Deducing surface chemistry and annealing conditions from observed nanoparticle shapes: A study of scandate cathodes

Since the early 1900s it has been understood that knowledge of the surface energies of stable crystal facets under given chemical conditions allows prediction of the equilibrium shape of the crystal via the Wulff construction. Here, we demonstrate a practical application of an inverse Wulff construction: leveraging computed temperature- and chemical-environment-dependent surface energies to determine the chemical conditions under which particles exhibiting an experimentally observed equilibrated shape were formed. We apply this approach to reveal the chemical conditions required to fabricate high-performing scandate thermionic cathodes. Thermionic cathodes are critical components in vacuum electron devices, and scandate cathodes have exhibited dramatically enhanced performance compared to state-of-the-art cathodes. Despite this, manufacturing difficulties limit their integration into devices. In the following we show that fabrication of high-performing scandate cathodes exhibiting a characteristic W particle shape requires processing in narrow windows of temperature and oxygen partial pressure. We further show that small variations from these conditions result in large changes in cathode work function (and therefore thermionic emission) and that the role of Sc in enhancing emission performance may not be to directly modify surface work functions, but rather to control chemical conditions to stabilize (Sc-free) low work function surface configurations.