# recoil from nature's best spring?

Percy Bridgeman remarked that "graphite is nature's best spring". I have attempted to quantify this with some bulk modulus expressions.
V = initial volume dV = change in volume (in cm^3) dP = change in pressure (gPA) B = Bulk Modulus of elasticity
For a given volume, bulk modulus, and applied pressure, how much will that volume shrink? dV = (dP*V)/B
Put a 17.6 carat diamond (1 Cm^3) into a perfectly ridged, incompressible and unbreakable box. Heat the diamond to about 4600 K to graphitize most of crystal. Graphite occupies 26% more volume than diamond at sea level. This is a very big change.
Rearranging the above equation to find the pressure change I get: dP = -B*(dV/V) dP = 34GPa*(1.26/1) dP = 42.84GPa
The graphite should be exerting over 422,000 atmospheres upon the sides of the perfect box.
Have I done this calculation correctly?
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no. see the phase diagram for carbon:
http://www.me.berkeley.edu/diamond/submissions/diam_intro/cphased.htm
you will produce liquid carbon at these temperatures. Additionally graphite is thermodynamically unstable above 14 GPa at any temperature, so you will never get to a higher pressure with your method.
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I will consider this more. Thank you for your input!
-Scott
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Annother error I made was overlooking rate of the conversion. I presumed that the reaction would proceed quickly and continually above 1700K and following the diamond-graphite equilibria curve like train following a track (pressure increasing with increasing temperature in a perfect container).
On of the warning signs was an anecdote from "the diamond makers" that explained how Percy Bridgeman subjected graphite and a diamond seed to thermite ignition (3000 deg c for a few seconds) at 30,000 bar. Dispite no diamond growth observed, the seed survived, indicating they were on the right track (can't grow diamond on a seed that gets destroyed in the process).
This link discusses the rate of diamond graphitization in low pressures. http://www.nanomedicine.com/NMI/9.3.5.3.4.htm
I gather from this link that It takes 10^84 sec for diamond (at STP) to revert to graphite, which to me is.. practically forever.
Kinetics is a facinating problem. I've read that solvent/catalysts are a double edge sword in HPHT synthesis. Molten iron is an effective graphite to diamond catalyst in the diamond stability field and conversely it can increase the rate of diamond to graphite conversion at sea level. This fact makes transition metal cemented diamond grit unstable above 800c, effectivly destroying the part.
Could there be a catalyst that enables graphitization of diamond but wouldn't aid diamondization of graphite? I suppose this would be the exact opposite of what Uncle Al is working on, right?
-Scott
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I fail to see any relevance to Percy Bridgeman's expression on "best Sping" in your hypothetical experiment.
You are actually talking about volume change under phase transformation.... not really what Bridgemen meant when talking about most perfect springs.
Incidentally, what is a "Best Spring" anyway, so we could all recognize it if we saw it?
Jim
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Bridgeman subjected graphite to over 400kBar at room temperature. It did not convert to diamond and it's volume remained unchanged. I don't know if "natures best" statement is a fact or just a lament in frustration. Hex is so dissimilar to fcc that it won't "collapse" without the aid of a lot of heat and time even under 100s of thousands of atmospheres of pressure.
What do you think he meant?
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It doesn't matter what I think.
I don't think about it cause I never read it or the context surrunding it.
Jim
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If you're into squeezing rocks you'd find Bridgeman very interesting :) Otherwise it probably sounds like sillyness.
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I read Bridgeman in the early 1960's and he was one of my scientific heros.
I feel that you have trivialized the work and thinking of a great man.
Jim
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trivialized? how?
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