Determination of the Thermal Expansion Coefficient of Different Phases of BaTiO₃ with Nanometer Resolution

Barium Titanite (BaTiO₃) exhibits several structural phase transformations over a range of 200 K, namely: rhombohedral → orthorhombic → tetragonal → cubic at temperatures around 183 K, 279 K and 385 K respectively [1]. Studies have suggested that phase transition temperature [2,3,4] and thermal expansion coefficient (TEC) [4,5] depend upon the particle sizes and the grain sizes. The ability to determine the TEC accurately across nm length scale is an important aspect in the design of miniaturized electronic devices.

Electron microscopy with its ability to probe low-loss electron energy loss spectroscopy (EELS) at high spatial resolution combined with in-situ temperature control of the sample enables us to measure the plasmon energy (E_p) at nanoscale. By combining these measurements with free electron model of E_p, we utilize a novel approach of non-contact thermometry to measure the thermal expansion coefficient (TEC) of BaTiO₃ with nm spatial resolution. The approach has previously been tested on 2D materials, such as graphene and MoS₂ [6]. In present work, we will extend the approach to BaTiO₃ nanoparticles to determine the TEC of its different phases (tetragonal and cubic). In addition, we will also explore the effect of particle size on phase transition temperature and TEC.

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[3] C. J. Xiao, et al., Sci 2011, 34, 963.

[4] M. Han, et al., Crystengcomm 2015, 17, 1944.

[5] X. Hu, et al., Phys Rev Lett 2018, 120, 055902.