Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A7B2C2_mC22_12_aij_h_i-001

This structure originally had the label A7B2C2_mC22_12_aij_h_i. Calls to that address will be redirected here.

If you are using this page, please cite:
D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comp. Mat. Sci. 161, S1-S1011 (2019). (doi=10.1016/j.commatsci.2018.10.043)

Links to this page

https://aflow.org/p/0J1F
or https://aflow.org/p/A7B2C2_mC22_12_aij_h_i-001
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Thortveitite ([Sc,Y]$_{2}$Si$_{2}$O$_{7}$, $S2_{1}$) Structure: A7B2C2_mC22_12_aij_h_i-001

Picture of Structure; Click for Big Picture
Prototype O$_{7}$Sc$_{2}$Si$_{2}$
AFLOW prototype label A7B2C2_mC22_12_aij_h_i-001
Strukturbericht designation $S2_{1}$
Mineral name thortveitite
ICSD 202633
Pearson symbol mC22
Space group number 12
Space group symbol $C2/m$
AFLOW prototype command aflow --proto=A7B2C2_mC22_12_aij_h_i-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak y_{2}, \allowbreak x_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}$

Other compounds with this structure

$\beta$Er$_{2}$Si$_{2}$O$_{7}$,  $\beta$Ho$_{2}$Si$_{2}$O$_{7}$,  $\beta$In$_{2}$Si$_{2}$O$_{7}$,  $\beta$Lu$_{2}$Si$_{2}$O$_{7}$,  $\beta$Sc$_{2}$Si$_{2}$O$_{7}$,  $\beta$Tm$_{2}$Si$_{2}$O$_{7}$,  $\beta$Y$_{2}$Si$_{2}$O$_{7}$,  $\beta$Yb$_{2}$Si$_{2}$O$_{7}$,  $\beta$[Y,  Sc]$_{2}$Si$_{2}$O$_{7}$,  $\beta$[Y,  Yb]$_{2}$Si$_{2}$O$_{7}$


  • Thortveitite is the primary source of scandium and is one of the simplest sorosilicates, minerals with isolated Si$_{2}$O$_{7}$ groups. (Bianchi, 1988)
  • Although the (4h) Wyckoff position is randomly occupied by both Sc and Y atoms, we use Sc to represent the site.
  • (Bianchi, 1988) gives structural information for several samples of thortveitite.
  • In addition, the Si (4i) site contains 2% aluminum.
  • We use the data from sample 1, collected in Iveland, Norway.

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

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $0$ = $0$ (2a) O I
$\mathbf{B_{2}}$ = $- y_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ (4h) Sc I
$\mathbf{B_{3}}$ = $y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ (4h) Sc I
$\mathbf{B_{4}}$ = $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ = $\left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ (4i) O II
$\mathbf{B_{5}}$ = $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ = $- \left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ (4i) O II
$\mathbf{B_{6}}$ = $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ = $\left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ (4i) Si I
$\mathbf{B_{7}}$ = $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ = $- \left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ (4i) Si I
$\mathbf{B_{8}}$ = $\left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5}\right) \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $\left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ (8j) O III
$\mathbf{B_{9}}$ = $- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ = $- \left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}- c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ (8j) O III
$\mathbf{B_{10}}$ = $- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ = $- \left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}- c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ (8j) O III
$\mathbf{B_{11}}$ = $\left(x_{5} + y_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $\left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}+c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ (8j) O III

References

  • R. Bianchi, T. Pilati, V. Diella, C. M. Gramacciou, and G. Mannucci, A re-examination of thortveitite, American Mineralogist 73, 601–607 (1988).

Found in

  • R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).

Prototype Generator

aflow --proto=A7B2C2_mC22_12_aij_h_i --params=$a,b/a,c/a,\beta,y_{2},x_{3},z_{3},x_{4},z_{4},x_{5},y_{5},z_{5}$

Species:

Running:

Output: