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Related Concept Videos

¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

2.0K
The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene...
2.0K
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

1.1K
In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must...
1.1K
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

1.2K
Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the...
1.2K
¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

1.4K
A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied...
1.4K
Moment of a Couple: Problem Solving01:30

Moment of a Couple: Problem Solving

1.2K
The moment of couple is an essential concept in physics and engineering, used to calculate the rotational force, or torque, that is created when a couple —two equal and opposite forces—acts on an object.
The moment of a couple is found by multiplying the magnitude of one of the forces by the perpendicular distance between the line of action of the two forces. This creates a twisting force, which can be used to rotate an object. The moment of a couple is used to solve problems...
1.2K
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

1.2K
Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
1.2K

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Related Experiment Video

Updated: Oct 7, 2025

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method
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Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method

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Mode Coupling at around M-Point in PZT.

Sergey Vakhrushev1, Alexey Filimonov2, Konstantin Petroukhno2

  • 1The Ioffe Physical-Technical Institute of the Russian Academy of Sciences, 194021 Saint-Petersburg, Russia.

Materials (Basel, Switzerland)
|January 11, 2022
PubMed
Summary

The microscopic origin of lead zirconate-titanate

Keywords:
antiferrodistortive modemode couplingperovskitessoft mode

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Area of Science:

  • Materials Science
  • Solid-State Physics
  • Crystallography

Background:

  • The M-superstructure and satellite peaks in Zr-rich lead zirconate-titanate (PZT) have been debated for 50 years.
  • Existing theories face contradictions regarding oxygen octahedra rotations or lead cation displacements.
  • Recent findings of an oxygen tilt soft mode in PZT2.4 did not resolve these contradictions.

Purpose of the Study:

  • To investigate the microscopic origin of the M-superstructure in PZT.
  • To resolve the contradiction between critical scattering selection rules and observed superstructure.
  • To understand the role of critical dynamics in PZT phase transitions.

Main Methods:

  • Inelastic X-ray scattering (IXS) study of phonon spectra.
  • Analysis of PZT2.4 around the M-point.
  • Detailed analysis of satellite patterns.

Main Results:

  • A strong coupling between lead and oxygen modes was identified.
  • Mode anticrossing and a wide, flat phonon dispersion curve were observed.
  • This flat dispersion corresponds to mixed lead-oxygen ion displacements, explaining the contradiction.

Conclusions:

  • The observed flat phonon dispersion is a prerequisite for incommensurate phase transitions.
  • Mixed lead-oxygen ion displacements explain the previously contradictory extinction rules.
  • The study provides a new understanding of the M-superstructure's origin in PZT.