Since natural carbon is 99% C-12 and 1% C-13, it's easier to make pure C-12 than C-13. The object was to make isotopically pure diamond, so "enriched" is appropriate. The bulk modulus should be independent of isotope, and is the highest of any material, 1.2 TPa. The speed of sound is also the highest of any material, 17.5 km/s, and should be slower for the heavier isotope by a factor of sqrt(12/13). That same factor should apply to phonon transport speed and thus to thermal conductivity. However, thermal conductivity is adversely degraded by crystal defects, as is evident from natural diamond vs, C-12 enriched. In Raman spectroscopy, the scattered light is downshifted in frequency by the vibration frequency of the scattering material. Again, it's a factor of sqrt(12/13) between the two isotopes. Since the vibration frequency varies with pressure, Raman can be used as a pressure sensor. These experimenters did something clever, by growing a thin layer of pure C-13 diamond on the tip of their diamond anvil, they could measure the pressure right at the tip, independent of the pressure within the bulk of the anvil. I'm not able to access the full paper from home, so I'm basing this on the abstract. Because C-13 has spin 1/2, it is well suited to NMR spectroscopy. This is standard in chemistry, but I'm not aware of it's use in medical imaging. -- Gene From: Bill Gosper <billgosper@gmail.com> To: math-fun@mailman.xmission.com Sent: Sunday, May 29, 2016 4:46 PM Subject: Re: [math-fun] Chinese tea puzzle Whoa, When Gene said enriched diamond I was imagining pure C13. I'd call crystalline C12 "depleted diamond"! Are the properties of C13 known? Hardness? Speed of sound? Thermal conductivity? Spin -1/2 shows up on NMR! Would you bet on 13C recycling centers by 2100? Oh, https://en.wikipedia.org/wiki/Isotopically_pure_diamond (incredibly, cited by neither https://en.wikipedia.org/wiki/Isotopes_of_carbon nor https://en.wikipedia.org/wiki/Carbon-13) just says " Isotopically pure 13C diamond layers 20 micrometers thick are used as stress sensors due to the advantageous Raman spectroscopy <https://en.wikipedia.org/wiki/Raman_spectroscopy> properties of 13C.[5] <https://en.wikipedia.org/wiki/Isotopically_pure_diamond#cite_note-5>" suggesting its other nonquantum properties are similar to pure 12C. --rwg Where's my lifetime diamond edged razor? (Actually, a certain Gillette Mach-3 is threatening to outlive me.) On 2016-05-29 11:04, Eugene Salamin via math-fun wrote:
This is for real. The heat content of a crystal is mainly due to phonons, quanta of vibration. Heat conduction is due to the transport of phonons. Phonons are scattered by inhomogeneities in the lattice, so that thermal conductivity is very sensitive to impurities, such as the random distribution of different mass isotopes.
Diamond is quite a remarkable substance. Since it is thermodynamically unstable with respect to graphite under ordinary temperature and pressure, its synthesis is tricky. The preferred technology today is chemical vapor deposition (CVD). On the other hand, it is just carbon. I expect that by year 2100, diamond synthesis will have become so cheap that recycling centers will have a bin for diamonds.
I wrote a report on diamond for a class I took on optomechanics at the University of Arizona.
http://fp.optics.arizona.edu/optomech/student%20reports/synopsis/SalaminRepo...
http://www.tlchm.bris.ac.uk/pt/diamond/pdf/rscreview.pdf
-- Gene
From: "rcs@xmission.com" <rcs@xmission.com> To: math-fun@mailman.xmission.com Cc: rcs@xmission.com Sent: Sunday, May 29, 2016 10:12 AM Subject: Re: [math-fun] Chinese tea puzzle
Notice that removing some of that 1.1% of C13 raises the heat conductivity of diamond by 50%. Magic or typo?
Rich
------- Quoting Bill Gosper <billgosper@gmail.com>:
Wow, I didn't know that C13 was 1.1% abundant: https://en.wikipedia.org/wiki/Carbon-13 and you can use this in mass spectrometry to count carbons in a molecule, or that there are three different kinds of photosynthesis, and Bill & Melinda Gates are funding a project to change rice from "C3" to "C4", promising a 50% yield increase, (Evil GMO! I'd rather you starve.) and that C13 enrichment may inhibit free radical aging. But how much C13 is too much? Deuterium can be toxic by deranging
relative
enzyme efficiencies. Is anybody working on enzymatic isotope separation? --rwg
I used "puzzle" in the subject line in keeping with math-fun tradition of implying I know the answer: The large surface area of the unimmersed bag outcompetes the cup liquid surface, so you should dunk infrequently. But now I'm less sure.
On 2016-05-28 10:12, Eugene Salamin via math-fun wrote:
Thermal conductivity at 25 C in W m^-1 K^-1
Silver 429 Copper 401 Diamond 2200C-12 enriched diamond 3300
-- Gene