The Goniometer

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The Goniometer
Rise and Fall of the Most Powerful
Crystallographic Instrument of the 18th and 19th
Century
Olaf Medenbach Institut für Geologie, Mineralogie
und Geophysik Ruhr-Universität Bochum Germany
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• Nicholas Steno
• (1636-1686)
• Danish scientist
• later pontifax of the Roman Catholic Church in
  Italy
• postulated the law of the constancy of
  interfacial angles in 1669

Quartz, Germany
Quartz, Namibia
Quartz, Italy
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• Jean-Baptiste L.
• Romé de l'Isle
• (1736 - 1790)
• French mineralogist
• compiled and described in 1772 all crystal forms
  hitherto known
• his student Arnould Carangeot invented the first
  contact goniometer for exact measurements of
  crystal angles, and thus made mineralogy a
  quantitative science

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Contact goniometer with detachable slotted
blades Stoe, Heidelberg, Germany, 1900
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cubic
abc abg90
Fluorite Tennessee/USA
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• René Just Haüy
• (1743 - 1822)
• Frech mineralogist
• postulated that crystals are composed by a close
  stacking of parallelepipeds ("molécules
  intégrantes", unit cells in modern parlance)

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Traité de minéralogie, 1801
Garnet, Canada
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• René Just Haüy
• (1743 - 1822)
• this explained that angles between crystal faces
  are not arbitrary but can be derived from the
  "molécule intégrante" by mathematic calculations
• law of rational indices

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• William Hyde
• Wollaston
• (1766 - 1828)
• British mineralogist
• invented the first optical reflecting goniometer
  in 1809

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Wollaston-type goniometer axis of rotation
oriented horizontally
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Combinations of trapezohedron 211 and
dodecahedron 110
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Wollaston goniometer with Degen's mirror
attachment French, unsigned, 1870
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• Eilhard Mitscherlich
• (1794 - 1863)
• German analytical chemist and chrystallographer

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Wollaston-Mitscherlich-type goniometer axis of
rotation oriented horizontally

• Mitscherlich applied optical telescopes with a
  signal (e.g. crosshairs) for increased precision

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Wollaston-Mitscherlich goniometer Meyerstein,
Göttingen, Germany, 1870
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Isomorphism

• Apatite Ca5 (P O4)3?Cl
• Pyromorphite Pb5 (P O4)3?Cl
• Mimetite Pb5 (As O4)3?Cl
• Vanadinite Pb5 (V O4)3?Cl

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Polymorphism

• Rutile TiO2 tetragonal P42
• Anatase TiO2 tetragonal amd
• Brookite TiO2 o'rhombic Pbca

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Wollaston-Mitscherlich goniometer Jünger,
Copenhagen, Denmark, 1878
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Malus-Babinet-type goniometer axis of rotation
oriented vertically
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Malus-Babinet goniometer Breithaupt, Kassel,
Germany, 1872
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• Quebec
• longitude 7112' W ?
• latitude 4649' N f

Two circle contact goniometer after
Goldschmidt Stoe, Heidelberg, Germany, 1900
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Two circle "theodolite-goniometer" Fuess,
Berlin, Germany, 1900
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Two circle "theodolite-goniometer" after
Goldschmidt Stoe, Heidelberg, Germany, 1900
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• Victor Mordechai
• Goldschmidt
• (1853 - 1933)
• German crystallographer
• published the 9 volume Atlas der
  Kristallformen, the most comprehensive work on
  crystal morphology
• designed the Goldschmidt two-circle goniometer
  fabricated by Peter Stoe in Heidelberg

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Gnomonic projection of the crystal forms of
calcite Goldschmidt, 1886
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• Epoch-making discoveries made
• through goniometry
• Steno-de l'Isle law of the constancy of
  interfacial angles
• Crystal symmetry the seven crystal systems
• Hauy's law of rational indices
• Isomorphism and polymorphism by Mitscherlich

Concept of crystals as three-dimensional periodic
arrays of unit cells with a certain chemical
composition Crystal Structure
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• Max von Laue
• (1879 - 1960)
• German physicist (Nobel Prize in 1914)
• showed in 1912 by one single genius experiment,
  that
• x-rays are an electromagnetic radiation
• crystals are composed of a three-dimensional
  periodic array of atoms, the crystal lattice

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Emerald, Columbia
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Goniometers

• . They are irreplaceable witnesses to
  cultural history and the history of the science
  of mineralogy and crystallography. In these
  specialized instruments the perfection of craft
  of the precision machinist and optician was
  combined with a large measure of esthetic
  sensibility.
• Burchard, 1998

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Malus-Babinet goniometer Dubosque, Paris,
France, 1870
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Contact goniometer, French, unsigned, 1830
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Two circle "theodolite-goniometer" after
Goldschmidt Stoe, Heidelberg, Germany, 1900
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Two circle "theodolite-goniometer" after
Goldschmidt Stoe, Heidelberg, Germany, 1900
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Malus-Babinet goniometer Fuess, Berlin, Germany,
1880
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tetragonal
ab?c abg90
Zirkon Russland
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trigonal
a1a2a3 abg ? 90
Dioptas Namibia
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hexagonal
a1a2a3 ab90, g120
Vanadinit, Marokko
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rhombisch
a ? b ? c abg90
Topas Ural/Russland
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monoklin
a ? b ? c ag90, b ?90
Gips Sizilien/Italien
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triklin
a ? b ? c a ? b ? g ?90
Rhodonit, Australien
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• NaCl - Steinsalz
• Die Elementarzelle hat eine Kantenlänge von
• 5,6 Å (0,00000000056 m)
• 4.000.000 Atome müssen aneinandergereiht werden
  um 1 mm Kantenlänge zu produzieren

Steinsalz, Fulda
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