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Related Concept Videos

Internal Energy and Formulation of the First Law01:19

Internal Energy and Formulation of the First Law

In thermodynamics, energy is used to describe and predict the behavior of physical systems. The internal energy (U) of a system is the sum of all microscopic forms of energy within the system, including molecular kinetic and potential energies, as well as contributions from electronic and nuclear energy levels. Although the individual components of internal energy cannot be measured directly, the internal energy of any system is well defined within thermodynamic theory.The first law of...
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Force and Potential Energy in One Dimension

Force can be calculated from the expression for potential energy, which is a function of position. The component of a conservative force, in a particular direction, equals the negative of the derivative of the corresponding potential energy with respect to the displacement in that direction. For regions where potential energy changes rapidly with displacement, the work done and force is maximum. Also, when force is applied along the positive coordinate axis, the potential energy decreases with...
Force and Potential Energy in Three Dimensions01:04

Force and Potential Energy in Three Dimensions

Consider a particle moving under the action of a conservative force that has components along each coordinate axis. Each component of force is a function of the coordinates. The potential energy function U is also a function of all three spatial coordinates. Force in one dimension can be written as the negative ratio of potential energy change to the displacement along that coordinate. For minimal displacement, the ratios become derivatives. If a function has many variables, the derivative only...
Energy Associated With a Charge Distribution01:21

Energy Associated With a Charge Distribution

The work done to bring a charge through a distance r is given by the potential difference between the initial and the final position. To assemble a collection of point charges, the total work done can be expressed in terms of the product of each pair of charges divided by their separation distance, defined with respect to a suitable origin. Solving this expression gives the energy stored in a point charge distribution.
Energy In A Magnetic Field01:24

Energy In A Magnetic Field

If a magnetic field is sustained, there must be a current in a closed circuit or loop, implying some energy has been spent in creating the field. If this energy is not dissipated via the circuit's resistance, it is stored in the field.
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Related Experiment Video

Updated: Jun 25, 2026

Finite Element Modelling of a Cellular Electric Microenvironment
08:23

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

Dislocation core energies and core fields from first principles.

Emmanuel Clouet1, Lisa Ventelon, F Willaime

  • 1CEA, DEN, Service de Recherches de Métallurgie Physique, F-91191 Gif-sur-Yvette, France.

Physical Review Letters
|March 5, 2009
PubMed
Summary
This summary is machine-generated.

Ab initio calculations reveal that screw dislocations in bcc iron create a unique dilatation field. This finding improves elastic modeling of atom displacements and core energy calculations.

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Computational Materials Science

Background:

  • Screw dislocations are fundamental defects in crystalline materials.
  • Understanding dislocation core structures is crucial for predicting material properties.
  • Previous models often simplified the complex atomic interactions at dislocation cores.

Purpose of the Study:

  • To investigate the atomic-scale behavior of a 111 screw dislocation in bcc iron.
  • To model the dislocation core field using anisotropic elastic theory.
  • To improve the accuracy of elastic energy calculations for dislocations.

Main Methods:

  • Performing ab initio calculations to simulate atom displacements.
  • Developing an elastic model incorporating force dipoles to represent the core field.
  • Comparing atom displacements from calculations with elastic modeling predictions.

Main Results:

  • Ab initio calculations identified a short-range dilatation field accompanying the Volterra elastic field.
  • Anisotropic elastic theory with force dipoles accurately reproduced atom displacements.
  • Incorporating the core field accelerated the convergence of elastic energy calculations.

Conclusions:

  • The study successfully modeled the complex core field of a 111 screw dislocation in bcc iron.
  • The refined elastic model provides a more accurate representation of atom displacements.
  • This approach leads to geometry-independent and efficiently computed dislocation core energies.