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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 Diagram01:19

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 Diagram01:24

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 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 Diagrams02:39

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...
Solid–Solid Solutions01:24

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.

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Phase Diagram Characterization Using Magnetic Beads as Liquid Carriers
12:37

Phase Diagram Characterization Using Magnetic Beads as Liquid Carriers

Published on: September 4, 2015

Geometry of phase separation.

Alberto Sicilia1, Yoann Sarrazin, Jeferson J Arenzon

  • 1Université Pierre et Marie Curie-Paris VI, LPTHE UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
PubMed
Summary
This summary is machine-generated.

This study analyzes domain geometry in binary mixtures during spinodal decomposition. We found that domain area distributions lack a cutoff, with large structures retaining initial morphologies and small ones becoming spherical.

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Area of Science:

  • Materials Science
  • Statistical Physics
  • Complex Systems

Background:

  • Spinodal decomposition is a fundamental process in materials science, describing the phase separation of unstable mixtures.
  • Understanding domain geometry, including area and perimeter distributions, is crucial for predicting material properties.
  • Existing theories, like Lifshitz-Slyozov-Wagner, primarily address minority phase structures and specific concentration limits.

Purpose of the Study:

  • To investigate the domain geometry during spinodal decomposition in a 50:50 binary mixture in two dimensions.
  • To derive approximate analytic results for the distributions of domain areas and perimeters.
  • To compare these distributions with existing theories and validate them using simulations.

Main Methods:

  • Developed approximate analytic methods by treating domain interfaces as moving independently.
  • Extended arguments from nonconserved coarsening dynamics to the conserved case.
  • Validated theoretical predictions using Monte Carlo simulations of the two-dimensional Ising model.

Main Results:

  • Derived a first-order approximation for domain area and perimeter distributions.
  • Found that domain area distributions in a 50:50 mixture do not exhibit a cutoff, unlike minority phase distributions.
  • Identified distinct scaling behaviors for large (cA-tau tail) and small (A1/2 scaling) domains, with a transition at A ~ t2/3.

Conclusions:

  • The study provides a novel analytic framework for understanding domain geometry in conserved spinodal decomposition.
  • Results indicate that large domains retain initial morphologies, while small domains evolve towards spherical shapes.
  • The findings offer valuable insights into the dynamics of phase separation and structure formation in binary mixtures.