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Related Concept Videos

Symmetry01:26

Symmetry

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The equation of an ellipse centered at the origin defines all points whose distances from the center maintain a constant ratio between the horizontal and vertical axes. This equation results in a smooth, closed curve that extends further along the x-axis than the y-axis, giving it a horizontal orientation. Such an ellipse demonstrates three kinds of symmetry: across the x-axis, across the y-axis, and about the origin. These symmetries are essential in understanding the graph's structure and...
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The double-stranded structure of DNA has two major advantages. First, it serves as a safe repository of genetic information where one strand serves as the back-up in case the other strand is damaged. Second, the double-helical structure can be wrapped around proteins called histones to form nucleosomes, which can then be tightly wound to form chromosomes. This way, DNA chains up to 2 inches long can be contained within microscopic structures in a cell. A double-stranded break not only damages...
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Range

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The range is one of the measures of variation. It can be defined as the difference between a dataset's highest and lowest values. For example, in the study of seven 16-ounce soda cans, the filled volume of soda was measured, thus producing the following amount (in ounces) of soda:
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Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
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A Fabrication and Measurement Method for a Flexible Ferroelectric Element Based on Van Der Waals Heteroepitaxy
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Long-range symmetry breaking in embedded ferroelectrics.

Hugh Simons1, Astri Bjørnetun Haugen2, Anders Clemen Jakobsen3

  • 1Department of Physics, Technical University of Denmark, Kongens Lyngby, Denmark. husimo@fysik.dtu.dk.

Nature Materials
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Ferroelectric materials

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Area of Science:

  • Materials Science
  • Solid-State Physics
  • Crystallography

Background:

  • Ferroelectric materials exhibit unique properties due to their crystalline symmetry.
  • Extrinsic strain can be introduced to manipulate this symmetry for novel material design.
  • Understanding strain distribution is crucial for predicting ferroelectric behavior.

Purpose of the Study:

  • To investigate the spatial extent and impact of symmetry-breaking strain fields around domain walls and grain boundaries in barium titanate (BaTiO3).
  • To determine if these extrinsic strain fields influence the entire material, leading to universal symmetry breaking.
  • To highlight the importance of considering these strain fields in computational material design.

Main Methods:

  • Utilized in situ dark-field X-ray microscopy to visualize and map lattice distortions.
  • Focused on deeply embedded domain walls and grain boundaries within BaTiO3 samples.
  • Analyzed the spatial extent of strain fields relative to domain widths.

Main Results:

  • Symmetry-breaking strain fields were observed to extend several micrometres from domain walls in BaTiO3.
  • This strain field extent significantly exceeds the average domain width.
  • Consequently, no region within the material remains elastically relaxed, indicating universal symmetry breaking.

Conclusions:

  • Extrinsic strains universally break the symmetry in ferroelectric materials like BaTiO3.
  • These strains are critical for defining local properties and the self-organization of domain walls.
  • Future computational material design approaches must incorporate these extrinsic strain effects for accurate predictions.