I've read somewhere on the Internet that heating graphite at 4200°K at a sufficiently high pressure would turn it into diamond.
This chart seems to support this idea: 
Is that doable industrially?
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$\begingroup$ The ° symbol is used for temperature scales other than kelvin. For example, 4200K, but 70°C or 98.6°F. $\endgroup$– Dietrich EppJul 11 '15 at 0:27
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It has been done since 1954 and has been a commercial success for some time. Many products now have diamond-like coatings, produced comparatively inexpensively through vapor deposition without need for high pressure.
BTW, in English "burning" means to set on fire, oxidize; I believe you mean "heating graphite", and, as your graph shows, pressure is needed as well as heat.
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$\begingroup$ Thanks for your answer. Are these synthetic diamonds as valuable as the natural ones ? I mean, do they have any use in jewelry ? $\endgroup$ Jul 10 '15 at 16:51
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$\begingroup$ There are many adds for man-made diamond jewelry, for example diamondnexus.com/pure-carbon-man-made-diamonds.html. As in synthetic sapphire, made since 1902, it is cheaper to make the artificial product (and the artificial material is also of more use in manufacture). Curiously, I believe natural quartz crystal (used in resonators etc.) are more used than the artificially grown crystals. $\endgroup$ Jul 10 '15 at 17:05
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$\begingroup$ @DrMoishePippik Apparently natural quartz is no longer common as natural quartz has many defects and impurities. Much like as you mention for sapphire, artificial quartz is more useful for manufacturing as it can be made in defect-less shapes that are simpler to cut appropriately. $\endgroup$ Jul 10 '15 at 17:26
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$\begingroup$ Thanks for the information, @Michael D. M. Dryden! Though I had read that Bell Labs had issues with growth of a polymorph of SiO2 taking over from the desired quartz after hydrothermal apparatus had been cycled a few times, I should have realized that problem would be overcome. $\endgroup$ Jul 10 '15 at 22:16
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You want to heat graphite at high pressure, not burn it - but yes, high-T, high-p will work.
Is that doable industrially?
There is a rather lengthy and informative Wikipedia article for synthetic diamond that illustrates (in part) the use of this process - HPHT, for "high pressure, high temperature"(using a high-purity source of carbon, not necessarily graphite) in industry. Note that there are several industrial processes mentioned in addition to HPHT.
answered Jul 10 '15 at 16:52