z-Pinch
I started thinking seriously about z-Pinches after receiving an e-mail with some suggestions about my earlier attempts at diamond synthesis.  Tom Wahl asked if I thought that crushing a hollow sphere of graphite with a high current pulse through a coil (as in a can crusher) might lead to diamond formation.  A few calculations convinced me that this would not generate sufficient pressure to convert graphite to diamond, but it got me thinking about how much pressure could be generated via a z-pinch and whether or not this applied to the process described in the Pike-Biegunsky Patent.

This drawing shows my analysis of the compressional force acting on a 0.001" graphite fiber carrying a current of 10,000 Amperes.  The formulas can be found on the web at HyperPhysics.  I have made only one assumption, namely that the current is confined primarily to the surface of the fiber.  If we are using a current pulse source such as a capacitor with a fast rise time, this should be true due to the "skin effect".  My calculations come up with a pressure of 200,000 atmospheres at the surface of the fiber.  Is this sufficient to convert graphite into diamond?

This is the phase diagram for carbon (taken from "Inorganic Chemistry" by Cotton and Wilkinson).  At one atmosphere of pressure, graphite is the only thermodynamically stable form of solid carbon.  So why does diamond exist?  There is also the issue of kinetic stability.  At reasonable temperatures the rate at which the conversion takes place is essentially zero.  However, at higher temperatures, the rate increases.  Heating a diamond to 4000º Kelvin at one atmosphere of pressure (of an inert gas, like argon) will convert it into graphite more or less instantly.  Likewise, although diamond is the only thermodynamically stable form of solid carbon at 200,000 atmospheres of pressure, the rate of conversion is slow below about 3000º K.  So, will a 10,000 Amp current heat a 0.001" graphite fiber to at least 3000º K?  Graphite has a resistivity of 1375.0 microohm-cm at 20º C.  If we have a one cm length of fiber, it will have a resistance of (0.001375 W-cm)(1 cm)/p(0.00127cm)2 = 271 W.  The rate of power dissipation will be (10,000 Amps)2(271 W) = 27.1 X 109 Joules/second.  At 3000º K graphite has a heat capacity of 2.5 Joules/gramºK.  Our hypothetical fiber contains 1.3 X 10-5 grams of graphite.  To raise its temperature from 295º K to 3000º K will require (2.5 J/gºK)(1.3 X 10-5 g)(2705º K) = 0.09 Joules of energy.  At a power level of 27 GW, this will take only 3.3 X 10-12 seconds.  No problem.  I am convinced that this method of diamond synthesis works because of the z-pinch phenomenon.

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