VN (Low-temperature) Structure: AB_tP8_111_n

Prototype	NV
AFLOW prototype label	AB_tP8_111_n_n-001
ICSD	none
Pearson symbol	tP8
Space group number	111
Space group symbol	$P \overline{4} 2 m$
AFLOW prototype command	aflow --proto=AB_tP8_111_n_n-001 --params= $a, c / a, x_{1}, z_{1}, x_{2}, z_{2}$

Above 205K vanadium nitride transforms into the rock salt ( $B 1$ ) structure.
We use the data taken at 150K.
(Kubel, 1988) place this structure in space group $P \overline{4} 2 m$ #111, but since $c / a \approx 1$ the default tolerance of AFLOW places this in the cubic space group $P \overline{4} 3 m$ #215. It is likely that first-principles calculations will place this compound in the higher symmetry space group.
The $P \overline{4} 2 m$ structure may be recovered from AFLOW using the commmand
aflow --proto=AB_tP8_111_n_n:N:V --params=a,c/a,x $_{1}$ ,z $_{1}$ ,x $_{2}$ ,z $_{2}$ --tolerance=0.001 .
We could not find an ICSD entry for (Kubel, 1988).

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

Basis vectors

		Lattice coordinates		Cartesian coordinates	Wyckoff position	Atom type
$B_{1}$	=	$x_{1} a_{1} + x_{1} a_{2} + z_{1} a_{3}$	=	$a x_{1} \hat{x} + a x_{1} \hat{y} + c z_{1} \hat{z}$	(4n)	N I
$B_{2}$	=	$- x_{1} a_{1} - x_{1} a_{2} + z_{1} a_{3}$	=	$- a x_{1} \hat{x} - a x_{1} \hat{y} + c z_{1} \hat{z}$	(4n)	N I
$B_{3}$	=	$x_{1} a_{1} - x_{1} a_{2} - z_{1} a_{3}$	=	$a x_{1} \hat{x} - a x_{1} \hat{y} - c z_{1} \hat{z}$	(4n)	N I
$B_{4}$	=	$- x_{1} a_{1} + x_{1} a_{2} - z_{1} a_{3}$	=	$- a x_{1} \hat{x} + a x_{1} \hat{y} - c z_{1} \hat{z}$	(4n)	N I
$B_{5}$	=	$x_{2} a_{1} + x_{2} a_{2} + z_{2} a_{3}$	=	$a x_{2} \hat{x} + a x_{2} \hat{y} + c z_{2} \hat{z}$	(4n)	V I
$B_{6}$	=	$- x_{2} a_{1} - x_{2} a_{2} + z_{2} a_{3}$	=	$- a x_{2} \hat{x} - a x_{2} \hat{y} + c z_{2} \hat{z}$	(4n)	V I
$B_{7}$	=	$x_{2} a_{1} - x_{2} a_{2} - z_{2} a_{3}$	=	$a x_{2} \hat{x} - a x_{2} \hat{y} - c z_{2} \hat{z}$	(4n)	V I
$B_{8}$	=	$- x_{2} a_{1} + x_{2} a_{2} - z_{2} a_{3}$	=	$- a x_{2} \hat{x} + a x_{2} \hat{y} - c z_{2} \hat{z}$	(4n)	V I

F. Kubel, W. Lengauer, K. Yvon, K. Knorr, and A. Junod, Structural phase transition at 205 K in stoichiometric vanadium nitride, Phys. Rev. B 38, 12908–12912 (1988), doi:10.1103/PhysRevB.38.12908.
H. T. Stokes and D. M. Hatch, {\em FINDSYM}: program for identifying the space-group symmetry of a crystal, J. App. Crystallogr. 38, 237–238 (2005), doi:10.1107/S0021889804031528.
D. Hicks, C. Oses, E. Gossett, G. Gomez, R. H. Taylor, C. Toher, M. J. Mehl, O. Levy, and S. Curtarolo, AFLOW-SYM: platform for the complete, automatic and self-consistent symmetry analysis of crystals, Acta Crystallogr. Sect. A 74, 184–203 (2018), doi:10.1107/S2053273318003066.
A. L. Speck, Single-crystal structure validation with the program PLATON, J. App. Crystallogr. 36, 7–13 (2003), doi:10.1107/S0021889802022112.

P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds (2013). ASM International.

Encyclopedia of Crystallographic Prototypes