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Phase Transitions: Melting and Freezing

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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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Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms. The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. The atoms within such a metallic solid are held together by a unique force known as metallic bonding that gives rise to many useful and varied bulk properties.
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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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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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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...
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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...
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Solidification of ternary melts with a two-phase layer.

L V Toropova1,2, A A Ivanov3, S I Osipov4

  • 1Laboratory of Mathematical Modeling of Physical and Chemical Processes in Multiphase Media, Department of Theoretical and Mathematical Physics, Ural Federal University, Ekaterinburg 620000, Russia.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|July 12, 2022
PubMed
Summary

This study models nonstationary solidification in three-component systems with two moving phase transition layers. Initial impurity concentration significantly impacts the two-phase layer lengths, influencing solidification dynamics.

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Area of Science:

  • Materials Science
  • Chemical Engineering
  • Thermodynamics

Background:

  • Solidification processes are crucial in materials science and engineering.
  • Understanding multi-component systems presents unique challenges.
  • Nonstationary and multi-phase solidification requires advanced modeling.

Purpose of the Study:

  • To develop and analyze a model for nonstationary solidification in three-component systems.
  • To investigate the influence of two moving phase transition regions.
  • To determine analytical solutions for temperature, concentration, and phase fraction distributions.

Main Methods:

  • Development of a non-linear moving boundary problem.
  • Analytical solution of the defined problem.
  • Theoretical consideration of a non-linear liquidus surface equation.

Main Results:

  • Defined analytical solutions for temperature and impurity concentration distributions.
  • Determined solid phase fractions within the phase transition regions.
  • Established the laws of motion for the boundaries of the main and cotectic layers.
  • Observed significant impact of initial impurity concentration on the ratio of two-phase layer lengths.

Conclusions:

  • The developed model accurately describes nonstationary solidification in complex systems.
  • Initial impurity concentration is a critical factor controlling solidification structure.
  • Analytical solutions provide valuable insights into phase transition dynamics.