Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

The Phase Rule01:20

The Phase Rule

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,...
Phase Transitions02:31

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 occupy...
Phase Transitions01:21

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 Transitions: Melting and Freezing02:39

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 Diagrams of Ternary Systems01:28

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 Transitions: Sublimation and Deposition02:33

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...

You might also read

Related Articles

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

Sort by
Same author

Introduction to the magnetic structures special issue.

Acta crystallographica Section B, Structural science, crystal engineering and materials·2025
Same author

Small-angle rigid-unit modes requiring linear strain compensation.

Acta crystallographica. Section A, Foundations and advances·2024
Same author

Chiral multiferroicity in two-dimensional hybrid organic-inorganic perovskites.

Nature communications·2024
Same author

Computational Screening and Stabilization of Boron-Substituted Type-I and Type-II Carbon Clathrates.

Journal of the American Chemical Society·2023
Same author

Electron Spin Decoherence Dynamics in Magnetic Manganese Hybrid Organic-Inorganic Crystals: The Effect of Lattice Dimensionality.

Journal of the American Chemical Society·2023
Same author

Enumeration and tabulation of magnetic (3+d)-dimensional superspace groups.

Acta crystallographica. Section A, Foundations and advances·2022

Related Experiment Video

Updated: Jul 14, 2026

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
08:55

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

Published on: June 7, 2018

Order parameters for phase transitions to structures with one-dimensional incommensurate modulations.

Harold T Stokes1, Branton J Campbell, Dorian M Hatch

  • 1Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA. stokesh@byu.edu

Acta Crystallographica. Section A, Foundations of Crystallography
|June 16, 2007
PubMed
Summary

This study details order parameters for incommensurate structural modulations in crystalline solids. It provides a comprehensive group-theoretical analysis of superspace groups and their isotropy subgroups for these phenomena.

More Related Videos

Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets
06:26

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

Published on: May 15, 2017

High-Contrast and Fast Photorheological Switching of a Twist-Bend Nematic Liquid Crystal
06:24

High-Contrast and Fast Photorheological Switching of a Twist-Bend Nematic Liquid Crystal

Published on: October 31, 2019

Related Experiment Videos

Last Updated: Jul 14, 2026

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
08:55

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

Published on: June 7, 2018

Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets
06:26

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

Published on: May 15, 2017

High-Contrast and Fast Photorheological Switching of a Twist-Bend Nematic Liquid Crystal
06:24

High-Contrast and Fast Photorheological Switching of a Twist-Bend Nematic Liquid Crystal

Published on: October 31, 2019

Area of Science:

  • Solid-state physics and materials science.
  • Crystallography and group theory.

Background:

  • Phase transitions leading to incommensurate structural modulations are common in crystalline solids.
  • These modulations impact magnetic, electronic, optical, and structural properties of materials.
  • Existing tables cover superspace-group symmetries for 1D modulations, but order parameters remain underexplored.

Purpose of the Study:

  • To systematically enumerate order parameters responsible for incommensurate structural modulations.
  • To provide a comprehensive group-theoretical framework for understanding these order parameters.
  • To connect theoretical findings to experimentally observed modulated structures.

Main Methods:

  • Utilized group-theoretical methods for analysis.
  • Performed an exhaustive enumeration of isotropy subgroups.
  • Investigated irreducible representations of (3+1)-dimensional superspace groups.

Main Results:

  • Presented a unique and exhaustive list of isotropy subgroups and their order-parameter directions.
  • Covered all incommensurate k points for the 230 crystallographic space groups.
  • Demonstrated that most observed incommensurate structures align with these derived order parameters.

Conclusions:

  • The study provides a complete theoretical basis for order parameters in incommensurately modulated structures.
  • This work is crucial for understanding and predicting the behavior of diverse functional materials.
  • The findings offer a valuable resource for experimentalists and theorists in condensed matter physics.