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Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

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Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
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Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
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Consider a ternary system, which is composed of three components: water (W), ethanoic acid (E), and trichloromethane (T). Here, Ethanoic acid (E) is fully miscible with both water (W) and trichloromethane (T), meaning it can mix entirely with either of them. However, water and trichloromethane have partial miscibility, meaning they can only mix to a certain extent, beyond which two separate phases will form.The phase diagram of a ternary system is represented as an equilateral triangle, where...
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Ionic crystals consist of two or more different kinds of ions that usually have different sizes. The packing of these ions into a crystal structure is more complex than the packing of metal atoms that are the same size.
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Related Experiment Video

Updated: Mar 27, 2026

Visualizing Uniaxial-strain Manipulation of Antiferromagnetic Domains in Fe1+YTe Using a Spin-polarized Scanning Tunneling Microscope
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Are Multiphase Competition and Order by Disorder the Keys to Understanding Yb(2)Ti(2)O(7)?

L D C Jaubert1, Owen Benton1, Jeffrey G Rau2

  • 1Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan.

Physical Review Letters
|January 15, 2016
PubMed
Summary

Magnetic frustration in Yb(2)Ti(2)O(7) leads to exotic behaviors. Thermal and quantum fluctuations drive multiple phase transitions, explaining material variability and offering insights into rare-earth pyrochlores.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Magnetism

Background:

  • Magnetic frustration often disrupts long-range magnetic order, as seen in spin liquids.
  • Understanding mechanisms that overcome frustration is key to discovering novel collective behaviors.

Purpose of the Study:

  • Investigate a minimal model capturing mechanisms relevant to the quantum spin ice candidate Yb(2)Ti(2)O(7).
  • Explain the expansion of a U(1) manifold stability against a splayed ferromagnetic state.

Main Methods:

  • Utilized a realistic minimal model.
  • Employed a range of numerical techniques.
  • Analyzed thermal and quantum fluctuations with order-by-disorder selection.

Main Results:

  • Demonstrated how fluctuations expand the U(1) manifold stability.
  • Observed multiple phase transitions, mirroring experimental findings in Yb(2)Ti(2)O(7).
  • Provided evidence linking multiphase competition to sample-to-sample variability.

Conclusions:

  • Multiphase competition is a key factor in the variability of Yb(2)Ti(2)O(7).
  • This study illuminates the role of chemical pressure in rare-earth pyrochlores.
  • The findings offer a path to understanding the intrinsic properties of Yb(2)Ti(2)O(7).