Historical research guide · 0534 · 2010
Energy density calculations for ball-lightning-like luminous silicon balls
Gerson S Paiva · Joacy V Ferreira · Cristiano C Bastos · Marcus V P dos Santos · Antonio C Pavão
In one minute
Ball lightning is one of the oldest unexplained sights in physics — a glowing sphere, often the size of a grapefruit, that drifts, bounces and burns for seconds after a lightning strike. Gerson Paiva, Antonio Pavão and their colleagues at the Federal University of Pernambuco make them on a bench: an electric arc struck on a silicon wafer throws off orange-white balls that spin, roll, leave smoke trails and last up to eight seconds. This paper answers the obvious next question — how much energy is packed inside one. The team weighs the white silicon-dioxide powder each ball leaves behind, reads the ball’s temperature off its own light spectrum, and computes the heat of the silicon-burning reaction from first principles with quantum chemistry. The answer is 31.9 joules inside a ball about 2.5 centimetres across, or 3.9 megajoules per cubic metre. That number sits squarely inside the range other researchers have inferred from the damage natural ball lightning does, which is exactly the authors’ point: the laboratory object belongs in the same family as the natural one.
Connection
Chapter 9 treats the long-lived luminous ball as a real, reproducible object rather than a curiosity, and this is the paper that puts a measured number on the energy inside one — an energy-density yardstick of 3.9 megajoules per cubic metre, obtained from a ball anyone can strike on a wafer with a welding transformer.
From the source
The luminous silicon ball is modelled as a hot condensed silicon core surrounded by an atmosphere of oxidising silicon, and the dominant energy source is the exothermic oxidation of gaseous silicon to silicon dioxide proceeding inside the sphere. This is the Abrahamson-Dinniss picture of natural ball lightning — lightning reduces silicon dioxide in the soil to metallic silicon, the vapour condenses into nanometre-scale particles, and the ball glows as that silicon burns back to oxide in air.Section 2, The silicon luminous ball model, Fig. 2
The balls are produced by an ordinary low-voltage arc, not by an exotic driver: a 2-inch p-type silicon wafer on a steel base electrode, a tungsten or graphite top electrode, 20 to 25 volts and 100 to 140 amperes, with the top electrode lifted one to two millimetres to strike the arc. The balls that fly off are 1 to 4 centimetres across, live up to 8 seconds, spin, leave spiral smoke trails, bounce, burn polystyrene on contact and ignite ethanol-soaked cotton, and decay leaving no trace — behaviour distinct from the hot fragments, which cool in about a second.Section 1, Introduction, Fig. 1 and Fig. 3
The ball’s colour does not change over its lifetime, indicating an almost constant temperature, and the temperature follows from the ball’s own emission spectrum. A portable spectrometer puts the Planck peak at 675 nanometres, and Wien’s law then gives a colour temperature of 4296 kelvin for the gaseous-silicon model.Section 3, Eq. (1) and Fig. 4
The energy released is measured through the ash. Each ball leaves a white powder trail averaging 7 thousandths of a gram, and Fourier-transform infrared spectroscopy confirms it is silicon dioxide through strong absorption bands at 1463 and 2924 reciprocal centimetres. Because the heat of reaction for gaseous silicon at that temperature has never been measured, the authors compute it with coupled-cluster quantum chemistry at the CCSD(T) level with correlation-consistent triple-zeta basis sets, obtaining minus 755 kilojoules per mole, or minus 273.4 kilojoules per mole once entropic effects are included — which gives 31.9 joules released per ball.Section 3, Results and discussions, the heat-of-reaction calculation and Fig. 5
Dividing that energy by the volume of a ball of mean radius 1.25 centimetres returns a mean energy density of 3.9 megajoules per cubic metre. The paper’s own comparison table places that beside published estimates inferred from the damage natural ball lightning causes — 0.8 from Barry, 6.25 from Imyanitov and Tikhii, 25.85 from Stakhanov, and higher figures for two of Stenhoff’s cases — so the laboratory ball falls inside the natural range and can be counted in the same category.Section 3, Eq. (2) and Table 1
The authors close with the discrepancy they say should be addressed next: a silicon sphere looks larger than it is, because a cloud of particulates travels with it. Stephan and Massey make the same point. If the true sphere is the roughly 1-centimetre object the photographs suggest rather than the 2.5-centimetre glowing cloud, the energy density is about sixteen times higher — which would place the bench-made ball among the more energetic natural estimates rather than the modest ones.Section 3, closing paragraph; Section 4, Conclusions
The way in
https://doi.org/10.3367/ufne.0180.201002g.0218How to cite it
Gerson S Paiva, Joacy V Ferreira, Cristiano C Bastos, Marcus V P dos Santos, Antonio C Pavão (2010) Energy density calculations for ball-lightning-like luminous silicon balls doi:10.3367/ufne.0180.201002g.0218