Related Experiment Video
Updated: Mar 24, 2026
10:27
A Uniaxial Compression Experiment with CO2-Bearing Coal Using a Visualized and Constant-Volume Gas-Solid Coupling Test System
Published on: June 12, 2019
9.2K
Free energy model for solid high-pressure phases of carbon
Manuel Schöttler1, Martin French1, Daniel Cebulla1
1Institute of Physics, University of Rostock, Albert-Einstein-Str. 23-24, 18059, Rostock Germany.
Summary
Free energy models for diamond, body-centered cubic (BC8), and simple cubic (SC) phases were developed using density functional theory. Anharmonic effects significantly shift phase transitions, improving agreement with experimental data.
Area of Science:
- Solid-state physics
- Materials science under extreme conditions
- Computational condensed matter physics
Background:
- Understanding the behavior of materials under high pressure is crucial for geophysics and materials science.
- Accurate thermodynamic models are needed to predict material properties at extreme conditions.
- Previous models often neglected anharmonic effects, limiting their predictive power.
Purpose of the Study:
- To develop accurate analytic free energy models for high-pressure solid phases (diamond, BC8, SC).
- To investigate the impact of anharmonicity on phase transitions and equations of state.
- To validate the models against experimental data from diamond anvil cells and Hugoniot experiments.
Main Methods:
- Density functional theory (DFT) calculations to establish ground states and properties.
- Molecular dynamics (MD) simulations to incorporate anharmonic effects in nuclear motion.
- Development of analytic free energy models incorporating density and temperature dependence.
- Thermodynamically constrained corrections to align with experimental equations of state.
Main Results:
- Analytic free energy models for diamond, BC8, and SC phases were successfully developed.
- Anharmonicity was found to significantly alter the predicted phase transition boundaries compared to harmonic approximations.
- The inclusion of anharmonic effects and thermodynamic corrections improved agreement with diamond anvil cell experimental data.
- The validated thermodynamic functions showed good performance when compared against Hugoniot experiments.
Conclusions:
- The developed free energy models provide an accurate description of high-pressure solid phases, including anharmonic contributions.
- Anharmonic effects are critical for precise predictions of phase transitions and equations of state under extreme pressures.
- The study validates the use of DFT and MD simulations for modeling materials under high-pressure conditions.
Related Concept Videos
02:39Phase Diagrams
51.5K
A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...
51.5K
01:19Phase Diagram
7.2K
The phase of a given substance depends on the pressure and temperature. Thus, plots of pressure versus temperature showing the phase in each region provide considerable insights into the thermal properties of substances. Such plots are known as phase diagrams. For instance, in the phase diagram for water (Figure 1), the solid curve boundaries between the phases indicate phase transitions (i.e., temperatures and pressures at which the phases coexist).
7.2K
01:24Phase Diagram
76
A phase diagram is a graphical representation of the physical states of a substance under different conditions of temperature and pressure. It shows the boundaries between solid, liquid, and gas phases and the conditions at which these phases coexist in equilibrium. An area in a phase diagram represents a single phase, whereas lines or phase boundaries represent the equilibrium between two phases.In the phase diagram of water, the boundary line between the solid and liquid states illustrates...
76
01:10Van der Waals Equation
6.9K
The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
6.9K
02:33Phase Transitions: Sublimation and Deposition
20.8K
Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and standard pressure, a piece of dry ice (solid CO2) sublimes, appearing to gradually disappear without ever forming any liquid. Snow and ice sublimate at temperatures below the melting point of water, a slow process that may be accelerated by winds and the reduced atmospheric pressures at high altitudes. When solid iodine is warmed, the solid sublimes...
20.8K
01:21Phase Transitions
43
A phase transition is the process in which a substance changes from one state of matter to another, like from a solid to a liquid, liquid to gas, or vice versa, at a specific temperature and under given pressure conditions. This change is spontaneous and is affected by alterations in temperature and pressure. These parameters impact the strength of the forces between molecules (intermolecular forces) in the substance.During a phase transition, both the initial and final phases of the substance...
43