Library of Crystallographic Prototypes

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =& - z_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3}& =& z_{1} \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Pd I} \\ \mathbf{B}_{2} & =& \frac12 \, \mathbf{a}_{1} + \left(\frac12 - z_{1}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{1}\right) \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, b \, \mathbf{\hat{y}} + z_{1} \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Pd I} \\ \mathbf{B}_{3} & =& - z_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3}& =& z_{2} \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Pd II} \\ \mathbf{B}_{4} & =& \frac12 \, \mathbf{a}_{1} + \left(\frac12 - z_{2}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{2}\right) \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, b \, \mathbf{\hat{y}} + z_{2} \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Pd II} \\ \mathbf{B}_{5} & =& x_{3} \, \mathbf{a}_{1} + \left(y_{3} - z_{3}\right) \, \mathbf{a}_{2} + \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}& =& x_{3} \, a \, \mathbf{\hat{x}} + y_{3} \, b \, \mathbf{\hat{y}} + z_{3} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \mbox{Sn I} \\ \mathbf{B}_{6} & =& - x_{3} \, \mathbf{a}_{1} - \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(z_{3} - y_{3}\right) \, \mathbf{a}_{3}& =& - x_{3} \, a \, \mathbf{\hat{x}} - y_{3} \, b \, \mathbf{\hat{y}} + z_{3} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \mbox{Sn I} \\ \mathbf{B}_{7} & =& \left(\frac12 + x_{3}\right) \, \mathbf{a}_{1} +\left(\frac12 - y_{3} - z_{3}\right) \,\mathbf{a}_{2} + \left(\frac12 - y_{3} + z_{3}\right) \, \mathbf{a}_{3}& =& \left(\frac12 + x_{3}\right) \, a \, \mathbf{\hat{x}} + \left(\frac12 - y_{3}\right) \, b \, \mathbf{\hat{y}} + z_{3} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \mbox{Sn I} \\ \mathbf{B}_{8} & =& \left(\frac12 - x_{3}\right) \, \mathbf{a}_{1} +\left(\frac12 + y_{3} - z_{3}\right) \,\mathbf{a}_{2} + \left(\frac12 + y_{3} + z_{3}\right) \, \mathbf{a}_{3}& =& \left(\frac12 - x_{3}\right) \, a \, \mathbf{\hat{x}} + \left(\frac12 + y_{3}\right) \, b \, \mathbf{\hat{y}} + z_{3} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \mbox{Sn I} \\ \mathbf{B}_{9} & =& x_{4} \, \mathbf{a}_{1} + \left(y_{4} - z_{4}\right) \, \mathbf{a}_{2} + \left(y_{4} + z_{4}\right) \, \mathbf{a}_{3}& =& x_{4} \, a \, \mathbf{\hat{x}} + y_{4} \, b \, \mathbf{\hat{y}} + z_{4} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \mbox{Sn II} \\ \mathbf{B}_{10} & =& - x_{4} \, \mathbf{a}_{1} - \left(y_{4} + z_{4}\right) \, \mathbf{a}_{2} + \left(z_{4} - y_{4}\right) \, \mathbf{a}_{3}& =& - x_{4} \, a \, \mathbf{\hat{x}} - y_{4} \, b \, \mathbf{\hat{y}} + z_{4} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \mbox{Sn II} \\ \mathbf{B}_{11} & =& \left(\frac12 + x_{4}\right) \, \mathbf{a}_{1} +\left(\frac12 - y_{4} - z_{4}\right) \,\mathbf{a}_{2} + \left(\frac12 - y_{4} + z_{4}\right) \, \mathbf{a}_{3}& =& \left(\frac12 + x_{4}\right) \, a \, \mathbf{\hat{x}} + \left(\frac12 - y_{4}\right) \, b \, \mathbf{\hat{y}} + z_{4} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \mbox{Sn II} \\ \mathbf{B}_{12} & =& \left(\frac12 - x_{4}\right) \, \mathbf{a}_{1} +\left(\frac12 + y_{4} - z_{4}\right) \,\mathbf{a}_{2} + \left(\frac12 + y_{4} + z_{4}\right) \, \mathbf{a}_{3}& =& \left(\frac12 - x_{4}\right) \, a \, \mathbf{\hat{x}} + \left(\frac12 + y_{4}\right) \, b \, \mathbf{\hat{y}} + z_{4} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \mbox{Sn II} \\ \end{array} \]