@TheDemonLord I think is one of those questions that's on the borderline of needing that tag but could be answered without it. An answer showing its math would be helpful but isn't necessary, IMO.

@AlexP Although I understand diamond>crust heat transfer cannot surpass mantle>diamond heat transfer, wouldn't convection currents cause cooled-off mantle to "drop off" the bottom of the diamond while hotter rock rises and comes into contact with it? There wouldn't be a "layer of mantle rock" next to the diamond, because the rock next to it would constantly cool and sink. If nothing else, I think the convection currents caused by this constant "radiator" effect would have notable consequences on the surface.

@John I doubt its thermal conductivity approaches the crust's, even at the temperatures here; I'm assuming at least 100 W/m/K even at 1400 K. Also, the atmosphere isn't relevant to this; as in the drawing, there's a multi-km-deep sheet of poorly-conducting earth/rock atop the diamond that heat must penetrate to reach the atmosphere. I chose diamond specifically because it's good at forming monolithic structures which don't collapse under their own weight; if granite can survive mountain formation, why would diamond "fracture" under the same conditions?

@BobaFit It has sunk to some extent, but it isn't as dense as the mantle, so it "floats" in the mantle like an iceberg. Some of it protrudes upwards into the crust. A portion of what protrudes into the crust protrudes above sea level. The force of the diamond's weight and the weight of the crust above the diamond are enough to "sink" the diamond to some extent, but not enough to make it irrelevant to the question. Also, it's not "roughly 50% more dense than ordinary crust rock"; the crust is 3150 kg/m^3 and the diamond is 3300 kg/m^3.

IMO, there's not enough info here to answer your question. The crust can be 3-43 miles thick. For all intent and purpose, the diamond is an indestructible theremal conductor, meaning the temperature on the upper surface is equal to the temperature on the lower surface. If the crust is 3 miles thick and geological time has past, it's likely that it's "melted off." If it's thicker, you might get a magma chamber, but there's no pressure, so no volcano (much less a supervolcano). Is this next to a large lake or ocean? Then you'll get hot springs and steam vents. Not near? No springs or vents.

@BobaFit I don't think density is enough to conclude that. The melting point of diamond is about 4000°C. The OP's stated condition is only 1127°C. I don't believe that's hot enough to materially soften diamond - but I could be wrong.

The more I think about it, assuming the diamond mountain really could be believed to float, the result would be a diamond surface exposed to the sky. The crust would be constantly melting off of it. The climate around the area would be interesting, but you would end up with a moat (not a sea) of molten lava around the diamond mountain. The crust can't build up fast enough for anything else. Now, what the mantle would do around the perimeter of the diamond mountain... that's a good question. It's only a guess, but the word "percolate" comes to mind.

Note that so long as the density of the diamond is greater than the density of the mantle, over geological time, the diamond will always sink.

@BobaFit This is not Earth. The crust is 3.15 g/cm^3, because it's made of other stuff than Earth's crust. Maybe the diamond is 3.5 g/cm^3, if that's the only density diamond can be at, but it's still not as dense as the mantle.

@JBH "A magma chamber without pressure" like what you said is what I want; it allows for relatively high surface heat fluxes, allowing things like hot springs, geothermal power, melted or at least shallower permafrost, etc.). The diamond isn't as dense as the mantle, albeit close (~3.5 g/cm^3 diamond, 3.6 g/cm^3 mantle); this isn't Earth, the mantle is different. If the crust constantly melted off the diamond, wouldn't the constant lava flows build the crust up thick enough that it wouldn't melt for long enough to creep over the diamond?

@JBH Basically, think of it as a shield volcano, except, instead of the magma coming out of the peak, it's formed on the sides, by crust constantly being pushed into the relatively hot diamond and then melted back down the flanks.

Ooops, I misread the crust density for the mantle density. Sorry about that. I'm still worried about the geological timelines. Any crust over the diamond would simply slough off. I don't think you'd get a shield volcano. At a guess, you'd get a moat around a whomping hot diamond that would generate fearsome storms about 50 klicks away.

@JBH Right, but where does sloughed-off crust go? As I understand it, the sloughed-off, molten crust will, on geological timescales, form a layer thick enough to cool, allowing solid crust to creep over it to reach parts of the diamond that are still exposed. The crust reaches those, melts, and adds more to the solid slopes around the diamond, allowing more crust to climb further still.

I suppose a better analogy would be taking a quadrilateral pyramid and pouring a bucket of sand on it from directly above its apex. Initially, the sand piles up at its base , but, over time, enough builds up to bury it, as more-recently poured sand builds up on the sand poured previously. And this won't encounter the issues normal mountains do, where too much rock slides down the sides; here, the crust encounters something it can't pass, so it just sort of peels back and pile on top of itself.

It's the same way Olympus Mons got so high: not by being tall and thin, which means you run into issues with the compressive strength of the rock, but by having so much stuff to the sides of it that it essentially builds a giant layer cake of molten crust with each eruption. It's just that, in this case, it's not an eruption, it's a tectonic plate trying to creep over the diamond (which is maybe something I should've made clearer in the original question).

Dirt falls atop of things for three reasons: wind (not very thick), volcanic eruption (up to hundreds of feet per eruption) and tectonic action. Tectonic action would take forever and crush the diamond mountain under the subduction zone of the two plates. In short, there's no "quick" method of replacing the dirt atop the mountain. On the other hand, the heat is almost immediate, melting everything atop of. At the most, you'd get a small ring of hills around the moat (sloughed-off dirt...

Let me underscore something I said. Tectonic mountain building is very slow. A mountain may grow an inch in centuries. The melting process is comparitively instantaneous, melting any soil deposited atop the diamond in days or, at worst, weeks. Worse, the subdcution process would either push the diamond up, onto the surface or down below it. In geological timeline terms, it wouldn't stay in the condition you're pitching for very long. This is one of those worldbuilding elements that you need...

... to declare to be so and move on. Making it substantially fit within the world of science is going to be difficult.

Gotcha. You're envisioning something like this, then?

The plates getting pushed into the magma area around the diamond, then melted before they have time to ride up the sides?

You're drawing crust over the top of the diamond I don't think would exist. Draw the green crust squared off over the top of the equator of the diamond and that's what I think will happen.

Well.... I can see your point about some encroachment of solid land... but not as much as you're showing.

The top's poking above sea level into the atmosphere. Green is crust, red is magma/lava/mantle.

There's no crust over it in this case, just air.

You said my idea would only work if the mountain was an upright cylinder; I presume that's based off of how shield volcanos work (i.e. central point in a circular mound, constantly spews lava down the sides)?

You're showing the crust encroaching over the top of the diamond, separated from the diamond by a layer of lava. I think you're showing about 300% more encroachment than would actually happen. You're correct about what I said about the cylinder. In fact, that's the issue I'm trying to resolve with your drawing. What you're showing would be true for a cylinder, but not a diamond.

Something more akin to this, then?

That's a lot closer. Think about it this way, the distance between the mantle and the crust without the diamond is the same distance from the angled surface of the diamond to the top of the crust. That's why a bit of encroachment would occur, but not much else. The diamond (simplistically) is acting as a nearly perfect conductor of heat.

Sorry, the thickness of the crust must be identical from the top of the natural mantle layer AND the angled sides of the diamond. Draw a vector over the natural mantle, then move that vector to a position perpendicular to the angled side of the diamond. I think that's what would happen.

Aye. There seem to be too many problems with this, as it currently is, for it to work.

Bummer. It's a cool idea. But, that's the way worldbuilding sometimes rolls. Cheers.

Thanks.

I wonder what about the diamond getting burned up by any oxide traversed by its side, at temp of 4000K a diamond could just trap oxygen off anything around and release more energy, allowing a chain reaction and eventual transmutation of that diamond into masses of CO/CO2.

It's not 4000K, it's 1400K. Much less.