Most of the big diamonds form deep in the Earth, between 410km and 660km (250 to 400 miles deep), and nearly all of them are older than 1 billion years. This is one reason why they are so interesting, because the mineral inclusions stuck inside these are essentially windows into Earth's geologic past and also a glance of what the deep Earth chemistry is like. Diamonds are the only way we can get samples of these inaccessible locations, but are critical for our understanding of Earth processes. Diamond research as been use to as evidence of the onset of plate tectonics, crustal recycling, as geobarometers and geothermometers, and as a source to discover new minerals that only grow in these parts of the Earth.
The deep diamonds are brought up by volcanic eruptions. These eruptions are not like regular volcanoes such has Hawaii or Mt. St. Helens, they are kimberlite eruptions, and one hasn't happened on Earth for over 70 million years, so we don't know exactly what they look like. Based on evidence of minerals trapped in diamonds, as well as associated minerals, we do know that they must have been brought up within an hour or so from 200+ miles below the surface of the Earth. If a diamond were to travel slowly from these depths, the diamond would begin to dissolve, and many of the gasses and fluids trapped within would escape.
Diamonds often contain new minerals in them. For example, the mineral bridgmanite is likely the most abundant mineral in the entire Earth. It would immediately breakdown if it were to be exposed to Earth surface pressures and temperatures, but because it is trapped in a diamond, it is preserved (again, until released from the diamond). This is pretty common for many diamond mineral inclusions, so experimental research on them can be quite challenging. The second most abundant mineral in Earth is called davemaoite, named after Caltech professor Dave Mao. The type specimen of davemaoite (see @nhmla_gems instagram page) is in the Mineral Sciences collection of NHMLAC.
Location of Diamond Formation
color
The origin of color in diamonds is quite complex, and difficult to resolve because overlapping effects and the difficulty in measuring the extremely low concentrations of impurities that impart the color. A diamond without any impurities is completely colorless, so it needs defects and/or elemental substitutions to generate a color center.
There is also a letter color grading scale that is marketed by the Gemological Institute of America for diamonds that are white to faint yellow, which are the most abundant types of diamonds. For the "fancy" diamonds (a term used to denote a colored diamond other than white/faint yellow), GIA has developed other grading methodologies that do not use a letter grade system. Many follow this nomenclature, but it is not universally used.
Brown, Red, Pink
After a diamond forms, it can be subjected to shear stresses that plastically push the planes of carbon atoms over each other. This deformation is on the atomic level, and induces a diffraction effect that scatters specific colors. It does not weaken the diamond, or change its hardness, but it does create an optical effect. The spacing between these shear planes, and the density of them, gives rise to these colors. Naturally, the color of the stone will change depending on how the light diffracts into your eye, so the gem cutter must pay special attention to this detail to maximize the desired color of the final polished gem. Reds and pinks fetch very high prices on the market, so these diamond cutters must be especially well trained.
Violet
Violet, and grayish-blue to violet, are rare colors of diamonds and are likely caused by hydrogen impurities (see 1, 2, 3).
Yellow
One of the most common colors in diamonds. This color is caused by nitrogen impurities that form clusters (type Ia) as isolated atoms within the structure (type Ib).
Green
The green color is caused by natural radiation damage to the gem. Natural gamma radiation from nearby radioactive minerals displace carbon atoms into other places in the crystal. Often the green color is only at the surface of the diamond, like a thin skin, be cause the gamma radiation doesn't penetrate deep into the stone. As a consequence, the diamond cutter can easily polish off the green parts of the crystal if they are not careful, and the resulting stone is a far less valuable white diamond. The green color can be removed by heating, but may result in a brown or possibly an orange diamond.
Blue
A highly desirable color of diamond, blue color come from impurities of boron in the crystal structure. The Hope diamond (a dark blue stone), has trace parts per billion boron in crystal, so it doesn't take much to impart the color.
Orange
The origin of this color is still not well understood, e.g. Wang & Lu, 2013
Black
Caused by lots of dark inclusions (like graphite) that limit the amount of transmittable light.
fluorescence
For diamonds to fluoresce, they need impurities or defects in their crystal structure. Common causes are nitrogen, hydrogen, nickel (for Ni, see examples 1, 2, 3, 4) and/or vacancies (empty atomic sites in the crystal). Fluorescence in diamonds can easily be seen using UV flashlights, and can even happen in direct sunlight (because sunlight has UV in it). Fluorescence is common in diamonds, anecdotal evidence suggests about 35% of all diamonds fluoresce.
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