58
7 The Crystalline Solid—Dislocations
Fig. 7.1 Continuous
re-emerging structures in a
crystal lattice
1. The first mechanical form of motion has already been discussed in detail. Elastic waves that transport mechanical energy through a solid (for example, the energy
of a hammer blow after I hit the end of a rod). Here, we can also say that signals
are transmitted through a solid with the sound velocity. It is of no importance that
we have only examined a one-dimensional lattice, the rod. The mathematical situation for three-dimensional lattices is more complicated (in fact generally far more
complicated) and results in a complicated system of directional and polarisational
dependent sound velocities.
1 However, nothing changes our fundamental physical
statement concerning the signal transmission with one of the sound velocities. In the
appendix, Chap. 25, we will discuss the simplest cases of a three- dimensional lattice
and continuum. Physically, this mechanical kind of motion of the lattice is generally
defined by the term elastic deformation. An atom takes a position inside of the elastically deformed crystal, from which it then moves back to its original lattice position
after the reason for the elastic deformation has been removed, see Figs. 7.4 and 7.5.
It is characteristic for an elastic deformation to completely disappear when the cause
for the deformation is removed. There are static and dynamic elastic deformations.
2. We have also made day-to-day experiences with the second mechanical kind of
motion. We bend a wire, roll a metal sheet, make a dent in a car, forge iron, stretch,
hammer, engrave, chisel, etc. The physical superimposed concept for this mechanical
kind of motion of atoms in a solid is plastic deformation. We can thus note:
1 We understand the direction of the oscillating vector s of an elastic displacement in comparison to
the direction of propagation k of the wave by polarisation. One speaks of longitudinal waves, when
s and k oscillate parallel to each other and one speaks of transversal waves when s and k oscillate
orthogonal to each other.
7 The Crystalline Solid—Dislocations
Fig. 7.1 Continuous
re-emerging structures in a
crystal lattice
1. The first mechanical form of motion has already been discussed in detail. Elastic waves that transport mechanical energy through a solid (for example, the energy
of a hammer blow after I hit the end of a rod). Here, we can also say that signals
are transmitted through a solid with the sound velocity. It is of no importance that
we have only examined a one-dimensional lattice, the rod. The mathematical situation for three-dimensional lattices is more complicated (in fact generally far more
complicated) and results in a complicated system of directional and polarisational
dependent sound velocities.
1 However, nothing changes our fundamental physical
statement concerning the signal transmission with one of the sound velocities. In the
appendix, Chap. 25, we will discuss the simplest cases of a three- dimensional lattice
and continuum. Physically, this mechanical kind of motion of the lattice is generally
defined by the term elastic deformation. An atom takes a position inside of the elastically deformed crystal, from which it then moves back to its original lattice position
after the reason for the elastic deformation has been removed, see Figs. 7.4 and 7.5.
It is characteristic for an elastic deformation to completely disappear when the cause
for the deformation is removed. There are static and dynamic elastic deformations.
2. We have also made day-to-day experiences with the second mechanical kind of
motion. We bend a wire, roll a metal sheet, make a dent in a car, forge iron, stretch,
hammer, engrave, chisel, etc. The physical superimposed concept for this mechanical
kind of motion of atoms in a solid is plastic deformation. We can thus note:
1 We understand the direction of the oscillating vector s of an elastic displacement in comparison to
the direction of propagation k of the wave by polarisation. One speaks of longitudinal waves, when
s and k oscillate parallel to each other and one speaks of transversal waves when s and k oscillate
orthogonal to each other.