Historical research guide · 0608 · 2014
Temperature Dependence of Excess Power in Two-laser Experiments
Peter L. Hagelstein · Dennis Letts
In one minute
Peter Hagelstein at MIT and Dennis Letts in Austin shine two weak lasers on a deuterium-loaded palladium cathode and tune the gap between their frequencies. That beat frequency is what matters: the excess heat peaks in three narrow bands, near 8.4, 15.1 and 20.7 terahertz, and two of them line up with calculated optical phonon modes of palladium deuteride — the lattice’s own preferred vibrations. This paper adds temperature to the picture. Re-reading the runs, the authors find excess power climbing with cell temperature the way a thermally activated barrier makes things climb, and a fresh experiment sharpens it: the same cathode gave about 220 milliwatts of excess power at 62 degrees Celsius and about 840 milliwatts at 72 degrees. Their explanation is that the reaction leaves helium sitting in the vacancy where it happened, plugging the active site, and heat is what scrubs the helium out — which turns a nuisance into a dial, with numbers another laboratory can check.
Connection
Chapter 12’s strongest form of the lattice claim is not that heat appears but that it appears on cue: this experiment names a frequency, a temperature and a magnetic-field orientation, and the excess power follows all three. That is what makes the two-laser work a control experiment rather than an anomaly, and it is where the terahertz phonon numbers that recur across this chapter come from.
From the source
Two lasers on a deuterated palladium cathode stimulate excess power at particular difference frequencies rather than at any frequency: fitting the accumulated data set puts the three resonances at about 8.4, 15.1 and 20.7 terahertz, and two of the three correspond to the Gamma point and the L point of the optical phonon modes of palladium deuteride, which had been predicted to be favoured because the compressional mode group velocity is zero there.Section 1, closing paragraph; Section 2, the fit shown in Figure 2
Excess power in these experiments is thermally activated: fitting it as a constant times the exponential of minus an activation energy divided by the thermal energy gives an activation energy near 0.42 electronvolts for the original data set and 0.54 electronvolts for the maximum-equilibrium-power spectrum, consistent with the 0.67 electronvolts Storms reported and the 0.63 electronvolts Swartz reported for Fleischmann–Pons cells.Sections 2 and 6, Figures 1 and 7
The dedicated test, experiment 669u,v: stimulated at a difference frequency of 21.0 terahertz with the electrolyte at 62.0 degrees Celsius, the cathode returned about 220 milliwatts of excess power; the cell was then heated to 72.05 degrees and re-illuminated at 21.6 terahertz, and returned about 840 milliwatts — an activation energy of 1.33 electronvolts, or 1.27 electronvolts if the temperature at the time of the heat is used.Section 4, Figure 3
Experiment 662a, previously reported at 521 milliwatts, was allowed to keep running and the excess power rose again to a level near 1400 milliwatts — so the quantity to compare between runs is the maximum power the cell equilibrates to, not the first plateau after stimulation.Section 5, Figures 4 and 5
The mechanism the authors work from: the active sites are palladium or gold vacancies, where the electron density is low enough for molecular D2 to form once loading is high, two deuterons make helium-4, and the nuclear energy is fractionated into a great many optical phonons before it thermalises — which accounts for the absence of energetic emissions. The helium then blocks the site, so the temperature dependence is the price of getting it out again: the calculated helium diffusion barrier in palladium and in gold is 0.72 electronvolts, and the binding of a single helium atom in a palladium vacancy about 2.4 electronvolts.Sections 7 and 8, with the vacancy stabilisation argument and the helium binding calculations of Zeng and of Laakmann
Excess power in this data set is mostly zero when no magnetic field is present, and the phonon theory offers a reason: the selection rules for the deuteron in the fractionation step allow only two of its three spin states to take part, so even a weak field raises the number of favourably aligned deuterons — and if fractionation limits the rate, the rate is exponential in that number.Section 3; Section 9, Magnetic Field Dependence
The way in
https://doi.org/10.70923/001c.72250How to cite it
Peter L. Hagelstein, Dennis Letts (2014) Temperature Dependence of Excess Power in Two-laser Experiments doi:10.70923/001c.72250