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I am writing a science fiction novel where dead humans are turned into diamonds by compacting cremated remains. What size of diamond would the amount of carbon in a human body form? I know that the size would vary somewhat depending on the weight of the person.
Specifically, would the diamond be small enough to be worn as an earring, or able to be worn as a necklace? Or would it be too large to practically be worn at all and be set as decoration?

Catlover
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    Isn't there a company that actually does this now? I'm sure it's a con but still. – oxide7 Nov 21 '17 at 16:39
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    After cremation, the body of a human adult is reduced to 1.8 to 2.7 kg of ashes, mostly calcium phosphate; very very little carbon remains, most of it being lost as carbon dioxide during the cremation process. So I'd say that maybe there is enough carbon to make a diamond suitable to use as a ring stone. – AlexP Nov 21 '17 at 16:44
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    The companies use a specified portion of ashes, and not all the ashes from a person. I am wondering about a futuristic society that is able to use all the carbon from a person in a diamond. – Catlover Nov 21 '17 at 16:46
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    @oxide7 quite a few actually... though judging by their spiel they talk about growing a diamond using carbon extracted from a persons ashes (or hair) as a foundation, so presumably very little carbon from a human is actually involved... – adaliabooks Nov 21 '17 at 16:47
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    It's considered a good idea to wait at least 24 hours before accepting an answer that way people from every time zone get a chance to weigh in. – sphennings Nov 21 '17 at 19:56
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    @AlexP, is that a comment or an answer? Sure looks like an answer... – RyanfaeScotland Nov 21 '17 at 23:04
  • On Star Trek it was a dodecahedron about 12" high. Or was that just minerals, not a gem? I forget. – davidbak Nov 21 '17 at 23:50
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    Welcome to Worldbuilding, if nobody did that already! While every Stack Exchange site has its own distinct differences, Worldbuilding is “more different” in some ways. In particular, you ought not Accept an answer before waiting at least 24 hours. A full explanation can be found on this meta post. – JDługosz Nov 22 '17 at 08:54
  • When a co-worker mentioned this, I noted that carbon atoms (of the same isotope) are fundamentally indistinguishable. And, a more practical memorial would be to make pencils, which your friends and loved ones (especially other engineers) would use and further memorialize you with. – JDługosz Nov 22 '17 at 08:58
  • Am i the only one that thinks wearing dead relative sounds horrible ? Or maybe as some kind of trophy. – Asoub Nov 22 '17 at 09:52
  • A number of societies, even now, consider burying not only the deceased, but also close personal items with them. In some cases, especially the ancient Egyptians, the actual content of burial chambers was considerable, including slaves - though much of this was not carbon based at all. Why though, should a burial process which reduced the deceased to a diamond not also be applied to other items relevant to the deceased which could also be treated in this way ceremonially? – Lee Leon Nov 22 '17 at 17:11

3 Answers3

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Before cremation

  • About 18.5% of the human body is carbon by composition.

  • One gram is five carats.

  • The average human being worldwide masses 62 kg. Note that people may be larger in some countries, e.g. in the United States is 88.3 kg.

$$ 62 \text{kg} \cdot 18.5\text{%} \cdot 1000 \text{ grams per kg} \cdot 5 \text{ carats per gram} \approx 57,000 \text{ carats}$$

So if we had some way of extracting all the carbon from a human body, you'd get an average of a fifty-seven thousand carat diamond. Or 5700 10-carat diamonds.

Post-cremation

But we're talking about post-cremation. There is much less carbon after cremation, as the carbon burns off as carbon dioxide in cremation.

  • According to a funeral urns seller, a rule of thumb is that one pound of person will result in less than one cubic inch of ashes 99.5% of the time.

$$ 62 \text{ kg} \cdot 2.2 \text{ pounds/kg} \cdot 1 \text{ in}^3 \text{ per pound} / 14.4375 \text{ in}^3 \text{ per cup} = 9.4 \text{ cups}$$

  • According to a cremation diamond seller, it takes two thirds of a cup of ashes to make a diamond. So that's 14 diamonds per average person. Each diamond is about .1 carats.

$$ 9.4 \text{cups} / (2/3 \text{ cup/diamond}) \cdot .1 \text{ carat per diamond} \approx 1.4 \text{ carats}$$

So the answer is that you could have a diamond as large as 1.4 carats using the current cremation diamond process' efficiency. If you harvested the hair prior to cremation, you could increase that. Hair is a better source of carbon than cremation ashes.

Note that we've been using the person's original mass to estimate the amount of ashes. It's worth noting that cremation will burn fat away. The amount of ashes is mostly based on the amount of bone in the body. So height would change that average more than weight.

Brythan
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  • Carbon converts one to one into diamond by weight? – Mazura Nov 21 '17 at 21:12
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    A diamond is carbon with some impurities. For this kind of calculation, I think it is close enough to say that the diamond will weigh as much as the carbon in it. – Brythan Nov 21 '17 at 21:28
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    @Brythan And the lower the impurities the higher the diamond will be rated. A perfect diamond is pure carbon. – Loren Pechtel Nov 21 '17 at 22:24
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    How much silicon is in the body? 'Cause I'd rather be made into chips. – davidbak Nov 21 '17 at 23:52
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    @davidbak's comment is actually an interesting idea. Making people into computers would be a cool idea. – worldsmith Nov 22 '17 at 02:27
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    @davidbak I think most of my mass came from chips, actually... – akaioi Nov 22 '17 at 05:28
  • @akaioi You are what you eat, afterall. – Neil Nov 22 '17 at 09:36
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    "136.4 cubic inches = 9.4 cups"... USA, you need to stop this silliness already – Lope Nov 22 '17 at 10:23
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    @davidbak, people are actually researching to use diamonds in place of silicone for semiconductors, so you can just specify in your will that you want to be a computer when grow up... https://spectrum.ieee.org/nanoclast/semiconductors/materials/diamondbased-semiconductors-take-a-step-foward. – ChP Nov 22 '17 at 10:41
  • @Mazura Yes, since we have conservation of mass. Of course, the volume will change (density of diamond is ~3.51 g/cm³, compared to ~2.16 g/cm³ for graphite), and there are likely some inefficiencies in the process. – MauganRa Nov 22 '17 at 11:57
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    Unpurified silicon is as worthless as one third of a sack of sand. – rackandboneman Nov 22 '17 at 15:20
  • Remind me to never visit your evil lair. – WernerCD Nov 22 '17 at 17:58
  • I wonder how easy it is to extract carbon from carbon dioxide. After asking Google it appears the answer is not very. Then again you're trying to create a diamond ring out of people. – Wayne Werner Nov 22 '17 at 19:56
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    I wonder if baking instead of burning (like how to make charcoal) would produce more carbon. – Wayne Werner Nov 22 '17 at 19:57
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    WFT! There is a company (in one of your links) that does this already! – Astor Florida Nov 22 '17 at 20:04
  • I just edited the question to clarify the calculations with tex formulas; however, I noticed that the final calculation is wrong. 9.4 x 2/3 x 0.1 = 0.626 not 1.4! – KareemElashmawy Nov 22 '17 at 21:26
  • 9.4 cups / 2/3 cups / diamond = 14 diamonds. – Brythan Nov 23 '17 at 03:59
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    You went from metric to imperial :(... very confusing! – Mixxiphoid Nov 23 '17 at 08:10
  • @WayneWerner Using a charcoal-like process should retain much more of the carbon, yes, but not all of it. Some is still lost as carbon monoxide and you might also get some tar and other gunk, such as happens when coal is coked. – David Richerby Nov 23 '17 at 11:35
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Prior Art

First it's worth noting that there is at least one company that actually does this. LifeGem creates diamonds from carbon extracted from cremated remains.

Per wikipedia:

The company can extract enough purified carbon from a single cremated human body to synthesize up to 50 gems weighing one carat (200 mg) each, or up to 100 diamonds of smaller size, while sending remaining ashes to the family.

This is about ten grams of gem. I think that's too heavy for an earring, but I don't wear earrings. It probably wouldn't hurt in a necklace.

Is this the limit?

The question literally asks

What size of diamond would the amount of carbon in a human body form?

According to wikipedia the human body is about 18% carbon by mass. This means that a 70 kilo person contains about 12.6 kilos of carbon.

If we made a diamond from all the carbon in a human body, we'd have a 12.6 kilo gem which is frankly a bit excessive. This is 63000 carats, and would be a record-size diamond. I don't think anyone would wear that.

However, cremation removes a significant portion of this carbon (as carbon dioxide gas). Wikipedia states that a typical cremation leaves 1.8-2.7 kilograms of ash, mostly calcium salts from the bones.

From that same article:

Cremated remains are mostly dry calcium phosphates with some minor minerals, such as salts of sodium and potassium. Sulfur and most carbon are driven off as oxidized gases during the process, although a relatively small amount of carbon may remain as carbonate.

I assume that's why LifeGem doesn't produce 12 kilo monster gems.

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Deolater
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    The current largest synthetic diamond is only a little over 10 carats. – sphennings Nov 21 '17 at 16:48
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    @sphennings that would be another good reason they don't produce 63000 carat monster gems! – Deolater Nov 21 '17 at 16:51
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    For more effective size measurements (since I have no idea what 63000 carats looks like), I used diamond's density of ~3.51 g/cm3 on the monster 12 kilogram gems... and came up with 3418.8 cubic centimeters; for an effective size comparison, that's roughly 10% smaller than a gallon of milk, or 10% larger than 3 liters. – Delioth Nov 21 '17 at 19:51
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    @Delioth is that bigger than a breadbox? – A. C. A. C. Nov 22 '17 at 21:37
  • @A.C.A.C. depends, are we talking metric or imperial breadboxes? – fgysin Nov 28 '17 at 10:10
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According to wikipedia, humans are 18% carbon by mass.

So a 70 kg human is made up of roughly 16 kg carbon.

The density of a diamond is roughly 3.5 g/cm^3

Assuming a lossless process where every atom of carbon is used in the resulting diamond this would result with a 4500 cm^3 diamond.

In the real world nothing is a lossless conversion. Memorial diamonds are being created by either using the cremated remains, or carbonized hair as the carbon source to create a lab grown diamond.

sphennings
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