Forsterite (Mg$_{2}$SiO$_{4}$, $S1_{2}$) Structure: A2B4C_oP28_62_ac_2cd

_{2}

BeO

_{4}

, Fe

_{2}

SiO

_{4}

(fayalite), Fe

_{2}

SiS

_{4}

, Mg

_{2}

GeO

_{4}

, Mg

_{2}

GeS

_{4}

, Mg

_{2}

GeS

_{4}

, Mn

_{2}

GeS

_{4}

, Tm

_{2}

ZnS

_{4}

Basis vectors

		Lattice coordinates		Cartesian coordinates	Wyckoff position	Atom type
$B_{1}$	=	$0$	=	$0$	(4a)	Mg I
$B_{2}$	=	$\frac{1}{2} a_{1} + \frac{1}{2} a_{3}$	=	$\frac{1}{2} a \hat{x} + \frac{1}{2} c \hat{z}$	(4a)	Mg I
$B_{3}$	=	$\frac{1}{2} a_{2}$	=	$\frac{1}{2} b \hat{y}$	(4a)	Mg I
$B_{4}$	=	$\frac{1}{2} a_{1} + \frac{1}{2} a_{2} + \frac{1}{2} a_{3}$	=	$\frac{1}{2} a \hat{x} + \frac{1}{2} b \hat{y} + \frac{1}{2} c \hat{z}$	(4a)	Mg I
$B_{5}$	=	$x_{2} a_{1} + \frac{1}{4} a_{2} + z_{2} a_{3}$	=	$a x_{2} \hat{x} + \frac{1}{4} b \hat{y} + c z_{2} \hat{z}$	(4c)	Mg II
$B_{6}$	=	$- (x_{2} - \frac{1}{2}) a_{1} + \frac{3}{4} a_{2} + (z_{2} + \frac{1}{2}) a_{3}$	=	$- a (x_{2} - \frac{1}{2}) \hat{x} + \frac{3}{4} b \hat{y} + c (z_{2} + \frac{1}{2}) \hat{z}$	(4c)	Mg II
$B_{7}$	=	$- x_{2} a_{1} + \frac{3}{4} a_{2} - z_{2} a_{3}$	=	$- a x_{2} \hat{x} + \frac{3}{4} b \hat{y} - c z_{2} \hat{z}$	(4c)	Mg II
$B_{8}$	=	$(x_{2} + \frac{1}{2}) a_{1} + \frac{1}{4} a_{2} - (z_{2} - \frac{1}{2}) a_{3}$	=	$a (x_{2} + \frac{1}{2}) \hat{x} + \frac{1}{4} b \hat{y} - c (z_{2} - \frac{1}{2}) \hat{z}$	(4c)	Mg II
$B_{9}$	=	$x_{3} a_{1} + \frac{1}{4} a_{2} + z_{3} a_{3}$	=	$a x_{3} \hat{x} + \frac{1}{4} b \hat{y} + c z_{3} \hat{z}$	(4c)	O I
$B_{10}$	=	$- (x_{3} - \frac{1}{2}) a_{1} + \frac{3}{4} a_{2} + (z_{3} + \frac{1}{2}) a_{3}$	=	$- a (x_{3} - \frac{1}{2}) \hat{x} + \frac{3}{4} b \hat{y} + c (z_{3} + \frac{1}{2}) \hat{z}$	(4c)	O I
$B_{11}$	=	$- x_{3} a_{1} + \frac{3}{4} a_{2} - z_{3} a_{3}$	=	$- a x_{3} \hat{x} + \frac{3}{4} b \hat{y} - c z_{3} \hat{z}$	(4c)	O I
$B_{12}$	=	$(x_{3} + \frac{1}{2}) a_{1} + \frac{1}{4} a_{2} - (z_{3} - \frac{1}{2}) a_{3}$	=	$a (x_{3} + \frac{1}{2}) \hat{x} + \frac{1}{4} b \hat{y} - c (z_{3} - \frac{1}{2}) \hat{z}$	(4c)	O I
$B_{13}$	=	$x_{4} a_{1} + \frac{1}{4} a_{2} + z_{4} a_{3}$	=	$a x_{4} \hat{x} + \frac{1}{4} b \hat{y} + c z_{4} \hat{z}$	(4c)	O II
$B_{14}$	=	$- (x_{4} - \frac{1}{2}) a_{1} + \frac{3}{4} a_{2} + (z_{4} + \frac{1}{2}) a_{3}$	=	$- a (x_{4} - \frac{1}{2}) \hat{x} + \frac{3}{4} b \hat{y} + c (z_{4} + \frac{1}{2}) \hat{z}$	(4c)	O II
$B_{15}$	=	$- x_{4} a_{1} + \frac{3}{4} a_{2} - z_{4} a_{3}$	=	$- a x_{4} \hat{x} + \frac{3}{4} b \hat{y} - c z_{4} \hat{z}$	(4c)	O II
$B_{16}$	=	$(x_{4} + \frac{1}{2}) a_{1} + \frac{1}{4} a_{2} - (z_{4} - \frac{1}{2}) a_{3}$	=	$a (x_{4} + \frac{1}{2}) \hat{x} + \frac{1}{4} b \hat{y} - c (z_{4} - \frac{1}{2}) \hat{z}$	(4c)	O II
$B_{17}$	=	$x_{5} a_{1} + \frac{1}{4} a_{2} + z_{5} a_{3}$	=	$a x_{5} \hat{x} + \frac{1}{4} b \hat{y} + c z_{5} \hat{z}$	(4c)	Si I
$B_{18}$	=	$- (x_{5} - \frac{1}{2}) a_{1} + \frac{3}{4} a_{2} + (z_{5} + \frac{1}{2}) a_{3}$	=	$- a (x_{5} - \frac{1}{2}) \hat{x} + \frac{3}{4} b \hat{y} + c (z_{5} + \frac{1}{2}) \hat{z}$	(4c)	Si I
$B_{19}$	=	$- x_{5} a_{1} + \frac{3}{4} a_{2} - z_{5} a_{3}$	=	$- a x_{5} \hat{x} + \frac{3}{4} b \hat{y} - c z_{5} \hat{z}$	(4c)	Si I
$B_{20}$	=	$(x_{5} + \frac{1}{2}) a_{1} + \frac{1}{4} a_{2} - (z_{5} - \frac{1}{2}) a_{3}$	=	$a (x_{5} + \frac{1}{2}) \hat{x} + \frac{1}{4} b \hat{y} - c (z_{5} - \frac{1}{2}) \hat{z}$	(4c)	Si I
$B_{21}$	=	$x_{6} a_{1} + y_{6} a_{2} + z_{6} a_{3}$	=	$a x_{6} \hat{x} + b y_{6} \hat{y} + c z_{6} \hat{z}$	(8d)	O III
$B_{22}$	=	$- (x_{6} - \frac{1}{2}) a_{1} - y_{6} a_{2} + (z_{6} + \frac{1}{2}) a_{3}$	=	$- a (x_{6} - \frac{1}{2}) \hat{x} - b y_{6} \hat{y} + c (z_{6} + \frac{1}{2}) \hat{z}$	(8d)	O III
$B_{23}$	=	$- x_{6} a_{1} + (y_{6} + \frac{1}{2}) a_{2} - z_{6} a_{3}$	=	$- a x_{6} \hat{x} + b (y_{6} + \frac{1}{2}) \hat{y} - c z_{6} \hat{z}$	(8d)	O III
$B_{24}$	=	$(x_{6} + \frac{1}{2}) a_{1} - (y_{6} - \frac{1}{2}) a_{2} - (z_{6} - \frac{1}{2}) a_{3}$	=	$a (x_{6} + \frac{1}{2}) \hat{x} - b (y_{6} - \frac{1}{2}) \hat{y} - c (z_{6} - \frac{1}{2}) \hat{z}$	(8d)	O III
$B_{25}$	=	$- x_{6} a_{1} - y_{6} a_{2} - z_{6} a_{3}$	=	$- a x_{6} \hat{x} - b y_{6} \hat{y} - c z_{6} \hat{z}$	(8d)	O III
$B_{26}$	=	$(x_{6} + \frac{1}{2}) a_{1} + y_{6} a_{2} - (z_{6} - \frac{1}{2}) a_{3}$	=	$a (x_{6} + \frac{1}{2}) \hat{x} + b y_{6} \hat{y} - c (z_{6} - \frac{1}{2}) \hat{z}$	(8d)	O III
$B_{27}$	=	$x_{6} a_{1} - (y_{6} - \frac{1}{2}) a_{2} + z_{6} a_{3}$	=	$a x_{6} \hat{x} - b (y_{6} - \frac{1}{2}) \hat{y} + c z_{6} \hat{z}$	(8d)	O III
$B_{28}$	=	$- (x_{6} - \frac{1}{2}) a_{1} + (y_{6} + \frac{1}{2}) a_{2} + (z_{6} + \frac{1}{2}) a_{3}$	=	$- a (x_{6} - \frac{1}{2}) \hat{x} + b (y_{6} + \frac{1}{2}) \hat{y} + c (z_{6} + \frac{1}{2}) \hat{z}$	(8d)	O III

Prototype	Mg $_{2}$ O $_{4}$ Si
AFLOW prototype label	A2B4C_oP28_62_ac_2cd_c-001
Strukturbericht designation	$S 1_{2}$
Mineral name	forsterite
ICSD	64744
Pearson symbol	oP28
Space group number	62
Space group symbol	$P nma$
AFLOW prototype command	aflow --proto=A2B4C_oP28_62_ac_2cd_c-001 --params= $a, b / a, c / a, x_{2}, z_{2}, x_{3}, z_{3}, x_{4}, z_{4}, x_{5}, z_{5}, x_{6}, y_{6}, z_{6}$

Encyclopedia of Crystallographic Prototypes

Forsterite (Mg $_{2}$ SiO $_{4}$ , $S 1_{2}$ ) Structure: A2B4C_oP28_62_ac_2cd_c-001

Simple Orthorhombic primitive vectors

References

Running:

Output:

Encyclopedia of Crystallographic Prototypes

Forsterite (Mg2​SiO4​, S12​) Structure: A2B4C_oP28_62_ac_2cd_c-001

Simple Orthorhombic primitive vectors

References

Running:

Output:

Forsterite (Mg $_{2}$ SiO $_{4}$ , $S 1_{2}$ ) Structure: A2B4C_oP28_62_ac_2cd_c-001