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A simple example of an EOS that is predicted by the Debye model for harmonic lattice vibrations is the Mie-Grünheisen equation of state: Such a relation is called an equation of state (EOS).
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To deduce the properties of minerals in the deep Earth, it is necessary to know how their density varies with pressure and temperature. Properties of materials Equations of state
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Second, large temperature gradients exist in the sample because only the portion of sample hit by the laser is heated. First, temperatures below 1200☌ are difficult to measure using this method. Laser heating is continuing to extend the temperature range that can be reached in diamond-anvil cell but suffers two significant drawbacks. Spectroscopy is used to measure black-body radiation from the sample to determine the temperature. Laser heating is done in a diamond-anvil cell with Nd:YAG or CO2 lasers to achieve temperatures above 6000k. Tungsten resistive heaters for BX90 DAC achieved temperatures of 1400☌. With an argon atmosphere, higher temperatures up to 1700☌ can be reached without damaging the diamonds. Temperatures below 700☌ can be reached in air due to the oxidation of diamond above this temperature. A large variety of heater designs are available including those that heat the entire diamond anvil cell (DAC) body and those that fit inside the body to heat the sample chamber. The application of a voltage to a wire heats the wire and surrounding area. Resistive heating is the most common and simplest to measure. Several methods are used to reach these temperatures and measure them. The sample can be heated to thousands of degrees.Īchieving temperatures found within the interior of the earth is just as important to the study of mineral physics as creating high pressures. The concentration of pressure at the tip of the diamonds is possible because of their hardness, while their transparency and high thermal conductivity allow a variety of probes can be used to examine the state of the sample. This is beyond the pressures at the center of the Earth. It can compress a small (sub-millimeter sized) piece of material to extreme pressures, which can exceed 3,000,000 atmospheres (300 gigapascals). The diamond anvil cell is a small table-top device for concentrating pressure. The diamond size is a few millimeters at most Schematics of the core of a diamond anvil cell. Recently, sintered diamond anvils have been developed for this type of press that can reach pressures of 90 GPa (2700 km depth). The apparatus is very bulky and cannot achieve pressures like those in the diamond anvil cell (below), but it can handle much larger samples that can be quenched and examined after the experiment.
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Pressures of about 28 GPa (equivalent to depths of 840 km), and temperatures above 2300 ☌, can be attained using WC anvils and a lanthanum chromite furnace. Unlike shock compression, the pressure exerted is steady, and the sample can be heated using a furnace. The method was developed by Kawai and Endo in Japan. The anvils are typically placed in a large hydraulic press. Typically the apparatus uses an arrangement eight cube-shaped tungsten carbide anvils to compress a ceramic octahedron containing the sample and a ceramic or Re metal furnace. Multi-anvil presses involve an arrangement of anvils to concentrate pressure from a press onto a sample. The conditions of the experiment must be interpreted in terms of a set of pressure-density curves called Hugoniot curves. The pressure is very non-uniform and is not adiabatic, so the pressure wave heats the sample up in passing. However, the method has some disadvantages. Pressures as high as any in the Earth have been achieved by this method. For a brief time interval, the sample is under pressure as the shock wave passes through. Many of the pioneering studies in mineral physics involved explosions or projectiles that subject a sample to a shock. Creating high pressures Shock compression