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Related Concept Videos

Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

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Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
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Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

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In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.
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Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

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NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of...
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Atomic Nuclei: Nuclear Magnetic Moment00:59

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All atomic nuclei are positively charged. When they have a nonzero spin, they behave like rotating charges. As a consequence of their charge and spin, these nuclei generate a magnetic field (B). This, in turn, gives rise to a magnetic moment (μ), which is randomly oriented in the absence of an external magnetic field. When an external magnetic field (B0) is applied, the magnetic moment vectors can align with the field or against it in 2 + 1 orientations. A hydrogen nucleus, which is just a...
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In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...
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Recrystallization: Solid–Solution Equilibria01:10

Recrystallization: Solid–Solution Equilibria

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Recrystallization is a purification technique used to separate impurities from solid compounds. In this technique, no chemical reactions occur. Instead, it exploits physical properties only, specifically, the solubility differences between the desired compound and impurities, either at a single temperature or at different temperatures, and under other selected conditions. The solid-solution equilibrium (solubility equilibrium) of each component in the solution represents a binary phase...
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Heterogeneous nucleation in the random field Ising model.

Liheng Yao1, Robert L Jack1,2

  • 1DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.

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|December 27, 2023
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Summary
This summary is machine-generated.

We studied how new phases form in a disordered Ising model. We found that nucleus size alone isn't enough to predict formation rates, requiring a new location-aware coordinate for better accuracy.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Computational Physics

Background:

  • The Ising model is a fundamental tool for understanding magnetism and phase transitions.
  • Nucleation dynamics describe the initial formation of a new phase within a metastable one.
  • Disorder and external fields significantly influence phase transition behavior.

Purpose of the Study:

  • To investigate the nucleation dynamics of the three-dimensional random field Ising model.
  • To determine appropriate reaction coordinates for nucleation in disordered systems.
  • To directly estimate nucleation rates and compare them with free energy barrier predictions.

Main Methods:

  • Umbrella sampling was employed to calculate the free-energy cost of critical nucleus formation.
  • Forward flux sampling was utilized for direct estimation of nucleation rates.
  • A novel reaction coordinate incorporating nucleus location was developed and tested.

Main Results:

  • Nucleus size is an inadequate reaction coordinate for moderate to strong disorder, unlike in the pure Ising model.
  • The new location-aware coordinate improves the prediction of nucleation rates.
  • Deviations between predicted and estimated rates increase with disorder, attributed to cluster shape fluctuations.

Conclusions:

  • The study introduces a more accurate method for describing nucleation in disordered systems.
  • Understanding nucleation dynamics is crucial for predicting material properties and phase transitions.
  • Finite-size effects on nucleation rates in the random field Ising model warrant further investigation.