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Phase Transitions

Phase Transitions

Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...

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 Transitions: Vaporization and Condensation

Phase Transitions: Vaporization and Condensation

The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase...

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...

Phase Transitions: Melting and Freezing

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...

Phase Transitions: Sublimation and Deposition

Phase Transitions: Sublimation and Deposition

Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and standard pressure, a piece of dry ice (solid CO2) sublimes, appearing to gradually disappear without ever forming any liquid. Snow and ice sublimate at temperatures below the melting point of water, a slow process that may be accelerated by winds and the reduced atmospheric pressures at high altitudes. When solid iodine is warmed, the solid sublimes...

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Related Experiment Video

Updated: Jun 23, 2025

High Resolution Phonon-assisted Quasi-resonance Fluorescence Spectroscopy

High Resolution Phonon-assisted Quasi-resonance Fluorescence Spectroscopy

Published on: June 28, 2016

Prediction of First-Order Phase Transition with Electron-Phonon Interaction.

Mario Graml^1,2, Kurt Hingerl¹

¹Center for Surface- and Nanoanalytics, Johannes Kepler Universität, Altenbergerstr. 69, A-4040 Linz, Austria.

The Journal of Physical Chemistry. C, Nanomaterials and Interfaces

|June 26, 2024

Summary

This summary is machine-generated.

This study reveals electron-phonon interactions drive first-order phase transitions in solids by altering free energies. Incorporating nuclear kinetic energy explains these transitions and their critical temperatures.

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Area of Science:

Condensed Matter Physics
Materials Science
Quantum Mechanics

Background:

Phase transitions in solids are traditionally explained by the balance between binding energies and entropy.
Existing models often do not fully account for quantum mechanical effects on nuclear behavior during transitions.

Purpose of the Study:

To investigate the role of electron-phonon interactions in driving first-order phase transitions in solids.
To incorporate the quantum mechanical kinetic energy of nuclei into theoretical models of phase transitions.
To derive methods for determining critical transition temperatures, latent heat, and nuclear displacement.

Main Methods:

Incorporation of electron-phonon interactions into the system's Hamiltonian.
Application of Bogoliubov's inequality to account for the quantum mechanical kinetic energy operator of the nucleus.
Derivation of an implicit equation for critical temperature and estimation of thermodynamic properties.

Main Results:

Electron-phonon interactions lead to distinct free energies at different temperatures, resulting in first-order phase transitions.
The inclusion of nuclear quantum effects via Bogoliubov's inequality confirms first-order phase transitions.
An equation for critical temperature is implicitly derived, alongside estimations for latent heat and nuclear positional displacement.

Conclusions:

Electron-phonon interactions are crucial for understanding first-order phase transitions, particularly when nuclear quantum effects are considered.
The derived theoretical framework allows for the prediction of transition temperatures and associated physical properties.
This work establishes parameter boundaries for distinguishing between first- and second-order phase transitions.