When diamonds "migrate" from deep underground to the surface, do they maintain pressure inside when there is no more pressure outside? If so, how?

Question

From Science News' A mineral found in a diamond’s flaws contains the source of some of Earth’s heat:

A tiny bit of rock trapped inside a diamond is now opening a brand-new window into what the planet’s lower mantle looks like. Inside the diamond is a newly identified silicate mineral dubbed davemaoite that can only have formed in Earth’s lower mantle, researchers report November 12 in Science. It’s the first time that scientists have managed to definitively prove that this type of lower mantle mineral — previously just predicted from laboratory experiments — actually exists in nature. The team named the mineral for well-known experimental high-pressure geophysicist Ho-kwang (Dave) Mao (SN: 3/16/04)

Scientists had previously estimated that about 5 percent to 7 percent of the lower mantle must be made up of this mineral, Tschauner says. But it’s fiendishly difficult to directly observe such deep-Earth minerals. That’s because minerals that are stable in the intense pressures of the lower mantle — which extends all the way to 2,700 kilometers below Earth’s surface — begin to rearrange their crystal structures as soon as the pressure lets up.

Even the planet’s most common mineral, a lower mantle magnesium iron silicate known as bridgmanite, was largely theoretical until 2014, when it was discovered to have naturally occurred within a meteorite that had slammed into Australia with a force that generated crushing, deep mantle-like pressures in the rock (SN: 11/27/14). To date, bridgmanite is the only other high-pressure silicate mineral confirmed to exist in nature.

Diamonds act like time capsules, locking in the original mineral forms on their journey to the surface. The discovery of davemaoite is not only a confirmation of its existence, but it also reveals the location of some sources of heat deep inside Earth.... By identifying the chemical makeup of davemaoite, researchers can now confirm where those elements reside.

That’s because the Botswana diamond also contained a high-pressure form of ice as well as another high-pressure mineral known as wüstite (SN: 3/8/18). The presence of those inclusions helped narrow down the rough pressures at which the davemaoite might have formed: somewhere between 24 billion pascals and 35 billion pascals, Tschauner says. It’s hard to say exactly what depth that corresponds to, he adds. But the discovery directly links heat generation (the radioactive materials), the water cycle (the ice) and the carbon cycle (represented by the formation of the diamond itself), all in the deep mantle, Tschauner says.

From the article I think that I'm being told that the diamond is preserving enough pressure to keep both the "davemaoite" and " a high-pressure form of ice" and the wüstite stable as well.

Am I understanding this correctly?

Question: When diamonds "migrate" from deep underground to the surface, do they maintain pressure inside when there is no more pressure outside? If so, how?

I would think that as the diamond rises to the surface and the pressure relaxes outside it would relax and expand uniformly and the pressure would relax inside as well. If that's not the case, why not?

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The tiny gray blobs of mineral embedded in this slice of clear diamond are the first samples of newly named davemaoite, a calcium silicate perovskite mineral that only forms in the lower mantle. AARON CELESTIAN/NATURAL HISTORY MUSEUM OF LOS ANGELES COUNTY

Answer 1

The question is in regard to pressure confining a rare, deep-mantle formed mineral visible within a diamond inclusion. The pressure on the inclusion within the diamond crystal is really the pressure of confinement within the crystalline lattice of carbon that makes a diamond what it is. Let's digress for a moment.

A diamond is a covalent crystal. Each carbon atom of a diamond crystal is bound to four equidistant carbon atoms tetrahedrally oriented about it, thereby forming a regular tetrahedron with a carbon atom at the center and one at each of four vertices, each atom sharing one electron in a covalent bond. This covalent crystal structure renders the diamond crystal as a single molecule. Among natural minerals, this covalent bonding also renders the diamond as extremely hard. Consequently, the crystalline structure is extraordinarily difficult to dislocate or shear, and will break, or fracture, as a consequence. This characteristic should be compared with the alternate crystalline form of carbon, namely, graphite. As we all know, graphite is extremely easy to shear and break. Without graphite, we would be without pencils.

Diamond crystals form at extraordinarily high temperatures and pressures deep within the earth's upper mantle. Nevertheless, the diamond crystal is unstable at temperatures and pressures where graphite is stable. The crystalline structure of diamond has unsatisfied bonding abilities on its crystal surface as the crystal-bonding elements there are not surrounded by other covalent bonding units. At the earth's surface, the crystal will reactively degenerate into graphite at a formidably slow rate, but will not readily oxidize unless by forced ignition. However, these extraordinarily strong covalent bonds result in an extremely high packing density of carbon atoms, and thereby also prevent the crystalline structure from alteration due to pressures existing where the crystal is unstable. Apparently there is little or no alteration in the dimensional stability of the crystalline structure of diamond due to changes in pressure. In other words, the dimensional stability of diamond is not sensitive to changes in pressure. Diamond cannot be compressed.

Inclusions of other minerals within the diamond crystal are rarely formed at the same pressure and temperature conditions under which the diamond was formed. These mineral inclusions are formed some considerable time before formation of the diamond and under conditions even more extreme. An inclusion is simply a formational artifact or otherwise a crystal of some other mineral contained within the diamond crystal. Inclusions may be typically small. Predominantly formational for gem-quality diamonds, these inclusions are graphite, or otherwise crystalline twinning of the diamond caused by irregularities in the crystal structure as the diamond was formed. But in some rare cases, these inclusions are of crystalline minerals that formed in deep time considerably before formation of the diamond, and at more extreme pressures deep within the mantle. Such inclusions may predate the formation of the diamond by billions of years. In other words, when the diamond crystal formed, it grew around this type of mineral inclusion.

As we can see, some diamonds may have a history that is very interesting. In particular regarding the present question, the small inclusions of davemaoite crystals would not exist at the earth's surface if not for the confining pressure formed consequent to the diamond's crystalline lattice of densely packed, covalently-bound carbon atoms. Recall that the crystalline structure of diamond is extraordinarily difficult to dislocate or shear, and the packing of carbon atoms in the crystal lattice is extraordinarily dense. Consequently, each davemaoite inclusion was trapped within the diamond crystal as the crystalline lattice grew around the inclusion. The unique crystalline covalent bonding structure of the diamond, itself, confines the davemaoite crystals at extreme pressure.

Answer 2

One of the more interesting examples of diamond maintaining high pressure in its lattice is discussed in this answer from Space Exploration SE. Put briefly, Ice VII inclusions have been found in diamonds at Earth's surface despite this phase of water requiring GPa pressure levels to form. In this case the required pressure must have been inherited within the diamond lattice within which the ice was found, and the calculated pressure from the lattice parameter is indeed between 8 and 11 GPa where Ice VII would be stable.

The tendency to maintain pressure internally is not entirely unique to diamond. Any solid formed under pressure can maintain such pressure internally in its crystal lattice. However, if the surrounding pressure is released then the material may also deform to relieve the internal pressure. So, roughly, only an amount of pressure similar to the yield strength (which is typically well below the bulk modulus) is expected to be retained. The mechanics behind this result is described below. For most solids this limit is so low that the inclusions end up in their "normal" low-pressure phases, not very interesting. What is unique about diamond is its much superior strength: [Ruoff1](https://doi.org/10.1063/1.326378) gives a yield strength of 35 GPa, enabling it to rentain enough internal pressure (if it is formed under such pressure) to stabilize Ice VII, perovskite-structured silicates, etc.

Reference

Arthur L. Ruoff (1979). "On the yield strength of diamond". Journal of Applied Physics 50, 3354. https://doi.org/10.1063/1.326378

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The pressure's on: How a solid matrix retains pressure ... or not

Consider a spherical particle of radius $r_p$ exerting pressure $P$ on a surrounding solid matrix. In the absence of a counterbalancing pressure from the outside, the imposed pressure from within generates a compressive stress $\sigma_c$ in the radial direction and a tensile stress $\sigma_t$ in the two orthogonal directions (along spheres concentric with the particle) through the volune of the surrounding solid. As shown in the picture below, both components decrease with the cube of the distance from the particle, and so have maximum magnitude at the particle surface. There the negative compressive stress is $-P$ and the positive tensile stress is $+P/2$.

We can apply the Von Mises yield criterion which states that the surrounding matrix yields, thus reducing the retained pressure, when

$(\sigma_1-\sigma_2)^2+(\sigma_2-\sigma_3)^2+(\sigma_3-\sigma_1)^2\ge2(YS)^2$

where $\sigma_1,\sigma_2,\sigma_3$ are the three orthogonal principal components of the stress tensor. Here $\sigma_1=\sigma_c=-P$ and $\sigma_2=\sigma_3=\sigma_t=+P/2$, from which the yield criterion then becomes

$P\ge(2/3)(YS)$

For a diamond lattice with a yield strength of 35 GPa this means the diamond can sustain a pressure up to 23 GPa, as quoted in the main text, around an Ice VII inclusions, whereas most other minerals would have yield stresses well below 1 GPa and thus fail to retain enough pressure to sustain Ice VII or other GPa-pressure phase inclusions.