Introduction to Dislocations

Derek Hull, D. J. Bacon

• Publisher: Butterworth-Heinemann
• Year: 2011
• ISBN:
  9780080966731
• Edition: 5
• Topic: Technology & Engineering
• Subtopic: Mechanical Engineering
• Index: Technology & Engineering

In materials science, dislocations are irregularities within the crystal structure or atomic scale of engineering materials, such as metals, semi-conductors, polymers, and composites. Discussing this specific aspect of materials science and engineering, Introduction to Dislocations is a key resource for students. The book provides students and practitioners with the fundamental principles required to understand dislocations. Comprised of 10 chapters, the text includes advanced computer modeling and very high-resolution electron microscopy to help readers better understand the structure of atoms close to the core of dislocations. It shows that atomic arrangement has a significant effect on the formation of dislocations and thereby on the properties of solids. The first two chapters of the book present an overview of dislocations. The crystal structures and the various defects and dislocations are discussed, and methods of observation and diagnosis of dislocations are covered. Chapters 3 to 5 discuss the behavior of dislocations and explain how changes in the structure and arrangement of atoms can affect the behavior of dislocations. The three chapters also discuss the mechanical properties of dislocations. The remaining chapters offer a detailed discussion of the mechanisms of dislocations and the mechanical strength of crystalline solids. The book is written for undergraduate- and graduate-level students in both materials science and mechanical engineering. Non-experts and novices working on mechanical properties, mechanisms of deformation and fracture, and properties of materials, as well as industrial and academic researchers, will find this book invaluable.

• Long-established academic reference by an expert author team, highly regarded for their contributions to the field.
• Uses minimal mathematics to present theory and applications in a detailed yet easy-to-read manner, making this an understandable introduction to a complex topic.
• Unlike the main competition, this new edition includes recent developments in the subject and up-to-date references to further reading and research sources.

Chapter 1. Defects in Crystals

1.1. Crystalline Materials

Dislocations are an important class of defect in crystalline solids and so an elementary understanding of crystallinity is required before dislocations can be introduced. Metals and many important classes of non-metallic solids are crystalline, i.e. the constituent atoms are arranged in a pattern that repeats itself periodically in three dimensions. The actual arrangement of the atoms is described by the crystal structure. The crystal structures of most pure metals are relatively simple: the three most common are the body-centered cubic, face-centered cubic and close-packed hexagonal, and are described in section 1.2. In contrast, the structures of alloys and non-metallic compounds are often complex.

The arrangement of atoms in a crystal can be described with respect to a three-dimensional net formed by three sets of straight, parallel lines as in Fig. 1.1(a). The lines divide space into equal sized parallelepipeds and the points at the intersection of the lines define a space lattice. Every point of a space lattice has identical surroundings. Each parallelepiped is called a unit cell and the crystal is constructed by stacking identical unit cells face to face in perfect alignment in three dimensions. By placing a motif unit of one or more atoms at every lattice site the regular structure of a perfect crystal is obtained.

Figure 1.1 (a) A space lattice, (b) unit cell showing positions of principal axes.

The positions of the planes, directions and point sites in a lattice are described by reference to the unit cell and the three principal axes, x, y and z (Fig. 1.1(b)). The cell dimensions OA=a, OB=b and OC=c are the lattice parameters, and these along with the angles

,

and

completely define the size and shape of the cell. For simplicity the discussion here will be restricted to cubic and hexagonal crystal structures. In cubic crystals a=b=c and α=β=γ=90°, and the definition of planes and directions is straightforward. In hexagonal crystals it is convenient to use a different approach, and this is described in section 1.2.

Any plane A′B′C′ in Fig. 1.2 can be defined by the intercepts OA′, OB′ and OC′ with the three principal axes. The usual notation (Miller indices) is to take the reciprocals of the ratios of the intercepts to the corresponding unit cell dimensions. Thus A′B′C′ is represented by

Figure 1.2 Cubic cell illustrating method of describing the orientation of planes.

and the numbers are then reduced to the three smallest integers in these ratios.

Thus from Fig. 1.2OA′=2a, OB′=3a, and OC′=3a, the reciprocal intercepts are

and so the Miller indices of the A′B′C′ plane are (322). Curved brackets are used for planes. A plane with intercepts OA, OB, and OC has Miller indices

or, more simply, (111). Similarly, a plane DFBA in Fig. 1.3 is

Figure 1.3 Cubic cell illustrating the method of describing directions and point sites. LM is parallel to OE.

or (110); a plane DEGA is

or (100); and a plane AB′C′ in Fig. 1.2 is

or (311). In determining the indices of any plane it is most convenient to identify the plane of lattice points parallel to the plane which is closest to the origin O and intersects the principal axis close to the origin. Thus plane A″B′C′ in Fig. 1.2 is parallel to ABC and it is clear that the indices are (111). Using this approach it will be seen that the planes ABC, ABE, CEA and CEB in Fig. 1.3 are (111),

,

and

respectively. The minus sign above an index indicates that the plane cuts the axis on the negative side of the origin. In a cubic crystal structure, these planes constitute a group of the same crystallographic type and are described collectively by {111}.

Any direction LM in Fig. ...