Library of Crystallographic Prototypes

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} + 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(1a\right) & \mbox{Mo I} \\ \mathbf{B}_{2} & = & x_{2} \, \mathbf{a}_{1} + 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(1a\right) & \mbox{P I} \\ \mathbf{B}_{3} & = & x_{3} \, \mathbf{a}_{1} + 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(1a\right) & \mbox{P II} \\ \mathbf{B}_{4} & = & x_{4} \, \mathbf{a}_{1} + 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(1a\right) & \mbox{P III} \\ \mathbf{B}_{5} & = & x_{5} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \left(x_{5}a+z_{5}c\cos\beta\right) \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + z_{5}c\sin\beta \, \mathbf{\hat{z}} & \left(1b\right) & \mbox{Mo II} \\ \mathbf{B}_{6} & = & x_{6} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(x_{6}a+z_{6}c\cos\beta\right) \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + z_{6}c\sin\beta \, \mathbf{\hat{z}} & \left(1b\right) & \mbox{Mo III} \\ \mathbf{B}_{7} & = & x_{7} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \left(x_{7}a+z_{7}c\cos\beta\right) \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + z_{7}c\sin\beta \, \mathbf{\hat{z}} & \left(1b\right) & \mbox{Mo IV} \\ \mathbf{B}_{8} & = & x_{8} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & \left(x_{8}a+z_{8}c\cos\beta\right) \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + z_{8}c\sin\beta \, \mathbf{\hat{z}} & \left(1b\right) & \mbox{Mo V} \\ \mathbf{B}_{9} & = & x_{9} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & \left(x_{9}a+z_{9}c\cos\beta\right) \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + z_{9}c\sin\beta \, \mathbf{\hat{z}} & \left(1b\right) & \mbox{Mo VI} \\ \mathbf{B}_{10} & = & x_{10} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & \left(x_{10}a+z_{10}c\cos\beta\right) \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + z_{10}c\sin\beta \, \mathbf{\hat{z}} & \left(1b\right) & \mbox{Mo VII} \\ \mathbf{B}_{11} & = & x_{11} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & \left(x_{11}a+z_{11}c\cos\beta\right) \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + z_{11}c\sin\beta \, \mathbf{\hat{z}} & \left(1b\right) & \mbox{Mo VIII} \\ \mathbf{B}_{12} & = & x_{12} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + z_{12} \, \mathbf{a}_{3} & = & \left(x_{12}a+z_{12}c\cos\beta\right) \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + z_{12}c\sin\beta \, \mathbf{\hat{z}} & \left(1b\right) & \mbox{P IV} \\ \mathbf{B}_{13} & = & x_{13} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + z_{13} \, \mathbf{a}_{3} & = & \left(x_{13}a+z_{13}c\cos\beta\right) \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + z_{13}c\sin\beta \, \mathbf{\hat{z}} & \left(1b\right) & \mbox{P V} \\ \end{array} \]