Determination of the c/a Ratio of a Submicrometer-Sized Crystal of Tetragonal Barium Titanate by the Synchrotron Radiation

The tetragonality of submicrometer-sized crystals of barium titanate, BaTiO3, has been investigated by the ultramicro single-crystal X-ray diffraction technique using synchrotron radiation. The c/a ratios have been determined using the splitting of Laue spots due to twinning to be 1.0072 (2) and 1.0106 (6) for crystals with conversion diameters of 0.56μm and 10μm, respectively. The c/a ratio of the 10μm crystal is approximately the same as that of the bulk crystal, while it is significantly small for the 0.56μm crystal, indicating that the size effect on the tetragonal-to-cubic phase transition is remarkable in the submicrometer region. No clear splitting due to tetragonal twinning was observed for the crystal with a conversion diameter of 0.25μm, suggesting that the critical size for the transition is close to this size.