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Abstract-Decomposition of the electromagnetic energy into its stored and radiated parts is instrumental in the evaluation of antenna Q and the corresponding fundamental limitations on antennas. This decomposition is not unique and there are several proposals in the literature. Here, it is shown that stored energy defined from the difference between the energy density and the far field energy equals the energy expressions proposed by Vandenbosch for many but not all cases. This also explains the observed cases with negative stored energy and suggests a possible remedy to them. The results are compared with the classical explicit expressions for spherical regions where the results only differ by the electrical size ka that is interpreted as the far-field energy in the interior of the sphere.

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High-temperature alloys are crucial to many important technologies that underpin our civilization. All these materials rely on forming an external oxide layer (scale) for corrosion protection. Despite decades of research on oxide scale growth, many open questions remain, including the crucial role of the so-called reactive elements and water. Here, we reveal the hitherto unknown interplay between reactive elements and water during alumina scale growth, causing a metastable 'messy' nano-structured alumina layer to form. We propose that reactive-element-decorated, hydroxylated interfaces between alumina nanograins enable water to access an inner cathode in the bottom of the scale, at odds with the established scale growth scenario. As evidence, hydride-nanodomains and reactive element/hydrogen (deuterium) co-variation are observed in the alumina scale. The defect-rich alumina subsequently recrystallizes to form a protective scale. First-principles modelling is also performed to validate the RE effect. Our findings open up promising avenues in oxidation research and suggest ways to improve alloy properties.

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