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The charge-density-wave ͑CDW͒ transitions in compounds R 5 Ir 4 Si 10 (Rϭrare-earth element͒ have been studied by x-ray-diffraction and electrical conductivity experiments for temperatures between 20 and 300 K. At T CDW incommensurate CDW's ͓q ជ ϭ(Ϯ0.25Ϯ␦)c ជ * with ␦Ϸ0.03] develop in compounds with RϭHo, Er, Tm, and (Lu 0.16 Er 0.84 ), while commensurate CDW's ͓q ជ ϭ(n/7)c ជ *͔ develop in compounds with RϭLu and (Lu 0.34 Er 0.66 ). T CDW varies between 83 K in RϭLu and 161.4 K in RϭHo. The compounds with an incommensurate CDW exhibit a second transition at T lock-in ϽT CDW , with T lock-in between 55 K in RϭEr and 111.5 K in RϭTm. In Ho 5 Ir 4 Si 10 and Er 5 Ir 4 Si 10 this is a pure lock-in transition at which ␦ becomes zero. In Tm 5 Ir 4 Si 10 and (Lu 0.16 Er 0.84 ) 5 Ir 4 Si 10 ␦ also becomes zero, but below T lock-in additional satellite reflections have been discovered, at commensurate positions (n/8)c ជ * in Tm 5 Ir 4 Si 10 and at incommensurate positions (n/8Ϯ␦ 2 )c ជ * with ␦ 2 Ϸ0.01 in (Lu 0.16 Er 0.84 ) 5 Ir 4 Si 10 . The development of this second CDW can be understood by a two-step mechanism similar to the mechanism for the development of the primary CDW in Er 5 Ir 4 Si 10 ͓Galli et al., Phys. Rev. Lett. 85, 158 ͑2000͔͒. At T lock-in the primary CDW becomes commensurate, leading to a partly restoration of the Fermi surface, as evidenced by an anomalous decrease of the electrical resistivity for T below T lock-in in Ho 5 Ir 4 Si 10 and Er 5 Ir 4 Si 10 . The modified Fermi surface then provides the favorable nesting conditions for the development of a second CDW in Tm 5 Ir 4 Si 10 and (Lu 0.16 Er 0.84 ) 5 Ir 4 Si 10 . The electronic character of this transition is suggested by the anomalous increase of the resistivity for T below T lock-in .

The incommensurately modulated structure of Sr(2)Nb(2)O(7) at room temperature is reported, as determined by single-crystal X-ray diffraction. The crystal structure of Sr(2)Nb(2)O(7) comprises slabs with a perovskite-type structure that are separated by planes of additional O atoms. The driving force for the modulation is shown to be internal strain around the Sr atoms that lie at the interface between the slabs. At room temperature, Sr(2)Nb(2)O(7) crystallizes in the superspace group Cmc2(1)(alpha00)0s0, with lattice parameters a = 3.9544 (7), b = 26.767 (6) and c = 5.6961 (8) A. The modulation wave vector is determined as q = 0.488 (3) a(*). X-ray diffraction data were collected at a synchrotron using a CCD area detector. A total of 3626 unique main reflections and 1262 unique first-order satellites with I > 3sigma(I) were obtained. Refinements using a single harmonic modulation wave converged at R = 0.057 (R = 0.051 for the main reflections and R = 0.121 for the satellite reflections). The modulated structure is interpreted in terms of rotations of NbO(6) octahedra and displacements of the Sr atoms.

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