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Phase Diagram01:19

Phase Diagram

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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).
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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...
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Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms. The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. The atoms within such a metallic solid are held together by a unique force known as metallic bonding that gives rise to many useful and varied bulk properties.
All metallic solids exhibit high thermal and electrical conductivity, metallic luster, and malleability....
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Overview of VSEPR Theory
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The internal energy of a substance—the total kinetic energy of all its molecules and the potential energy of their associated forces—depends on the strength of the intermolecular forces in the condensed phases and the pressure exerted on the substance. The internal energy of a substance is the highest in the gaseous state, the lowest in the solid state, and intermediate in the liquid state. Phase transitions are caused by changes in physical conditions, such as temperature and...
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The equation of state is an equation that relates physical quantities, such as pressure, volume, temperature, and the number of moles, of a thermodynamics system with each other. The equation relating physical quantities with each other can be a simple mathematical expression or too complicated to express in mathematical form. In either case, a relationship between physical quantities exists. If the equation of state cannot be expressed in a mathematical form, then experimental data and...
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Updated: Nov 12, 2025

Phase Diagram Characterization Using Magnetic Beads as Liquid Carriers
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Diverse densest binary sphere packings and phase diagram.

Ryotaro Koshoji1, Mitsuaki Kawamura1, Masahiro Fukuda1

  • 1Institute for Solid State Physics, The University of Tokyo, Kashiwa 277-8581, Japan.

Physical Review. E
|March 19, 2021
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Summary

Researchers updated the phase diagram for densest binary sphere packings (DBSPs) by discovering 12 new structures. These findings reveal how packing structures achieve high densities and can serve as prototypes for complex crystal structures.

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Crystallography

Background:

  • Understanding densest binary sphere packings (DBSPs) is crucial for materials science and condensed matter physics.
  • Previous studies have explored DBSPs, but an updated phase diagram and comprehensive structural analysis are needed.

Purpose of the Study:

  • To update the phase diagram of densest binary sphere packings (DBSPs) under periodic boundary conditions.
  • To discover new putative densest structures and analyze their packing characteristics.
  • To investigate the relationship between DBSPs and known crystal structures.

Main Methods:

  • Developed an unbiased random search approach combining piling-up and iterative balance methods.
  • Efficiently explored densest binary sphere packings (DBSPs) by optimizing unit cell volume and minimizing sphere overlap.
  • Conducted an exhaustive search to discover diverse dense packing structures.

Main Results:

  • Discovered 12 new putative densest binary sphere packings (DBSPs), updating the existing phase diagram.
  • Identified five new DBSPs in the radius ratio range of 0.42≤α≤0.50, with competitive packing fractions.
  • Found that high packing fractions are achieved through structural distortion and the combination of local dense units.

Conclusions:

  • The updated phase diagram provides a more comprehensive understanding of densest binary sphere packings (DBSPs).
  • Many structural units in real crystals, including high-pressure phases, can be represented by DBSPs.
  • Densest sphere packings serve as effective structural prototypes for discovering complex crystal structures, particularly high-pressure phases.