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Acta Cryst. (2003). B59, 17±27 Alla Arakcheeva et al.  K3In(PO4)2 17 research papers Acta Crystallographica Section B Structural Science ISSN 0108-7681 The incommensurate structure of K3In(PO4)2 Alla Arakcheeva,a,b Gervais Chapuis,a* Vaclav Petr???c?ek,a,c Michal Dus?eka,c and Andreas Schoènlebera aUniversite? de Lausanne, Institut de Cristallo- graphie, BSP Dorigny, CH-1015 Lausanne, Switzerland, bBaikov Institute of Metallurgy, RAS, 119991 Moscow, Russia, and cInstitute of Physics, Academy of Science of the Czech Republic, Na Slovance 2, 182 21 Praha, Czech Republic Correspondence e-mail: gervais.chapuis@ic.unil.ch # 2003 International Union of Crystallography Printed in Great Britain ± all rights reserved The incommensurately modulated structure of K3In(PO4)2 has been solved and re?ned. The origin of the modulation relates to the ordering of K cations within the hexagonal close packing of the PO4 anions. The driving forces for the modulation of the other cations are InDP and KDP interactions. The modulation of O atoms of rigid PO4 units follows the cations in order to stabilize the InO6 octahedron. It is shown that the previously published three-dimensional structure re?ned from powder diffraction data obtained at room temperature is an average structure. Therefore the incommensurately modulated phase of K3In(PO4)2 is the only one that has been unequivocally identi?ed at room tempera- ture. The origin of the modulation is discussed in comparison with the structures of Na3InP2, - and -Na3In(PO4)2, Na3Fe(PO4)2 and Rb3In(PO4)2. Received 31 August 2002 Accepted 19 November 2002 1. Introduction Potassium indium double phosphate, K3In(PO4)2, was ?rst obtained (Zhizhin et al., 2002) as powder and single-crystal specimens by sintering In2O3, KH2PO4 and K2CO3 at the temperatures 1173 K and 1473 K, respectively. Preliminary X-ray investigation (Zhizhin et al., 2002) gave identical monoclinic unit cells for both powder and single-crystal specimens. In addition, a few wea