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Phase Transitions

Phase Transitions

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...

Phase Diagram

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 Diagrams of Ternary Systems

Phase Diagrams of Ternary Systems

Consider a ternary system, which is composed of three components: water (W), ethanoic acid (E), and trichloromethane (T). Here, Ethanoic acid (E) is fully miscible with both water (W) and trichloromethane (T), meaning it can mix entirely with either of them. However, water and trichloromethane have partial miscibility, meaning they can only mix to a certain extent, beyond which two separate phases will form.The phase diagram of a ternary system is represented as an equilateral triangle, where...

Phase Diagram

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 Diagrams

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...

States of Matter and Phase Changes

States of Matter and Phase Changes

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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Related Experiment Video

Updated: Mar 30, 2026

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Published on: June 7, 2018

A phase diagram for jammed matter.

Chaoming Song¹, Ping Wang, Hernán A Makse

¹Levich Institute and Physics Department, City College of New York, New York, New York 10031, USA.

|May 30, 2008

Summary

This summary is machine-generated.

This study statistically describes jammed sphere packing, interpreting random close packing as a ground state. It reveals a maximum density limit of 63.4% for hard sphere packings and a unifying phase diagram.

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Last Updated: Mar 30, 2026

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Published on: June 7, 2018

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Published on: May 15, 2017

Phase Diagram Characterization Using Magnetic Beads as Liquid Carriers

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Published on: September 4, 2015

Area of Science:

Statistical Mechanics
Materials Science
Computational Physics

Background:

Sphere packing, a problem with historical roots, has practical applications in diverse fields like granular processing and logistics.
Experimental studies show random loose packing (RLP) at ~55% density and random close packing (RCP) at ~64% density, but lack physical interpretation.
Existing models struggle to provide a unified understanding of the various states of sphere packing.

Purpose of the Study:

To provide a statistical description of jammed states in sphere packing.
To interpret random close packing (RCP) as the ground state within a statistical ensemble.
To establish a theoretical density limit for random packings of hard spheres.

Main Methods:

Development of a statistical mechanics framework for jammed states.
Analysis of hard sphere packings in three dimensions.
Construction of a phase diagram to unify packing behaviors.

Main Results:

Random close packing (RCP) is identified as the ground state of the jammed matter ensemble.
A theoretical upper density limit of approximately 63.4% is demonstrated for random hard sphere packings.
A comprehensive phase diagram is presented, unifying various packing states including random loose packing (RLP).

Conclusions:

The statistical description provides a physical interpretation for the observed densities in sphere packing.
The 63.4% density limit offers a fundamental constraint for random packings of hard spheres.
The phase diagram serves as a valuable tool for understanding and predicting sphere packing behaviors.