Coupled In/Te and Ni/vacancy ordering and the modulated crystal structure of a B8 type, Ni_3±xIn_1-yTe _2+y solid solution phase

The commensurate superstructures of a NiAs/Ni₂In type parent structure, Ni_3.32InTe₂ and Ni_3.12In_0.86Te_2.14 (q=γ[0 0 1]^*, γ=2/3) as well as one dimensionally incommensurate structure of Ni₃InTe₂ (γ=0.71) were refined from neutron powder diffraction data (R_wp=4.77%, 4.53% and 4.91% for the three structures, respectively, at 298 K). The commensurate structures were refined in the P6₃/mmc space group (c=3c_NiAs). The stacking sequence at the hcp array is -In/Te/Te/- and the trigonal bipyramidal site within the In layer, Ni(2), is partially occupied while it is empty in the Te layers. The octahedral position in between the In and Te layers, Ni(1a), is fully occupied while the octahedral position in between two adjacent Te layers, Ni(1b), is partially occupied. With decreasing In and Ni content, the modulation wave vector, γ, was found to increase continuously until γ=1. From this, crenel functions to describe the whole homogeneity range of the solid solution were constructed with the length of the atomic domains Δ^Te=γ (and hence Δ^In=Δ^Ni=1-γ) and Δ^Ni(1b)=γ/2 (and hence Δ^Ni(1a)=1-γ/2) which were then used for the refinement of the incommensurate structure of Ni₃InTe₂. The corresponding effect in real space is that the single In layers separating double layers of Te occur less frequent when γ in increasing until at γ=1 the CdI₂ type structure of Ni_1+xTe₂ is reached.