Role of Finite Size in Triggering Excess Heat: Why Nanoscale PdD Crystals Turn on Faster

Two persistent questions have been: 1. Why is a finite triggering time required after the near full-loading condition (PdD$_x$, 0.85 \approx < x \rightarrow1$) before the Excess Heat effect\footnote{ C.G. Beaudette, \underline{Excess Heat: Why Cold Fusion Research Prevailed.} (Oak Grove Press, Bristol, ME, 2002)} is observed? 2. Is it possible to identify physical properties of the materials and/or crystals that are used that might be playing a role in the length of the interval of time associated with this phenomenon? In the talk, through a generalization\footnote{ S.R. Chubb, ``Role of Broken Gauge Symmetry on Conduction of Charged and Neutral Particles in Finite Lattices,'' submitted to Proc Roy. Soc Series A (2005).} of conventional energy band theory, as it applies to infinitely-repeating, periodic lattices to situations involving finite lattices, I have been able to address both questions. In particular, the tunneling time depends on crystal size. Crystals with dimensions $\approx <$6 nm, which have tunneling times $\approx$ microseconds, either can not provide enough momentum to initiate d+d$\rightarrow ^4$He reactions or conduct ion charge so rapidly that collisions occur. Crystals with dimensions $\approx$ 60nm create heat and load rapidly ($\approx$ 3 ms). But crystals with dimensions $>\approx$60 microns have tunneling times that are longer than a month.