[Wien] Surface dipole of a metal

[Fecher, Gerhard]

Maybe you find something useful in:
Springer Tracts in Modern Physics Vol. 85 Solid Surface Physics  (1979)
J. HöIzl F.K.Schulte "Work Function of Metals"

It should be available online as pdf


Ciao
Gerhard

DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:
"I think the problem, to be quite honest with you,
is that you have never actually known what the question is."

====================================
Dr. Gerhard H. Fecher
Institut of Physics
Johannes Gutenberg - University
55099 Mainz
________________________________________
Von: Wien [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von Laurence Marks [laurence.marks at gmail.com]
Gesendet: Dienstag, 6. Juni 2023 18:37
An: A Mailing list for WIEN2k users
Betreff: Re: [Wien] Surface dipole of a metal

Dear Saeid,

Thanks for the suggestion. One can certainly calculate a surface dipole for an adsorbate using the method you suggest, subtracting that for a clean surface from the adsorbed case.

However, what I want is the dipole of just the metal, e.g. the classic Lang-Kohn form https://doi.org/10.1103/PhysRevB.3.1215. I want to separate the dipole from the mean-inner potential component.

--
Professor Laurence Marks (Laurie)
Department of Materials Science and Engineering, Northwestern University
www.numis.northwestern.edu<http://www.numis.northwestern.edu>
"Research is to see what everybody else has seen, and to think what nobody else has thought" Albert Szent-Györgyi

On Tue, Jun 6, 2023, 11:26 <sjalali at sci.ui.ac.ir<mailto:sjalali at sci.ui.ac.ir>> wrote:

Dear Prof. Laurence Marks,
Hi,
Thank you for your inquiry. Calculating the surface dipole of a metal can be an interesting and challenging task. While I cannot provide a personal account of testing the DIPOLE option in AIM, I can suggest an approach that might be helpful.

The surface dipole moment, denoted as $\mu$ in Debye, can be calculated using the Helmholtz equation:

$\Delta\Phi = \frac{1}{2\pi\Theta}\frac{\mu}{A}$,

where $\Delta\Phi$ is the work-function change in eV, $A$ is the area per ($1\times1$) surface unit cell in $\text{\AA}^2$, $\Theta$ represents the adsorbate coverage in monolayers. The equation expressing the surface dipole moment is given by Eq. (4) of  Ref. [Physical Review B, 73, 165424 (2006)], see also Fig. 2 of this reference, where $\mu$ and $\Delta \Phi$ are shown as a function of coverage for O in the fcc-hollow site.

The work function, as the difference between the electrostatic potential in the middle of the vacuum and the Fermi energy of the slab, can be calculated using Eq. (1) of  Ref. [http://dx.doi.org/10.1016/j.commatsci.2009.09.027], you would also see Fig. 2 of [http://dx.doi.org/10.1063/1.3486216].

I hope this suggestion is helpful to you. Should you have any further questions or require more specific guidance, please feel free to ask.
Good luck with your research!
Warmest Regards,
Saeid




Quoting Laurence Marks <laurence.marks at gmail.com<mailto:laurence.marks at gmail.com>>:

I wonder if anyone has a good suggestion for calculating the surface dipole of a metal (e.g. Al). The DIPOLE option in aim might do it, although I have no idea if that works. If anyone has tested it please let me know; alternatively, if you have an inspiration on how to test it against a calibrant that would be informative.

I am always hopeful...

--
Professor Laurence Marks (Laurie)
Department of Materials Science and Engineering
Northwestern University
www.numis.northwestern.edu<http://www.numis.northwestern.edu>
"Research is to see what everybody else has seen, and to think what nobody else has thought", Albert Szent-Györgyi



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