Ab initio investigation of barium-scandium-oxygen coatings on tungsten for electron emitting cathodes

Microwave, x-ray, and radio-frequency radiation sources require a cathode emitting electrons into vacuum. Thermionic B-type dispenser cathodes consist of ${\text{Ba}}_{x}{\text{O}}_{z}$ coatings on tungsten (W), where the surface coatings lower the W work function and enhance electron emission. The new and promising class of scandate cathodes modifies the B-type surface through inclusion of Sc, and their superior emissive properties are also believed to stem from the formation of a low work function surface alloy. In order to better understand these cathode systems, density-functional theory (DFT)-based ab initio modeling is used to explore the stability and work function of ${\text{Ba}}_{x}{\text{Sc}}_{y}{\text{O}}_{z}$ on W(001) monolayer-type surface structures. It is demonstrated how surface depolarization effects can be calculated easily using ab initio calculations and fitted to an analytic depolarization equation. This approach enables the rapid extraction of the complete depolarization curve (work function versus coverage relation) from relatively few DFT calculations, useful for understanding and characterizing the emitting properties of novel cathode materials. It is generally believed that the B-type cathode has some concentration of Ba-O dimers on the W surface, although their structure is not known. Calculations suggest that tilted Ba-O dimers are the stable dimer surface configuration and can explain the observed work function reduction corresponding to various dimer coverages. Tilted Ba-O dimers represent a new surface coating structure not previously proposed for the activated B-type cathode. The thermodynamically stable phase of Ba and O on the W surface was identified to be the ${\text{Ba}}_{0.25}\text{O}$ configuration, possessing a significantly lower $\ensuremath{\Phi}$ value than any of the Ba-O dimer configurations investigated. The identification of a more stable ${\text{Ba}}_{0.25}\text{O}$ phase implies that if Ba-O dimers cover the surface of emitting B-type cathodes, then a nonequilibrium steady state must dominate the emitting surface. The identification of a stable and low work function ${\text{Ba}}_{0.25}{\text{Sc}}_{0.25}\text{O}$ structure suggests that addition of Sc to the B-type cathode surface could form this alloy structure under operating conditions, leading to improved cathode performance and stability. Detailed comparison to previous experimental results of ${\text{Ba}}_{x}{\text{Sc}}_{y}{\text{O}}_{z}$ on W surface coatings are made to both validate the modeling and aid in interpretation of experimental data. The studies presented here demonstrate that ab initio methods are powerful for understanding the fundamental physics of electron emitting materials systems and can potentially aid in the development of improved cathodes.