$\beta$–Pu Structure: A_mC34_12_ah3i2j

Picture of Structure; Click for Big Picture
Prototype : $\beta$–Pu
AFLOW prototype label : A_mC34_12_ah3i2j
Strukturbericht designation : None
Pearson symbol : mC34
Space group number : 12
Space group symbol : $\mbox{C2/m}$
AFLOW prototype command : aflow --proto=A_mC34_12_ah3i2j
--params=
$a$,$b/a$,$c/a$,$\beta$,$y_{2}$,$x_{3}$,$z_{3}$,$x_{4}$,$z_{4}$,$x_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$,$x_{7}$,$y_{7}$,$z_{7}$


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} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(2a\right) & \mbox{Pu I} \\ \mathbf{B}_{2} & =& - y_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + \frac12 \, \mathbf{a}_{3}& =& \frac12 \, c \, \cos\beta \, \mathbf{\hat{x}}+ y_{2} \, b \, \mathbf{\hat{y}}+ \frac12 \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4h\right) & \mbox{Pu II} \\ \mathbf{B}_{3} & =& y_{2} \, \mathbf{a}_{1} - y_{2} \, \mathbf{a}_{2} + \frac12 \, \mathbf{a}_{3}& =& \frac12 \, c \, \cos\beta \, \mathbf{\hat{x}}- y_{2} \, b \, \mathbf{\hat{y}}+ \frac12 \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4h\right) & \mbox{Pu II} \\ \mathbf{B}_{4} & =& 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) & \mbox{Pu III} \\ \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) & \mbox{Pu III} \\ \mathbf{B}_{6} & =& 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) & \mbox{Pu IV} \\ \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) & \mbox{Pu IV} \\ \mathbf{B}_{8} & =& x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3}& =& \left(x_{5} \, a \, + \, z_{5} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ z_{5} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4i\right) & \mbox{Pu V} \\ \mathbf{B}_{9} & =& - x_{5} \, \mathbf{a}_{1} - x_{5} \, \mathbf{a}_{2} - z_{5} \, \mathbf{a}_{3}& =& - \left(x_{5} \, a \, + \, z_{5} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- z_{5} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4i\right) & \mbox{Pu V} \\ \mathbf{B}_{10} & =& \left(x_{6} - y_{6}\right) \, \mathbf{a}_{1} + \left(x_{6} + y_{6}\right) \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3}& =& \left(x_{6} \, a \, + \, z_{6} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{6} \, b \, \mathbf{\hat{y}}+ z_{6} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(8j\right) & \mbox{Pu VI} \\ \mathbf{B}_{11} & =& \left(x_{6} + y_{6}\right) \, \mathbf{a}_{1} + \left(x_{6} - y_{6}\right) \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3}& =& \left(x_{6} \, a \, + \, z_{6} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{6} \, b \, \mathbf{\hat{y}}+ z_{6} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(8j\right) & \mbox{Pu VI} \\ \mathbf{B}_{12} & =& \left(y_{6} - x_{6}\right) \, \mathbf{a}_{1} - \left(x_{6} + y_{6}\right) \, \mathbf{a}_{2} - z_{6} \, \mathbf{a}_{3}& =& - \left(x_{6} \, a \, + \, z_{6} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{6} \, b \, \mathbf{\hat{y}}- z_{6} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(8j\right) & \mbox{Pu VI} \\ \mathbf{B}_{13} & =& - \left(x_{6} + y_{6}\right) \, \mathbf{a}_{1} + \left(y_{6} - x_{6}\right) \, \mathbf{a}_{2} - z_{6} \, \mathbf{a}_{3}& =& - \left(x_{6} \, a \, + \, z_{6} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{6} \, b \, \mathbf{\hat{y}}- z_{6} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(8j\right) & \mbox{Pu VI} \\ \mathbf{B}_{14} & =& \left(x_{7} - y_{7}\right) \, \mathbf{a}_{1} + \left(x_{7} + y_{7}\right) \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3}& =& \left(x_{7} \, a \, + \, z_{7} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{7} \, b \, \mathbf{\hat{y}}+ z_{7} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(8j\right) & \mbox{Pu VII} \\ \mathbf{B}_{15} & =& \left(x_{7} + y_{7}\right) \, \mathbf{a}_{1} + \left(x_{7} - y_{7}\right) \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3}& =& \left(x_{7} \, a \, + \, z_{7} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{7} \, b \, \mathbf{\hat{y}}+ z_{7} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(8j\right) & \mbox{Pu VII} \\ \mathbf{B}_{16} & =& \left(y_{7} - x_{7}\right) \, \mathbf{a}_{1} - \left(x_{7} + y_{7}\right) \, \mathbf{a}_{2} - z_{7} \, \mathbf{a}_{3}& =& - \left(x_{7} \, a \, + \, z_{7} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{7} \, b \, \mathbf{\hat{y}}- z_{7} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(8j\right) & \mbox{Pu VII} \\ \mathbf{B}_{17} & =& - \left(x_{7} + y_{7}\right) \, \mathbf{a}_{1} + \left(y_{7} - x_{7}\right) \, \mathbf{a}_{2} - z_{7} \, \mathbf{a}_{3}& =& - \left(x_{7} \, a \, + \, z_{7} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{7} \, b \, \mathbf{\hat{y}}- z_{7} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(8j\right) & \mbox{Pu VII} \\ \end{array} \]

References

  • W. H. Zachariasen and F. H. Ellinger, The Crystal Structure of Beta Plutonium Metal, Acta Cryst. 16, 369–375 (1963), doi:10.1107/S0365110X63000992.

Found in

  • J. Donohue, The Structure of the Elements (Robert E. Krieger Publishing Company, Malabar, Florida, 1982)., pp. 162-165.
  • P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn., pp. 5022.

Geometry files


Prototype Generator

aflow --proto=A_mC34_12_ah3i2j --params=

Species:

Running:

Output: