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The Phase Rule

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The phase rule describes the relationship between the variance (degrees of freedom), the number of components, and the number of phases in a system at equilibrium.Variance is a concept that denotes the number of independent intensive properties (properties are those that do not depend on the amount of material in the system), such as temperature, pressure, and composition, that can be altered without impacting the number of phases in equilibrium.In a single-component system, such as pure water,...

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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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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 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...

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Related Experiment Video

Updated: Jun 16, 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

Entropy Decoding the Fundamental Law of Phase Competition in Glass Formation.

Benke Huo¹, Zhengqing Cai¹, Bingtao Wang¹

¹Center for Advanced Structural Materials, State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao, P. R. China.

Advanced Science (Weinheim, Baden-Wurttemberg, Germany)

|June 15, 2026

Summary

Entropy engineering using low melting entropies of phases aids in designing optimal glass-forming compositions in multi-component alloys. This method reveals phase competition mechanisms crucial for glass formation.

Keywords:

entropy engineering glass formation melting entropy metallic glass phase competition

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Last Updated: Jun 16, 2026

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

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Published on: June 7, 2018

Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets

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Cooling Rate Dependent Ellipsometry Measurements to Determine the Dynamics of Thin Glassy Films

Cooling Rate Dependent Ellipsometry Measurements to Determine the Dynamics of Thin Glassy Films

Published on: January 26, 2016

Area of Science:

Materials Science
Thermodynamics
Alloy Design

Background:

Understanding optimal glass-forming compositions in multi-component alloys is complex.
Current methods like deep eutectic principles and trial-and-error have limitations.

Purpose of the Study:

To investigate a novel entropy engineering strategy for designing optimal glass-forming compositions.
To elucidate the phase competition mechanism in glass formation.

Main Methods:

Systematic study of glass compositions using entropy engineering.
Integration of eutectic or intermetallic phases with low melting entropies.
Comparison with conventional deep eutectic principles and empirical methods.

Main Results:

A correlation between glass-forming ability and melting entropies of initial phases was identified in Cu-Zr-Ti alloys.
An optimal glass-forming composition (Cu59.99Zr28.75Ti11.26) was designed using low-entropy phases.
The designed composition closely matched a known optimal composition (Cu60Zr30Ti10).

Conclusions:

Entropy engineering provides a quantitative approach to understanding phase competition in glass formation.
Melting entropies are critical for screening and balancing competing phases during glass formation.
This strategy offers a new pathway for designing advanced metallic glasses.