Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: AB2C4_oC28_63_c_ac_fg-001

This structure originally had the label AB2C4_oC28_63_c_bc_fg. 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)

Links to this page

https://aflow.org/p/A786
or https://aflow.org/p/AB2C4_oC28_63_c_ac_fg-001
or PDF Version

Na$_{2}$CrO$_{4}$ ($H1_{8}$) Structure: AB2C4_oC28_63_c_ac_fg-001

Picture of Structure; Click for Big Picture
Prototype CrNa$_{2}$O$_{4}$
AFLOW prototype label AB2C4_oC28_63_c_ac_fg-001
Strukturbericht designation $H1_{8}$
ICSD 76001
Pearson symbol oC28
Space group number 63
Space group symbol $Cmcm$
AFLOW prototype command aflow --proto=AB2C4_oC28_63_c_ac_fg-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak y_{2}, \allowbreak y_{3}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}$

Other compounds with this structure

Li$_{2}$SO$_{4}$,  LiFeP$_{4}$,  Na$_{2}$FeO$_{4}$,  Na$_{2}$SO$_{4}$ (III),  NaCaVO$_{4}$,  NaMnPO$_{4}$,  NaVCdO$_{4}$,  Tl$_{2}$SeO$_{4}$


  • This structure was originally determined by (Miller, 1936), who placed it in space group $Pnna$ #52, and (Gottfried, 1938) uses this data for Strukturbericht $H1_{8}$. Subsequently (Niggli, 1954) rather acerbically pointed out that Miller's coordinates were consistent with the more compact $Cmcm$ #63 space group. This does not change the positions of the atoms in the conventional cell, so we use the compact structure as our prototype for Strukturbericht designation $H1_{8}$.
  • This structure is stable up to 413°C. (Amirathanlingam, 1982)

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

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $0$ = $0$ (4a) Na I
$\mathbf{B_{2}}$ = $\frac{1}{2} \, \mathbf{a}_{3}$ = $\frac{1}{2}c \,\mathbf{\hat{z}}$ (4a) Na I
$\mathbf{B_{3}}$ = $- y_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ = $b y_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ (4c) Cr I
$\mathbf{B_{4}}$ = $y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ = $- b y_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ (4c) Cr I
$\mathbf{B_{5}}$ = $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ = $b y_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ (4c) Na II
$\mathbf{B_{6}}$ = $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ = $- b y_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ (4c) Na II
$\mathbf{B_{7}}$ = $- y_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ = $b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ (8f) O I
$\mathbf{B_{8}}$ = $y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- b y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8f) O I
$\mathbf{B_{9}}$ = $- y_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $b y_{4} \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8f) O I
$\mathbf{B_{10}}$ = $y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ = $- b y_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ (8f) O I
$\mathbf{B_{11}}$ = $\left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ = $a x_{5} \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ (8g) O II
$\mathbf{B_{12}}$ = $- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ = $- a x_{5} \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ (8g) O II
$\mathbf{B_{13}}$ = $- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ = $- a x_{5} \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ (8g) O II
$\mathbf{B_{14}}$ = $\left(x_{5} + y_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ = $a x_{5} \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ (8g) O II

References

  • A. Niggli, Die Raumgruppe von Na$_{2}$CrO$_{4}$, Acta Cryst. 7, 776 (1954), doi:10.1107/S0365110X54002368.
  • J. J. Miller, The Crystal Structure of Anhydrous Sodium Chromate, Na$_{2}$CrO$_{4}$, Z. Kristallogr. 94, 131–136 (1936), doi:10.1524/zkri.1936.94.1.131.
  • C. Gottfried, ed., Strukturbericht Band IV 1936 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1938).
  • V. Amirathanlingam and K. S. Venkateswarlu, Te Thermal Expansion and Crystallographic Phase Transformation of Na$_{2}$CrO$_{4}$, Thermochimica Acat 58, 107–109 (1982), doi:10.1016/0040-6031(82)87145-1.

Prototype Generator

aflow --proto=AB2C4_oC28_63_c_ac_fg --params=$a,b/a,c/a,y_{2},y_{3},y_{4},z_{4},x_{5},y_{5}$

Species:

Running:

Output: