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Trends in Lattice Energy: Ion Size and Charge02:54

Trends in Lattice Energy: Ion Size and Charge

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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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The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
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A stationary charge creates and interacts with the electric field, while a moving charge creates a magnetic field.
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Imagine a bucket of water. It contains many molecules, of the order of 1026 molecules. Thus, although it contains discrete elements (molecules) at the microscopic level, macroscopically, it can be considered continuous. Small volume elements of water, infinitesimal compared to the bulk of the bucket's volume, still contain many molecules. Under this framework, quantized matter is approximated as continuous for practical purposes.
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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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A charged particle experiences a force when moving through a magnetic field. Consider the field to be uniform and the charged particle to move perpendicular to it. If the field is in a vacuum, the magnetic field is the dominant factor determining the motion. Since the magnetic force is perpendicular to the direction of motion, a charged particle follows a curved path. The particle continues to follow this curved path until it forms a complete circle. Another way to look at this is that the...
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Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light
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Localization and persistent currents in a quasiperiodic disordered helical lattice.

Taylan Yildiz1, B Tanatar2

  • 1Department of Physics, Bilkent University, 06800, Ankara, Türkiye.

Scientific Reports
|October 24, 2025
PubMed
Summary
This summary is machine-generated.

We explored how magnetic fluxes and disorder affect electron behavior in a special lattice. We found that these factors control whether the material conducts electricity or acts as an insulator.

Keywords:
Helical latticeLocalizationPersistent currentQuasiperiodic disorder

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Area of Science:

  • Condensed Matter Physics
  • Quantum Materials
  • Disordered Systems

Background:

  • Understanding electron localization and persistent currents is crucial for designing novel electronic devices.
  • Helical lattices with quasiperiodic potentials and magnetic fluxes present complex quantum phenomena.

Purpose of the Study:

  • To investigate the interplay of disorder, magnetic fluxes, and quasiperiodic potentials on electron localization and persistent currents.
  • To map the phase diagram separating extended, mixed, and localized electronic regimes.
  • To explore the control over conductive and insulating states.

Main Methods:

  • Exact diagonalization of a helical tight-binding lattice model.
  • Analysis of localization using inverse participation ratio (IPR) and normalized participation ratio (NPR).
  • Calculation of persistent currents in toroidal and poloidal directions.

Main Results:

  • Identified distinct electronic regimes (extended, mixed, localized) based on potential strength and inter-ring coupling.
  • Observed decaying oscillations in persistent currents with increasing disorder in the metallic regime, vanishing at the localization threshold.
  • Demonstrated flux-insensitivity of currents in the localized regime.
  • Showed that magnetic fluxes, hopping, and potential amplitudes tune the critical disorder threshold.

Conclusions:

  • Tuning system parameters offers control over the transition between conductive and insulating states.
  • The helical lattice serves as a versatile platform for disorder- and flux-controlled electronic switching.
  • Results provide insights into quantum transport in complex disordered systems.