Chapter 7
The Crystalline Solid—Dislocations
Since time out of mind, the continuous re-emerging forms of crystals have occupied
the thoughts of mankind—be it that their constantly new, self-generating, unchangeable structural order in the domain of the microscopes gives them the aura of eternity,
or that their valuable mechanical properties lay hidden in these regularities. In 1912,
M. v. Laue made a decisive contribution in the decoding of the basic principles of
this order with his famous diffraction experiments. The atoms (or groups of atoms)
of an ideal crystal are thus arranged in a periodical, infinite, three-dimensional space
lattice in such a manner, that one can always distinguish a group of atoms whose
continuous translation in three different independent directions could lead to a continuously expanding crystal, see Fig. 7.1. Here, we examine only monocrystalline
structures, not polycrystals made up of many single crystals. Independent of this,
every real crystal that can thus only have a finite expansion must principally differ
from the ideal symmetry alone by its boundaries.
If one sends X -rays through such a crystal whose wavelength is about as large as
the distance between two lattice planes, the well-known Laue diagrams are produced.
With the help of these diagrams, we can calculate the structure of the lattice, see
Fig. 7.2.
Crystallography deals with the mathematically possible details and arrangements
of lattice structures. For our purposes, it will be sufficient to use a simple cubic lattice.
Even the properties of this lattice will be made of restricted use in the passing to the
limit to the continuum mechanics. In fact, here we only need a modelled extension
of our observed linear chain in three-dimensional space.
A very important fact when dealing with lattices is that we are dealing with two
completely different possible mechanical kinds of motion not including the third
possible kind of motion, the motion of the complete lattice as a rigid solid, which
does not interest us.
© The Editor(s) (if applicable) and The Author(s), under exclusive
license to Springer Nature Singapore Pte Ltd. 2020
H. Günther, Elementary Approach to Special Relativity,
https://doi.org/10.1007/978-981-15-3168-2_7
57
The Crystalline Solid—Dislocations
Since time out of mind, the continuous re-emerging forms of crystals have occupied
the thoughts of mankind—be it that their constantly new, self-generating, unchangeable structural order in the domain of the microscopes gives them the aura of eternity,
or that their valuable mechanical properties lay hidden in these regularities. In 1912,
M. v. Laue made a decisive contribution in the decoding of the basic principles of
this order with his famous diffraction experiments. The atoms (or groups of atoms)
of an ideal crystal are thus arranged in a periodical, infinite, three-dimensional space
lattice in such a manner, that one can always distinguish a group of atoms whose
continuous translation in three different independent directions could lead to a continuously expanding crystal, see Fig. 7.1. Here, we examine only monocrystalline
structures, not polycrystals made up of many single crystals. Independent of this,
every real crystal that can thus only have a finite expansion must principally differ
from the ideal symmetry alone by its boundaries.
If one sends X -rays through such a crystal whose wavelength is about as large as
the distance between two lattice planes, the well-known Laue diagrams are produced.
With the help of these diagrams, we can calculate the structure of the lattice, see
Fig. 7.2.
Crystallography deals with the mathematically possible details and arrangements
of lattice structures. For our purposes, it will be sufficient to use a simple cubic lattice.
Even the properties of this lattice will be made of restricted use in the passing to the
limit to the continuum mechanics. In fact, here we only need a modelled extension
of our observed linear chain in three-dimensional space.
A very important fact when dealing with lattices is that we are dealing with two
completely different possible mechanical kinds of motion not including the third
possible kind of motion, the motion of the complete lattice as a rigid solid, which
does not interest us.
© The Editor(s) (if applicable) and The Author(s), under exclusive
license to Springer Nature Singapore Pte Ltd. 2020
H. Günther, Elementary Approach to Special Relativity,
https://doi.org/10.1007/978-981-15-3168-2_7
57