Some Thoughts on LENR, Vibrations, Chrystals, Phonons, and Quantum Mechanics

I’ve posted a fair number of things on Cold Fusion or LENR or whatever they are calling it these days.

I think I have a handle on how to make it go more reliably. The “bottom line” (here at the top) is that you need to wiggle the atoms and protons and electrons around, faster is better, until they collide enough to join.

The more Quantum Mechanical point of view is that you need to have rapid change of the electromagnetic fields so that the particle Hamiltonians will have a diabatic change and thus have a move to a new Hamiltonian instead of staying on the same one. (or, shake them until they bang hard enough to fuse ;-)

So a lot of detail follows, but the practical implication is that once you have H or D loaded into Pd or Ni (or potentially other metals with a metalic or partially metalic bond) you need to induce atomic and electronic oscillations so the little dears bang into the walls, so to speak. That can be with high speed change of mag fields, electric fields, electric flows, light (such as UV) whacking the surfaces, thermal energy (hotter is better), ultrasonics (make those phonons wobble!) and maybe more. So some folks have cavitation LENR. Some have hot LENR (Rossi). Some have high frequency e-field LENR (Brillouin), and the Papp engine uses thermal spikes with UV and E-field spikes from a giant spark.

You can load the H or D via raw pressure, or via electric pressure via electrolysis. Just get it loaded. More is better. Probably best is some of both. Then whack it with change. Preferably controllable change so it doesn’t blow up…

The Background

Hard sledding comes first. The QM stuff.

No, I don’t fully understand this. A lot of it looks like F.M. to me… er… ‘Friendly’ Magic ;-) but it is what it is. So here’s my take on the QM of it all… First off, a Hamilton.

https://en.wikipedia.org/wiki/Hamiltonian_%28quantum_mechanics%29

In quantum mechanics, the Hamiltonian is the operator corresponding to the total energy of the system. It is usually denoted by H, also Ȟ or Ĥ. Its spectrum is the set of possible outcomes when one measures the total energy of a system. Because of its close relation to the time-evolution of a system, it is of fundamental importance in most formulations of quantum theory.

Key Bits: It’s just talking about the energy of the system. Note the “time-evolution”. That matters as we need to control the rate of change of things to kick particles out of their Hamiltonian ruts.

Another word to know:

https://en.wikipedia.org/wiki/Quantum_mechanics

Generally, quantum mechanics does not assign definite values. Instead, it makes a prediction using a probability distribution; that is, it describes the probability of obtaining the possible outcomes from measuring an observable. Often these results are skewed by many causes, such as dense probability clouds. Probability clouds are approximate, but better than the Bohr model, whereby electron location is given by a probability function, the wave function eigenvalue, such that the probability is the squared modulus of the complex amplitude, or quantum state nuclear attraction.[21][22] Naturally, these probabilities will depend on the quantum state at the “instant” of the measurement. Hence, uncertainty is involved in the value. There are, however, certain states that are associated with a definite value of a particular observable. These are known as eigenstates of the observable (“eigen” can be translated from German as meaning “inherent” or “characteristic”).

So most of the time things are an ill-defined muddle of probability (so unusual things DO happen) but sometimes they have a more definite value. That is called an “eigenstate”. So eigenstates are more definite, the rest is a bit probabilistic.

The time evolution of a quantum state is described by the Schrödinger equation, in which the Hamiltonian (the operator corresponding to the total energy of the system) generates the time evolution. The time evolution of wave functions is deterministic in the sense that – given a wavefunction at an initial time – it makes a definite prediction of what the wavefunction will be at any later time.

So we are packing a crystal lattice of metal with Protons (H without the e-) and with a metallic bond cloud of electrons. (In covalent bonds, the electron is shared between two nuclei. In ionic bonds, one wins the struggle and captures the electron into the outer electron shell, so Na+ is down one and Cl- is up one in salt. In metalic bonds, the electrons run around in a loose soup of electrons. That’s why we can have electricity move and why they are metallic shiny as photons bounce off of the e- cloud. For colored metals, like gold, only the low energy bounces off and the high energy gets absorbed and the metal is blue deficient in reflections and looks golden. All thanks to that electron cloud wandering between atoms in the crystals.) Once packed, we’d like those e- wave functions to get smushed up with some P+ wave functions and become N. Slow neutrons that get stuck into a nucleus somewhere. Normally the e- and P+ don’t get close enough for that. We need a way to collapse their wave functions into a new thing. A way to get each off of their own Hamiltonian and onto a new common one.

Note the words “time evolution” again. So we need to do things that screw around with the motion / time aspect. Get those suckers smacked around by other atomic wave functions, and fast, so they get pushed over the hump into a new N function.

That’s hinted at in this quote:

Wave functions change as time progresses. The Schrödinger equation describes how wavefunctions change in time, playing a role similar to Newton’s second law in classical mechanics. The Schrödinger equation, applied to the aforementioned example of the free particle, predicts that the center of a wave packet will move through space at a constant velocity (like a classical particle with no forces acting on it). However, the wave packet will also spread out as time progresses, which means that the position becomes more uncertain with time. This also has the effect of turning a position eigenstate (which can be thought of as an infinitely sharp wave packet) into a broadened wave packet that no longer represents a (definite, certain) position eigenstate

We want those particles sitting there, broadening their wave functions, until if finds itself overlapping with another wave function ( the e- and P+) and then whack them FAST into one new wave function that takes less space… by forcing them into a known smaller space… by having the atoms around them crush them together into that eigenstate space.

Enter The Phonon

Now you and I might just call this vibration. Or vibrating atoms. But now, now we need a new name for it. Sigh. Just like “eigenstates” means “that stuff you always knew that was not probabilistic”, phonon means that vibration you always thought was just a vibration, but is now more, er, QM special…

https://en.wikipedia.org/wiki/Phonon

In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids. Often referred to as a quasiparticle,[1] it represents an excited state in the quantum mechanical quantization of the modes of vibrations of elastic structures of interacting particles.

Phonons play a major role in many of the physical properties of condensed matter, such as thermal conductivity and electrical conductivity. The study of phonons is an important part of condensed matter physics.

The concept of phonons was introduced in 1932 by Russian physicist Igor Tamm. The name phonon comes from the Greek word φωνή (phonē), which translates as sound or voice because long-wavelength phonons give rise to sound. Shorter-wavelength higher-frequency phonons give rise to heat.

So, in short, we want those suckers vibrating. In a quantum mechanical kind of way since they are small things…

Now any particle collection larger than a single hydrogen is essentially beyond description as a Hamiltonian. Too many states and too much flux. Our goal is to add a whole lot of particles and a whole lot of flux so some of those QM states end up squashing some wave functions into a new particle. How to do that?

Well, one clue is that these are thermal. So heating stuff up moves it that way. Another clue is that they make sound, so sound vibrations will move things that way. Try “hot sound” and you ought to be getting even more energetic Hamiltonians, even if you can’t write them down. Some, in that QM Probability kind of way, ought to kick some P+ and e- into being a nice Neutron. Perhaps some into turning Ni into Cu as a next step (or maybe via direct additions?)

There is some nice eye candy graphics on that page, so take a look and watch beads oscillating…

A phonon is a quantum mechanical description of an elementary vibrational motion in which a lattice of atoms or molecules uniformly oscillates at a single frequency. In classical mechanics this is known as a normal mode. Normal modes are important because any arbitrary lattice vibration can be considered as a superposition of these elementary vibrations (cf. Fourier analysis). While normal modes are wave-like phenomena in classical mechanics, phonons have particle-like properties as well in a way related to the wave–particle duality of quantum mechanics.

So those wobbles can have the nature of one whopper of a particle. And they have a spectrum of vibrations.

For example, a rigid regular, crystalline, i.e. not amorphous, lattice is composed of N particles. These particles may be atoms, but they may be molecules as well. N is a large number, say ~10^23, and on the order of Avogadro’s number, for a typical sample of solid. If the lattice is rigid, the atoms must be exerting forces on one another to keep each atom near its equilibrium position. These forces may be Van der Waals forces, covalent bonds, electrostatic attractions, and others, all of which are ultimately due to the electric force. Magnetic and gravitational forces are generally negligible. The forces between each pair of atoms may be characterized by a potential energy function \, V that depends on the distance of separation of the atoms. The potential energy of the entire lattice is the sum of all pairwise potential energies:

It is electro-magnetic in character, as well as dipping a toe in the Van der Waals pond. Just what we need to get something else that is resisting joining together (via those same electro-magnetic and Van der Waals forces) nudged into doing what it doesn’t want to do. This also implies that some electrical and / or magnetic forces can be used to stimulate more phonons. So things like a microwave excitation of short harmonic wires, or UV absorption into metals, or VHF magnetic fields. (Shades of Tesla and his spikes of HF fields and the assertion that the did odd things…) In short, we can make more, and potentially bigger aggregations of electromagnetic and Van der Waals forces inside a crystal lattice via induction of large phonon activity.

Cram metals with H or D and loads of excess e-, then induce lots of phonons. That ought to be about it. Having a metallic H bond would likely help, too. (More on that later).

The wiki goes on to point out that the math is intractable so a load of simplifying assumptions are made. I suspect we want the non-simple real actions and are looking to exploit a low probability edge case, but one big enough to make things hot. Take a Trillion atoms, and a ‘one in a billion per second’ reaction becomes very usable.

Solids with more than one type of atom – either with different masses or bonding strengths – in the smallest unit cell, exhibit two types of phonons: acoustic phonons and optical phonons.

Acoustic phonons are coherent movements of atoms of the lattice out of their equilibrium positions. If the displacement is in the direction of propagation, then in some areas the atoms will be closer, in others farther apart, as in a sound wave in air (hence the name acoustic). Displacement perpendicular to the propagation direction is comparable to waves in water. If the wavelength of acoustic phonons goes to infinity, this corresponds to a simple displacement of the whole crystal, and this costs zero energy. Acoustic phonons exhibit a linear relationship between frequency and phonon wavevector for long wavelengths. The frequencies of acoustic phonons tend to zero with longer wavelength. Longitudinal and transverse acoustic phonons are often abbreviated as LA and TA phonons, respectively.

Optical phonons are out-of-phase movement of the atoms in the lattice, one atom moving to the left, and its neighbour to the right. This occurs if the lattice is made of atoms of different charge or mass. They are called optical because in ionic crystals, such as sodium chloride, they are excited by infrared radiation. The electric field of the light will move every positive sodium ion in the direction of the field, and every negative chloride ion in the other direction, sending the crystal vibrating. Optical phonons have a non-zero frequency at the Brillouin zone center and show no dispersion near that long wavelength limit. This is because they correspond to a mode of vibration where positive and negative ions at adjacent lattice sites swing against each other, creating a time-varying electrical dipole moment. Optical phonons that interact in this way with light are called infrared active. Optical phonons that are Raman active can also interact indirectly with light, through Raman scattering. Optical phonons are often abbreviated as LO and TO phonons, for the longitudinal and transverse modes respectively.

Notice that light or sound are both able to set things jiggling, and that having different species in the crystal lattice lets you get both kinds of phonons. So hydrogen loading opens the door (and perhaps some other minor elements in the mix could make it interesting too. B or Li? Other metal alloys?) and then phonons make the smashing happen. The differing mass of H and Ni implies optical phonons, and that might be important. It could also explain why things only start when loading nears 1:1 ratio.

There’s more in that article, but for now it can wait. Just realize that this activity of phonons relates to sound and light, and also to emissions of EM waves like microwaves and such. The implication being that those energies going back in can create the phonon activity as well.

So what happens next?

https://en.wikipedia.org/wiki/Adiabatic_process_%28quantum_mechanics%29

This is where it gets pulled together.

Avoided Crossing of two Hamiltonians

Original image and attribution

The caption says:

Figure 2. An avoided energy-level crossing in a two-level system subjected to an external magnetic field. Note the energies of the diabatic states, \scriptstyle{|1\rangle} and \scriptstyle{|2\rangle} and the eigenvalues of the Hamiltonian, giving the energies of the eigenstates \scriptstyle{|\phi_1\rangle} and \scriptstyle{|\phi_2\rangle} (the adiabatic states).

Hopefully the Greek characters come through. If not, click to the article and read it there until I learn Greek ;-) Drat. Didn’t work. OK, that’s for later…

What it is showing is two Hamiltonians, the red curve and the blue curve, with the avoided crossover between them. Our goal is to get things to take that black line from one corner to the other and change from one Hamiltonian to the other. What does it say enhances this outcome?

Figure 2 shows the dependence of the diabatic and adiabatic energies on the value of the magnetic field; note that for non-zero coupling the eigenvalues of the Hamiltonian cannot be degenerate, and thus we have an avoided crossing. If an atom is initially in state \scriptstyle{|\phi_1(t_0)\rangle} in zero magnetic field (on the red curve, at the extreme left), an adiabatic increase in magnetic field \scriptstyle{\left(\frac{dB}{dt}\rightarrow0\right)} will ensure the system remains in an eigenstate of the Hamiltonian \scriptstyle{|\phi_1(t)\rangle} throughout the process(follows the red curve). A diabatic increase in magnetic field \scriptstyle{\left(\frac{dB}{dt}\rightarrow\infty\right)} will ensure the system follows the diabatic path (the solid black line), such that the system undergoes a transition to state \scriptstyle{|\phi_2(t_1)\rangle}. For finite magnetic field slew rates \scriptstyle{\left(0<\frac{dB}{dt}<\infty\right)} there will be a finite probability of finding the system in either of the two eigenstates. See below for approaches to calculating these probabilities.

Basically saying things stay on the red or blue line… but what can make things NOT stay on that line? A very fast magnetic slew rate. Or, I’d speculate, a very fast electric slew rate, or phonon slew rate.

In an adiabatic process the Hamiltonian is time-dependent i.e, the Hamiltonian changes with time (not to be confused with Perturbation theory, as here the change in the Hamiltonian is not small; it’s huge, although it happens gradually). As the Hamiltonian changes with time, the eigenvalues and the eigenfunctions are time dependent.

Time.

Deriving conditions for diabatic vs adiabatic passage

The math in that article is quite thick at this point, but what I think it is saying is just that if you move things fast enough, they can’t be elastic enough to stay on their Hamiltonian, and things get forced into other shapes when moved very fast. I.e. onto that black line between Hamiltonians.

In 1932 an analytic solution to the problem of calculating adiabatic transition probabilities was published separately by Lev Landau and Clarence Zener,[7] for the special case of a linearly changing perturbation in which the time-varying component does not couple the relevant states (hence the coupling in the diabatic Hamiltonian matrix is independent of time).

The key figure of merit in this approach is the Landau-Zener velocity:

v_{LZ} = {\frac{\partial}{\partial t}|E_2 – E_1| \over \frac{\partial}{\partial q}|E_2 – E_1|} \approx \frac{dq}{dt},

where \scriptstyle{q} is the perturbation variable (electric or magnetic field, molecular bond-length, or any other perturbation to the system), and \scriptstyle{E_1} and \scriptstyle{E_2} are the energies of the two diabatic (crossing) states. A large \scriptstyle{v_{LZ}} results in a large diabatic transition probability and vice versa.

Using the Landau-Zener formula the probability, \scriptstyle{P_D}, of a diabatic transition is given by

So if I’ve got that right, the more rapid and stronger the energy changes, the more likely a diabatic transition.

So high frequency EM fields, bright light, ultrasonics, and even high heat can add some increased probability.

That would explain why high temp E-Cat cells are prone to instability. They start to heat up even faster and make more heat that makes it go faster and… So make it ‘warm enough’, then modulate with something faster to switch, like HF electricity, microwaves, or even ultrasonics.

OK, that’s my theoretical whack at it. Now for a Modest Suggestion on how to make a cell.

Nano-Diamonds and Ultrasonics

There’s a nice PDF on this that I’ve got, but I need to find the link again. For now, a bit less descriptive but flashy link. How to make nano-diamonds with oil and sound:

http://www.hielscher.com/ultrasonic-synthesis-of-nanodiamonds.htm

The chamber is filled with an appropriate slurry, and ultrasound does the rest. It makes tiny spots of heat and pressure so high you get diamonds to form.

What I propose is that the same apparatus ought to make LENR happen. Use a powder of Ni in water, saturated with high pressure H2, or perhaps with a transverse electric current to load the metal, then turn on the ultrasonics to provide the phonon kicker.

Call it the Smith LENR Cell if it works, and I’ll be happy ;-)

Ah, there’s the PDF:

http://www.chm.bris.ac.uk/pt/diamond/pdf/drm17-931.pdf

Up to 10% conversion of organic to diamond. Temps of about 120 C in the bulk liquid. Not exactly hard to engineer. Perhaps we could get a master mechanic like P.G. to build one in the garage… First get it to make diamonds, then swap the liquid for a metal in water slurry with H loading and stand back. (Crank up the ultrasonics slowly in case it works too well ;-)

Ultrasonic Diamond Rig

Now I can also think of other ways to create the phonon activity. Make a bundle of metal rods. Bathe them in microwaves that match their length. Anyone who has put a metal trimmed bit of china in a microwave knows how that can vaporize the metal if strong enough. So keep the microwaves under control. Load the metal with H or D via pressure, or electrolysis, or whatever, then slowly add the microwaves. As radiation, or as a directly coupled electric current. (Think “antenna in a hydrogen bath”).

But wait, there’s more!

It ought to also be possible to use this same insight to make a system excited by light (just pick a color that the particular metal absorbs). Or any other phonon creating method.

And about that Papp Engine…

These folks claim they have it working: http://www.pappengine.com/

Some other links:

http://revolution-green.com/unconventional-green-energy/the-papp-engine-history-and-current-progress/

http://www.infinite-energy.com/iemagazine/issue51/papp.html

Perhaps, just perhaps, as a speculative bit, the Papp Engine can work. It has a massive spark in the top from something like 6 over grown spark plugs. Lots of UV, EM, and heat there, along with a SNAP from the spark. It has a cyclic compression cycle, so heat is produced, along with lots of molecular agitation. The metals might well involve things like Ni in a stainless steel. Could it be that either a noble gas itself reacts, or that the ‘special treatment’ involved the introduction of some small amount of hydrogen into the noble gas?

I have to wonder what would happen if you had a ‘side chamber’ like in precombustion chamber Diesels, or Sterling engines, with a Ni gauze in it, and used Hydrogen gas in the noble gas mix, with loads of spark, and that external magnetic coil, add in some sound from a big fat spark, and maybe even duct in a bit of microwave energy; if somewhere in that mix enough phonons and hydrogen could get together in that gauze to heat the gas enough to make a net gain…

There’s a lot more I’d like to say, but I’m once again out of time. It will have to wait. Things like what crystal lattice looks best. ( I looked at all metal lattice types and crossed it with what is known to happen in excess energy production AND transmutations. Body centered cubic, and perhaps some face centered cubic look to dominate). Also some on metallic bonded H. Ni and Pd do it, some others don’t. Having metallic H bonding, with the right crystal type, with the bond distances the right size for H or D to fit, but only just, looks like the key magic sauce. Some oxides might also work, along with some alloys. Study the bond lengths, look for cubic crystallization, and try for metallic bonded hydrogen… Yes, I’ve got a load of papers to link for that set of ideas. But for now, it’s time to call it a day and have dinner. But at least I’ve put the marker down ;-)

(Also things like my usual typo pass and QA will have to wait, along with a how-to-do-Greek HTML study…)

It is a large search area, so lots of opportunities to bypass patents on things like Ni/H with something else like a B/Cu alloy or??? FWIW, Cu/Ni makes a cubic crystal, and ought to work as well as Ni. I’d add a touch of metal from each side of Ni and Pd and see what happens with H, D, and T loading. Slight variations in bond lengths and spaces ought to enhance some reactions. Perhaps even the ones you want…

In Conclusion

So that’s my theory and practical idea (if any LENR can be called ‘practical’) in one go. I’ve deliberately avoided the deep weeds of quantum mechanical math, while hopefully showing where it has a theoretical opening for this to work, and suggesting ways to make it go.

That also points at why there are so many ways reported as doing interesting things. From cavitation cells to those with electrolysis to others. And why some work and others don’t. It could be as simple as one guy doing his glass electrolysis cell with an open window pointed at the local airport radar…

I don’t know when I can get a chance to try any of these ideas, nor do I see any way I could make a living out of it (given my present circumstances) so I’m tossing into the Copy Left and Free world. If you can make it go, all I ask is a foot note of attribution. (Though if you make $Billions on it, a few $Million would be nice too! ;-)

At any rate, I hope it gives some order to ways to think about the LENR process and ways to make it more likely to work. Some ideas on ways to stimulate phonons, to get crystal lattices that are prone to multiple modes even if the H loading is low (like a bimetallic matrix with H added in smaller than unity amounts) and even some ideas on how to make a better Papp Engine go POP!

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