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Related Concept Videos

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...
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 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...
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Trends in Lattice Energy: Ion Size and Charge

An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
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Atomic Spectroscopy: Effects of Temperature

Atomization, converting samples into gas-phase atoms and ions, is essential for atomic spectroscopy. The flame temperature required for atomization affects the efficiency of the atomic spectroscopic methods by increasing the atomization efficiency and the relative population of the excited and ground states.
At thermal equilibrium, the relative populations of excited and ground state atoms can be estimated using the Maxwell–Boltzmann distribution. For example, an increase in temperature from...

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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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Coulomb phase diagnostics as a function of temperature, interaction range, and disorder.

Arnab Sen1, R Moessner, S L Sondhi

  • 1Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany.

Physical Review Letters
|March 26, 2013
PubMed
Summary

We developed a theory explaining pinch points in spin ice, revealing how their shape indicates monopole interaction strengths and resolves experimental observations at high temperatures.

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Area of Science:

  • Condensed Matter Physics
  • Magnetism
  • Statistical Mechanics

Background:

  • Spin ice materials exhibit a Coulomb phase characterized by emergent gauge fields.
  • Pinch points in the spin structure factor (S) are experimental signatures of these gauge fields.
  • Understanding the behavior of pinch points under various conditions is crucial for characterizing spin ice physics.

Purpose of the Study:

  • To develop a comprehensive theory for the behavior of pinch points in spin ice.
  • To investigate the influence of temperature, spin types, interaction ranges, and disorder on pinch points.
  • To establish a method for determining the relative strengths of entropic and magnetic Coulomb interactions of monopoles.

Main Methods:

  • Theoretical modeling of the spin structure factor (S) in reciprocal space.
  • Analysis of pinch point features under varying physical conditions (temperature, spin properties, interactions, disorder).
  • Comparison of theoretical predictions with experimental observations in materials like Ho(1.7)Y(0.3)Ti(2)O(7).

Main Results:

  • The theory successfully describes the fate of pinch points across different temperatures and material parameters.
  • The detailed shape of pinch points provides a quantitative measure of monopole interaction energies.
  • The theory explains the high-temperature observation of pinch points in disordered spin ice.

Conclusions:

  • Pinch point analysis is a powerful tool for probing the fundamental interactions in spin ice.
  • The developed theory offers a unified framework for understanding diverse experimental observations in spin ice.
  • This work clarifies the role of emergent gauge fields and monopole interactions in spin ice thermodynamics.