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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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Gauss's Law: Cylindrical Symmetry01:20

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A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
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Gauss's Law in Dielectrics01:17

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Consider a polar dielectric placed in an external field. In such a dielectric, opposite charges on adjacent dipoles neutralize each other, such that the net charge within the dielectric is zero. When a polar dielectric is inserted in between the capacitor plates, an electric field is generated due to the presence of net charges near the edge of the dielectric and the metal plates interface. Since the external electrical field merely aligns the dipoles, the dielectric as a whole is neutral. An...
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Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

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A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
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Bewley Lattice Diagram01:12

Bewley Lattice Diagram

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The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
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Electrostatic Boundary Conditions01:16

Electrostatic Boundary Conditions

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Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
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Related Experiment Video

Updated: Jul 16, 2025

1,3,5-Triphenylbenzene and Corannulene as Electron Receptors for Lithium Solvated Electron Solutions
06:56

1,3,5-Triphenylbenzene and Corannulene as Electron Receptors for Lithium Solvated Electron Solutions

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Cosmological Lithium Solution from Discrete Gauged B-L.

Seth Koren1

  • 1Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA.

Physical Review Letters
|September 18, 2023
PubMed
Summary
This summary is machine-generated.

The cosmological lithium problem is addressed by a new physics model involving cosmic strings. These strings may have altered primordial lithium abundance after the Big Bang nucleosynthesis.

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Area of Science:

  • Cosmology
  • Particle Physics
  • Nuclear Astrophysics

Background:

  • The cosmological lithium problem highlights a significant discrepancy between predicted and observed primordial lithium abundances.
  • Decades of research by cosmologists, nuclear physicists, and astronomers have failed to resolve this issue within the standard model.

Purpose of the Study:

  • To propose a novel new physics mechanism that can explain the observed lithium abundance.
  • To investigate the role of cosmic strings in modifying primordial lithium nuclei after Big Bang nucleosynthesis.

Main Methods:

  • Revisiting the cosmological lithium problem within an extended standard model featuring gauged baryon minus lepton number.
  • Analyzing spontaneous symmetry breaking via a scalar with charge six, leading to cosmic string formation.
  • Investigating a Callan-Rubakov effect analog involving an electric-magnetic interplay on cosmic strings to amplify proton-to-positron conversion.

Main Results:

  • Cosmic strings can support interactions converting three protons into three positrons.
  • An amplified, strong-scale cross section for this conversion process is proposed.
  • It is suggested that cosmic strings disintegrated a significant fraction of primordial lithium nuclei.

Conclusions:

  • This study presents the first new physics mechanism with microphysical justification for post-Big Bang nucleosynthesis modification of lithium abundance.
  • The proposed cosmic string interactions offer a potential solution to the cosmological lithium problem.
  • Further investigation is required to confirm the viability of this scheme.