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Related Concept Videos

Mass Spectrometry: Isotope Effect01:13

Mass Spectrometry: Isotope Effect

Most elements exist in nature as a mixture of isotopes. The isotopes differ in weight due to their respective number of neutrons. The molecular weight of a molecule is different depending on the specific isotope of its elements involved. As a result, the mass spectrum of the molecule exhibits peaks from the same fragment at multiple positions. The positions of these mass signals depend on the mass differences between isotopes. Furthermore, the intensity of these signals is dependent on the...
Nuclear Overhauser Enhancement (NOE)01:06

Nuclear Overhauser Enhancement (NOE)

Irradiation of a spin-active nucleus causes an increase or decrease in the signal intensity of neighboring nuclei that are not necessarily chemically bonded or involved in J-coupling. This phenomenon, called the nuclear Overhauser enhancement (NOE), results from through-space interactions between the nuclear spins. The NOE effect decreases with increasing internuclear distance and is generally not observed beyond 4 angstroms. In NOE, dipole-dipole interactions between neighboring spin-active...
Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
Atomic Radii and Effective Nuclear Charge03:08

Atomic Radii and Effective Nuclear Charge

The elements in groups of the periodic table exhibit similar chemical behavior. This similarity occurs because the members of a group have the same number and distribution of electrons in their valence shells.
Nuclear Binding Energy02:13

Nuclear Binding Energy

The difference between the calculated and experimentally measured masses is known as the mass defect of the atom. In the case of helium-4, the mass defect indicates a “loss” in mass of 4.0331 amu – 4.0026 amu = 0.0305 amu. The loss in mass accompanying the formation of an atom from protons, neutrons, and electrons is due to the conversion of that mass into energy that is evolved as the atom forms. The nuclear binding energy is the energy produced when the atoms’ nucleons are bound together;...
Nuclear Stability03:18

Nuclear Stability

Protons and neutrons, collectively called nucleons, are packed together tightly in a nucleus. With a radius of about 10−15 meters, a nucleus is quite small compared to the radius of the entire atom, which is about 10−10 meters. Nuclei are extremely dense compared to bulk matter, averaging 1.8 × 1014 grams per cubic centimeter. If the earth’s density were equal to the average nuclear density, the earth’s radius would be only about 200 meters.
To hold positively charged protons together in the...

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Related Experiment Video

Updated: May 11, 2026

Neutron Crystallography Data Collection and Processing for Modelling Hydrogen Atoms in Protein Structures
10:10

Neutron Crystallography Data Collection and Processing for Modelling Hydrogen Atoms in Protein Structures

Published on: December 1, 2020

Modeling nuclear volume isotope effects in crystals.

Edwin A Schauble1

  • 1Department of Earth and Space Sciences, University of California, Los Angeles, CA 90095.

Proceedings of the National Academy of Sciences of the United States of America
|May 8, 2013
PubMed
Summary

Mass-independent isotope fractionations, driven by nuclear volume and shape differences, are predicted using density functional theory (DFT-PAW). This method accurately models nuclear volume effects in elements like cadmium and mercury, agreeing with experimental data.

Keywords:
Mössbauer spectroscopymass independent fractionationnuclear field shift

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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Published on: June 7, 2018

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Last Updated: May 11, 2026

Neutron Crystallography Data Collection and Processing for Modelling Hydrogen Atoms in Protein Structures
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Neutron Crystallography Data Collection and Processing for Modelling Hydrogen Atoms in Protein Structures

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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
08:55

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Published on: June 7, 2018

Area of Science:

  • Computational Chemistry
  • Isotope Geochemistry
  • Nuclear Physics

Background:

  • Mass-independent isotope fractionations, influenced by nuclear volume and shape (field shift effect), are observed in various elements.
  • All-electron relativistic calculations predict these effects but are computationally demanding and limited to small systems.
  • Density functional theory with the projector augmented wave method (DFT-PAW) offers a faster alternative, compatible with periodic boundary conditions.

Purpose of the Study:

  • To calibrate DFT-PAW calculations against high-level ab initio methods for estimating nuclear volume isotope effects.
  • To investigate nuclear volume contributions to isotope fractionation in cadmium and mercury systems.
  • To explore the relationship between field shift energies, Mössbauer isomer shifts, and mass-independent fractionations.

Main Methods:

  • Performed DFT-PAW calculations, validated against Dirac-Hartree-Fock and coupled-cluster methods.
  • Calculated nuclear volume contributions to isotope fractionation for cadmium and mercury between vapor and various mineral phases.
  • Related field shift energies to Mössbauer isomer shifts for tin-bearing crystals.

Main Results:

  • DFT-PAW accurately reproduces nuclear electron density changes, crucial for the field shift effect.
  • Calculated Cd and Hg isotope fractionations between vapor and minerals show good agreement with experimental data.
  • Calculations indicate preferential incorporation of neutron-rich isotopes in oxidized, ionically bonded Cd and Hg phases.
  • Mössbauer isomer shift data can simplify mass-independent fractionation calculations for other elements.

Conclusions:

  • DFT-PAW is a viable and efficient method for calculating nuclear volume isotope effects.
  • The study provides quantitative predictions for Cd and Hg isotope fractionation, aiding geochemical interpretations.
  • Mössbauer spectroscopy offers a pathway to predict mass-independent isotope fractionations in elements like Pt and U.