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First Experimental Proof of Raizer–Zeldovich Theorem (or RZ-Theory). SID SENADHEERA Mechanical Engineering Department Ryerson University. Different methods of producing nanofibers. Experimental Setup. Computer simulation of heat dissipation in laser ablation.

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sid senadheera mechanical engineering department ryerson university

First Experimental Proof of

Raizer–Zeldovich Theorem

(or RZ-Theory)

SID SENADHEERAMechanical Engineering DepartmentRyerson University


* Initially, the vapor expansion proceeds along the Poisson adiabat with : PVγ= const.

P-V diagram with the Causius-Clapeyron equation

  • *The Poisson adiabat crosses the saturation adiabat defined by the Clausius-Clapeyron equation.
  • * The corresponding critical temperature is defined as Tc

According to RZ-theory the following equation can be written

Condensation rate : dx/dt

Nucleation rate : dν/dt

Atomic clustering rate : dg/dt

x(t) = ν(t).g(t)

Nucleation rate can be expanded as :


*The sharp increment in nucleation occurs at phase transformation

*The time component for Graphite and Silicon can be theoretically graphed as below to estimate the times for phase transformations.


The first theoretical analysis of condensation dynamics in a rapidly expanding vapor was performed by

Raizer et al. in 1958. Anisimov et al. did the next detailed study on the theory with the results below.

(a) Temperature Variations

(d) Nucleation rate is ν(t)

(b) Supercooling Parameter

(e) Cluster dimension variation

(c) Vapor condensationx(t)

(f) Atomic clustering g(t)





Graphite Silicon

* Crystallization and formation of fibers start at a lower pulse

frequency for Graphite crystals (less than 1 MHz) and for Silicon (~2MHz)




Starts nucleation at 2 MHz

Starts nucleation at 1 MHz

Interpulse time unit ~ 0.5 μs

Interpulse time unit ~ 1 μs

*Theoretical estimates

(below graph) are in close agreement with the experimental values (above).


R(t) ~ (Eo/ro)1/5 t2/5




Supernova expansion


H-Bomb testing



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Yakov B. Zeldovich (left), Andrei Sakharov (middle),

and David A. Frank-Kamenetskii in Sarov, 1950s

-Russian Academy of Sciences