Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

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...

Solid–Solid Solutions

Solid–Solid Solutions

The temperature-composition phase diagram of two solids, A and B, which are immiscible in the solid phase but form miscible liquids, shows that when the temperature is low, these two exist as separate, pure solids (A and B). As the temperature increases, they transition into a single-phase liquid solution where A and B coexist. Moving from point a1 to a2 in the phase diagram, the composition changes such that solid B begins to separate from the solution, enriching the remaining liquid with A.

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 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

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...

Molecular and Ionic Solids

Molecular and Ionic Solids

Crystalline solids are divided into four types: molecular, ionic, metallic, and covalent network based on the type of constituent units and their interparticle interactions.
Molecular Solids
Molecular crystalline solids, such as ice, sucrose (table sugar), and iodine, are solids that are composed of neutral molecules as their constituent units. These molecules are held together by weak intermolecular forces such as London dispersion forces, dipole-dipole interactions, or hydrogen bonds, which...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

From Triangular Correlated Paramagnet to Multi-q Noncoplanar Spin State in Spinel GeFe_{2}O_{4}.

Physical review letters·2026

Same author

Antiferroelectricity in BiFeO_{3} Thin Films.

Physical review letters·2025

Same author

Dynamics of Polar Vortex Crystallization.

Physical review letters·2024

Same author

Electric Control of Magnetism in Multiferroic Rare-Earth-Substituted BiFeO_{3} with Ferrielectricity.

Physical review letters·2024

Same author

Crossover from Linear to Quadratic Electro-optic Behavior in BaTiO_{3} and (Ba, Sr)TiO_{3} Solid Solution.

Physical review letters·2024

Same author

Motion and teleportation of polar bubbles in low-dimensional ferroelectrics.

Nature communications·2024

Search research articles

Related Experiment Video

Updated: Jul 18, 2026

Synthesis and Exfoliation of Discotic Zirconium Phosphates to Obtain Colloidal Liquid Crystals

Synthesis and Exfoliation of Discotic Zirconium Phosphates to Obtain Colloidal Liquid Crystals

Published on: May 25, 2016

Phase diagram of pb(Zr,Ti)O3 solid solutions from first principles.

Igor A Kornev¹, L Bellaiche, P-E Janolin

¹Physics Department, University of Arkansas, Fayetteville, Arkansas 72701, USA.

Physical Review Letters

|December 13, 2006

Summary

A new computational method reveals hidden phases and multiphase points in lead zirconate titanate (Pb(Zr1-xTix)O3) near its morphotropic phase boundary, resolving long-standing scientific debates.

More Related Videos

Synthesis of Non-uniformly Pr-doped SrTiO3 Ceramics and Their Thermoelectric Properties

Synthesis of Non-uniformly Pr-doped SrTiO₃ Ceramics and Their Thermoelectric Properties

Published on: August 15, 2015

Combining Solid-state and Solution-based Techniques: Synthesis and Reactivity of Chalcogenidoplumbates(II or IV)

Combining Solid-state and Solution-based Techniques: Synthesis and Reactivity of Chalcogenidoplumbates(II or IV)

Published on: December 29, 2016

Related Experiment Videos

Last Updated: Jul 18, 2026

Synthesis and Exfoliation of Discotic Zirconium Phosphates to Obtain Colloidal Liquid Crystals

Synthesis and Exfoliation of Discotic Zirconium Phosphates to Obtain Colloidal Liquid Crystals

Published on: May 25, 2016

Synthesis of Non-uniformly Pr-doped SrTiO3 Ceramics and Their Thermoelectric Properties

Synthesis of Non-uniformly Pr-doped SrTiO₃ Ceramics and Their Thermoelectric Properties

Published on: August 15, 2015

Combining Solid-state and Solution-based Techniques: Synthesis and Reactivity of Chalcogenidoplumbates(II or IV)

Combining Solid-state and Solution-based Techniques: Synthesis and Reactivity of Chalcogenidoplumbates(II or IV)

Published on: December 29, 2016

Area of Science:

Materials Science
Condensed Matter Physics
Computational Materials Science

Background:

Lead zirconate titanate (Pb(Zr1-xTix)O3) is a crucial material for piezoelectric applications.
Understanding its phase behavior near the morphotropic phase boundary is complex due to competing ferroelectric and antiferrodistortive orders.

Purpose of the Study:

To develop a first-principles-derived computational scheme for studying finite-temperature properties of Pb(Zr1-xTix)O3.
To investigate the complex phase diagram of Pb(Zr1-xTix)O3, particularly near its morphotropic phase boundary.

Main Methods:

A first-principles-derived computational scheme was developed, incorporating ferroelectric and antiferrodistortive degrees of freedom.
The scheme was applied to study the finite-temperature properties of the Pb(Zr1-xTix)O3 solid solution.

Main Results:

The computational method resolved controversies regarding the monoclinic ground state for specific titanium compositions.
An previously overlooked phase within the Pb(Zr1-xTix)O3 system was discovered.
Three multiphase points, each involving four distinct phases, were identified.

Conclusions:

The developed computational scheme provides new insights into the phase behavior of Pb(Zr1-xTix)O3.
The findings, supported by neutron diffraction data, advance the understanding of ferroelectric materials.
This work clarifies the complex phase diagram near the morphotropic phase boundary, aiding future material design.