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Recently I checked a picture about the geologic layers of the Earth, and I saw that the mantle is divided into upper and lower mantle. What's the reason of this differentiation?

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The boundary between the upper and lower mantle is today believed to be due to the phase change because of increasing pressure of:

$$\text{Ringwoodite} \xrightarrow{\text{660 km, about 24.5 GPa}} \text{Mg-Perovskite} + \text{Mg-Wüstite}$$

The boundary was originally found in the form of a seismic discontinuity (the "660 km discontinuity"). This information was combined with the knowledge that the most primitive meteorites have roughly the chemistry of the bulk Earth. Accounting for the chemical differentiation (into crust, mantle and core) the chemistry of the mantle was known. Additional clues for the chemistry come from mantle-xenoliths. The crystal structure (important for the density of a chemical compound or mineral) can be deduced from high pressure experiments and natural laboratories such as meteorite impact craters. For example, the mineral majorite was found, which is also postulated for the lower mantle.

Some literature on this: http://mahi.ucsd.edu/shearer/PDF/30NT92a.pdf

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