An extensive study of the crystal structure and phase transitions in Na0.5Bi0.5TiO3\ud has been carried out using neutron/x-ray powder, and single-crystal x-ray, diffraction\ud techniques. This has been complemented with optical and Raman studies. The sequence\ud of phase transitions from the high-temperature prototypic cubic structure (above 813 K),\ud to one of tetragonal (673-773 K) and then rhombohedral structure (5-528 K) has been\ud established in Na0.5Bi0.5TiO3. Coexisting tetragonal/cubic (773-813 K) and\ud rhombohedral/tetragonal (528-673 K) phases have also been observed. Rietveld\ud refinements have revealed the rhombohedral phase, space group Ric, exhibits an\ud antiphase, a-a-a- oxygen octahedra tilt system, with parallel cation displacements. The\ud tetragonal phase, space group P4bm, possesses an unusual combination of in-phase,\ud a0a0c+ oxygen octahedra tilts and antiparallel cation displacements along the polar axis.\ud This structure type is unprecedented amongst the perovskites. A high-pressure study\ud using synchrotron and neutron diffraction has revealed the ambient pressure\ud rhombohedral structure undergoes a phase transition to an orthorhombic structure with\ud Pnma symmetry and the a-b+a- oxygen octahedra tilt system together with antiparallel A-cation\ud ordering along . The pure rhombohedral structure persists up to 8 kbar;\ud between 10-19.4 kbar a rhombohedral/orthorhombic coexistence region was observed\ud and above 26.2 kbar the purely orthorhombic phase was seen.\ud Structural variations as a function of temperature, pressure and doping across the\ud (Na1-xKx)0.5Bi0.5TiO3 series are also presented. With increasing potassium doping across\ud this series, phase transitions from the rhombohedral structure with octahedral tilting to a\ud non-tilted rhombohedral structure (space group, Ram) and then to a tetragonal structure\ud (space group P4mm) was observed. A basic phase diagram for this series has been\ud assembled outlining phase boundaries across the series and as a function of temperature.\ud In this study, the optimum conditions used for the fabrication of powders,\ud ceramics and single crystals of the perovskite compound Na0.5Bi0.5TiO3 and the solid\ud solution across the (Na1-xKx)0.5Bi0.5TiO3 series have been established. A detailed analysis\ud of this A-site substituted distorted perovskite compound is made with structural\ud variations, cation displacements and octahedral distortions for the different phases being\ud reported. The A-site substituted compounds are thoroughly discussed in the context of\ud modem perovskite science
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