# Mineral physics

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Mineral physics

Mineral physics is the science of materials that compose the interior of planets, particularly the Earth. It overlaps with petrophysics, which focuses on whole-rock properties. It provides information that allows interpretation of surface measurements of seismic waves, gravity anomalies, geomagnetic fields and electromagnetic fields in terms of properties in the deep interior of the Earth. This information can be used to provide insights into plate tectonics, mantle convection, the geodynamo and related phenomena.

Laboratory work in mineral physics require high pressure measurements. The most common tool is a diamond anvil cell, which uses diamonds to put a small sample under pressure that can approach the conditions in the Earth's interior.

## Creating high pressures

The pace of progress in mineral physics has been determined, to a large extent, by the technology for reproducing the high pressures and temperatures in the Earth's interior. The most common tools for achieving this have been:

### Shock compression

Many of the pioneering studies in mineral physics involved explosions or projectiles that subjected a sample to a shock. For a brief time interval, the sample is under pressure as the shock wave passes through. Pressures as high as any in the Earth have been achieved by this method. However, the method has some disadvantages. The pressure is very non-uniform and is not adiabatic, so the pressure wave heats the sample up in passing. The conditions of the experiment must be interpreted in terms of a set of pressure-density curves called the Hugoniot curves.[1]

### Multi-anvil press

Multi-anvil presses involve an arrangement of anvils to concentrate pressure from a press onto a sample. Unlike shock compression, the pressure exerted is steady, and the sample can be heated using a furnace. Pressures equivalent to depths of 700 km and temperatures of 1500°C can be attained. The apparatus is very bulky and cannot achieve pressures like those in the diamond anvil cell (below), but they can handle much larger samples that can be examined after the experiment.[2]

### Diamond anvil cell

Schematics of the core of a diamond anvil cell. The diamond size is a few millimeters at most

The diamond anvil cell is a small table-top device for concentrating pressure. It can compress a small (sub-millimeter sized) piece of material to extreme pressures, which can exceed 3,000,000 atmospheres (300 gigapascals).[3] This is beyond the pressures at the center of the Earth. The concentration of pressure at the tip of the diamonds is possible because of their hardness, while their transparency and high electrical conductivity allow a variety of probes can be used to examine the state of the sample. The sample can be heated to thousands of degrees.

## Properties of materials

### Equations of state

To deduce the properties of minerals in the deep Earth, it is necessary to know how their density varies with pressure and temperature. Such a relation is called an equation of state (EOS). A simple example of an EOS that is predicted by the Debye model for harmonic lattice vibrations is the Mie-Grünheisen equation of state:

$\left(\frac{dP}{dT} \right) = \frac{\gamma_D}{V}C_V,$

where CV is the heat capacity and γD is the Debye gamma. The latter is one of many Grünheisen parameters that play an important role in high-pressure physics. A more realistic EOS is the Birch–Murnaghan equation of state.[4]

### Interpreting seismic velocities

Inversion of seismic data give profiles of seismic velocity as a function of depth. These must still be interpreted in terms of the properties of the minerals. A very useful heuristic was discovered by Francis Birch: plotting data for a large number of rocks, he found a linear relation of the compressional wave velocity vp of rocks and minerals of a constant average atomic weight $\overline{M}$ with density ρ:[5][6]

$v_p = a \overline{M} + b \rho$.

This makes it possible to extrapolate known velocities for minerals at the surface to predict velocities deeper in the Earth.

## References

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