Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: AB_tI8_141_a_b

  • M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
  • 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)
  • 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)

NbP ("$40$") Structure: AB_tI8_141_a_b

Picture of Structure; Click for Big Picture
Prototype : NbP
AFLOW prototype label : AB_tI8_141_a_b
Strukturbericht designation : $"40"$
Pearson symbol : tI8
Space group number : 141
Space group symbol : $\text{I4}_{1}\text{/amd}$
AFLOW prototype command : aflow --proto=AB_tI8_141_a_b
--params=
$a$,$c/a$


  • When $c/a = 2$, the atoms in this lattice are on the sites of the face-centered cubic lattice. Thus (Lu, 1991) use this lattice for their structural stability studies, and arbitrarily assign this lattice a Strukturbericht designation of "40". Note that (Schönberg, 1954) gives the space group as I4122, but as (Villars, 1991) notes, the coordinates given increase the symmetry to I41/amd

Body-centered Tetragonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & - \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, c \, \mathbf{\hat{z}}\\ \mathbf{a}_2 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, c \, \mathbf{\hat{z}}\\ \mathbf{a}_3 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} - \frac12 \, c \, \mathbf{\hat{z}}\\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & =&\frac78 \, \mathbf{a}_{1}+ \frac18 \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&\frac34 \, a \, \mathbf{\hat{y}}+ \frac18 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \text{Nb} \\ \mathbf{B}_{2} & =&\frac18 \, \mathbf{a}_{1}+ \frac78 \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \frac38 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \text{Nb} \\ \mathbf{B}_{3} & =&\frac58 \, \mathbf{a}_{1}+ \frac38 \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&\frac14 \, a \, \mathbf{\hat{y}}+ \frac38 \, c \, \mathbf{\hat{z}}& \left(4b\right) & \text{P} \\ \mathbf{B}_{4} & =&\frac38 \, \mathbf{a}_{1}+ \frac58 \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \frac18 \, c \, \mathbf{\hat{z}}& \left(4b\right) & \text{P} \\ \end{array} \]

References

  • Z. W. Lu., S.–H. Wei, and A. Zunger, Long–range order in binary late–transition–metal alloys, Phys. Rev. Lett. 66, 1753 (1991), doi:10.1103/PhysRevLett.66.1753.

Found in

  • P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn., pp. 4511.

Geometry files


Prototype Generator

aflow --proto=AB_tI8_141_a_b --params=

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