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It is worth reviewing the old killer flux arguments. Another motivation is that peterP has discovered a new electrostatic principle why they don't work which he will share with us:

I have made enough mistakes in my life to cope with valid disagreement. The problem is you don't understand electrostatics. This is proven by your "killer flux" invention. If you apply the principle of superposition correctly you will find things are not as you now seem to believe.

So - first what is the killer flux argument?

Given flat plates a surface charge of 50C/m^2 would lead to fields of 7MV/u in the gap between the plate charge and the (opposing) dielectric charge. This field is high enough to ionise any lattice, therefore such surface charge can't exist.

There are a number of subtleties about this argument. The first issue is that you could it appears use it to show that normal ceramic capacitors don't work:

Given flat plates a surface charge of 0.25C/m^2 would lead to fields of 35,000V/u in the gap between the plate charge and the (opposing) dielectric charge. This field is high enough to ionise any lattice, therefore such surface charge can't exist.

The induced field still looks probably too high! But that leaves out the dielectric. If you have ionic polarization equal to this surface charge there is no field on distances larger than the charge movement distance for ionic polarization: less than one lattice cell. So all is OK. The problem with killer flux is that the surface charge is higher than any possible ionic polarization. What makes ionic polarization so special? We have other polarization methods after all. It is that it happens with very small charge movements. So does classic electronic polarization, and that would do equally well but does not to give k much higher than 2 or so. Such a low k does not reduce the killer flux's killer field enough to be helpful.

So flux kills when it cannot be (nearly) balanced by polarization. The limit for electronic and ionic polarization with all charges bound to a lattice cell is around 1C/m^2. If you allow charge exchange polarization between the ions in a bicubic cell the limit goes up to maybe 1.5C/m^2.

The second issue is the gap between the plates and the opposing charge. You might argue this is so small that the killer field does not have enough room to develop, and quantum effects save the day. The trouble is that quantum effects also limit the volume charge density in material to around 1 electron per lattice cell. Pauli exclusion means that piling lots of electrons into a small volume is impossible without giving them extra energy. The effect is that at the edges of charged conductors charge spreads out a bit into the interior.

At 50C/m^2 this spreading out effect is large. How large TP can perhaps help us with. I suspect there are some nice formulae we could use to approximate it. Anyway, I'll investigate further if challenged on this point. I maintain large enough that the depth of uncancelled surface charge, and hence volume which experiences killer field, is large enough for voltage to exceed bandgap by a large factor, even given some cancellation from electronic polarization (inner electron shells). Suppose the k from these inner electron shells is 7 (a gross overestimate). There remains 1MV/u or 1000V/nm field. So one lattice cell (0.4nm typically) of this is enough to give 400V - much larger than any bandgap.

One amusing issue of this nanoscopic view of the killer field is that it kills only by making whatever it touches conduct. So killer field inside the metal plate is fine, because charge is free to move to an equilibrium position and conduction no problem. Why can't we have conduction everywhere? Something insulating must separate the plate killer charge from the opposing charge. Otherwise Coulomb attraction between the two would mean that they cancelled each other out, and are capacitor becomes a conductor. It does not matter whether the opposing charge is another plate, or space charge moving inside a dielectric: it must the the same size as the plate charge, and there must be an insulating barrier to stop it joining the space charge. That barrier is made to conduct by the killer field from the two sets of opposing charge.

You don't need Gauss to calculate this - you can do it all by considering Coulomb force on any charge in the insulating barrier (that is just another way of describing the induced filed of course).

What about space charge inside the dielectric? The best way to think of this is to ask: "what is it that stops the space charge from moving all the way through the dielectric?". Whatever that insulating section is, the killer field argument will then apply to it.

The third issue is what if the plates are not really flat? For example suppose the plate (or dielectric) has conducting needles, like a forest, which interlock with similar needles from the other plate. Charge is free to move along each needle (because it conducts) but not to hop between adjacent needles.

The effect here is to make the plates much higher effective surface area than they appear to be. And it really is a get-out for the killer flux argument, because the effective surface charge is now divided by the "fractal expansion ratio" - the amount the plates have increased in surface area.

If anyone wants to kill the killer flux argument for this reason I agree. I stated this as a caveat "fractal plates" three years ago (?) when I first wrote up killer flux in detail. All that has changed since then is I understand more about how difficult it is for fractal plates to store high ED. Here is what I was summarising two years ago, which still seems about right. I'd link the original Gauss disproof threads but can't seem to find them.

Theoretically, if fractal plates could be made with a weird dielectric (and TP, always the optimist, sees this as likley) they could just nicely explain the current EEstor measurements. They could however not go much higher than 1000J/cc - as TP and others would agree.

Now I await with baited breath for PeterP's argument against this. He is clear that I don't understand electrostatics. Fair enough - let us have some better understanding posted here.

Thread rules: stick to electrostatics and related matters.

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There are many amateur mistakes in ee-tom's post- for instance there is no gap, the matter is contiguous. No more of a gap exists between plate and dielectric than between plate atoms or between dielectric atoms. Also his 1 C/m^2 calculation is much too obscure to be considered. I heat echoes of the same basic misunderstandings that can be seen in his and TP's earlier posts. A prime example is that electrons cannot travel more than a unit cell when it is already established that there are Bloch electrons present which are delocalized. EE-tom's wall of text is liberally sprinkled with lack of understanding that electrostatics is a macroscopic theory and microscopic features do not matter to it. For instance high local fields do not matter since they are not applied to macroscopic matter and therefore cannot cause breakdown.

As far as ee-tom's Pauli exclusion argument its completely incorrect as a crystal is already a Pauli exclusion domain with exceedingly many electrons.

Since brevity is the soul of wit, and tediousness the limbs and outward flourishes, I will be brief:

 

Been here. Read that. Still wrong.

Adding to Jcat's post I must say that I have observed ee-tom's inventions to correspond with the phases of the moon which I first recognized by mapping his walls of text to tidal cycles.

I'll wager he and TP have up late concocting this latest sham. I expect him and maybe even EEntangible to join in later.

I answer your points below.

JCatania said:

There are many amateur mistakes in ee-tom's post- for instance there is no gap, the matter is contiguous. No more of a gap exists between plate and dielectric than between plate atoms or between dielectric atoms.

You misunderstand. The "gap" indeed may be 0 thickness. But it must insulate. And the field in teh surrounding lattice must be killer. That is becaus ethe charge density on eitehr side cannot be infinitely thin, for the reasons given.

Also his 1 C/m^2 calculation is much too obscure to be considered. I heat echoes of the same basic misunderstandings that can be seen in his and TP's earlier posts.

You will have to be explicit. But TP has been doing this stuff with his PhD supervisor for two years now, I doubt he makes elementary mistakes!

A prime example is that electrons cannot travel more than a unit cell when it is already established that there are Bloch electrons present which are delocalized.

You misunderstand again. I never said electrons cannot travel more than one unit cell - what do you think space charge is? But if more than one unit cell then the killer field extends also kore than one unit cell, so it does not help. The distinction is that where polarization is on a very fine grain (less than one unit cell) it can cancel the filed without killer field over multiple lattice cell ectent. It is then possible that higher fields can be accomodated, because teh intra-atomic fields are very high anyway.

EE-tom's wall of text is liberally sprinkled with lack of understanding that electrostatics is a macroscopic theory and microscopic features do not matter to it. For instance high local fields do not matter since they are not applied to macroscopic matter and therefore cannot cause breakdown.

I'm, sorry Jcat this is just wrongly applied. I'm not using anything except Maxwell eqns, which work microscopic. k applies to the average field, obviously, and is an approximation. The whole point is that high fields are applied to > 1 lattice cell for the reasons I've given - the charge on both sides must be distributed.

As far as ee-tom's Pauli exclusion argument its completely incorrect as a crystal is already a Pauli exclusion domain with exceedingly many electrons.

Talk to TP about his DFT simulations. I'm right that electrons cannot be squeezed so close to an edge. I'll leave the details of why for later. TP will do a better job than me of describing them.

Matt - i thought better of you. You have never before (to my knowledge) given arguments against. Perhaps I missed them. Facts don't go away just cos you choose to disbelieve them, so this is not adequate.

Matt said:

Since brevity is the soul of wit, and tediousness the limbs and outward flourishes, I will be brief:

 

Been here. Read that. Still wrong.

B - glad to see your commentary on my psyche is back to near its old inimitable level!

B said:

Adding to Jcat's post I must say that I have observed ee-tom's inventions to correspond with the phases of the moon which I first recognized by mapping his walls of text to tidal cycles.

ee-tom said, You misunderstand. The "gap" indeed may be 0 thickness. But it must insulate. And the field in teh surrounding lattice must be killer. That is becaus ethe charge density on eitehr side cannot be infinitely thin, for the reasons given.

Are you saying there's no semantic difference between a 0 width gap and no gap but there is a physical difference?

Dear all,

Please help poor PeterP. He has stated categorically that the above argument is wrong but I strongly suspect cannot correctly show this. You lot are not doing is work for him. Jcat tried though. Thanks Jcat.

You should take some time to convince yourself that macroscopic theory is correct and has been verified. There is no theory to replace it. Your mistake about the constitutive relations is indeed grave but it should be obvious that there are plenty here who can help you understand it. DFT does not trump macroscopic theory as Imperial College, even for its name does not trump science. Let's say for instance I measure 100.00 volts on a meter and DFT told me its really 3.45356 volts, should I believe it?

Jcat, perhaps you could explain what in my argument precisely is incorrect? Maxwell's equations do not replace macroscopic theory, but they complement it and they allow a deeper understanding at a microscopic level which is helpful and not covered by macroscopic theory at all.

I think perhaps my "mistake about the constitutive relations" is what you will wish to expand. I am aware of no such mistake and I think for others to understand it would need to be made clear. For example, you could propose a system for which my argument above falls apart?

JCatania said:

You should take some time to convince yourself that macroscopic theory is correct and has been verified. There is no theory to replace it. Your mistake about the constitutive relations is indeed grave but it should be obvious that there are plenty here who can help you understand it. DFT does not trump macroscopic theory as Imperial College, even for its name does not trump science. Let's say for instance I measure 100.00 volts on a meter and DFT told me its really 3.45356 volts, should I believe it?

I have explained all that. For instance you still need to answer this question: Are you saying there's no semantic difference between a 0 width gap and no gap but there is a physical difference?

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