Goldschmidt's rule

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The Goldschmidt tolerance factor , named after Victor M. Goldschmidt , states that a complete isomorphism only between such atoms is possible whose ionic radius is no longer differs by 10-15%. The rule was discovered by Goldschmidt in 1926. He found that this can still occur in crystals with a perovskite structure if the condition for the sums of radii is fulfilled in the form with a tolerance factor t = 0.8 ... 1.1. The tolerance factor is therefore also called Goldschmidt's tolerance factor and corresponds to the thermodynamic and structural stability of the material. Below 0.8 an ilmenite or corundum structure is formed. Above 1 the calcite or aragonite structure develops . Chlorides and sulphides tend to have lower values ​​than oxides and fluorides. In 1962, Sleight and Ward extended the rule for more complex perovskites.

The rules of substitution for atoms in crystals found by Goldschmidtsche state:

  1. Elements can substitute for one another if they have the same charge and similar ionic radius.
  2. If the charge is the same, the element with the smaller radius is preferred.
  3. If the radius is the same, the element with the higher charge is preferred.

With the help of these rules it can be predicted that, for example, the trace element rubidium in potassium- rich minerals such as potassium feldspar and mica can substitute for potassium and that chromium and nickel can take the lattice site for magnesium in magnesium- rich minerals such as olivine and the pyroxene . They also explain the substitution of Fe 2+ and Mg 2+ , which can be observed very frequently in nature , such as in the minerals olivine, orthopyroxene , clinopyroxene , garnet and hornblende . All of these minerals form seamless rows of mixed crystals between iron and magnesium-rich end members, because Fe 2+ and Mg 2+ are very similar in their chemical properties. Fe 2+ and Mg 2+ can also be substituted by Mn 2+ , but this occurs to a lesser extent since manganese occurs less frequently.

The findings formulated by Goldschmidt (also called Goldschmidt's law) can be summarized in such a way that the crystal structure of a solid connection is determined by the ratio of number, radii and polarizability of the atoms that make it up.

Individual evidence

  1. ^ VM Goldschmidt: The laws of crystal chemistry . In: The natural sciences . tape 14 , no. 21 , 1926, pp. 477-485 , doi : 10.1007 / BF01507527 .
  2. ^ Will Kleber, Hans-Joachim Bautsch, Joachim Bohm, Detlef Klimm: Introduction to crystallography . Oldenbourg Verlag, 2010, ISBN 978-3-486-59885-8 , pp. 170 ( limited preview in Google Book search).
  3. ↑ Pascal Granger, Vasile I. Parvulescu, Serge Kaliaguine, Wilfrid Prellier: Perovskites and Related Mixed Oxides Concepts and Applications . John Wiley & Sons, 2016, ISBN 978-3-527-33763-7 , pp. 370 ( limited preview in Google Book search).
  4. ↑ George T. Rado, Harry Suhl: Spin Arrangements and Crystal Structure, Domains, and Micromagnetics A Treatise on Modern Theory and Materials . Academic Press, 2013, ISBN 978-1-4832-6832-3 , pp. 5 ( limited preview in Google Book search).
  5. ^ DD Eley: Advances in Catalysis, Volume 36 . Academic Press, 1989, ISBN 978-0-08-056540-8 , pp. 241 ( limited preview in Google Book search).
  6. ^ Richard JD Tilley: Perovskites Structure-Property Relationships . John Wiley & Sons, 2016, ISBN 978-1-118-93563-7 , pp. 6 ( limited preview in Google Book search).
  7. ^ AP Jones, F. Wall, CT Williams: Rare Earth Minerals Chemistry, Origin and Ore Deposits . Springer Science & Business Media, 1995, ISBN 978-0-412-61030-1 , pp. 47 ( limited preview in Google Book search).
  8. ^ A b O. Adrian Pfiffner, Larryn Diamond, Martin Engi, Klaus Mezger: Erdwissenschaften . UTB, 2015, ISBN 978-3-8252-4381-4 , pp. 285 ( limited preview in Google Book search).
  9. ↑ Harrry J. Emeleus, JS Anderson: Results and Problems of Modern Inorganic Chemistry . Springer-Verlag, 1954, ISBN 978-3-642-86628-9 , pp. 77 ( limited preview in Google Book search).