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Introduction to Structural Chemistry pp 329–356Cite as

Crystal Structure: Real

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Abstract

An ideal crystal is thought of as an infinite repetition of an elementary unit cell in three dimensions, described by the crystal lattice. The real structure of even a good-quality crystal is far from this ideal picture; the periodicity is perturbed by thermal motion of atoms, static disorder (local or ‘global’) in the arrangement of atoms, chemical impurities and/or violations of stoichiometry of the main component, and defects of various types. Thermal motion is discussed in relation to thermal expansion (normal and negative) and melting of solids, which occurs (according to Lindemann’s hypothesis) when the amplitude reaches certain critical fraction (L-factor) of interatomic distances. A similar approach can be extended to boiling. Defects are classified according to their dimensionality: point (vacancy or interstitial atom), linear (edge or screw dislocation), planar (e.g. phase boundary) and bulk (e.g. voids) and type (Frenkel or Shottky). High concentration of defects created by shock compression, can affect the symmetry of crystals. All defects tend to depress and blur the melting point, as illustrated by nano-materials.

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Authors and Affiliations

  1. Institute of Structural Macrokinetics and Materials Science, Russian Academy of Sciences, Academician Osipyan str. 8, 142432, Chernogolovka, Moscow Region, Russia

    Prof. Stepan S. Batsanov

  2. Chemistry Department, Durham University, Science Site, South Road, DH1 3LE, Durham, United Kingdom

    Andrei S. Batsanov Ph.D.

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  1. Prof. Stepan S. Batsanov
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Correspondence to Stepan S. Batsanov .

Appendices

Appendix

6.1.1 Supplementary Tables

Table S6.1 Critical factors for the threshold of melting in metals, according to Lindemann (δL) and Batsanov (δB). [6.1]
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Table S6.2 Experimental values of sound velocity at melting and boiling points (c m and c b in m/s), evaporation heats (ΔН v in kJ/g), coordination numbers of atoms in melts and critical amplitudes of atomic vibrations (as fractions of the bond lengths) at boiling temperatures
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Table S6.3 Experimental atomization energies (kJ/mol), the negative pressures of rupture (GPa), the increase of volume V R/V o and the maximum amplitude of vibrations of atoms at the rupture pressure, δ P
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Table S6.4 Thermal energy (kJ/mol) and the maximum amplitude of atomic vibrations at boiling points
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Table S6.5 Minimum sizes of crystallites (D min), further reduction of which results in amorphization
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Supplementary References

  • 6.1 Batsanov SS (2009) Russ J Phys Chem 83:1836

  • 6.2 Boivineau M, Arlès L, Vermeulen JM, Thévenin T (1993) Intern J Thermophysics 14:427

  • 6.3 Boivineau M, Arlès L, Vermeulen JM, Thévenin T (1993) Physica B190:31

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Batsanov, S., Batsanov, A. (2012). Crystal Structure: Real. In: Introduction to Structural Chemistry. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4771-5_6

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