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Related Concept Videos

Phase Diagram01:19

Phase Diagram

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).
Phase Diagram01:24

Phase Diagram

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...
Phase Diagrams02:39

Phase Diagrams

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...
Two Components: Liquid–Liquid Systems01:27

Two Components: Liquid–Liquid Systems

A pressure-composition phase diagram explicitly describes the behavior of an ideal solution of two volatile liquids under varying pressures and compositions. A pressure-composition diagram has two main curves. The bubble point curve represents the plot of pressure versus liquid mole fraction. It indicates the pressure at which the first bubble of vapor forms from the liquid phase as the system pressure decreases.The dew point curve is the pressure versus vapor mole fraction. It indicates the...
Recrystallization: Solid–Solution Equilibria01:10

Recrystallization: Solid–Solution Equilibria

Recrystallization is a purification technique used to separate impurities from solid compounds. In this technique, no chemical reactions occur. Instead, it exploits physical properties only, specifically, the solubility differences between the desired compound and impurities, either at a single temperature or at different temperatures, and under other selected conditions. The solid-solution equilibrium (solubility equilibrium) of each component in the solution represents a binary phase...
Phase Transitions: Melting and Freezing02:39

Phase Transitions: Melting and Freezing

Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...

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Related Experiment Video

Updated: May 30, 2026

Synthesis and Microdiffraction at Extreme Pressures and Temperatures
07:26

Synthesis and Microdiffraction at Extreme Pressures and Temperatures

Published on: October 7, 2013

Equilibrium lines and crystal phases under pressure.

P M Marcus1, S L Qiu

  • 1IBM Research Division, T J Watson Research Center, Yorktown Heights, NY 10598, USA.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|August 6, 2011
PubMed
Summary
This summary is machine-generated.

The study reveals a universal relationship between a crystal phase's bulk modulus and its elastic constants under varying pressure. This finding offers insights into material properties and phase stability.

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Area of Science:

  • Materials Science
  • Solid-State Physics
  • Crystallography

Background:

  • Crystalline solids exhibit distinct phases under varying thermodynamic conditions.
  • Understanding the static and dynamic properties of these phases is crucial for materials design.
  • Elastic constants and bulk modulus quantify a material's mechanical response to stress.

Purpose of the Study:

  • To investigate the relationship between bulk modulus and elastic constants for a crystal phase in equilibrium.
  • To explore the calculation of equilibrium lines and material properties from thermodynamic potentials.
  • To determine if a universal relation exists between bulk modulus and specific elastic constants.

Main Methods:

  • Calculating the equilibrium line in structure space for a crystal phase under changing pressure.
  • Deriving static properties, including elastic constants and bulk modulus, from Gibbs free energy and internal energy.
  • Analyzing the stress-strain relationships along the equilibrium line.

Main Results:

  • A crystal phase in equilibrium under changing pressure defines a unique line in structure space.
  • The bulk modulus along this equilibrium line exhibits a universal relationship with specific elastic constants.
  • This universal relation is independent of pressure and relates to the stability-controlling elastic constants.

Conclusions:

  • The study establishes a pressure-independent universal relation between bulk modulus and stability-controlling elastic constants.
  • This finding simplifies the prediction of mechanical properties for crystalline phases.
  • The methods provide a framework for calculating equilibrium lines and associated properties from fundamental energy calculations.