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Effective Mass Centrifuge

  1. Oct 10, 2012 #1
    Hello you all!

    What about a slightly exotic idea? Here I propose to measure the "effective" mass of charge carriers by centrifugal force.

    Electrons in vacuum have a mass, and when moving in a solid an other mass, often called "effective" (as if the vacuum mass were ineffective). Centrifugal force creates unequal voltages across dissimilar materials that give a different mass to electrons, and with a proper setup, this voltage seems measurable - which I feel funny.

    Referring to the attached sketched (click to magnify if logged in):

    Along a radial leg, the centrifugal force creates a voltage of mA * 0.5*(V2-v2) /q in the material A, or mB etc in the material B, with V the outer speed and v the inner one. By making the odd legs of material A and even legs of material B, and putting many leg pairs in series, we get a significant voltage.

    At least with metals, the electron work function won't vary with the minute amount of electrons added or subtracted, and nor will the contact potential; other materials need an ohmic contact. And yes, I believe electric power could be harvested, which would be provided mechanically by the shaft, but is technologically uninteresting.

    One excellent choice for the disk is a silicon wafer; I take D=2 inches here. An other choice would be a platter of a hard disk drive with its spindle already. Silicon can rotate at 600 m/s (and much more); the inner speed shall be 400 m/s. Take materials that give masses of 1.5*m0 and -1.2*m0 for instance, then each pair of legs offers 1.5 µV; a pitch of 100µm permits 1000 pairs of legs (not all drawn here) resulting in 1.5 mV.

    Metal thermocouples can develop 20 µV/K for instance, so the outer and inner temperatures must be much closer than 0.1K: nothing special within metals or silicon, but it must impose to rotate in vacuum.

    1.5 mV DC is easy to measure, but not on a disk rotating at 3800 Hz (226,000 rpm). Capacitive coupling with the stator simplifies it and can serve as a welcome chopper. Take a gap of 0.2mm and an electrode width of 0.5mm between r = 10 mm and R = 15 mm: you can put 2*40 of them, resulting in 4.4 pF /2 and 150 kHz, so the signal is 1.5 mV pk at 150 kHz through -j*480 kohm, so easy.

    Take a Fet or Mos amplifier, polarize its inputs with 100 Mohm, you get 2.3 kohm noise equivalent from the polarization - or use a pair of diodes for that. The amplifier's noise is similar and the legs can sum to 40 kohm if made of 2 µm thick metal. Noise over a 10 Hz band is 0.1 µV only; with semiconductor legs, shunt the resistance at 150 kHz by a rotating capacitor of few pF on silicon. A 3.5" platter at 7200 rpm would still provide some 15 µV signal.

    Hydrodynamic bearings
    of proper dimensions dampen vibrations, see Dubbel for instance. Silicone and fluorosilicone oils have a negligible vapour pressure but beware they're very under-newtonian at high shear.

    In metals, electron mass may be less exciting, but it is important in semiconductors. Known materials like silicon may serve as an electron standard, possibly with a metal (silver?) as an intermediate mass standard. What about superconductors, where heavy holes are allegedly essential? Or graphene and nanotubes? Or even electrolytes, to determine the degree of solvation?

    Marc Schaefer, aka Enthalpy
     

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  3. Oct 10, 2012 #2

    mfb

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    Looks interesting.

    The v^2-scaling suggests to use other materials - flywheels can exceed 1km/s, improving that v^2 a factor of >=2 (even more if the inner velocity is lower). With ~50cm disk radius and 20cm inner radius, you can pack ~5000 inner contacts (10000 legs) on that disk and get 30mV.
    In addition, flywheels exist as commercial products, including vacuum, and they are good insulators. Disadvantage: Needs a method to fix the conductors on the wheel.
     
  4. Oct 10, 2012 #3
    Enthalpy - you are evidently not aware the proposed centrifuge would be acting as a perpetuum mobile if it worked as hoped. Centripetal acceleration forces are acting in effect as a an artificial 'g' field deriving from a conservative potential. The resulting 'voltage' is felt by conduction charges, but it cannot act like a true emf source capable of driving a current through a circuit. [STRIKE]One should expect a compensating 'junction potential difference' wherever the two media join[/STRIKE] [1]. Just ask yourself - where would any back-reaction torque act to slow the centrifuge if such a current did flow? Especially problematic given sign and magnitude of 'g' forces are independent of rotation direction

    [1]: On second thought that is no answer. 'Junction PD's' should overall cancel out assuming no variation in magnitude between an inner and outer radius 'junction PD'. Cannot honestly conceive of any plausible mechanism that would provide the needed bias - e.g. centripetal stress-induced variation. That would be sensitive to means of mechanical support of circuit material. So, just how it all balances out is unclear to me at least for now.
     
    Last edited: Oct 10, 2012
  5. Oct 10, 2012 #4
    Thanks for your interest!

    This idea is far from obvious, isn't it? :confused: I believe rotation does produce a voltage, which would even be useable at some current (not interesting for technology, but vital for logic!).

    The power for it comes from the shaft, as I imagine it. As heavy electrons flow outwards, their tangential speed increases because they're pushed by the conductor's edge (and resulting field), which consumes torque and power from the shaft. As they come back inwards as lighter electrons they lose tangential speed and do give back some torque and power to the conductor and shaft, but less than on the way outwards, because the electrons are now lighter.:cool:

    So this look possible to me. Not a perpetuum mobile but a mechanical-to-electrical power converter, that is, a generator.

    On the contact potential... It took some time to convince me :uhh:. If the acceleration (or gravitation) potential varies between both contacts to compensate the centrifugal force actingon effective mass, then the idea won't work. But why should the contact potential vary? It's linked with the electron work function. I see only the density of electrons in the metal that would change it, and this variation is so tiny!

    So my position is: voltage doesn't balance out and doesn't have to because it wouldn't create a perpetuum mobile. But err... You know, the idea is simple enough (especially with metals and insulating layers deposited on the platter of a hard disk drive) that it can be tested quickly, and thereafter, many people will be able to predict how it necessarily had to behave...:biggrin:
     
  6. Oct 10, 2012 #5

    mfb

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    post 3 --> post 4 is very similar to my own line of thought before I posted :).

    "Heavy electrons" flow outwards (=> get much energy from rotation), "light electrons" flow inward (give less energy to rotation), slowing the thing - independent on the direction of rotation.
     
  7. Oct 10, 2012 #6
    Well it is interesting! :bugeye:
    Right there!
    You make one good point here I had missed - IF the true inertial mass of conduction charges varies just as for effective mass in lattice, then inward and outward radial mass flow-rates are unequal and a net Coriolis torque is acting! Which will reverse sense in keeping with rotation sense of ω such as to act as a power drain. Looking good so far. But wait - dp/dt = mdv/dt + vdm/dt, and there is a flow-speed dependent reaction force ~ vdm/dt across those junctions in keeping with overall mass flow continuity. Another thing needing to be conserved though is angular momentum. And that guarantees that any net Coriolis torques owing to unequal radial mass flows must be exactly compensated by the net tangential 'kick' forces in junctions owing to that vdm/dt effect. This immediately rules out any possibility of compensating mechanical power drain. Which sadly implies no electrical current after all :frown: - assuming you have not inadvertently discovered free energy! :eek:

    [Oh my. Just realized above is not the real answer. Junction vdm/dt fix to counter Coriolis torque won't work consistently. Sign and magnitude of that junction force depends solely on current flow direction and speed relative to that junction - independent of direction of centrifuge ω. Whereas Coriolis forces reverse with sense of ω. So to salvage both conservation of energy and angular momentum, seems awfully certain that charge carrier in-lattice effective mass cannot be equated to inertial mass. The latter must then, apart from tiny relativistic variation, be invariant. Hence no centripetally induced emf. Bottom-line remains sadly as before - no output to detect.]
    I agree there is no plausible contact potential type explanation. Maybe you should build it just for peace of mind - with a certain Nobel prize if it does work! But I would suggest thinking a lot about what is really going on before committing to any action plan.
    Think about above points - but if you think it can be done quickly (and cheaply)....:smile: See above edit!
     
    Last edited: Oct 10, 2012
  8. Oct 10, 2012 #7

    mfb

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    Here another setup which might be easier to build: Build several strips as before, but connect them to a circle with a voltmeter in the center. The voltmeter has to rotate, and needs some way to store or transmit its data, but the whole setup needs less parts.
     
  9. Oct 10, 2012 #8
    The remark about dp containing as well V*dm is disturbing!
    Let's see...

    - The different metals will be superimposed, according to usual semiconductor processes, and current may flow there in any direction chosen by the design. So possible hot electron injection as happens in heterojunctions, which would be parallel here to the rotation axis, should play no role.

    - Electron speed due to the current is much smaller than the rotation and should have no importance.

    - Imagine the momentum of electron+both metals is conserved (could it be different ?) when the electron crosses the contact: this is exactly what I need! It means no torque is created there.

    - I feel this terrain very uncomfortable... I haven't thought through what the momentum-energy relation of electrons in a solid really means. Could it be that, for a given electron kinetic energy in a solid, the difference of momentum to what it would be in vacuum lays in the crystal? What would this imply for the paths outwards and inwards?

    Back to the same situation: better try first, and predict afterwards.:tongue:

    -----

    Nobel: I have the strongest doubts this thing deserves one. And anyway, I feel my electrostatic alternator is much more significant than a measurement of effective mass
    http://saposjoint.net/Forum/viewtopic.php?f=66&t=1684&start=20#p19961
    http://saposjoint.net/Forum/viewtopic.php?f=66&t=1684&start=40#p20451

    Test this electron dryer by myself: I have absolutely nothing here to build it! I came here with my backpack and received my computer meanwhile, that's all more or less. Someone else will have to try.
     
  10. Oct 10, 2012 #9
    But necessary if an actual charge carrier inertial mass change is occurring. Even if the only change is in charge carrier number density there must be a junction impulse. More on that later.
    No escape here. Even if flow across the junction itself is axial, current must make a sharp turn to resume tangential flow, and altered mass will show up in ensuing centripetal contribution there. And btw I neglected to fully round this out last time - additional contributions to any overall torques occurs owing to fully in-plane centripetal forces at corners of circuit. Of course in the end this is moot as conservation of angular momentum guarantees no net mechanical torque or power. Still, it's important to know whether carrier effective mass meff and inertial mass mi can be equated, and I'm confident they cannot for reasons already given, and notwithstanding some corrections listed later.
    The actual charge carrier speeds - averaged over direction of current - are typically ~ 106m/s and much greater than rotation speed, but owing to a correspondingly tiny fraction of available conduction band charge carriers. See under 'The Sommerfeld Model of Conductivity', pp 4/7, 5/7 here: https://www.physicsforums.com/attachment.php?attachmentid=38139&d=1313832109 Many sites and even textbooks get that one quite wrong. Not that it really matters here. What matters is the product of mean flow speed and carrier density, and of course potentially any fractional difference in inertial mass. I made an error in blue-text edit in #6 in stating only current speed and direction relative to junction mattered re junction impulse. There are additional contributions, but overall they do not matter. More later.
    That won't do. Consider case of a single circuit comprised of two semicircular wires of different materials joined at obviously two junctions to form overall a circular loop. Suppose this loop is stationary but carries a steady circulating current. If effective/inertial masses differ, there must be an imbalance of centripetal forces in the two halves. If you reject that a compensating impulse exists in those two junctions.....need I add the rest?!

    But now for admission. My last blue text edit in #6 was mistaken in that there must be additional contribution to junction impulse owing to circuit rotation. Suppose above circular loop with steady current flowing now rotates about it's own major axis. Just suppose in this case mean charge speed around circuit is uniform and exactly countered by mechanical rotation speed. No centripetal accelerations exist, so no junction impulse will exist either. Had forgotten there must be Bernoulli-type contributions that depend on overall motions. And also any carrier concentration differential in addition to and separate from any actual mi differential. For instance in above loop circuit, non-rotating, suppose carrier densities are different in two halves. Then mean flow speeds will also vary inversely to densities. It's easy to then show centripetal force imbalance exists weighted towards greater force in lower carrier density half. Again, there must be a compensating impulse in the junctions. Bernoulli-type effect I imagine well understood by those versed in solid-state physics. However all of these additional contributions cancel out in respect of a possible emf existing in your rotating circuit arrangement, which can only depend on whether a real differential in mi exists.
    And the major stumbling block there continues to be conservation of angular momentum and energy.
    Of course if carrier meff = mi varies, it is implied the crystal lattice absorbs the difference. But that has no bearing on whether an emf in your proposed arrangement is possible - that depends only on whether meff = mi. And energy-momentum conservation laws are saying no.
    Your choice. :uhh:
    Had a quick look at links. Some interesting ideas - but not the place in this section to discuss - maybe General Physics if you want to.
    I suppose you are aware electrons never get wet - not as far as I know!!! :rofl: Or maybe just a diction error. :tongue:
     
    Last edited: Oct 10, 2012
  11. Oct 11, 2012 #10

    mfb

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    I think we need a different approach - the acceleration will change the electron potentials and therefore the band-structure itself. The effect might look small, but it is the one which generates potential potential differences (:D).
     
  12. Oct 11, 2012 #11
    Is this something fundamentally different to effective mass meff (if = inertial mass mi) differentials? Can it apply to a cascaded series arrangement of OP - i.e. are we talking just a one-shot inner-to-outer radius PD, or actual emf around cascaded structure? Because best I can tell, impossible to get an emf via centripetal effects without it breaking those conservation laws. Now if it turns out meff does equate to mi, that would be real interesting!
     
  13. Oct 11, 2012 #12

    mfb

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    Ok, another simplified setup: Make a single loop, orthogonal to the disk. This way, we do not have any movement in phi-direction. In equilibrium (current, electron density & potentials), conservation of angular momentum (in particular: the component orthogonal to the disk) enforces a constant spinning rate. Therefore, with a finite resistance, we cannot have a constant current inside.

    The discussed effect would be present in this simple setup, too, but we cannot get a potential here. Therefore, the original setup should not have a potential either.
    However, I do not know how to explain that in terms of electron density. We would need different situations at inner vs. outer connection, which depends on the potentials? Looks strange. But we have quantum mechanics, so a potential-dependence is indeed possible.
     
  14. Oct 11, 2012 #13
    Meaning I take it with loop on centrifuge periphery, and loop major axis tangent to periphery of disc it's mounted on. That does side-step conservation of momentum issue it's true, but still implies 'free energy' since it's now 'even more impossible' for any energy balance - assuming we are talking having an emf in loop circuit.
    Potential difference, or emf? If only the former, any initial centripetally generated PD likely rapidly neutralized via charge redistribution. Which is how I believe it works for a bar electret. Unlike for a bar magnet where free magnetic charges do not exist. For an emf none of that matters.
    Are we still talking effective/inertial mass differences in circuit, or something else?
     
  15. Oct 12, 2012 #14

    mfb

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    That is my point. We cannot get a permanent current. However, a voltage difference in the original setup would allow to get a permanent current in my setup, therefore we cannot get a voltage difference in the original setup.

    Effective mass, band structure and electron density.
     
  16. Oct 12, 2012 #15
    Not exactly sure what you mean here, but a circuital emf is ruled out in either setup if conservation of energy applies. Given I can see no mechanism to oppose a net emf if mi were to vary similarly for meff with material, this basically says mi is fixed at m0, or we have exciting 'new physics'. No bets on that one.
    Knowing so little about effective mass, decided to check out Wiki here
    Which suggests it does not have any actual linkage to inertial mass mi as suspected. Also highly directional in many crystals - although averaged value for polycrystaline materials still can markedly vary from usual mass. Maybe an actual experiment would show some kind of linkage between meff and mi, but all in all I'd say dim prospects for OP.
     
  17. Oct 16, 2012 #16
    The "effective" mass is the one that, combined with the force, decides acceleration, so it is the "inertial" mass. And since inertial and gravitational masses are identical until we abandon Relativity, the "effective" mass is the "gravitational" mass as well.

    Because mass has no other effect known to me, I say the "effective" mass is the mass.
    That is what I meant in the first message with:
    called "effective" (as if the vacuum mass were ineffective)

    This interpretation may be somewhat disturbing, but is the only consistent one I imagine.

    I wanted first to observe gravity's action on electron mass, but centrifugal force gives a bigger signal. Though, if one came to observe a signal due to centripetal acceleration but rule out one due to gravitation, that would be closer to the Nobel suggested in Q-reeus' message.

    Mass depends on (here non-relativistic) energy and momentum in solids, following a dispersion relation, where mass can be positive, negative, heavier or lighter than in vacuum. And when the kinetic energy is seriously bigger than the interaction with the lattice, say with a beta ray, you naturally take in the solid the same electron mass as in vacuum for the considered energy.

    The conservation of mass-energy implies that when an electron passes from one solid lattice to an other and its mass change, the mass of the lattices changes in the opposite direction, including in anisotropic manner where needed. This results as well from the conservation of momentum in the same situation, where the lattice's momentum change compensates the electron's momentum change.

    Though, the lattice's relative mass change is small because atoms are heavier than electrons. Also, measuring this lattice mass without the electrons looks seriously uneasy.
     
  18. Oct 16, 2012 #17
    Enthalpy - you may just be correct which is why I have not flatly ruled it out but merely said prospects are dim. My knowledge of solid-state physics is at best rudimentary, and it may pay for you to field this idea in that section of PF. Unless I'm mistaken, concept of holes in semiconductors is synonymous with negative effective mass for certain electronic states (in fact it is stated as such early on here:http://en.wikipedia.org/wiki/Electron_hole). Which means you may be better off doing such an experiment, but using doped semiconductors or semimetals. All I urge is, before committing to something costly in time if not money, is that you consult with experts in solid-state physics first. Things like mobility may be just as important as effective mass when it comes to magnitude of any possible effects. And if you feel there is commercial potential - diagnostic wise, not as useful energy source - consider applying for a provisional patent first (there is the slight problem of prior public disclosure! :tongue2:).
     
  19. Oct 16, 2012 #18
    I could convince myself that mechanical speed and angular momentum at the contacts between the different materials don't change the contact potential.

    Imagine first a translation speed: it acts on both the lattices and the electrons, and because all inertial reference frames are equivalent, the (electrostatic) contact potential measured by an "immobile" observer equals the one measured when moving together with the contact.

    Take now a rotation at the same peripheral speed and on a huge radius: it is equivalent to a translation for all local phenomena and won't change the contact potential. Though, it has the same speed as the rotation at small radius, and a bigger angular momentum.

    -----

    Still an other reason is that momentum is conserved, and any effect by the contact on an electron is local since electrons thermalize over a short distance, so the electron, the contact and their very local surroundings keep the sum of their momenta.

    As the electron keeps its rotation speed but changes its mass, the lattices keep their rotation speed and change their masses to compensate the electron. This keeps the cumulated rotation momentum around the contact, giving no torque there as an electron passes it.

    The question of the electron work function varying with the gravitation potential remains open; I believe it's vanishingly small in a metal.

    -----

    About electron speed in lattices: depending on the band structure, moveable electrons can have a small wavelength and a big momentum. In isotropic materials the band structure is symmetrical , but in piezoresistivity this is observed, and in heterojunctions as well, where only electrons pertaining to some conduction valleys have the proper direction to cross a junction.

    However, the momentum is associated with the wave number which depends on the phase speed, or the position of the conduction valley, while the speed of an electron is its group speed, related with the curvature of the conduction valley. So a big momentum comes with a small speed here. Consistently, mass is defined through a momentum variation.
     
  20. Oct 16, 2012 #19
    Metals have holes as well. In fact, about half of all metals, among the most common ones. It depends only on how the band is curved where the Fermi level lies.

    It's the only reason why students are told to measure the Hall effect on silver: silver happens to have positive electron mass, close to the mass in vacuum - and even better, about one electron per atom. This way, students are properly mislead into believing they have understood their good teacher :approve: . Any cheap metal (aluminium wrap foil) would give a voltage as good, and a semiconductor would be hugely more efficient, but then students would ask "why is the voltage in the wrong direction" - and teaching isn't about giving doubts, is it?

    Expert in solid state: despite having learnt it at University for my microelectronics degree, I don't consider myself an expert. And the stuff is complicated enough that true experts will answer "try first, predict later" as I did :rofl:.

    Commercial potential: which one? It can serve once for every material to determine the electron mass. Anyway, if I wanted to take a patent, I wouldn't have described it here first. But citing my name if papers result from this idea would be nice.
     
  21. Oct 16, 2012 #20
    Fun: in the USA and formerly in Europe, ideas had to be feasible to get a patent.

    Presently in Europe, incredible numbers of perpetuum mobile are patented.
    But previously in Europe, some valid ideas were rejected.

    Example: a French inventor described the transformer at about the same time as Tesla did, but his "impossible" idea was rejected by the clerk.

    And what about non-obvious ideas like the injector (see Wiki)? Get vapour from the boiler, expand it to accelerate, let it suck liquid water, and the momentum pushes all the vapour and the liquid into the boiler at full pressure. Observers didn't believe Giffard even after demonstrations. Imagine a patent clerk...

    Now imagine a patent clerk and describe him a rotating disk with metal strips and electrons who change their mass...:rofl:
     
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