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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 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...

States of Matter

States of Matter

Solids, liquids, and gases are the three states of matter commonly found on Earth. A solid is rigid and possesses a definite shape. A liquid flows and takes the shape of its container, except it forms a flat or slightly curved upper surface when acted upon by gravity. Both liquid and solid samples have volumes nearly independent of pressure. A gas takes both the shape and volume of its container.
Scientists have discovered a fourth state of matter, plasma, that occurs naturally in the interiors...

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 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

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Phase Behavior of Charged Vesicles Under Symmetric and Asymmetric Solution Conditions Monitored with Fluorescence Microscopy

Phase Behavior of Charged Vesicles Under Symmetric and Asymmetric Solution Conditions Monitored with Fluorescence Microscopy

Published on: October 24, 2017

Quarter-filled supersolid and solid phases in the extended Bose-Hubbard model.

Kwai-Kong Ng¹, Y C Chen, Y C Tzeng

¹Department of Physics, Tunghai University, Taichung 40704, Taiwan.

Journal of Physics. Condensed Matter : an Institute of Physics Journal

|March 12, 2011

Summary

We numerically studied the Bose-Hubbard model, finding a stable supersolid phase. Competition between solid phases leads to a first-order phase transition, revealing key insights into quantum materials.

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Area of Science:

Condensed Matter Physics
Quantum Many-Body Systems

Background:

The two-dimensional hard-core Bose-Hubbard model describes interacting bosons on a lattice.
Understanding its phase diagram is crucial for designing quantum devices.

Purpose of the Study:

Investigate the ground state phase diagram of the Bose-Hubbard model with nearest- and next-nearest-neighbor interactions.
Identify and characterize supersolid and solid phases at quarter filling.

Main Methods:

Numerical simulations using canonical and grand canonical quantum Monte Carlo (QMC) methods.
Complementary analysis with mean-field calculations.

Main Results:

Evidence for a commensurate supersolid phase.
Identification of two distinct solid phases and one stable supersolid phase.
Observation of a first-order phase transition between solid phases driven by interaction parameters (2V(2) ~ V(1)).

Conclusions:

The study confirms the existence of a stable supersolid phase in the investigated model.
The competition between different ordering tendencies dictates the phase transitions.
Detailed characterization of phase transitions and order parameter behavior provides valuable data for quantum simulations.