Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A4B3_tI28_141_cd_ae-002

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H. Eckert, S. Divilov, M. J. Mehl, D. Hicks, A. C. Zettel, M. Esters. X. Campilongo and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 4. Submitted to Computational Materials Science.

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Paramelaconite (Cu $_{4}$ O $_{3}$ ) Structure: A4B3_tI28_141_cd_ae-002

Prototype	Cu $_{4}$ O $_{3}$
AFLOW prototype label	A4B3_tI28_141_cd_ae-002
Mineral name	paramelaconite
ICSD	100566
Pearson symbol	tI28
Space group number	141
Space group symbol	$I 4_{1} / am d$
AFLOW prototype command	aflow --proto=A4B3_tI28_141_cd_ae-002 --params= $a, c / a, z_{4}$

(O'Keeffe, 1968) indicate that the atom they call O(2) (our O-I) is located at the (4a) Wyckoff position, but give the coordinates of the (4b) Wyckoff position. The coordinates are correct, however we shift the origin so that the O-I atom is on the (4a) site. This maps their atom Cu(1) to our Cu-II, and Cu(2) to Cu-I.

a_{1} a_{2} a_{3} = = = - \frac{1}{2} a \hat{x} + \frac{1}{2} a \hat{y} + \frac{1}{2} c \hat{z} \frac{1}{2} a \hat{x} - \frac{1}{2} a \hat{y} + \frac{1}{2} c \hat{z} \frac{1}{2} a \hat{x} + \frac{1}{2} a \hat{y} - \frac{1}{2} c \hat{z}

Picture of Structure; Click for Big Picture

Basis vectors

		Lattice coordinates		Cartesian coordinates	Wyckoff position	Atom type
$B_{1}$	=	$\frac{7}{8} a_{1} + \frac{1}{8} a_{2} + \frac{3}{4} a_{3}$	=	$\frac{3}{4} a \hat{y} + \frac{1}{8} c \hat{z}$	(4a)	O I
$B_{2}$	=	$\frac{1}{8} a_{1} + \frac{7}{8} a_{2} + \frac{1}{4} a_{3}$	=	$\frac{1}{2} a \hat{x} - \frac{1}{4} a \hat{y} + \frac{3}{8} c \hat{z}$	(4a)	O I
$B_{3}$	=	$0$	=	$0$	(8c)	Cu I
$B_{4}$	=	$\frac{1}{2} a_{1} + \frac{1}{2} a_{3}$	=	$\frac{1}{2} a \hat{y}$	(8c)	Cu I
$B_{5}$	=	$\frac{1}{2} a_{2}$	=	$\frac{1}{4} a \hat{x} - \frac{1}{4} a \hat{y} + \frac{1}{4} c \hat{z}$	(8c)	Cu I
$B_{6}$	=	$\frac{1}{2} a_{3}$	=	$\frac{1}{4} a \hat{x} + \frac{1}{4} a \hat{y} - \frac{1}{4} c \hat{z}$	(8c)	Cu I
$B_{7}$	=	$\frac{1}{2} a_{1} + \frac{1}{2} a_{2}$	=	$\frac{1}{2} c \hat{z}$	(8d)	Cu II
$B_{8}$	=	$\frac{1}{2} a_{2} + \frac{1}{2} a_{3}$	=	$\frac{1}{2} a \hat{x}$	(8d)	Cu II
$B_{9}$	=	$\frac{1}{2} a_{1}$	=	$- \frac{1}{4} a \hat{x} + \frac{1}{4} a \hat{y} + \frac{1}{4} c \hat{z}$	(8d)	Cu II
$B_{10}$	=	$\frac{1}{2} a_{1} + \frac{1}{2} a_{2} + \frac{1}{2} a_{3}$	=	$\frac{1}{4} a \hat{x} + \frac{1}{4} a \hat{y} + \frac{1}{4} c \hat{z}$	(8d)	Cu II
$B_{11}$	=	$(z_{4} + \frac{1}{4}) a_{1} + z_{4} a_{2} + \frac{1}{4} a_{3}$	=	$\frac{1}{4} a \hat{y} + c z_{4} \hat{z}$	(8e)	O II
$B_{12}$	=	$z_{4} a_{1} + (z_{4} + \frac{1}{4}) a_{2} + \frac{3}{4} a_{3}$	=	$\frac{1}{2} a \hat{x} + \frac{1}{4} a \hat{y} + c (z_{4} - \frac{1}{4}) \hat{z}$	(8e)	O II
$B_{13}$	=	$- (z_{4} - \frac{3}{4}) a_{1} - z_{4} a_{2} + \frac{3}{4} a_{3}$	=	$\frac{3}{4} a \hat{y} - c z_{4} \hat{z}$	(8e)	O II
$B_{14}$	=	$- z_{4} a_{1} - (z_{4} - \frac{3}{4}) a_{2} + \frac{1}{4} a_{3}$	=	$\frac{1}{2} a \hat{x} - \frac{1}{4} a \hat{y} - c (z_{4} - \frac{1}{4}) \hat{z}$	(8e)	O II

References

M. O'Keeffe and J.-O. Brovin, The crystal structure of paramelaconite, Cu $_{4}$ O $_{3}$ , Am. Mineral. 63, 180–185 (1978).

Encyclopedia of Crystallographic Prototypes

Paramelaconite (Cu $_{4}$ O $_{3}$ ) Structure: A4B3_tI28_141_cd_ae-002

Body-centered Tetragonal primitive vectors

References

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Encyclopedia of Crystallographic Prototypes

Paramelaconite (Cu4​O3​) Structure: A4B3_tI28_141_cd_ae-002

Body-centered Tetragonal primitive vectors

References

Running:

Output:

Paramelaconite (Cu $_{4}$ O $_{3}$ ) Structure: A4B3_tI28_141_cd_ae-002