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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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Size-Dependent Permittivity for Alumina Powders.

Tien-Fu Yang1, Hsien-Wen Chao1, Bo-Wie Tseng2

  • 1Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan.

Nanomaterials (Basel, Switzerland)
|April 13, 2026
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Summary

The study shows that smaller alumina powder sizes increase dielectric constant and loss tangent. This size-dependent permittivity can be used to engineer composite materials for applications like stealth technology.

Keywords:
dielectric measurementhybrid modelpermittivity enhancementpermittivity manipulationsurface-charge effect

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Area of Science:

  • Materials Science
  • Electrical Engineering
  • Physics

Background:

  • Alumina is a widely used ceramic with desirable electrical and thermal properties.
  • The size effect of powdery materials is critical for composite material development in electronic devices.
  • Understanding the dielectric properties of alumina powders is essential for advanced applications.

Purpose of the Study:

  • To measure and analyze the size-dependent dielectric properties of alumina powders.
  • To introduce and validate the field-enhancement method (FEM) for characterizing powder permittivity.
  • To explore the relationship between alumina powder size and its complex permittivity.

Main Methods:

  • Utilized the field-enhancement method (FEM) to measure resonant frequency (f0) and quality factor (Q) of packed alumina powders.
  • Employed contour mapping and high-frequency structure simulation (HFSS) to determine effective complex permittivity.
  • Retrieved complex permittivity using a hybrid model and effective medium theories (EMTs), comparing with the Landau-Lifshitz-Looyenga (LLL) model.

Main Results:

  • The dielectric constant and loss tangent of alumina powder increase as particle size decreases.
  • A power relation was established to describe permittivity across nano- to micrometer sizes.
  • A surface-charge scaling argument was proposed to explain the observed size effect.

Conclusions:

  • Alumina powder permittivity is strongly dependent on particle size, particularly at smaller scales.
  • The findings enable new methods for manipulating permittivity in composite materials.
  • Potential applications include stealth/absorber technology and controlling grain growth during sintering.