The Killer Flux and all that stuff

[ee-tom]

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.

[JCatania]

That sounds like parallel's argument that that since temperatures are rising they're not- its just fudged data that makes us think so. Also similar is what Al Capone told the Feds; "Our boys will be here, in the heart of Chicago where you want to drive your armored cars, you see? So, er, drive them around this way, near the outskirts and they'll be safe. Ya got that?"

ee-tom said:

As I said in the OP, the killer flux argument does not rule out these measurements. It makes them require a weird mechanism swapping P for E, but E is low enough as measured that that does not seem impossible, just unlikely.

I tried for 2 years to find loopholes. I have documented the P for E swap one in the OP.

I posted this because Peterp said he had an argument against. That, weirdly, is progressing on another thread.

GKR said:

Ee-tom, shouldn't you be trying harder to find the loopholes in your argument, given the latest measurements in the PR?

[JCatania]

Actually long range charge movement gives the short range fields. In the case of surface charge the range is zero. 
ee-tom thinks if he can force there to be high fields theoretically the proper theory will have to be abandoned so he manufactured a lie that field wawsn't cancelled at the surface.
EEntangible said:

Tom, why is it that only short range charge movements matter in your argument?

As a thought experiment, suppose we have Frenkel defects en masse where the barium ions move from one end of the entire lattice to the other, so that they fill nearly every lattice site closest to the electrode. Regardless of the physical plausibility of this state of affairs, wouldn't it rapidly attenuate much of the field as you enter into the lattice?

Or take JCat's suggestion about Bloch electrons. If they are extremely polarized such that the electron spends nearly all of its time at the absolute edge of the dielectric, wouldn't this also rapidly screen the field?

I don't claim to understand this stuff very well... I don't see why you suppose that the mechanism must be a short range charge movement rather than any mechanism capable of rapidly screening the field. Could you elaborate on this for me?

[Technopete]

Guys, you might all get somewhere if you moved the way you talked about these things to conform to the "band theory" approach.  Then it is pretty clear what is and what is not possible.  At the moment you are all taking in isolated concepts which don't join up very well.

For instance, Tom's "killer flux" is the normal field experienced at 0.15 Angstroms from an unscreened proton.  But talking in terms of the potential (e.g. of metal electron Fermi levels and dielectric valence and conduction bands) will tell you whether an electron is going to move to where it should not be to start a breakdown or leakage process.

For those of you who know the spoof London underground station game known as "Mornington Crescent" may have more of an inkling as to what this sort of talking at cross purposes really means!

And if you don't know band theory - spend a few hours learning it.

 

Regards,

TP

[JCatania]

Band theory doesn't enter into it. Macroscopic theory has explained it. Don't tell me correct theory is superedesd by wildly inaccurate DFT. Macroscopic theory is a check on DFT and DFT rarely comes close to living up to it. DFT is not a theory but a calculation approximation.

There is no killer flux, breakdown occurs at breakdown not way before it. You are denying the very foundations of thought. It would be silly for you to continue. Occam has eliminated killer flux. Why don't unscreened protons cause breakdown in neutral matter with no applied field.

[ee-tom]

Hi Jcat. I can't evaluate these qualitative arguments. The thing that influences me is simply Gauss applied to the charge on either side of the edge. That is not DFT. Macroscopic theory does not apply here because it assumes the dielectric is homogeneously polarised, whereas we are assuming in this case electrons moving a longish distance and therefore charged regions of macroscopic size at edges.

JCatania said:

Band theory doesn't enter into it. Macroscopic theory has explained it. Don't tell me correct theory is superedesd by wildly inaccurate DFT. Macroscopic theory is a check on DFT and DFT rarely comes close to living up to it. DFT is not a theory but a calculation approximation.

There is no killer flux, breakdown occurs at breakdown not way before it. You are denying the very foundations of thought. It would be silly for you to continue. Occam has eliminated killer flux. Why don't unscreened protons cause breakdown in neutral matter with no applied field.

[ee-tom]

TP - I worked out above in example field at interface and extent of field, getting a potential of 40X a high band gap.  I agree that field on its own is not the issue. Also, near to a nucleus the potential will be much larger than the bandgap - but this is irrelevant because there is no unfilled band for charge to move into (all the inner orbitals are full). I'm saying if:

(1) the extent of the field is several lattice cells (actually even one lattice cell would be enough)

(2) the extent X field >> bandgap

then it must result in conduction.

So if you could get ionic polarization high enough this argument would not apply, of course, because the extent of the field would be absolutely tiny.

That is clear, but seems not accepted on this site!

Technopete said:

Guys, you might all get somewhere if you moved the way you talked about these things to conform to the "band theory" approach.  Then it is pretty clear what is and what is not possible.  At the moment you are all taking in isolated concepts which don't join up very well.

For instance, Tom's "killer flux" is the normal field experienced at 0.15 Angstroms from an unscreened proton.  But talking in terms of the potential (e.g. of metal electron Fermi levels and dielectric valence and conduction bands) will tell you whether an electron is going to move to where it should not be to start a breakdown or leakage process.

For those of you who know the spoof London underground station game known as "Mornington Crescent" may have more of an inkling as to what this sort of talking at cross purposes really means!

And if you don't know band theory - spend a few hours learning it.

 

Regards,

TP

[ee-tom]

Jcat, I'm sorry for surface charge at high density the range is not zero, because the charge spreads out over multiple cells. Where otherwise can the electrons go/come from? electrons are not point charges!

The exception would be where the "surface charge" was simply small distortion of existing orbitals, as in ionic or electronic polarization. But that cannot get up to 50C/m^2

JCatania said:

Actually long range charge movement gives the short range fields. In the case of surface charge the range is zero. 
ee-tom thinks if he can force there to be high fields theoretically the proper theory will have to be abandoned so he manufactured a lie that field wawsn't cancelled at the surface.
EEntangible said:

Tom, why is it that only short range charge movements matter in your argument?

As a thought experiment, suppose we have Frenkel defects en masse where the barium ions move from one end of the entire lattice to the other, so that they fill nearly every lattice site closest to the electrode. Regardless of the physical plausibility of this state of affairs, wouldn't it rapidly attenuate much of the field as you enter into the lattice?

Or take JCat's suggestion about Bloch electrons. If they are extremely polarized such that the electron spends nearly all of its time at the absolute edge of the dielectric, wouldn't this also rapidly screen the field?

I don't claim to understand this stuff very well... I don't see why you suppose that the mechanism must be a short range charge movement rather than any mechanism capable of rapidly screening the field. Could you elaborate on this for me?

[JCatania]

The material is homogeneous therefore the k is constant and the applied field constant. That's macroscopic theory. It is known to apply.

ee-tom said:

Hi Jcat. I can't evaluate these qualitative arguments. The thing that influences me is simply Gauss applied to the charge on either side of the edge. That is not DFT. Macroscopic theory does not apply here because it assumes the dielectric is homogeneously polarised, whereas we are assuming in this case electrons moving a longish distance and therefore charged regions of macroscopic size at edges.

JCatania said:

Band theory doesn't enter into it. Macroscopic theory has explained it. Don't tell me correct theory is superedesd by wildly inaccurate DFT. Macroscopic theory is a check on DFT and DFT rarely comes close to living up to it. DFT is not a theory but a calculation approximation.

There is no killer flux, breakdown occurs at breakdown not way before it. You are denying the very foundations of thought. It would be silly for you to continue. Occam has eliminated killer flux. Why don't unscreened protons cause breakdown in neutral matter with no applied field.

[JCatania]

Electrons are point charges! This is not to say the plate electron wave functions don't have spatial extent. The theory is sound and has yet to be overturned, furthermore it successfully explains the physics of dielectrics. The electrons in the metal are bound to the potential of the metal crystal. This does not mean they are not cancelled by positive charge in the dielectric. Again, if I add a surface of electrons to a k=33500 crystal I most certainly am within the breakdown voltage by definition. Use the definition and there is no mistake possible.

ee-tom said:

Jcat, I'm sorry for surface charge at high density the range is not zero, because the charge spreads out over multiple cells. Where otherwise can the electrons go/come from? electrons are not point charges!

The exception would be where the "surface charge" was simply small distortion of existing orbitals, as in ionic or electronic polarization. But that cannot get up to 50C/m^2

JCatania said:

Actually long range charge movement gives the short range fields. In the case of surface charge the range is zero. 
ee-tom thinks if he can force there to be high fields theoretically the proper theory will have to be abandoned so he manufactured a lie that field wawsn't cancelled at the surface.
EEntangible said:

Tom, why is it that only short range charge movements matter in your argument?

As a thought experiment, suppose we have Frenkel defects en masse where the barium ions move from one end of the entire lattice to the other, so that they fill nearly every lattice site closest to the electrode. Regardless of the physical plausibility of this state of affairs, wouldn't it rapidly attenuate much of the field as you enter into the lattice?

Or take JCat's suggestion about Bloch electrons. If they are extremely polarized such that the electron spends nearly all of its time at the absolute edge of the dielectric, wouldn't this also rapidly screen the field?

I don't claim to understand this stuff very well... I don't see why you suppose that the mechanism must be a short range charge movement rather than any mechanism capable of rapidly screening the field. Could you elaborate on this for me?

[ee-tom]

JCatania said:

Electrons are point charges!

All evidence is that in lattices electronic charge is distributed in orbitals, not point. I'll not make a philosophical point here, but a point charge would have indeterminate large momentum...

This is not to say the plate electron wave functions don't have spatial extent. The theory is sound and has yet to be overturned, furthermore it successfully explains the physics of dielectrics. The electrons in the metal are bound to the potential of the metal crystal. This does not mean they are not cancelled by positive charge in the dielectric.

I think I can agree with all of this, but I'm not entirely sure what is "the theory".

Again, if I add a surface of electrons to a k=33500 crystal I most certainly am within the breakdown voltage bydefinition. Use the definition and there is no mistake possible.

The issue is how many electrons you have to add. I maintain that 60C/m^2 will be too many electrons for them to exist coplanar, or without several lattice cells depth. This is a quantum effect so if you consider classical theory you will not find it, but it is real. Would you like me to find evidence for the thickness of surface charge in conductors (for these electrons all to sit on the edge in a charged dielectric you need the body of the dielectric to conduct)?

3 electrons/A^2, or 50/sq lattice cell, is I think too many for 4A thickness without energy way higher than bandgap. Shall we work out the "particle in a box" equations?

ee-tom said:

Jcat, I'm sorry for surface charge at high density the range is not zero, because the charge spreads out over multiple cells. Where otherwise can the electrons go/come from? electrons are not point charges!

The exception would be where the "surface charge" was simply small distortion of existing orbitals, as in ionic or electronic polarization. But that cannot get up to 50C/m^2

JCatania said:

Actually long range charge movement gives the short range fields. In the case of surface charge the range is zero. 
ee-tom thinks if he can force there to be high fields theoretically the proper theory will have to be abandoned so he manufactured a lie that field wawsn't cancelled at the surface.
EEntangible said:

Tom, why is it that only short range charge movements matter in your argument?

As a thought experiment, suppose we have Frenkel defects en masse where the barium ions move from one end of the entire lattice to the other, so that they fill nearly every lattice site closest to the electrode. Regardless of the physical plausibility of this state of affairs, wouldn't it rapidly attenuate much of the field as you enter into the lattice?

Or take JCat's suggestion about Bloch electrons. If they are extremely polarized such that the electron spends nearly all of its time at the absolute edge of the dielectric, wouldn't this also rapidly screen the field?

I don't claim to understand this stuff very well... I don't see why you suppose that the mechanism must be a short range charge movement rather than any mechanism capable of rapidly screening the field. Could you elaborate on this for me?

[JCatania]

ee-tom says,"The issue is how many electrons you have to add. I maintain that 60C/m^2 will be too many electrons for them to exist coplanar, or without several lattice cells depth. This is a quantum effect so if you consider classical theory you will not find it, but it is real. Would you like me to find evidence for the thickness of surface charge in conductors (for these electrons all to sit on the edge in a charged dielectric you need the body of the dielectric to conduct)?'

 

I don't consider 3 to 4 electrons per sq Angstrom to be unusually dense no matter what theory you try to invoke. Certainly the cmbt surface will have some features. I don't agree that the electrons we are speaking of are necessarily localized therefore your several lattice cell depths is a difficult case to make- it sounds like no quantum effect I'm aware of. Also I've never maintained the electron wavefunctions need to be localized to the surface. But there is some theorization wrt to separate surface states.

[ee-tom]

Ok, so what is the depth of the wave functions of these electrons do you reckon: and i'll do the approx calcs.

JCatania said:

ee-tom says,"The issue is how many electrons you have to add. I maintain that 60C/m^2 will be too many electrons for them to exist coplanar, or without several lattice cells depth. This is a quantum effect so if you consider classical theory you will not find it, but it is real. Would you like me to find evidence for the thickness of surface charge in conductors (for these electrons all to sit on the edge in a charged dielectric you need the body of the dielectric to conduct)?'

 

I don't consider 3 to 4 electrons per sq Angstrom to be unusually dense no matter what theory you try to invoke. Certainly the cmbt surface will have some features. I don't agree that the electrons we are speaking of are necessarily localized therefore your several lattice cell depths is a difficult case to make- it sounds like no quantum effect I'm aware of. Also I've never maintained the electron wavefunctions need to be localized to the surface. But there is some theorization wrt to separate surface states.