Direct measurements of space-charge-regions in individual nanometer-scale crystals of Al₂O₃-rich magnesium-aluminate-spinel using off-axis electron holography and electron energy-loss spectroscopy

Space charge regions (SCR) in ionic solids, a result of an uneven distribution of point defects, alter their thermodynamic, transport, mechanical, and optical properties. We examine the formation of SCR in nanometer-scale sized crystals of magnesium-aluminate-spinel with excess Al₂O₃, MgO·1.27Al₂O₃. For this composition, the expected dominant point defects are anti-sites and cation vacancies. We determine the types, distribution and formation energies of charged point defects that form the SCR. Off-axis electron holography and electron energy-loss spectroscopy enabled to measure the electrostatic potential and distribution of Al^·_Mg anti-site charged point defects, respectively in individual crystals. We extract the width of the SCR, L_SCR, between 1.7 and 2.1 nm. We measured the formation energy of charged vacancies following two extreme states, only aluminum or magnesium vacancies resulting in E_f^V″′_Al=1.09±0.16eV and E_f^V″_Mg=1.04±0.19eV, respectively. For crystals considerably larger than L_SCR, V^'''_Al and Vʺ_Mg cation vacancies are the majority species at the particle core resulting in a negative charge density. When approaching the surface of the crystal, the space charge region is richer in Al^·_Mg defects. Finally, we examine the SCR as the crystal size is reduced, approaching L_SCR. Measurements at particle cores of these crystals results in a positive charge due to the overlap of the SCR.