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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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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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The earth's gravitational field produces a 'twisting force' perpendicular to the angular momentum of a spinning mass (such as a spinning top) that causes the mass to 'wobble' around the gravitational field axis in a phenomenon called precession. Similarly, the magnetic moment (μ) of a spinning nucleus precesses due to an external magnetic field directed along the z-axis. The precession of the magnetic moment vector about the magnetic field is called Larmor precession,...
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The number of nuclear spins aligned in the lower energy state is slightly greater than those in the higher energy state. In the presence of an external magnetic field, as the spins precess at the Larmor frequency, the excess population results in a net magnetization oriented along the z axis. When a pulse or a short burst of radio waves at the Larmor frequency is applied along the x axis, the coupling of frequencies causes resonance and flips the nuclear spins of the excess population from the...
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An applied magnetic field causes loosely bound π-electrons in organic molecules to circulate, producing a local or induced diamagnetic field over a large spatial volume. As the molecules tumble in solution, the field generated by π-electrons in spherical substituents results in a zero net field. However, the net field generated by π-electrons in non-spherical substituents is not zero. The effect of this induced field depends on the orientation of the molecule with respect to B0,...
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The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
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Updated: Jan 16, 2026

Sample Preparation and Experimental Design for In Situ Multi-Beam Transmission Electron Microscopy Irradiation Experiments
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Collective Rotation Mode in Lattice Migration under Electron Irradiation.

Jiajian Guan1,2, Wuxin Yang1, Richard F Webster3

  • 1Department of Chemical and Materials Engineering, University of Auckland, Auckland 1010, New Zealand.

Nano Letters
|January 15, 2026
PubMed
Summary
This summary is machine-generated.

Nanoparticles rotate and merge due to transient thermal spikes from electron beams. This collective rotation mechanism, driven by asymmetric temperature gradients, explains nanocrystal migration and coalescence under irradiation.

Keywords:
electron-beam irradiationin situ TEMlattice rotationnanoparticlethermal spike

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Area of Science:

  • Materials Science
  • Nanotechnology
  • Surface Science

Background:

  • Atomic migration dynamics are key for nanomaterial synthesis and modification.
  • A universal nanoscale rotation mode is observed during annealing and electron-beam irradiation.
  • The activation and driving forces of this rotation mode, especially under electron irradiation, are poorly understood.

Purpose of the Study:

  • To elucidate the collective rotation mechanism of nanoparticles under electron irradiation.
  • To understand how this rotation drives nanoparticle migration and coalescence.
  • To identify the fundamental origins of the observed rotation behavior.

Main Methods:

  • In situ transmission electron microscopy (TEM) to observe nanoparticle behavior.
  • Molecular dynamics (MD) simulations to model atomic interactions.
  • Small-strain theory to analyze mechanical behavior.

Main Results:

  • A collective rotation mechanism induced by transient thermal spikes under electron irradiation was identified.
  • Platinum (Pt) and AuPt nanoparticles coalesced into larger islands with coherent {111} twin structures via nonrandom lattice rotation.
  • Asymmetric temperature gradients were demonstrated as the fundamental cause of the rotation behavior.

Conclusions:

  • Transient thermal spikes under electron irradiation induce collective nanoparticle rotation.
  • This rotation mechanism drives nanoparticle coalescence into specific twin structures.
  • Asymmetric temperature gradients are the fundamental drivers of electron-beam-induced nanocrystal migration and rotation.