Work function and surface stability of tungsten-based thermionic electron emission cathodes

Materials that exhibit a low work function and therefore easily emit electrons into vacuum form the basis of electronic devices used in applications ranging from satellite communications to thermionic energy conversion. W-Ba-O is the canonical materials system that functions as the thermionic electron emitter used commercially in a range of high power electron devices. However, the work functions, surface stability, and kinetic characteristics of a polycrystalline W emitter surface are still not well understood or characterized. In this study, we examined the work function and surface stability of the eight lowest index surfaces of the W-Ba-O system using Density Functional Theory methods. We found that under the typical thermionic cathode operating conditions of high temperature and low oxygen partial pressure, the most stable surface adsorbates are Ba-O species with compositions in the range of Ba0.125O to Ba0.25O per surface W atom, with O passivating all dangling W bonds and Ba creating work function-lowering surface dipoles. Wulff construction analysis reveals that the presence of O and Ba significantly alters the surface energetics and changes the proportions of surface facets present under equilibrium conditions. Analysis of previously published data on W sintering kinetics suggests that fine W particles in the size range of 100-500 nm may be at or near equilibrium during cathode synthesis, and thus may exhibit surface orientation fractions well-described by the calculated Wulff construction.


Main
Electron emission cathodes are found in high power, high frequency vacuum electronic devices (VEDs) such as traveling wave tubes, magnetrons and klystrons. 1 These high power VEDs are used in an array of applications, such as military and civilian infrastructure and communications, industrial food preparation, medical imaging, scientific research, and satellites. 2,3 All of these applications require low work function electron cathodes that provide ample electron emission to generate the electron beam necessary for the function of the VEDs.
Recently, there has also been considerable interest in using electron emission cathodes in thermionic energy conversion devices. 4,5 In thermionic energy converters, the excess energy of an electron emitted into vacuum and re-absorbed by a material of lower work function results in a voltage difference capable of doing useful work; the excess energy of the hot electrons can also be coupled to a heat engine which can generate steam to power a turbine. In particular, the creation of hot electrons using solar energy could result in high efficiency, energy-generating VEDs that use thermionic electron cathodes. [4][5][6][7] Researchers have published numerous studies detailing novel classes of materials spanning a large composition space that all show promise as low work function electron emitters in future VEDs. For example, adding Sc 2 O 3 to traditional W-based cathodes (creating so-called scandate cathodes) lowers the work function, making scandate cathodes promising candidates for commercial high-power microwave VEDs. [8][9][10][11][12][13][14] Pure oxides have also been explored, e.g., perovskite oxides have been experimentally shown to function as a work function-lowering coating for field emitters, [15][16][17] and the perovskite work function physics and novel low work function surfaces have been investigated computationally. [18][19][20] Dichalcogenide materials have been a material class of interest for thermionic energy converters, with promising materials possessing predicted work functions less than 1 eV. 21 As a last example, work function engineering of two-dimensional materials has also garnered interest, with an investigation demonstrating graphene can exhibit work functions as low as 1 eV 22 and alloyed MXenes (two dimensional carbides and nitrides) have predicted work functions of about 1.5 eV. 23 As is clear from the examples provided here, materials for use as electron emitters include a variety of material classes. The successful engineering of these materials as electron emitters will require understanding the complex interplay of the composition, chemistry, structure, and resultant properties in a full device environment. To guide the development of next generation materials it is particularly important to better understand the systems that are already in use, like W-Ba-O.
W-Ba-O is a canonical thermionic cathode materials system used in commercial high power VEDs. Bare W has a high average work function on the order of 4.6 eV for a polycrystalline sample. 24 To be useful for device applications, the work function of W must be lowered, and a work function of about 2 eV can be achieved via the adsorption of Ba-O species on the emitting surfaces. [25][26][27] These Ba-O adsorbates produce electropositive dipoles which electrostatically reduce the work function directly at the emitting surface. 28 12,13,[41][42][43] The emitting properties of W have been studied previously with Density Functional Theory (DFT)-based approaches, including the stability and work function of Ba, Sc and O on the (001) surface, 41 the expected crystal structures and electronic properties of Os-doped W, 44 and the stability and emission characteristics of W coated with various oxide films and adsorbed alkali metals. 45 However, an in-depth investigation examining the stability and work function of numerous crystal faces of W with adsorbed Ba-O is still missing. This study addresses that gap and provides in-depth computational examination of the W-Ba-O system. Our goals include understanding the stable W and W-Ba-O surfaces, including the stable Ba and O structures on W surfaces, and how these structures impact surface stability and work functions under physically relevant temperature and oxygen partial pressure conditions. An in-depth analysis of W-Ba-O can enable improved experimental cathode characterization and design, provide a framework to guide future examinations of more complex electron emitter materials systems, and generally enhance the basic understanding of electron emission from the W-Ba-O system, which forms the basis of most commercial thermionic electron emitters used in high power VEDs.
All calculations in this study were performed using Density Functional Theory (DFT) as implemented in the Vienna Ab-Initio Simulation Package (VASP). 46 The generalized gradient approximation (GGA) exchange and correlation functional with Perdew, Burke and Ernzerhof (PBE)-type pseudopotentials and the projector augmented wave (PAW) method were used for the W, Ba and O atoms. 47,48 The planewave energy cutoff was set to be 500 eV for all calculations. Wulff construction analysis was used to determine the predicted equilibrium shape of W under different thermodynamic environments. 49 All surface slabs and Wulff constructions were generated using the tools contained in the Pymatgen code package. 50 The starting structure used as input for making surface slabs with Pymatgen was the fully relaxed 2-atom conventional BCC W unit cell (2 atoms, space group Im 3 m, a=b=c=3.1847 Å). The work function and surface energies for each surface configuration were calculated using methods well-documented in previous studies. 13,18,41,51 The reference states of O and Ba used for surface energy calculations were taken as the O 2 gas energy from the Materials Project 52 and rocksalt BaO, respectively, and our designation of "thermionic cathode operating conditions" corresponds to temperature (T) and oxygen partial pressure (p(O 2 )) values of 1200 K and 10 -8 Torr, respectively. Following previous studies, we apply a shift for the O chemical potential to account for the vibrational energy differences between O in the gas and surface adsorbed phase (this shift approximately cancels for the Ba chemical potential). 14,41 This was done by using an Einstein model with Einstein   The results for the Ba-adsorbed surfaces (red data) show that the majority of surfaces with adsorbed Ba are less stable than their bare variants. This indicates that metallic Ba will tend to desorb from the W surface to form BaO. In contrast to the adsorbed O surfaces, the electropositive nature of Ba substantially reduces the work function. Here, we discuss the structural and chemical characteristics which give rise to the most stable W-Ba-O structures for each surface orientation.    Figure 3D. 59  synthesis. The length scale of these partially sintered crystals is about 100-500 nm. Our observed qualitative agreement between experimental and predicted crystal shapes suggests that the kinetics of W diffusion among these 100-500 nm sized particles is sufficiently fast for the system to be at or near equilibrium during synthesis.
To further assess the expected length and time scales of W surface kinetics during sintering, we calculated diffusion lengths as a function of time for typical sintering temperatures 60-62 between 1500-1700 ˚C (see Figure S1 of the Supplementary Material) using a basic Arrhenius relationship and activation barriers for W diffusion during sintering obtained from the literature (see Supplementary Material for more details). [63][64][65] Based on the work of Kothari, et al., 63 Vasilos, et al., 65  nm may be at or near equilibrium. However, we note here that many emitter cathodes use W powders with particle sizes of 1 µm or larger, and it would take approximately two days of sintering for W to move a distance of about 1 µm at 1700 ˚C, which is much longer than typical sintering times (to equilibrate with a W diffusion length of about 1 µm in a sintering time of one hour would require sintering at 2050 ˚C, a much higher temperature than what is typically used to sinter tungsten). Thus, larger grain sizes may result in sintered grains whose fractions of surface facets deviate from those predicted by the Wulff construction as a result of kinetic limitations of W surface diffusion during the sintering process. In addition, other nonequilibrium processing steps, such as machining, etching or cleaning, may result in the presence of surface terminations that are not expected based on thermodynamic predictions alone. Therefore, the processing steps of preparing W powders used to construct thermionic dispenser cathodes may significantly affect which surface orientations are present, directly impacting the value of the overall measured work function and performance of the cathode.
In summary, we used DFT methods to analyze the work function and surface stability of conditions. Finally, we used previously published data of W sintering kinetics to show that the precise sintering temperature, time, and W particle size may play a significant role in setting the fraction of surfaces present in a real cathode. The results and methods employed in this work may directly influence experimental and computational investigations of other thermionic cathode systems such as scandate, Os-Ru, or oxide cathodes, and offer basic investigative principles useful for Cs-coated metal or semiconductor cathodes used extensively in thermionic conversion devices.
Supplementary Material: See supplementary material for calculated data of work function and surface energy for all surfaces examined in this study, essential calculation input files and final structures, and an analysis of W diffusion during sintering.