THE DISTORTION OF A CRYSTAL BY POINT IMPERFECTIONS

Abstract

The distortion of a crystal lattice is discussed form the standpoint of calculations using the elastic displacement appropriate to a center of dilatation in an infinite medium. This displacement gives a nonzero stress at the surface of the solid. The treatment shows the necessity for additional image displacement in certain applications to insure that this stress vanishes. In particular, if image displacement is omitted the volume change due to one or more point singularities can be underestimated by a factor of 1.5 for metals or 1.8 for alkali halides. If the effects of the free boundary are ignored, any nonspherical body uniformly filled with point singularities would suffer a change of shape as well a change of size. When the boundary effect is considered, there is a change of volume without change of shape. Moreover, for this case, a calculation of the change of x-ray lattice constant gives a result consistent with the geometrical deformation only if the image displacements are included.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1953
Accession Number
AD0018045

Entities

People

  • J. D. Eshelby

Organizations

  • University of Illinois Urbana–Champaign

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Bodies
  • Boundaries
  • Bulk Modulus
  • Crystal Lattices
  • Crystal Structure
  • Crystals
  • Diffraction
  • Displacement
  • Distortion
  • Elastic Properties
  • Equations
  • Materials
  • Measurement
  • Navy
  • Shear Modulus
  • X Rays
  • X-Ray Diffraction

Readers

  • Electromagnetic Wave Scattering and Antenna Radiation Engineering
  • Mechanical Engineering/Mechanics of Materials.
  • Theoretical Analysis.