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Position and Displacement Vectors01:00

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To describe the motion of an object, one should first be able to describe its position (where it is at any particular time). More precisely, the position needs to be specified relative to a convenient frame of reference. A frame of reference is an arbitrary set of axes from which the position and motion of an object are described. Earth is often used as a frame of reference to describe the position of an object in relation to stationary objects on Earth.
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The position of an object defines its location relative to a convenient frame of reference at any particular time. A frame of reference is an arbitrary set of axes from which the position and motion of an object are described. Earth is often used as a frame of reference, and we often describe the position of an object as it relates to stationary objects on Earth. For example, a rocket launch could be described in terms of the position of the rocket with respect to Earth as a whole. On the other...
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Ampère's law, in its usual form, does not work in places where the current changes with time and is not steady. Thus, Maxwell suggested including an additional contribution, called the displacement current, Id, to the real conduction current I.
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A displacement current is analogous to a real current in Ampère's law, participating in Ampère's law the same way as the usual conduction current. However, it is produced by a changing electric field. Displacement current is defined in terms of a time-varying electric field, and also has an associated displacement current density. By adding a term accounting for displacement current, Maxwell modified the existing Ampère's law, which is now called generalized Ampère's law.
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The atomic anisotropic displacement tensor – completing the picture.

Gunnar Thorkildsen1, Helge B Larsen1

  • 1Department of Mathematics and Natural Science, University of Stavanger, N-4036 Stavanger, Norway.

Acta Crystallographica. Section A, Foundations and Advances
|July 2, 2015
PubMed
Summary

A simplified method for calculating the equivalent isotropic displacement parameter (EDP) is introduced. This approach analyzes tensor properties under point-group operations, providing essential data for crystallographic symmetry analysis.

Keywords:
anisotropic displacement tensorequivalent isotropic displacement parametersite-symmetry restrictionstransformations among tensor representations

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Area of Science:

  • Crystallography
  • Solid-state physics
  • Materials science

Background:

  • The accurate determination of atomic displacement parameters is crucial in crystallography.
  • Understanding site symmetry is fundamental for interpreting crystal structures.
  • Existing methods for calculating equivalent isotropic displacement parameters can be complex.

Purpose of the Study:

  • To present a simplified approach for calculating the equivalent isotropic displacement parameter (EDP).
  • To analyze the transformation properties of the tensor representation U under point-group operations.
  • To compile comprehensive tables of symmetry restrictions for crystallographic tensors.

Main Methods:

  • Development of a simplified calculation method for EDP.
  • Analysis of the transformation of the U tensor under point-group operations.
  • Compilation of tables based on site symmetry and special positions from International Tables for Crystallography.

Main Results:

  • A simplified procedure for calculating EDP has been established.
  • The transformation properties of the U tensor concerning point-group operations are elucidated.
  • Complete tables detailing symmetry-imposed restrictions on the U tensor for all special positions are provided.

Conclusions:

  • The presented simplified approach facilitates the calculation of EDP.
  • The analysis of tensor transformation properties enhances understanding of crystallographic symmetry.
  • The compiled tables serve as a valuable resource for crystallographers studying site symmetry effects.