On Dec 30, 2009, at 8:01 AM, fznidar...@aol.com wrote:
I see where my mistake was now that I read the work of Horrace.
It was in the elastic constant K. I just used the electrical force
on the proton and the lattice spacing
to compute the elastic constant.
I did not factor in that total force on a stationary proton is
zero. I needed to
calculate the force on a slightly displaced proton as a subtraction
of opposing forces.
You have showed me the way.
Now what is the difference between the palladium and the dissolved
deuterium lattice vibrations?
They are, I believe, similar in frequency. The phase may be the
big difference. The adjacent
lattice vibrations at the shortest wavelengths are 180 deg out of
phase.
I already gave this approach to computing (Pd) lattice vibrations:
The deuterons actually are screened from each other by lattice
electrons. They exist in lattice potential wells. They essentially
move at lattice speeds due to lattice vibrations, except when
tunneling between lattice sites. These lattice vibrations might be
considered to achieve resonance when lambda = N * 2 * (lattice
constant), which for Pd is 7.78x10^-10 m. The resonant frequency is
given by:
f = v / lambda
where v is the speed of sound in the medium, or 3070 m/s, so:
f = ( 3070 m/s) / (7.78x10^-10 m) = 3.946 x 10^12 Hz
which is not far off from the other frequency I gave, which was
computed from the deuteron 1 dimensional mechanical resonance. The
lattice sites occupied by the hydrogen are points of lowest potential
between lattice atoms, e.g. tetrahedral sites. The value of k varies
with the speed of sound in the lattice and thus temperature and other
factors. The presence of hydrogen itself affects this, i.e. the
loading phase. The problem is the vibrations of the hydrogen and the
PD vary because the forces are non-linear. In other words k is a
function of x.
Still, I think the above is very much on the wrong track.
The entire dissolved hydrogen lattice my be vibrating in phase as a
single quantum system.
Well, here is a good hint for you. The most thoroughly linked system
is the electron system. The nuclei are rigidly enclosed in electron
cages. The cages weigh 3 orders of magnitudes less than the nuclei.
It is the *cages* that move in unison. If there is any collection of
things in the lattice that are powerfully coupled it is the
*electrons*. It is primarily the electrons that respond to external
stimuli, such as sound or x-rays. What happens when the electron
cages move, and the nuclei are hence moved out of the locus of the
center of charge, is the electron flux through the nuclei momentarily
increases. The lumbering nuclei comparatively slowly respond with
motion.
Also of interest is the imbedded nano-particle. It's electron cage
is small and somewhat disconnected from the overall lattice. It
responds to external stimuli somewhat independently of the overall
lattice. This is the realm between the quantum and the macro
worlds. The nuclei of a nano-particle are more likely to move in
unison, and thus the relative motion is highly suppressed unless
there is extreme stimulation. The phonon energies are quantized, so
all the movements of the electron cage across the nano-particle tend
to be in unison. All the phonon exchanges are quantized to E = (N +
1/2)*h*f. The nuclei thus experience much less motion than the
electrons for a given quantum of exchange. This tends to keep the
forces on the nuclei in unison, and all relative nucleus motion in
unison. This has the obvious makings for nuclear condensate
wavefunctions, and Bose condensate fusion. It also provides the
perfect makings for *simultaneous* deflated state hydrogen, and thus
multi-body heavy element transmutation LENR.
I believe that cold fusion is an affect of a big difference in the
way dissolved hydrogen vibrates.
What do you think?
I disagree. I think the focus on coordinated lattice nucleus
vibration and ordinary atomic diffusion rates (as opposed to hydrogen
diffusion by *tunneling* rates, a separate variable) is a blunder of
major proportions, and has slowed down development in the field.
Any fusion that occurred purely as a result of lattice vibrations
would have the same branching ratios as hot fusion. Such a kinetics
based system would have little prospect of explaining heavy element
LENR. Much work has been done on this basis for 20 years with nominal
progress. I'm hoping the deflation fusion model will stimulate some
improved experimental approaches.
Horrace, did you go back to school or what?
Unfortunately no.
Your work is orders of magnitude better than it was a few short
years ago.
Thanks, but maybe that is just a mirage. Every day is a learning and
re-learning experience. I'm a bit up on CF right now. I've
forgotten about all I know about gravity or EM propulsion. In a
while I'll be back to work on EM propulsion and will have forgotten
most all I know about CF. Or, maybe I'll work on gravity and forget
all I know about EM propulsion. Or maybe I'll add to the 10 chapters
of the book I was writing on Boolean algebra. Or maybe I'll just
forget everything and have to vegetate. It's ultimately a losing
battle in the war of aging. What were we talking about?
Best regards,
Horace Heffner
http://www.mtaonline.net/~hheffner/
