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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 Spin State Overview01:03

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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 one, the...
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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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Paramagnetism01:30

Paramagnetism

3.0K
Paramagnets are materials with unpaired electrons that possess a finite magnetic moment. In the absence of a magnetic field, these moments are randomly oriented, and thus the net moment is zero. Under an external field, a torque acting on the moments tends to align them along the field's direction. However, the random thermal motion of electrons produces a torque opposite to the external field and tries to disorient the moments. These two competing effects align only a few moments along the...
3.0K
Atomic Nuclei: Types of Nuclear Relaxation01:28

Atomic Nuclei: Types of Nuclear Relaxation

1.0K
Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
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Valence Bond Theory02:42

Valence Bond Theory

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Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
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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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Eigenstate-specific temperatures in two-level paramagnetic spin lattices.

Mark B Masthay1, Calley N Eads2, Amber N Johnson1

  • 1Department of Chemistry, University of Dayton, 300 College Park, Dayton, Ohio 45469-2357, USA.

The Journal of Chemical Physics
|December 10, 2017
PubMed
Summary
This summary is machine-generated.

Eigenstate-specific temperatures (ESTs) are derived for paramagnetic spin lattices. While not true thermodynamic temperatures for small systems, ESTs serve as valuable estimators, especially for nanothermometers.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Quantum Systems

Background:

  • Growing interest in thermodynamics of small/isolated systems.
  • Recent observations of negative temperatures in ultracold optical lattices.
  • Need for estimating conventional temperature (Tc^conv) using eigenstate-specific temperatures (ESTs).

Purpose of the Study:

  • Derive four distinct ESTs for two-level paramagnetic spin lattices (PSLs).
  • Analyze the behavior of ESTs for small (N < 1000) and large N.
  • Assess the validity of ESTs as thermodynamic temperatures and their potential applications.

Main Methods:

  • Derivation of continuous and discrete canonical/microcanonical ESTs for PSLs.
  • Analysis of ESTs' intensity, deviation from Tc^conv, and adherence to thermodynamic laws.
  • Investigation of thermodynamic uncertainty relation and sign conventions of ESTs.

Main Results:

  • For large N, ESTs are intensive, equal Tc^conv, and obey thermodynamic laws.
  • For N < 1000, ESTs are non-intensive, differ from Tc^conv, and violate thermodynamic laws.
  • ESTs are not true thermodynamic temperatures but serve as good estimators for small PSLs.

Conclusions:

  • ESTs exhibit unique energy dependencies, quantifying deviations from Tc^conv.
  • Thermodynamic uncertainty relation is obeyed only by small canonical PSLs.
  • ESTs have potential applications in nanothermometry and systems with long-range interactions.