Effective Mass Centrifuge

[Enthalpy]

Hello everyone and everybody!

 

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.

 

 

Along a radial leg, the centrifugal force creates a voltage of m_A * 0.5*(V²-v²) /q in the material A, or m_B 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 extraction potential 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

[EquisDeXD]

Well, if what your doing is extracting energy from the potentially energy that was already stored in the material itself as you found it or mined, then this could easily be a source of energy. The only other option is that the energy you are spending to create this process is equal to or less than the output energy, so you should make sure of that, that the electricity used is less than the energy your getting out of the device because otherwise the explanation is that the energy your getting is from the transformation of electricity that your putting into running the device rather than "releasing" the potential energy in an energy source.

Edited October 7, 2012 by EquisDeXD

[Enthalpy]

The paragraph about energy was just a side remark for people wondering if some physics law prevents the buildup of a voltage. The aim here is not to produce power, but to measure effective masses.

 

My language mistake: instead of "extraction potential", please read "electron work function".

[Enthalpy]

More trouble in sight... because if we were to follow similar reasons, gravity should produce a measureable voltage! Here's a setup:

 

 

This one has D=600mm and can use a bicycle wheel. It rotates at 0.4Hz so gravity exceeds centrifugal force, and this latter cancels out anyway along the conductor path.

 

The conductors are macroscopic wires of metals whose electron "effective" mass differ by 3 vacuum masses. 2*200 wires shall then produce 18nV at 0.4Hz. Yes, it needs shielding. It also needs a uniform temperature that doesn't cycle at 0.4Hz.

 

The amplifier rotates with the wheel. Build an instrumentation amplifier with an LTC6241 for instance: at 70nV/sqrt(Hz) around 0.4Hz for each opamp, an FFT must accumulate data for some 5 min to get 5 sigma signal-to-noise ratio.

 

-----

 

Trouble... Very probably, this one doesn't work for being a perpetuum mobile. The only possibility would be that the shaft brings power, just like when you rotate a tube with a ball in it, and for a short time, the ball's movement means true work. This is the only reason why I take a CMOS opamp here: it's more noisy but if the total charge of the signal is limited then a CMOS is more likely to pick it.

 

What if the centrifuge produces a signal and gravity doesn't? Uncomfortable... It could be that electrons in a metal respond differently to acceleration and to gravity - something new.

 

And what if neither the centrifuge nor gravity produce a signal? Then maybe the contact electric potential changes with the gravity potential.

 

Marc Schaefer, aka Enthalpy

Edited October 21, 2012 by Enthalpy

[Enthalpy]

I've convinced myself that the acceleration acting on electrons' mass creates a potential gradient, and that this potential depends on the mass in each material. While the series of couples in my previous attempt won't accumulate the voltage, one couple can deliver a charge, much like the gate material of a Mos transistor influences the threshold voltage. Even better: this wouldn't obtain a permanent power from a gravity field.

So here's a design, not as easy because the voltage is smaller.

 

A platter spins at 15,000rpm=250Hz to reuse the spindle and motor of an Scsi disk drive, but the new platter has D=300mm. Any alloyed aluminium fits, other materials too, and it must be insulated, for instance by anodisation. A smaller but faster platter is possible. Air drag is strong; shallower gaps reduce it, vacuum too. An active air cushion instead of the spindle would ease balancing and can rotate the platter; the flow must center the platter.

The radial tracks extend from r=25mm to mean R=135mm, where the squares differ by 208m/s. If the electrons weigh +0.5*m0 in one material and -1.0*m0 in the other, the voltage must be 185nV (peak, symmetric) or 131nV rms symmetric.

Air capacitances to the stator bring the signal as AC to the electronics. 106 stripes of each material, 2mm wide, overlap the stator electrodes over 20mm radius at 1mm gap. They transmit the 26.5kHz signal through 37pF or -j160kohm (unsymmetric).



Each signal goes through a low-capacitance buffer before the difference is amplified and observed for instance on a signal analyzer. The OPA827 offers 4nV/rHz, 2.2fA/rHz (all typ at 25°C), and a 10*22Mohm polarization 8.5fA/rHz, cumulating 6.0nV/rHz on -j160kohm over both channels. An analyzer equivalent noise bandpass of 4.8Hz gives 20dB S/N and 48mHz 40dB.

To reduce the input capacitance, much of the buffer follows the output's potential: the shielding (differs between + and - signal), the inverting input and the op amp's supplies.

22Mohm to 0.90*Vout would worsen the current noise. Regulators referenced at the output may replace the zeners and bipolars if stable. The Jfet pair LSK489 is quieter (each 1.8nV/rHz, 1pA and 3pF) than the OPA827, worth a design. The design can also be unsymmetric, with one capacitor circular abd wide at the centre.

Work functions, contaminants and more reasons will create a strong signal too. The effect of the centrifugal force must be observed from the differences at varied speeds, needing to tinker the drive's electronics.

Marc Schaefer, aka Enthalpy

[MigL]

Correct me if I'm wrong Marc, but all I know about effective mass is from a 4th yr course in solid state physics, and if I remember correctly it is simply the 'apparent' mass of the electron as it moves through a semiconductor under the influence of various fields and other particles. The effective mass is, then, related to the material ( and its properties ) that its moving through.

 

In effect it is a simplification of the problem, where the change to effective mass allows us to disregard the material and its properties in our calculations.

[Enthalpy]

A cleaner signal needs a very narrow bandpass filter, but the platter's rotation isn't that accurate. A spectrum analyzer or special hardware would use a Fourier transform, but drifts in the rotation frequency are still a worry.

Extra hardware can measure the platter's instantaneous angle to synchronize the Fourier transform - and then a complete Fourier isn't needed.

Or, as inspired by radioastronomy, we can split the pickup of the signal in two, say at two half-circles, have two independent amplification chains, and compute the correlation between both. This extracts the signal, which is correlated at both pickups, from the local thermal noise, which isn't correlated and sums up inefficiently in the integrator.

The correlation detects a signal even if the frequency isn't known. Approximate filtering remains useful. Correlation doesn't protect against noise sources common to both channels.

----------

Instead of electrons conductors, we can rotate electrolytes. The signal is stronger because ions are heavier: 114,000 times for NO₃^-. It adds all ion types: mass divided by the signed charge. The buyoancy reduces the force through the solvent's displaced mass, so that the number of solvent molecules per ion has no direct effect; this rare feature can be interesting for analysis methods.

Marc Schaefer, aka Enthalpy

 

(Hi MigL, answering soon)

[Enthalpy]

[...] the 'apparent' mass of the electron as it moves through a semiconductor under the influence of various fields and other particles. The effective mass is, then, related to the material ( and its properties ) that its moving through. [...]

 

The electron's wavefunction in a solid is a huge mess. First, because electrons interact, and very strongly. Though, all models want independent electrons; while this may hold more or less in a semiconductor, it must have consequences in a metal - I still want an explanation why metals' heat capacity want very few mobile electrons but the Hall effect sees roughly one per atom.

 

Then, because electrons deep in the atoms influence the valence and conduction electrons. This must be and is accounted for in numerical models; it explains why diamond, silicon and germanium have different band diagrams despite the identical crystal structure.

 

The standard method is to deduce band diagrams as linear combinations of the orbitals of individual atoms. This reasonably tells that electrons are denser near the nuclei and that the electron's energy depends fundamentally on how its wavelength compares with the crystal lattice. Though, this isn't manageable by hand.

 

As a workaround, people noticed that only the relative variation of the wavenumber versus the energy is interesting, and only over a small span of energies, because this determines how a thermal electron is localized and changes its speed - keywords phase speed and group speed.

 

Once the relation between wavenumber and energy is known, or rather their relative local variation, the details of the wavefunctions are unimportant. Only the interferences of waves having nearly the same energy locates the particle and tells teh speed and acceleration.

 

So we can gladly replace the solid's linear combination of orbitals by plane waves typical of vacuum, that is, the trapped electron by a free one (shocks are still absent from such models), as long as the "dispersion relation" between E and k is the same. This is the huge simplification. The only thing added to the vacuum situation is that the mass differs.

 

Though, the different mass isn't a result of our assimilation with a free particle. It results from the dispersion relation itself, as given by each material (and may depend on the direction, the local valley, and other things).

[John Cuthber]

A cleaner signal needs a very narrow bandpass filter, but the platter's rotation isn't that accurate. A spectrum analyzer or special hardware would use a Fourier transform, but drifts in the rotation frequency are still a worry.

 

Extra hardware can measure the platter's instantaneous angle to synchronize the Fourier transform - and then a complete Fourier isn't needed.

 

Or, as inspired by radioastronomy, we can split the pickup of the signal in two, say at two half-circles, have two independent amplification chains, and compute the correlation between both. This extracts the signal, which is correlated at both pickups, from the local thermal noise, which isn't correlated and sums up inefficiently in the integrator.

 

The correlation detects a signal even if the frequency isn't known. Approximate filtering remains useful. Correlation doesn't protect against noise sources common to both channels.

 

----------

 

Instead of electrons conductors, we can rotate electrolytes. The signal is stronger because ions are heavier: 114,000 times for NO₃^-. It adds all ion types: mass divided by the signed charge. The buyoancy reduces the force through the solvent's displaced mass, so that the number of solvent molecules per ion has no direct effect; this rare feature can be interesting for analysis methods.

 

Marc Schaefer, aka Enthalpy

 

(Hi MigL, answering soon)

I have no idea whether or not you can "centrifuge" the effective mass of an electron (or anything else come to think of it) But this may be able to help with the filter/ signal/ noise ratio problems

http://en.wikipedia.org/wiki/Lock-in_amplifier

You can lock it to the rotating "wheel" so, if the speed drifts it doesn't matter too much.

 

you might also want to look at this sort of thing

http://en.wikipedia.org/wiki/Boxcar_averager

[Sensei]

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).

It's not just "mass of electron in vacuum".

 

Take for example radioactive beta decay minus, which emits electron. Probably the best example is Tritium decay:

 

[math]T \rightarrow _2^3He + e^- + \bar{V}_e + 18.6 keV[/math]

 

mass of Tritium is 3.0160492777 u

3.0160492777 u * 931494061 * 1.602176565*10^-19 / 299792458^2 = 5.00826721404019E-027 kg (if you prefer kilograms)

 

mass of Helium-3 is 3.0160293191 u

3.0160293191 u * 931494061 * 1.602176565*10^-19 / 299792458^2 = 5.00823407200808E-027 kg (if you prefer kilograms)

 

But these masses (from isotopes database) are nucleus plus electrons around them.

So we need to subtract masses of of electrons and have:

 

3.0160492777 * 931494061 - 510998.9 = mass-energy of Tritium nucleus alone.

3.0160293191 * 931494061 - 2*510998.9 = mass-energy of Helium-3 nucleus alone.

 

Right, but Tritium is emitting free electron.

 

So full equation looks like:

(3.0160492777 * 931494061 - 510998.9)-(3.0160293191 * 931494061 - 2*510998.9) - 510998.9 = 18591.3173662185 eV (+- few electron volts)

And that's typically rounded to 18.6 keV decay energy of Tritium.

Which also shows true mass-energy of electron.

If it would be different, we wouldn't be able to predict/calculate decay energy.

Edited April 8, 2015 by Sensei

[Enthalpy]

I have no idea whether or not you can "centrifuge" the effective mass of an electron [...]

 

And so would say most people working in solid pysics. I changed my mind several times about the contacts between both materials cancelling or not the effect on the electrons. What convinces me presently is that the contact can't cancel out the rotation-induced voltage over all the stripes length. The best bet to my eyes is to experiment first, and later make the perfectly logic, definite and irrefutable prediction.

 

Even if no voltage were observed, we'd have learned something.

[...] This may be able to help with the filter/ signal/ noise ratio problems

http://en.wikipedia.org/wiki/Lock-in_amplifier

You can lock it to the rotating "wheel" so, if the speed drifts it doesn't matter too much.

 

Yes, it's the kind of setup I had in mind. If integrating over 1000s to make an accurate measure, the platter rotates 250,000 times and 2*106 stripes pass by. Even if the platter's rotation and the spectrum analyzer were driven by oven-controlled crystal oscillators, they would drift too much for a Fourier transform, hence the angle sensor at the platter and the locking.

 

It's easier at the electrolyte. Maybe I check the drift time of the ions, a possible difficulty; a blood centrifuge takes an acceptable time.

It's not just "mass of electron in vacuum". [...] The decay energy of Tritium [...] shows the true mass-energy of the electron.

 

When the electron has in the solid a different mass from the one in vacuum, the crystal lattice can also have an other mass, so both compensate. As far as I know, such an effect isn't accessible to measures.

 

There are other possibilities. Moving electrons at moderate energy (for instance 26meV) in a solid tests the mass only around a very limited energy spectrum; the mean value over a wider energy spectrum could converge to the vacuum mass. The so-called "effective" mass being a differential anyway, its mean value must be simple.

Edited April 9, 2015 by Enthalpy

[Enthalpy]

This setup solves the technical and conceptual difficulties of the centrifugal designs. It creates instead a rotational oscillation to observe the electrons' inertia. The acceleration is huge and its azimutal direction lets a long stripe of a single material accumulate signal amplitude.

The stripe can have at identical radius both contacts with the amplifier's material if this is any worry; or even, it could drive a transformer whose primary winding is of the stripe's material. Though, I expect no difficulty at the contacts.

The design uses the vibration deformation of one single part to achieve the acceleration. The tube that rotates a disk is just an example I detail, and the figures serve only to illustrate it; this design is very adaptable in shape and sizes, and for instance the disk could be tapered like a turbine, the stripe could be a helix on a longer tube instead of a spiral on a disk, it could spiral its second layer and have more layers...



A strong mechanical resonance makes the acceleration, so I don't consider a glued wire. By thin film methods, the disk gets an insulation layer (anodized?), a patterned stripe layer, an insulation, a second patterned stripe layer. An additional insulation and a shield layer shouldn't be necessary.

AA7075 aluminium brings a good acceleration; it may need a new heat treatment after the thin film process. Copper alloys like Cu-Cr1Zr accept a hotter process but give a weaker acceleration. Titanium alloys like Ti-Al6V4 are too resistive for an actuator to be described, ceramic is obviously worse. Steel is ferromagnetic or uncomfortably resistive. Composites have mechanical losses.

----------

With the dimension examples of the sketch, AA7075 T651 (2810kg/m³, G=27GPa) serves at 100MPa shear to survive for some hours; exaggerate the transition radii. At R=25mm, the 4mm disk transmits 1500N*m to accelerate 560*10^-6 kg*m² by 2.8Mrd/s². The R=25mm r=19mm tube has GI=11*10³ N*m²/rd stiffness; a slightly shorter R=22mm cylinder, optionally with a small bore, would also resist 1500N*m.

2400Hz is a high flute note; vacuum would relieve the experimenters and widen the choice. 87mm tube length gives the 127kN*m/rd.

A second disk vibrates with opposite phase; with e=20mm and additional 87mm/5 tube length, it provides a vibration node on the tube where a shoulder permits to hold the part with low losses. Percussion instruments know some methods like wires. The accurate shoulder's position may need trials.

The thin disk has a vibration peak amplitude of 2.8Mrd/s², 186rd/s and 12mrd. At the stripe's mean r56 it translates to peak 157km/s², 10m/s and 0.67mm, and at the disk's R75 to peak 211km/s², 14m/s and 0.90mm, whoop.

----------

The stripe spirals from r=35 to R=75mm or weighed mean r=56mm. Two layers of 80 turns make it 56m long, so electrons as heavy as in vacuum create an open-loop peak voltage of 50µV, or 35µV rms, wow. Aluminium for instance, 250µm*40µm, would have only 157ohm with 1.6nV/rHz noise, to which an LT1028 or BC550C adds little. Even a 100Mohm semiconductor stripe would make only 1.3µV/rHz noise.

The disk' center is less shaky for the preamplifier; wires could also exit from there, possibly through the shoulder, to an external preamplifier.

The rotation of the closed spiral doesn't pick an external induction if uniform and constant. 50µV spurious would result from a gradient of 250µT over one spiral diameter, and two opposite spirals improve that; Earth's induction is about 40µT. Or an axial external induction of 2nT at 2400Hz would create such a spurious.

----------

Monocrystalline semiconductors would need to glue a wafer on the disk perfectly, or grind a boule into the disk+tube+shoulder+disk, or recrystallize the stripe - difficult. Amorphous semiconductors are easier.

Nice for graphene as well. And if one can bring nanotubes in the stripe shape, this setup measures a carrier mass where the Hall effect can't. Miniaturize the design on silicon? Or prefer the previous centrifugal design?

Electrolytes are less natural here because of diffusion times. I didn't investigate.

Superconductors are an obvious target, as Hall has drawbacks, but they will need interpretation... Does the translating and rotating charged lattice freeze the superconducting population? Which electrons do we observe?

A description of an actuator should come.
Marc Schaefer, aka Enthalpy

[Enthalpy]

The torsional resonator needs a good motor. Radiation loses very little, air viscosity only 0.2W, but at hypothetic Q=10,000 the metal dissipates ~40W rms. Here are qualitative ideas until I debug my design.

A violin's bow is good for early trials but too weak. It can inspire a rotating slip-stick disk, with rosin and strong hairs, rotated around 2m/s and pressed against the thick disk.

A hydraulic flow can provide a strong oscillation at 2400Hz, but I didn't investigate - it could resemble a magnetron.

An induction motor might be designed so its torque drops with the slip speed between 0 and 4m/s. This one would accept an imprecise rotation or field speed.

A rotor with many magnetic poles can run at usual speed around or near the thick disk which would have many teeth, so that currents induced in the teeth when facing the poles let the disk cog at 2400Hz.

Marc Schaefer, aka Enthalpy

[Enthalpy]

Here's a convenient motor design with design flexibility. This "transmotor" doesn't touch the resonator to avoid damping. It's an electromagnetic actuator, similar to any motor or actuator, but it has transformers to inject current in the rotor without contact.

 

 

Comments aided by figures should come.

Marc Schaefer, aka Enthalpy

 

[Enthalpy]

Figures for the transmotor. They don't use sizes of existing magnets and coil formers, hence are only an example.

----------

The motor disk has mean 10mm thickness: only 4mm at the rim, thicker elsewhere, to rotate with peak 1.1Mrd/s² - 74rd/s - 4.8mrd. Around R60 where the force is created, this translates to peak 67km/s² - 4.5m/s - 0.29mm. 18 spokes push each 1.0N peak to provide arbitrary 40W rms.

5+5mm thick Nd magnets (N38SH: 915kA/m µ=1.06) create 0.8T in 0.5+4+0.5mm gap. The outer 2*1.7mm at the shorter edge are polarized to avoid leaks and make the induction more even where the spokes move; I didn't check these losses. Peak 89A over 14mm make the force.

The 2400Hz current spreads over 4mm thickness but only ~4mm width in 54nohm*m AA7075. 0.12mohm per spoke lose 8.3W rms in the rotor. I estimate the rotor's leakage inductance to 15nH per spoke, whose j0.23mohm is good, as it creates 20mV but the movement 72mV. Instead of the sketched coils but with the magnetic cores at the same places, stacked flexible printed circuits could circulate the primary current parallel to the rotor current loops to minimize both this leakage inductance and the eddy currents in the magnets.

Neglecting the stiffness of the outer ring, its mass adds like extra 18mm to the 20mm long spokes, so 7mm width lets these resonate at 4000Hz, well over 2400Hz. Each spoke accelerates by 79km/s² 1.4g (0.0014kg) of the outer ring and 0.8g of its own mass; 22mm distance need 3.8N*m, stressing the spoke with 118MPa.

Magnets induce at each spoke peak 50mV, so the transformer cores must pass 6.7µWb or 6mm*5mm*220mT. To waste -j10A*turn, the parallel inductance of 660nH needs a permeability >1300, hence the wound metal core. The eighteen 35mm long primaries occupying each 40% of 2*2mm*13mm have 30µohm*N² each; at peak 46A, they dissipate together 0.6W rms.

Each 80mm² spoke side radiates 4mW sound; they cancel much an other out.

----------

Individual fluxes induce peak 100mV in 400mm² spoke pairs at 10mm distance. The core contributes most but radiates little, the air flux makes 28mV. At 110mm distance, each loop would induce 100mV in the spiral's 2*80*120cm².

• They cancel much an other out;
• The experimenter can adjust individual primary currents to optimize the cancellation;
• The upper disk shields /5;
• The primary on a flexible printed circuit would improve a lot;
• Magnetic shielding (better than a conductor) shall do the rest, preferably as spaced thin sheets;
• Active shielding would have been possible.

Each 0.57A*m² magnet would create in open space at 0.11m a gradient <<120mT/m, not the desired <<1.7mT/m.

• Their magnetic circuit is nearly closed;
• They cancel much an other out;
• The already desired magnetic shielding does the rest. Easier than the previous one.

A resonating cylinder would be 0.34m long and attenuate the induction 28 times better than the disks and cylinder. Just fold the spiral and the motor on the cylinder.

----------

The experimenter has many means to check the signal's origin:

• Operate outside the resonance;
• Turn the motor power on and off, observe the signal during the transients;
• Turn the motor's stator, observe the signal's phase;
• Add a dummy magnet pair and its shoes, swap magnets, and so on;
• Observe if more shielding still improves;
• Compare electron with hole conduction.

Almost ready to draw and build.
Marc Schaefer, aka Enthalpy