Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A2B_hP12_194_cg_f

  • 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)

$\beta$–Tridymite (SiO2, $C10$) Structure: A2B_hP12_194_cg_f

Picture of Structure; Click for Big Picture
Prototype : SiO2
AFLOW prototype label : A2B_hP12_194_cg_f
Strukturbericht designation : $C10$
Pearson symbol : hP12
Space group number : 194
Space group symbol : $\text{P6}_{3}\text{/mmc}$
AFLOW prototype command : aflow --proto=A2B_hP12_194_cg_f
--params=
$a$,$c/a$,$z_{2}$


Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}}\\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \text{O I} \\ \mathbf{B}_{2}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \text{O I} \\ \mathbf{B}_{3}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ z_{2} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+\frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ z_{2} \, c \, \mathbf{\hat{z}}& \left(4f\right) & \text{Si} \\ \mathbf{B}_{4}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \left(\frac12 + z_{2}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(4f\right) & \text{Si} \\ \mathbf{B}_{5}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}- z_{2} \, c \, \mathbf{\hat{z}}& \left(4f\right) & \text{Si} \\ \mathbf{B}_{6}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ \left(\frac12 - z_{2}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(4f\right) & \text{Si} \\ \mathbf{B}_{7}& = &\frac12 \, \mathbf{a}_{1}& = &\frac14 \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}4 \, a \, \mathbf{\hat{y}}& \left(6g\right) & \text{O II} \\ \mathbf{B}_{8}& = &\frac12 \, \mathbf{a}_{2}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}4 \, a \, \mathbf{\hat{y}}& \left(6g\right) & \text{O II} \\ \mathbf{B}_{9}& = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}& = &\frac12 \, a \, \mathbf{\hat{x}}& \left(6g\right) & \text{O II} \\ \mathbf{B}_{10}& = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}4 \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \text{O II} \\ \mathbf{B}_{11}& = &\frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}4 \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \text{O II} \\ \mathbf{B}_{12}& = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \text{O II} \\ \end{array} \]

References

  • K. Kihara, Thermal change in unit–cell dimensions, and a hexagonal structure of tridymite, Zeitschrift für Kristallographie 148, 237–253 (1978), doi:10.1524/zkri.1978.148.3-4.237.

Found in

  • P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn., pp. 4759.

Geometry files


Prototype Generator

aflow --proto=A2B_hP12_194_cg_f --params=

Species:

Running:

Output: