Library of Crystallographic Prototypes

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =& \frac12 \, \mathbf{a}_{2}& =& \frac12 \, a \, \mathbf{\hat{y}}& \left(2c\right) & \mbox{Pd I} \\ \mathbf{B}_{2} & =& \frac12 \, \mathbf{a}_{1} + \frac12 \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Pd I} \\ \mathbf{B}_{3} & =& \frac14 \, \mathbf{a}_{3}& =& \frac14 \, c \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Pd II} \\ \mathbf{B}_{4} & =& \frac34 \, \mathbf{a}_{3}& =& \frac34 \, c \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Pd II} \\ \mathbf{B}_{5} & =&x_{3} \, \mathbf{a}_{1}+ y_{3} \, \mathbf{a}_{2}& =&x_{3} \, a \, \mathbf{\hat{x}}+ y_{3} \, a \, \mathbf{\hat{y}}& \left(4j\right) & \mbox{Pd III} \\ \mathbf{B}_{6} & =&- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}& =&- x_{3} \, a \, \mathbf{\hat{x}}- y_{3} \, a \, \mathbf{\hat{y}}& \left(4j\right) & \mbox{Pd III} \\ \mathbf{B}_{7} & =&- y_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&- y_{3} \, a \, \mathbf{\hat{x}}+ x_{3} \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(4j\right) & \mbox{Pd III} \\ \mathbf{B}_{8} & =&y_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&y_{3} \, a \, \mathbf{\hat{x}}- x_{3} \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(4j\right) & \mbox{Pd III} \\ \mathbf{B}_{9} & =&x_{4} \, \mathbf{a}_{1}+ y_{4} \, \mathbf{a}_{2}+ z_{4} \, \mathbf{a}_{3}& =&x_{4} \, a \, \mathbf{\hat{x}}+ y_{4} \, a \, \mathbf{\hat{y}}+ z_{4} \, c \, \mathbf{\hat{z}}& \left(8k\right) & \mbox{S} \\ \mathbf{B}_{10} & =&- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+ z_{4} \, \mathbf{a}_{3}& =&- x_{4} \, a \, \mathbf{\hat{x}}- y_{4} \, a \, \mathbf{\hat{y}}+ z_{4} \, c \, \mathbf{\hat{z}}& \left(8k\right) & \mbox{S} \\ \mathbf{B}_{11} & =&- y_{4} \, \mathbf{a}_{1}+ x_{4} \, \mathbf{a}_{2}+ \left(\frac12 + z_{4}\right) \, \mathbf{a}_{3}& =&- y_{4} \, a \, \mathbf{\hat{x}}+ x_{4} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(8k\right) & \mbox{S} \\ \mathbf{B}_{12} & =&y_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+ \left(\frac12 + z_{4}\right) \, \mathbf{a}_{3}& =&y_{4} \, a \, \mathbf{\hat{x}}- x_{4} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(8k\right) & \mbox{S} \\ \mathbf{B}_{13} & =&- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}& =&- x_{4} \, a \, \mathbf{\hat{x}}- y_{4} \, a \, \mathbf{\hat{y}}- z_{4} \, c \, \mathbf{\hat{z}}& \left(8k\right) & \mbox{S} \\ \mathbf{B}_{14} & =&x_{4} \, \mathbf{a}_{1}+ y_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}& =&x_{4} \, a \, \mathbf{\hat{x}}+ y_{4} \, a \, \mathbf{\hat{y}}- z_{4} \, c \, \mathbf{\hat{z}}& \left(8k\right) & \mbox{S} \\ \mathbf{B}_{15} & =&y_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+ \left(\frac12 - z_{4}\right) \, \mathbf{a}_{3}& =&y_{4} \, a \, \mathbf{\hat{x}}- x_{4} \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(8k\right) & \mbox{S} \\ \mathbf{B}_{16} & =&- y_{4} \, \mathbf{a}_{1}+ x_{4} \, \mathbf{a}_{2}+ \left(\frac12 - z_{4}\right) \, \mathbf{a}_{3}& =&- y_{4} \, a \, \mathbf{\hat{x}}+ x_{4} \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(8k\right) & \mbox{S} \\ \end{array} \]