# Work functions of ceramics/insulators

Is anyone aware of or know of a good source or means of estimating the work function of a ceramic material? Typically, work functions are given for pure elemental metals, rather than for compounds, such as oxides or nitrides.

The definition of work function that I am using is: the minimum thermodynamic work (i.e. energy) needed to remove an electron from a solid to a point in the vacuum immediately outside the solid surface.

This could be viewed in the context of the photoelectric effect, the minimum energy photon required, incident to a surface, to liberate an electron from the material with zero kinetic energy.

One example that I have found successfully, is for lanthanum hexaboride $(LaB_{6})$, often used as a cathode because of its low work function (2.5 eV) and high melting point. But aside from this, I haven't been able to find work functions of other materials. Perhaps because LaB6 is ubiquitous in charged particle optics as a cathode that its work function is readily available.

For instance, I'd be interesting in knowing the work function for silica $(SiO_{2})$, alumina $(Al_{2}O_{3})$, magnesia $(MgO)$, and potassium oxide $(K_{2}O )$, among others, however, in searching, I typically find their secondary electron emission coefficient instead, when checking sources such as CRC Handbook of Chemistry and Physics, or other fundamental texts and databases for material properties.

Where can reliable sources for work functions of compounds (primarily ceramics) be found?

• You may have to spell out what you mean when you say work function of (isolating) ceramics. The usual definition, the energy difference between an unbound electron and one in the metallic conduction band, does not make sense. Are you by any chance talking about the first ionization energy, the energy to lift the least well-bound electron into an unbound state? – pyramids Feb 26 '15 at 17:55
• @pyramids I've edited the question to show the definition, which is the amount of energy required to remove an electron on the surface of a solid to a point in vacuum immediately outside the solid surface. – iwantmyphd Feb 26 '15 at 18:43
• That makes sense for a metal, where "on the surface" implies being inside the conduction band (and in fact at the highest populated energy level inside it). The ceramics you are interested in appear to be isolators which, unlike the conductor lanthanum hexaboride, do not have an obvious equivalence. – pyramids Feb 26 '15 at 18:47
• @pyramids Does that mean that work functions only apply to conductors and not insulators? – iwantmyphd Feb 26 '15 at 23:31
• I think that is a question of definition. If you want to communicate about it with me, you have to define what a "work function" is to you such that I may understand you rather than make my own guess and likely talk about something entirely different. Otherwise, you may have to limit yourself to other respondents who already believe they know the answer to if, and possibly how, a work function applies to insulators. – pyramids Feb 27 '15 at 8:54

## 1 Answer

The definition of work function that I am using is: the minimum thermodynamic work (i.e. energy) needed to remove an electron from a solid to a point in the vacuum immediately outside the solid surface.

This could be viewed in the context of the photoelectric effect, the minimum energy photon required, incident to a surface, to liberate an electron from the material with zero kinetic energy.

This is the (first) ionization energy of your material. Try looking for the answer under that keyword.

Note that the concept of a work function is most commonly used where no charged material is left behind. This will most likely not describe the behavior of your isolating ceramics of interest. Hence the details, including the fact that at seperation the electron will need lots of kinetic energy to be counted as unbound (able to escape electrostatic attraction), will differ from what most people will associate with the term work function.

There is an argument to be made that "work function" is a historical term, used before engineers had a good understanding of the quantumchemistry of metals. Hence you will rarely find it outside of contexts where this concept proved good enough, such as cathodes in vacuum tubes, and where history tends to be retold, such as high school physics lessons. It's not well-suited for generalization because it ignores the internal structure of the material, misleading you to expect a uniform reservoir of quasi-free electrons (the electron gas that exists in the metallic conduction band) essentially only differing from free electrons outside the metal by an energy difference. That is simply not the case in materials that do not closely resemble metallic conductors.

• To clarify, I am looking for the first ionization potential/energy of the compounds in question (Al2O3, MgO, SiO2, etc.)? – iwantmyphd Feb 27 '15 at 13:06
• That is what I would call it, so, as a suggestion, yes. A quick search did not turn up anything, so you may bwant to also consider approximations e.g. based on adding and subtracting other energies: lattice energy, enthalpy of formation, individual single ion ionization or second ionization energy (depending on which one you take the electron from in an idealized ionic crystal only), etc. That's obviously error-prone, though, considering one needs a perfect understanding of the model behind all these and assume a purely ionic crystal before and, after, with the electron defect process. – pyramids Feb 28 '15 at 9:17
• I think your "no charged material left behind" distinction for the usual definition of a work function is a good one, and makes it essentially impossible to define a work function for an insulator. – Floris Sep 10 '15 at 23:08