Chapter 1- Introduction to Fleischmann Pons Fusion Mechanism
(Feb . 19, 2008)
After years of experiments and a brush with a runaway reaction, Fleischmann and Pons announced their “excess heat” electrolysis using heavy water and a palladium cathode in 1989. These experiments eventually acquired the apt designation: “cold fusion”. The scientific community was first excited, then skeptical, and finally dismissive of the experiments, as well as the years of cooberating work since then. At first, in lite of the difficulty replicating the “excess heat” and lacking theoretical support, the skepticism was justified. Curiously, as the experimental evidence mounted, physicists did not consider the possibility of a solid-state mechanism. The main objections, to the claim of fusion, were the requirement for three “miracles”. Namely:
1) Overcoming the electrostatic repulsion of deuterons
2) Reacting with little or no “nuclear ash”; neutrons or tritium
3) Dissipation of the heat with no by-products; neutrons & gamma rays
Solid-state physics is one of the most difficult environments to probe, as the dearth of photon emitting interactions denies direct access to electron behavior. Quantum mechanic modeling and indirect measurements are the general tools used very successfully to study solid-state electrons. The modeling used here will be straight forward, with derivations taken from basic quantum mechanics texts. With these simple, robust models and a touch of insight, we will show how to overcome the “3 miracles”. With this in mind, let us delve into this intriguing mystery and reveal the wondrous and surprisingly simple behavior hidden below Fermi’s sea.
Chemically Catalyzed Fusion
Chemically induced fusion is not unprecedented. Overcoming the electrostatic repulsion of two deuterons has been convincingly demonstrated (and accepted by physicists) using muons to replace the electron in a deuterium molecule. Although solid-state “cold fusion” is not the result of muon catalysis, a brief look at this reaction leads to some important insight.
The muon (a short-lived particle) is 207 times the mass of an electron, while possessing the same charge. On solving the Schrodinger equation for muon-bonded deuterium, d2, the bond length is found to be 207 times shorter than the same electron bound molecule. The average bond length, of the muon bound deuterium molecule, is about 0.005 angstroms (500 fermis), with a total bound muon energy of just over 3000 eV. This allows for a fusion reaction in mili-seconds of confinement time. Thus, if we can uncover a mechanism for an electron to achieve this kind of binding energy, one of the miracles above may be circumvented.
Introduction to “Cold Fusion”
Let us suspend disbelief for a moment and assume there is an electron bond between two deuterons, in the palladium lattice, on the order of tens of thousands of electron volts. If this could be true, then, according to the “uncertainty principle”, the electron would be contained to an average radius of ~0.01 angstrom, and the deuterons would have an average bond length on the order of ~0.001 angstrom. This would be sufficient for the deuterons to react in short order. How could this possibly happen? Although at first glance appearing preposterous, the mechanism will be shown as straightforward electron physics that has been accepted and practiced since the inception of quantum mechanics; true alchemy.
We will show how helium, the high energy by product of fusion, catalyzes the fusion chain reaction:
He + d => [He-d]
[He-d] + d => [He-2d]
[He-2d] => [Be]
[Be] => 2 He + ~24 MeV
{restart cycle}
The reaction cycle starts with the channeling of helium at 100- 300 eV, in the palladium deuteride lattice. The channeling probability is controlled by the deuterium loading and crystal quality. The deuterium loading is critical for two reasons; 1) the deuterium is half of the guiding molecular crystal structure, and 2) the “active” concentration of deuterium is proportional to the deuterium loading. So in a sense, the reaction is third order in deuterium; two from the reaction of two deuterons and one from the channeling dependence on concentration. Any missing deuterium along the channel path diminishes the capture forces proportionately. Defects in the crystal will de-channel the helium lowering the reaction probability. The critical travel distance of the helium channeled in the lattice is ~100 to 200 angstroms. Natural crystal defects occur in about this same length scale depending on the processing history, making the sample preparation a critical factor to a successful experiment.
The channeled helium’s path is the volume filled with the tetrahedral (alpha phase) location of deuterium (see figure). At high deuterium loading in the palladium lattice, the tetrahedral locations contain about 1% of the total deuterium in equilibrium with the octahedral sites (beta phase) where the other 99% resides.
With at least ~20 to 50 eV center of mass activation energy, the helium will collide with and bond to deuterium in the tetrahedral position, giving He-d. A localized “free electron” forms the bond. The solid-state environment forces the electron into linear momentum states. There are no angular momentum states available. The He-d linear momentum bond energy is over 100,000 eV. The wave functions of the helium and deuterium nuclei, and the free electrons, must overlap appreciably with the {He-d + electron} activation state, for the reaction to proceed. The crystal palladium deuteride provides the proper potential constraints to align the three particle wave functions (He, d, electron), for a high probability transition to an electron in localized linear momentum states; bonding the helium with deuterium. The palladium is acting as a true catalyst. This is the first miracle; overcoming the coulomb repulsion. The ground state of the He-d molecule will be analyzed after an introduction to the relevant quantum mechanics. In a later chapter, the transition state will be analyzed.
With enough translational kinetic energy, He-d will continue down the crystal channel and react with another deuterium using the same linear momentum state bonding. This will give the molecule Hed2. The rate of energy loss of the channeled helium is a critical factor in the chain reaction, as this controls the distance the helium will travel. The distance traveled controls the probability of intercepting two deuterons. The temperature dependence of the reaction found experimentally is simply the slight shifting of the equilibrium concentration of deuterium toward the alpha phase (in the channel) relative to the beta phase at higher temperatures. The higher alpha phase concentration increases the reaction probability. The success with nano-sized crystals, in the Arrata and Navy work, is the result of alpha phase deuterium favored at the crystal surfaces due to well-known surface electron effects. The increased concentration, of the alpha phase, then raises the probability the Helium will intercept two deuterons, before its kinetic energy drops below the transition state activation energy.
Once the Hed2 “molecule” forms (with He-d bond energies over 100,000 eV) it is only a matter of time before both deuterons tunnel to the helium nucleus at the same time. The reaction time (half-life) of the Hed2 is calculated using a modified reverse alpha emission model. The probabilities of the two deuterons are calculated using their wave functions. When, eventually, the two deuterons simultaneously enter the helium nucleus, a compound beryllium nucleus forms. The beryllium promptly decomposes into two ~12 MeV alpha particles (helium nuclei). Another two miracles; no neutrons, tritium or gamma rays. As the resulting high-energy alpha particles slow below ~1000 eV, they acquire electrons to become high velocity helium atoms. If the environment is favorable to channeling, and the alpha phase deuterium concentration high enough, the reaction probability will be greater than 50%, and the chain reaction continues. The difficulty in achieving these two criteria is the cause of the many failed experiments; the “lack of reproducibility”.
The usual fusion reactions, d+d => Tr +p or He3+n, are shown to be completely suppressed due to angular momentum constraints in the Hed2 molecule. The angular momentum is a consequence of the helium nuclei wave function, dictated by the potential in the crystal “felt” by the helium, as it reacts with the deuterium. The same constraints conspire to give several chemically stable angular momentum states, of Hed2, having different half-lives (~micro-seconds to ~hours). The differing half-lives, along with the macroscopic crystal structure, lead to most of the interesting experimental behavior; including the trace tritium.
After analyzing the fusion mechanism, three major experiments will be discussed, revealing the logic behind the improbable behavior. The three representative experiments are;
1) The Fleischmann and Pons bulk palladium electrolysis,
2) the Arrata palladium black in a palladium tube, and
3) the Navy co-deposition of palladium and deuterium.
Unfortunately, some understanding of quantum mechanics is required for these discussions. A brief introduction to the appropriate quantum mechanic principles is given next in hopes of allowing the non-physics reader to follow along. We first explore the quantum mechanics of solid-state “free” electrons, and then, the hydrogen atom. Understanding the difference between linear momentum states of free electrons, and the angular momentum states of localized atomic electrons, is essential to understanding the mystery of cold fusion.