Thermionic Emission from Hot Metal Surfaces: A First Principles Study Johannes Voss,* 1 Sharon Chou, 2,3 Aleksandra Vojvodic, 1,4 Igor Bargatn, 2,3,5 Frank Abild-Pedersen, 4 Piero A. Pianeta, 3,6 Roger T. Howe, 2,3 Jens K. Nørskov 1,4 Traditonal thermionic energy converters and also photon-enhanced thermionic emission [PETE – see J.W. Schwede, I. Bargatn, D.C. Riley, B.E. Hardin, S.J. Rosenthal, Y. Sun, F. Schmit, P. Pianeta, R.T. Howe, Z.-X. Shen, N.A. Melosh, Nature Mat. 9, 762 (2010)] converters require electrode materials with low work functons. A low cathode work functon φ E is needed to allow for sufcient thermionic emission from the hot metal surface. An even lower anode work functon φ C is re- quired to provide sufcient voltage V out . We aim at fnding new materials with ultra- low work functons, allowing thermionic energy converters to be run at lower cathode temperatures and more efciently. The current density due to thermionic emission is described by the Richardson- Dushman equaton: Besides the work functon φ, this equaton is determined by the Richardson-Dushman constant A, which accounts for electronic tunneling probabilites out of the surface. Cesiated transiton metal surfaces show low work functons due to surface dipoles induced by the cesium adsorbates. Here, we calculate, based on frst principles density functonal theory (DFT), the tunneling probabilites through adsorbate-induced dipole barriers. Movaon *[email protected] 1 Department of Chemical Engineering, Stanford University 2 Center of Interfacial Engineering for Microelectromechanical Systems (CIEMS) at Stanford 3 Department of Electrical Engineering, Stanford University 4 SUstainable eNergy through CATalysis (SUNCAT) center 5 Department of Mechanical Engineering, University of Pennsylvania 6 Stanford Synchrotron Radiaton Lightsource (SSRL) Authors’ Affiliaons and Acknowledgments DFT Modeling of Transport Properes Tunneling Through the Dipole Barrier Thermionic Current Densies The Surface States Contribung to Emission (Average) dipole tunneling barrier induced by cesium absorbed on a tungsten (110) surface. Scheme of a thermionic energy converter. We use density functonal theory calculatons (as implemented in the plane-wave code DACAPO [htps://wiki.fysik.dtu.dk/dacapo]) to model bulk and surface propertes of transiton metals. Surfaces are studied with help of supercells, where transiton metal slabs (including adsorbates) are separated by sufcient amounts of vacuum layers. Surface slab ● ● ● ● Bulk 'lead' Scattering region Cesium Tungsten φ Outlook Populaton of the electronic states according to Fermi-Dirac statstcs connects the trans- mission functons to current densites. The lower work functon of cesiated tungsten at inter- mediate coverage leads to a current density at e.g. 1500 K that is three tmes higher than the value for unit coverage. Current densites for cesiated tungsten (110) at intermediate and high coverage. Note that the emited electrons are assumed here to dissipate into vacuum once the dipole barrier is passed, i.e. there is no anode. In our future studies, we will address in partcular the possibility to engineer interactons between the cesium adsorbates. The Cs-induced work functon reducton is strongly infuenced by covalent interactons between the adsorbates [Chou, Voss, Bargatn, Vojvodic, Howe, Abild-Pedersen, J. Phys.: Condens. Mater 24, 445007 (2012)]. Tailoring the Cs-Cs interacton by e.g. surface defects could thus open up design pathways for new materials allowing for higher current densites. We will furthermore study the transmission probabilites of other surfaces. Top: Real space resolved transmission probabilites at about 0.1 eV above the vacuum level of cesiated tungsten (volume integral yields total transmission). Shown are isosurfaces corresponding to 1/3 of the maximum density. Cs W Right: Cesium-induced work functon reducton for tungsten (110) as a functon of coverage. A ft including orbital overlap terms [Chou et al., see above] shows that the onset of covalent bonding between Cs atoms limits the minimum work functon that can be reached. If these Cs-Cs interactons can be screened, only electrostatc point-dipole interac tons will limit the minimum work functon. Screening of covalent interactions would allow for lower work functions. Contributions of tungsten 5d- and 6s-states Crystal structure plots created with VESTA [K. Momma and F. Izumi, J. Appl. Crystallogr. 44, 1272 (2011)] Despite lower projected DOS near the vacuum level (~1.5eV) the transmission functon is higher at intermediate coverage (i.e. with more exposed tungsten states) for low energies. The dominant contributon to the trans- mission functon and the surface density of states near the vacuum level is due to tungsten 5d- and 6s-states; the partally occupied t 2g -manifold shows the largest contributons (shown above). Also the unoccupied e g -states contribute to the transmission functon. T 2g -contributons to surface DOS (leſt) and transmission functon (right) at intermediate and high coverage of cesiated tungsten. Higher transmission at intermediate coverage for lower (and hence important) energies Cs W Schematc plots of tungsten 6s- and 5d- (surface) states, which dominate the thermionic emission propertes. We have calculated the transmission functons (normalized here to a 2x2 surface area) of cesiated, close-packed tungsten surfaces at intermediate coverage, where the work functon is approximately at its minimum (~1.3eV), and at high coverage (work functon: ~1.6eV). At intermediate coverage the transmission becomes fnite at lower energies due to a lower work functon (about 0.3eV lower than at unit coverage = 1 Cs atom/30Å 2 ). But also at slightly higher energies < 2eV, the transmission is higher at intermediate coverage. The surface density of states (DOS) shows slight changes for different coverages. The DOS at low energies is actually lower at intermediate coverage. Nevertheless, transmission is higher, i.e. more transport channels are available at these energies due to a larger exposed transiton metal surface area. At high coverage, however, there is signifcant covalent bonding between the cesium adsorbates, which both leads to a strong depolarizaton of the surface dipoles and also to a reduced coupling of the transiton metal surface states to vacuum, resultng in lower transmission. Higher transmission at intermediate coverage for lower (and hence important) energies Higher transmission at unit coverage for higher energies (which are unimportant for thermionic emission)
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Thermionic Emission from Hot Metal Surfaces: A First Principles Study Johannes Voss,*1 Sharon Chou,2,3 Aleksandra Vojvodic,1,4 Igor Bargatn,2,3,5 Frank Abild-Pedersen,4 Piero A. Pianeta,3,6 Roger T. Howe,2,3 Jens K. Nørskov1,4
Traditonal thermionic energy converters and also photon-enhanced thermionic emission [PETE – see J.W. Schwede, I. Bargatn, D.C. Riley, B.E. Hardin, S.J. Rosenthal, Y. Sun, F. Schmit, P. Pianeta, R.T. Howe, Z.-X. Shen, N.A. Melosh, Nature Mat. 9, 762 (2010)] converters require electrode materials with low work functons.A low cathode work functon φE is needed to allow for sufcient thermionic emission from the hot metal surface.An even lower anode work functon φC is re-quired to provide sufcient voltage Vout.
We aim at fnding new materials with ultra-low work functons, allowing thermionic energy converters to be run at lower cathode temperatures and more efciently.
The current density due to thermionic emission is described by the Richardson-Dushman equaton:
Besides the work functon φ, this equaton is determined by the Richardson-Dushman constant A, which accounts for electronic tunneling probabilites out of the surface.
Cesiated transiton metal surfaces show low work functons due to surface dipoles induced by the cesium adsorbates.Here, we calculate, based on frst principles density functonal theory (DFT), the tunneling probabilites through adsorbate-induced dipole barriers.
Motivation
*[email protected] 1Department of Chemical Engineering, Stanford University2Center of Interfacial Engineering for Microelectromechanical Systems (CIEMS) at Stanford 3Department of Electrical Engineering, Stanford University4SUstainable eNergy through CATalysis (SUNCAT) center5Department of Mechanical Engineering, University of Pennsylvania6Stanford Synchrotron Radiaton Lightsource (SSRL)
Authors’ Affiliations and Acknowledgments
DFT Modeling of Transport Properties
Tunneling Through the Dipole Barrier Thermionic Current Densities
The Surface States Contributing to Emission
(Average) dipole tunneling barrier induced by cesium absorbed on a tungsten (110) surface.
Scheme of a thermionic energy converter.
We use density functonal theory calculatons (as implemented in the plane-wave code DACAPO [htps://wiki.fysik.dtu.dk/dacapo]) to model bulk and surface propertes of transiton metals.Surfaces are studied with help of supercells, where transiton metal slabs (including adsorbates) are separated by sufcient amounts of vacuum layers.
Surface slab
● ●
●
●
Bulk 'lead'
ScatteringregionCesium
Tungsten
φ
Outlook
Populaton of the electronic states according to Fermi-Dirac statstcs connects the trans-mission functons to current densites.
The lower work functon of cesiated tungsten at inter-mediate coverage leads to a current density at e.g. 1500 K that is three tmes higher than the value for unit coverage.
Current densites for cesiated tungsten (110) at intermediate and high coverage.Note that the emited electrons are assumed here to dissipate into vacuum once the dipole barrier is passed, i.e. there is no anode.
In our future studies, we will address in partcular the possibility to engineer interactons between the cesium adsorbates.
The Cs-induced work functon reducton is strongly infuenced by covalent interactons between the adsorbates [Chou, Voss, Bargatn, Vojvodic, Howe, Abild-Pedersen, J. Phys.: Condens. Mater 24, 445007 (2012)].
Tailoring the Cs-Cs interacton by e.g. surface defects could thus open up design pathways for new materials allowing for higher current densites.
We will furthermore study the transmission probabilites of other surfaces.
Top: Real space resolved transmission probabilites at about 0.1 eV above the vacuumlevel of cesiated tungsten (volume integral yields total transmission).Shown are isosurfaces corresponding to 1/3 of the maximum density.
Cs
W
Right: Cesium-induced work functon reducton for tungsten (110) as a functon of coverage.A ft including orbital overlap terms [Chou et al., see above] shows that the onset of covalent bonding between Cs atoms limits the minimum work functon that can be reached.If these Cs-Cs interactons can be screened, only electrostatc point-dipole interactons will limit the minimum work functon.
Screening of covalent interactions would allow for lower work functions.
Contributions oftungsten 5d- and 6s-states
Crystal structure plots created with VESTA[K. Momma and F. Izumi, J. Appl. Crystallogr. 44, 1272 (2011)]
Despite lower projected DOS near the vacuum level (~1.5eV) the transmission functon is higher at intermediate coverage (i.e. with more exposed tungsten states) for low energies.
The dominant contributon to the trans-mission functon and the surface density of states near the vacuum level is due to tungsten 5d- and 6s-states; the partally occupied t2g-manifold shows the largest contributons (shown above).Also the unoccupied eg-states contribute to the transmission functon.
T2g-contributons to surface DOS (left) and transmission functon (right) at intermediate and high coverage of cesiated tungsten.
Higher transmission at intermediate coverage for lower (and hence important) energies
Cs
W
Schematc plots of tungsten 6s-and 5d- (surface) states,which dominate the thermionic emission propertes.
We have calculated the transmission functons (normalized here to a 2x2 surface area) of cesiated, close-packed tungsten surfaces at intermediate coverage, where the work functon is approximately at its minimum (~1.3eV), and at high coverage (work functon: ~1.6eV).
At intermediate coverage the transmission becomes fnite at lower energies due to a lower work functon (about 0.3eV lower than at unit coverage = 1 Cs atom/30Å2).But also at slightly higher energies < 2eV, the transmission is higher at intermediate coverage.
The surface density of states (DOS) shows slight changes for different coverages.The DOS at low energies is actually lower at intermediate coverage.Nevertheless, transmission is higher, i.e. more transport channels are available at these energies due to a larger exposed transiton metal surface area.
At high coverage, however, there is signifcant covalent bonding between the cesium adsorbates, which both leads to a strong depolarizaton of the surface dipoles and also to a reduced coupling of the transiton metal surface states to vacuum, resultng in lower transmission.
Higher transmission at intermediate coverage for lower (and hence important) energies
Higher transmission at unit coverage for higher energies (which are unimportant for thermionic emission)
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