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Related Concept Videos

Lattice Energies of Ionic Crystals01:27

Lattice Energies of Ionic Crystals

Lattice energy represents the energy released when gaseous cations and anions combine to form an ionic solid, reflecting the strength of electrostatic interactions within the crystal. This process is fundamentally governed by Coulombic attraction between oppositely charged ions, where the potential energy varies inversely with the interionic distance and directly with the product of ionic charges. As ions approach one another, the electrostatic energy becomes increasingly negative, indicating a...
Measurements of Strain01:27

Measurements of Strain

Strain quantifies the deformation of a material under force, typically measured as normal strain, which represents the change in length when compared with the original length. Electrical strain gauges are used for enhanced accuracy. These devices consist of a conductive wire mounted on a paper backing that adheres to the material's surface. These gauges operate on the piezoresistive effect, where the wire's electrical resistance changes in response to mechanical deformation. The strain gauge...
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Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
Imperfections in Crystal Structure: Stoichiometric Point Defects01:26

Imperfections in Crystal Structure: Stoichiometric Point Defects

Schottky defects arise when some lattice points in a crystal, such as those in NaCl, remain unoccupied, creating lattice vacancies without disturbing the overall electrical neutrality of the crystal. This defect is common in ionic crystals where the positive and negative ions are similar in size, as seen in sodium chloride and cesium chloride. The presence of Schottky defects enables the crystal to conduct electricity to a small extent through an ionic mechanism. Electric fields cause nearby...
X-ray Crystallography02:18

X-ray Crystallography

The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
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Picometer-Precision Atomic Position Tracking through Electron Microscopy
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Quantifying Lattice Strains in Elastically Deformed Covalent Crystals.

Jiayi Li1, Heyi Wang1, Juzheng Chen1

  • 1The University of Hong Kong, Department of Mechanical Engineering, Hong Kong, China.

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|June 26, 2026
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Summary

Researchers observed pure lattice elongation in silicon and diamond, clarifying the origin of their ultralarge elasticity. This finding guides the design of advanced electronic and photonic devices through deep elastic strain engineering.

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Area of Science:

  • Materials Science
  • Solid-State Physics
  • Nanotechnology

Background:

  • Covalent semiconductor crystals like silicon and diamond exhibit ultralarge elastic strains at micro/nanoscales.
  • These properties are crucial for strain-engineered electronic and optoelectronic devices.
  • The origin of this elasticity (lattice displacement vs. atomic rearrangement) is not fully understood.

Purpose of the Study:

  • To directly observe and understand the in situ elastic-lattice response of silicon and diamond under tensile loading.
  • To determine if ultralarge elasticity arises from pure lattice elongation or atomic rearrangements.
  • To establish a quantitative link between macroscopic strain and lattice deformation.

Main Methods:

  • Utilized high-resolution transmission electron microscopy (HRTEM) and four-dimensional scanning transmission electron microscopy (4D-STEM).
  • Performed in situ uniaxial tensile loading on microfabricated single-crystalline silicon and diamond bridges at room temperature.
  • Quantified deep-strained atomic coordinates and mapped elastic lattice strains with sub-pixel precision.

Main Results:

  • Directly observed pure lattice elongation in silicon and diamond under tensile strain.
  • Confirmed the absence of extended defects or phase transformations contributing to the elasticity.
  • Established a quantitative correlation between applied macroscopic strain and the resulting lattice deformation.

Conclusions:

  • Elucidated the fundamental nature of ultralarge elasticity in covalent materials as pure lattice elongation.
  • Provided direct experimental evidence clarifying the origin of elasticity in silicon and diamond.
  • Offers guidelines for designing novel silicon and diamond-based devices with enhanced properties via deep elastic strain engineering.