Not sure what’s driving this discussion, or the fascination with carbon isotopes, but here are some things to consider: 1) Beta-brass is a 50-50 mixture of Cu and Zn (atomic numbers 29 & 30) on a bcc lattice. Above about 1200K the two types of atoms are equally likely to be on either of the two cubic sub-lattices (this doesn’t preclude some short-range order). Because the phase transition to the ordered state, of Cu and Zn perfectly segregated on the two sub-lattices, is second order the segregation is small just below 1200K. By quenching to low temperature, the mostly random occupation of sites by Cu and Zn is preserved — in other words, the phase transition has negligible effect on the information content. The rate of a Cu-Zn pair swapping positions is given by the product of an atomic oscillation frequency, several terahertz for brass, and an exponential factor exp(-c T_D / T), where T = temperature, T_D = 340K is the Debye temperature, and c is a numerical constant of order unity. Most atom pairs, in a chunk of beta-brass in equilibrium with the balmy 3K microwave background of the cosmos, will not have changed places over the lifetime of the universe. 2) A different, temperature-independent, exponential suppression factor takes over at low temperatures. The exponent scales as the square root of the product of the atomic mass and the potential energy barrier. The system most studied in this regime is He, which forms a crystal under pressure. Atom-swapping in both He3-He4 mixture crystals and pure He3 can be studied because He3 has a nuclear spin-1/2 that serves as a label. The dominant quantum tunneling mechanisms in these crystals are small permutation cycles (I recall 3- and 4-cycles occur at higher rates than pair-exchange). These quantum effects actually order the crystal, now at temperatures below mK. Missing atoms in the crystal (“vacancies”) greatly enhance the rate of position scrambling, much like the Sam Loyd 15-puzzle. 3) We asked Feynman in Physics-X what he thought about the net effect of human civilization on the entropy balance of the universe. He told us he had compared illuminated manuscript production (middle ages) with a bottle of gas and that it wasn’t even close. -Veit
On Jun 6, 2016, at 1:21 AM, Henry Baker <hbaker1@pipeline.com> wrote:
Hi Keith:
Although I don't know enough quantum physics to do the calculation, my gut still tells me that the probability of exchanging an adjacent C12 for a C13 nucleus is non-negligible.
The problem with crystal lattices is that the constituent atoms are usually the same -- e.g., diamond or graphene. In the case of crystals like NaCl, there is no hope of exchanging a Na for a Cl, and if a Na<->Na happened or a Cl<->Cl happened, we'd not notice.
In the case of a metal, the electrons become smeared all over the crystal, so they can't be localized at all.
In the case of a diamond crystal, the location of "a" carbon nucleus is localized to within the distance to its 4 (?) nearest neighbors.
https://en.wikipedia.org/wiki/Diamond_cubic
Delocalizing a carbon nucleus would make diamond look a lot more like a liquid.
Diamond won't melt at 1 atmosphere, as 1 atmosphere is below its triple point at 107 atmospheres and 7820 degrees F. So I would guess that the probability of an adjacent C12<->C13 exchange would be dramatically improved with 100x atmospheric pressure, and floating on top of molten tungsten at 6500-7000 degrees F.
However, if we heat up diamond at 1 atmosphere, past about 3500F it first turns to graphite before finally melting at ~7600F.
So somewhere in the vicinity of 3500F and 1 atmosphere, the localization of the carbon atoms must start to break down, and the exchange probability must rise sharply.
So the real question is: what is the falloff in exchange probability as we lower the temperature from 3500F to 100F ?
https://en.wikipedia.org/wiki/File:Carbon_basic_phase_diagram.png
At 02:13 PM 6/5/2016, Keith F. Lynch wrote:
Henry Baker <hbaker1@pipeline.com> wrote:
Re adjacent C12/C13 swapping: in a quantum universe, never say "never". The probability & half-life of such swapping should be calculable.
The atoms are locked into a rigid lattice. It's enormously more likely that the lattice will break down than that atoms will swap in an intact lattice. So it's the half-life of the lattice that you should calculate.
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