Incommensurately modulated LT″-Ni1+δSn (δ=0.60, 0.63): Rietveld refinement, line-broadening analysis and structural relation with LT- and LT′-Ni1+δSn

X-ray powder diffraction data of NiAs/Ni2In-type Ni1.60Sn and Ni1.63Sn alloys annealed at or below about 573 K reveal the development of an incommensurately ordered phase called LT″. In this phase Ni(2) atoms occupy partially the trigonal–bipyramidal interstices formed by five Sn within an NiAs-type arrangement Ni(1)Sn. The modulated occupational ordering of Ni(2) in the LT″ phase can be described in the superspace group Cmcm(α00)0 s 0, and the parameters describing this occupational modulation were refined together with atomic displacement modulations using the Rietveld method. The structure parameters revealed close structural analogies of the LT″ phase with the previously reported commensurate LT-Ni1+δSn and incommensurate LT′-Ni1+δSn phases (A. Leineweber, J. Solid State Chem. 177 (2004) 1197–1212), which both occur for lower Ni contents than the LT″ phase. The 1st-order satellite reflections visible in the powder-diffraction patterns exhibit, with respect to the fundamental reflections, a considerable diffraction-line broadening, caused by a small size of the particularly ordered domains. This small-domain-size broadening was successfully described by a recently developed reflection-index (hklm) dependent (anisotropic) line-broadening model (A. Leineweber, V. Petricek, J. Appl. Crystallogr. 40 (2007) 1027–1034) designed to consider the effect of fluctuations of the lattice metrics on the peak widths in powder diffraction patterns of incommensurately modulated crystal structures. The small domain sizes encountered for the LT″ phase indicate that domain coarsening is much more difficult than for the LT and LT′ phases. This special feature of the LT″ phase goes along with a compared to the LT and LT′ phases absent orthorhombic distortion and the low ordering temperature, which are discussed as a consequence of the ordering patterns due to the Ni(2) atoms.