Structure of Solid Matter

  • Harald Ibach
  • Hans Lüth
Part of the Advanced Texts in Physics book series (ADTP)


When atoms are chemically bound to one another they have well-defined equilibrium separations that are determined by the condition that the total energy is minimized. Therefore, in a solid composed of many identical atoms, the minimum energy is obtained only when every atom is in an identical environment. This leads to a three-dimensional periodic arrangement that is known as the crystalline state. The same is true for solids that are composed of more than one type of element. In this case, certain “building blocks” comprising a few atoms are the periodically repeated units. Periodicity gives rise to a number of typical properties of solids. Periodicity also simplifies the theoretical understanding and the formal theory of solids enormously. Although a real solid never possesses exact three-dimensional periodicity, one assumes perfect periodicity as a model and deals with the defects in terms of a perturbation (Sect. 2.7). Three-dimensional periodic arrangements of atoms or “building blocks” are realized in many different ways. Basic elements of the resulting crystal structures are described in Sects. 2.1–2.5.


Free Enthalpy Burger Vector Point Group Mirror Plane Solid Matter 
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Chapter 2

  1. 2.1
    K. Urban, P. Kramer, M. Wilkens: Phys. Bl. 42, 373 (1986)CrossRefGoogle Scholar
  2. 2.2
    T.B. Massalski (ed.): Binary Alloy Phase Diagrams, 2nd edn. (American Society for Metals, Metals Park, Ohio 44073, 1990 )Google Scholar
  3. A database is available under the name TAPP of ES Microwave, 2234 Wade Court, Hamilton, OH 45013, USAGoogle Scholar

Further Reading

  1. Burzlaff, H., Thiele, G. (eds.): Kristallographie — Grundlagen und Anwendungen (Thieme, Stuttgart 1977), insbesondere: Burzlaff, H, Zimmermann, H.: “Symmetrielehre”, Bd. IGoogle Scholar
  2. Hamermesh, M.: Group Theory and Its Application to Physical Problems ( Addison-Wesley/Pergamon, London Paris 1962 )zbMATHGoogle Scholar
  3. Heine, V.: Group Theory in Quantum Mechanics ( Pergamon, London 1960 )zbMATHGoogle Scholar
  4. Koster, G.F., Dimmock, J.O., Wheeler, R.G., Statz, H.: Properties of the 42 Point Groups ( MIT Press, Cambridge, MA 1963 )Google Scholar
  5. Streitwolf, H.: Gruppentheorie in der Festkörperphysik ( Akademische Verlagsges., Leipzig 1967 )zbMATHGoogle Scholar
  6. Tinkham, M.: Group Theory and Quantum Mechanics ( McGraw-Hill, New York 1964 )zbMATHGoogle Scholar
  7. Vainshtein, B.K.: Fundamentals of Crystals: Symmetry and Methods of Structural Crystallography, Springer Ser. Modern Crystallography, Vol. 1 ( Springer, Berlin Heidelberg 1994 )Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Harald Ibach
    • 1
    • 2
  • Hans Lüth
    • 1
    • 2
  1. 1.Institut für Schichten und GrenzflächenForschungszentrum Jülich GmbHJülichGermany
  2. 2.Rheinisch-Westfälische Technische HochschuleAachenGermany

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