci. 161, S1-S1011 (2019). (doi=10.1016/j.commatsci.2018.10.043)
  • D. Hicks, M.J. Mehl, M. Esters, C. Oses, O. Levy, G.L.W. Hart, C. Toher, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 3, Comp. Mat. Sci. 199, 110450 (2021). (doi=10.1016/j.commatsci.2021.110450)

M–carbon Structure: A_mC16_12_4i

Picture of Structure; Click for Big Picture
Prototype : C
AFLOW prototype label : A_mC16_12_4i
Strukturbericht designation : None
Pearson symbol : mC16
Space group number : 12
Space group symbol : $C2/m$
AFLOW prototype command : aflow --proto=A_mC16_12_4i
--params=
$a$,$b/a$,$c/a$,$\beta$,$x_{1}$,$z_{1}$,$x_{2}$,$z_{2}$,$x_{3}$,$z_{3}$,$x_{4}$,$z_{4}$


  • This structure was originally found by Oganov and Glass, (Oganov, 2006) and was refined and designated M–Carbon by Li et al. (Li, 2009)

Base-centered Monoclinic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac12 \, b \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, b \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \cos\beta \, \mathbf{\hat{x}} + c \sin\beta \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & \left(x_{1}a+z_{1}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{1}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \text{C I} \\ \mathbf{B}_{2} & = & -x_{1} \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2}-z_{1} \, \mathbf{a}_{3} & = & \left(-x_{1}a-z_{1}c\cos\beta\right) \, \mathbf{\hat{x}}-z_{1}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \text{C I} \\ \mathbf{B}_{3} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \left(x_{2}a+z_{2}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{2}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \text{C II} \\ \mathbf{B}_{4} & = & -x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2}-z_{2} \, \mathbf{a}_{3} & = & \left(-x_{2}a-z_{2}c\cos\beta\right) \, \mathbf{\hat{x}}-z_{2}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \text{C II} \\ \mathbf{B}_{5} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \left(x_{3}a+z_{3}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{3}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \text{C III} \\ \mathbf{B}_{6} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & \left(-x_{3}a-z_{3}c\cos\beta\right) \, \mathbf{\hat{x}}-z_{3}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \text{C III} \\ \mathbf{B}_{7} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \left(x_{4}a+z_{4}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{4}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \text{C IV} \\ \mathbf{B}_{8} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & \left(-x_{4}a-z_{4}c\cos\beta\right) \, \mathbf{\hat{x}}-z_{4}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \text{C IV} \\ \end{array} \]

References

  • Q. Li, Y. Ma, A. R. Oganov, H. Wang, H. Wang, Y. Xu, T. Cui, H.–K. Mao, and G. Zou, Superhard Monoclinic Polymorph of Carbon, Phys. Rev. Lett. 102, 175506 (2009), doi:10.1103/PhysRevLett.102.175506.
  • A. R. Oganov and C. W. Glass, Crystal structure prediction using em ab initio evolutionary techniques: Principles and applications, J. Chem. Phys. 124, 244704 (2006), doi:10.1063/1.2210932.

Geometry files


Prototype Generator

aflow --proto=A_mC16_12_4i --params=

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