Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: AB3C_mP60_14_3e_9e_3e-001

This structure originally had the label AB3C_mP60_14_3e_9e_3e. Calls to that address will be redirected here.

If you are using this page, please cite:
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)

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https://aflow.org/p/XADC
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Parawollastonite (CaSiO$_{3}$, $S3_{3}$(II)) Structure: AB3C_mP60_14_3e_9e_3e-001

Picture of Structure; Click for Big Picture
Prototype CaO$_{3}$Si
AFLOW prototype label AB3C_mP60_14_3e_9e_3e-001
Strukturbericht designation $S3_{3}$(II)
Mineral name parawollastonite
ICSD 34908
Pearson symbol mP60
Space group number 14
Space group symbol $P2_1/c$
AFLOW prototype command aflow --proto=AB3C_mP60_14_3e_9e_3e-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak x_{1}, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}$

  • (Trojer, 1968) refined the original structure of (Barnick, 1936). While Barnick referred to this structure as wollastonite, in modern terminology it is called parawollastonite, with the original name used for the triclinic CaSiO$_{3}$ form.
  • (Gottfried, 1938) gave this structure the $S3_{3}$ designation, but (Gottfried, 1937) had already used this label for crancrinite, Na$_{6}$Ca$_{2}$Al$_{6}$Si$_{6}$O$_{24}$(CO$_{3}$)$_{2}$. We will refer to parawollastonite as $S3_{3}$(II) and crancrinite as $S3_{3}$(I).

\[ \begin{array}{ccc} \mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}} \end{array}\]

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $x_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ = $\left(a x_{1} + c z_{1} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{1} \,\mathbf{\hat{y}}+c z_{1} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Ca I
$\mathbf{B_{2}}$ = $- x_{1} \, \mathbf{a}_{1}+\left(y_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{1} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- \left(a x_{1} + c \left(z_{1} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b \left(y_{1} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{1} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Ca I
$\mathbf{B_{3}}$ = $- x_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ = $- \left(a x_{1} + c z_{1} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{1} \,\mathbf{\hat{y}}- c z_{1} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Ca I
$\mathbf{B_{4}}$ = $x_{1} \, \mathbf{a}_{1}- \left(y_{1} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $\left(a x_{1} + c \left(z_{1} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b \left(y_{1} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Ca I
$\mathbf{B_{5}}$ = $x_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ = $\left(a x_{2} + c z_{2} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+c z_{2} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Ca II
$\mathbf{B_{6}}$ = $- x_{2} \, \mathbf{a}_{1}+\left(y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- \left(a x_{2} + c \left(z_{2} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b \left(y_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Ca II
$\mathbf{B_{7}}$ = $- x_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ = $- \left(a x_{2} + c z_{2} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}- c z_{2} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Ca II
$\mathbf{B_{8}}$ = $x_{2} \, \mathbf{a}_{1}- \left(y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $\left(a x_{2} + c \left(z_{2} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Ca II
$\mathbf{B_{9}}$ = $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ = $\left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Ca III
$\mathbf{B_{10}}$ = $- x_{3} \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- \left(a x_{3} + c \left(z_{3} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Ca III
$\mathbf{B_{11}}$ = $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ = $- \left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}- c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Ca III
$\mathbf{B_{12}}$ = $x_{3} \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $\left(a x_{3} + c \left(z_{3} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Ca III
$\mathbf{B_{13}}$ = $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ = $\left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O I
$\mathbf{B_{14}}$ = $- x_{4} \, \mathbf{a}_{1}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- \left(a x_{4} + c \left(z_{4} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O I
$\mathbf{B_{15}}$ = $- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ = $- \left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}- c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O I
$\mathbf{B_{16}}$ = $x_{4} \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $\left(a x_{4} + c \left(z_{4} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O I
$\mathbf{B_{17}}$ = $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $\left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O II
$\mathbf{B_{18}}$ = $- x_{5} \, \mathbf{a}_{1}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- \left(a x_{5} + c \left(z_{5} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O II
$\mathbf{B_{19}}$ = $- x_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ = $- \left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}- c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O II
$\mathbf{B_{20}}$ = $x_{5} \, \mathbf{a}_{1}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $\left(a x_{5} + c \left(z_{5} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O II
$\mathbf{B_{21}}$ = $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $\left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}+c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O III
$\mathbf{B_{22}}$ = $- x_{6} \, \mathbf{a}_{1}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- \left(a x_{6} + c \left(z_{6} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O III
$\mathbf{B_{23}}$ = $- x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ = $- \left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}- c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O III
$\mathbf{B_{24}}$ = $x_{6} \, \mathbf{a}_{1}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $\left(a x_{6} + c \left(z_{6} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O III
$\mathbf{B_{25}}$ = $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ = $\left(a x_{7} + c z_{7} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{7} \,\mathbf{\hat{y}}+c z_{7} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O IV
$\mathbf{B_{26}}$ = $- x_{7} \, \mathbf{a}_{1}+\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- \left(a x_{7} + c \left(z_{7} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O IV
$\mathbf{B_{27}}$ = $- x_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ = $- \left(a x_{7} + c z_{7} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{7} \,\mathbf{\hat{y}}- c z_{7} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O IV
$\mathbf{B_{28}}$ = $x_{7} \, \mathbf{a}_{1}- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $\left(a x_{7} + c \left(z_{7} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O IV
$\mathbf{B_{29}}$ = $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ = $\left(a x_{8} + c z_{8} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}+c z_{8} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O V
$\mathbf{B_{30}}$ = $- x_{8} \, \mathbf{a}_{1}+\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- \left(a x_{8} + c \left(z_{8} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O V
$\mathbf{B_{31}}$ = $- x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ = $- \left(a x_{8} + c z_{8} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{8} \,\mathbf{\hat{y}}- c z_{8} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O V
$\mathbf{B_{32}}$ = $x_{8} \, \mathbf{a}_{1}- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $\left(a x_{8} + c \left(z_{8} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O V
$\mathbf{B_{33}}$ = $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ = $\left(a x_{9} + c z_{9} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}+c z_{9} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O VI
$\mathbf{B_{34}}$ = $- x_{9} \, \mathbf{a}_{1}+\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- \left(a x_{9} + c \left(z_{9} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O VI
$\mathbf{B_{35}}$ = $- x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ = $- \left(a x_{9} + c z_{9} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}- c z_{9} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O VI
$\mathbf{B_{36}}$ = $x_{9} \, \mathbf{a}_{1}- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $\left(a x_{9} + c \left(z_{9} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O VI
$\mathbf{B_{37}}$ = $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ = $\left(a x_{10} + c z_{10} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}+c z_{10} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O VII
$\mathbf{B_{38}}$ = $- x_{10} \, \mathbf{a}_{1}+\left(y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- \left(a x_{10} + c \left(z_{10} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O VII
$\mathbf{B_{39}}$ = $- x_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ = $- \left(a x_{10} + c z_{10} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}- c z_{10} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O VII
$\mathbf{B_{40}}$ = $x_{10} \, \mathbf{a}_{1}- \left(y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $\left(a x_{10} + c \left(z_{10} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O VII
$\mathbf{B_{41}}$ = $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ = $\left(a x_{11} + c z_{11} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{11} \,\mathbf{\hat{y}}+c z_{11} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O VIII
$\mathbf{B_{42}}$ = $- x_{11} \, \mathbf{a}_{1}+\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- \left(a x_{11} + c \left(z_{11} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O VIII
$\mathbf{B_{43}}$ = $- x_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ = $- \left(a x_{11} + c z_{11} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{11} \,\mathbf{\hat{y}}- c z_{11} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O VIII
$\mathbf{B_{44}}$ = $x_{11} \, \mathbf{a}_{1}- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $\left(a x_{11} + c \left(z_{11} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O VIII
$\mathbf{B_{45}}$ = $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ = $\left(a x_{12} + c z_{12} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{12} \,\mathbf{\hat{y}}+c z_{12} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O IX
$\mathbf{B_{46}}$ = $- x_{12} \, \mathbf{a}_{1}+\left(y_{12} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- \left(a x_{12} + c \left(z_{12} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b \left(y_{12} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{12} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O IX
$\mathbf{B_{47}}$ = $- x_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ = $- \left(a x_{12} + c z_{12} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{12} \,\mathbf{\hat{y}}- c z_{12} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O IX
$\mathbf{B_{48}}$ = $x_{12} \, \mathbf{a}_{1}- \left(y_{12} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $\left(a x_{12} + c \left(z_{12} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b \left(y_{12} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) O IX
$\mathbf{B_{49}}$ = $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ = $\left(a x_{13} + c z_{13} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{13} \,\mathbf{\hat{y}}+c z_{13} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Si I
$\mathbf{B_{50}}$ = $- x_{13} \, \mathbf{a}_{1}+\left(y_{13} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- \left(a x_{13} + c \left(z_{13} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b \left(y_{13} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Si I
$\mathbf{B_{51}}$ = $- x_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ = $- \left(a x_{13} + c z_{13} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{13} \,\mathbf{\hat{y}}- c z_{13} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Si I
$\mathbf{B_{52}}$ = $x_{13} \, \mathbf{a}_{1}- \left(y_{13} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $\left(a x_{13} + c \left(z_{13} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b \left(y_{13} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Si I
$\mathbf{B_{53}}$ = $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ = $\left(a x_{14} + c z_{14} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{14} \,\mathbf{\hat{y}}+c z_{14} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Si II
$\mathbf{B_{54}}$ = $- x_{14} \, \mathbf{a}_{1}+\left(y_{14} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{14} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- \left(a x_{14} + c \left(z_{14} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b \left(y_{14} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{14} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Si II
$\mathbf{B_{55}}$ = $- x_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ = $- \left(a x_{14} + c z_{14} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{14} \,\mathbf{\hat{y}}- c z_{14} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Si II
$\mathbf{B_{56}}$ = $x_{14} \, \mathbf{a}_{1}- \left(y_{14} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $\left(a x_{14} + c \left(z_{14} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b \left(y_{14} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Si II
$\mathbf{B_{57}}$ = $x_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ = $\left(a x_{15} + c z_{15} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{15} \,\mathbf{\hat{y}}+c z_{15} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Si III
$\mathbf{B_{58}}$ = $- x_{15} \, \mathbf{a}_{1}+\left(y_{15} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{15} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- \left(a x_{15} + c \left(z_{15} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b \left(y_{15} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{15} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Si III
$\mathbf{B_{59}}$ = $- x_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ = $- \left(a x_{15} + c z_{15} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{15} \,\mathbf{\hat{y}}- c z_{15} \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Si III
$\mathbf{B_{60}}$ = $x_{15} \, \mathbf{a}_{1}- \left(y_{15} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $\left(a x_{15} + c \left(z_{15} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b \left(y_{15} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ (4e) Si III

References

  • F. J. Trojer, The crystal structure of parawollastonite, Z. Krystallogr. 127, 291–308 (1968), doi:10.1524/zkri.1968.127.16.291.
  • M. Barnick, Strukturuntersuchung des natürlichen Wollastonits (1936). Dissertation.
  • C. Gottfried, ed., Strukturbericht Band IV 1936 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1938).
  • C. Gottfried and F. Schossberger, eds., Strukturbericht Band III 1933-1935 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).

Prototype Generator

aflow --proto=AB3C_mP60_14_3e_9e_3e --params=$a,b/a,c/a,\beta,x_{1},y_{1},z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14},x_{15},y_{15},z_{15}$

Species:

Running:

Output: