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contact goniometer
contact goniometer


Wollaston goniometer

Wollaston goniometer


Mitscherlich type goniometer

Mitscherlich type goniometer


horizontal circle reflecting goniometer

horizontal circle reflecting goniometer


two-circle contact goniometer

two-circle contact goniometer



 
Goniometers


Introduction
Already in 1669 Niels Stensen proved the constancy of interplanar angles in quartz crystals. Still it took more than a century before it was recognized that this property holds for all crystal species and not just for quartz crystals. It was Jean Baptiste Louis de Romé de l’Isle (1736-1790) who generalized this fundamental law of crystallography that is presently known as "Steno's law".

Actually this property was incidentally discovered by de l'Isle's assistant, Arnould Carrangeot, in the course of making terra cotta models of the crystals in de l'Isle's collection. For this purpose in 1780 he developed a simple instrument to measure the angles between crystal faces. The instrument that became known under the names of "application goniometer" or "contact goniometer" was nothing more than two limbs connected by a joint. The limbs could be applied to two adjacent crystal faces and eventually the angle between the limbs could be measured. The accuracy of the contact goniometer was about 15' at best.

In 1809 Wollaston developed an optical goniometer where the reflection of light was used to exactly position a set of crystal planes belonging to one crystallographic zone. For this purpose the crystal was mounted on a rotatable horizontal axis. This axis was connected to a graduated circle. The crystal was positioned such that a zone axis (and as such the edge between two adjacent crystal faces belonging to that zone) was parallel to the rotation axis of the graduated circle. Upon rotation of the circle, the crystal faces to be measured reflected the light from a source located at long distance, at specific angular positions. As such the angle between the normals to the respective crystal faces could be measured. With this instrument, known as the "Wollaston goniometer" or "Wollaston reflecting goniometer", accuracies down to 5' could be obtained.

Later, a mirror was added to improve the positioning of the reflections from the crystal faces. This could also be accomplished by means of a low powered observation telescope and measurements down to accuracy of 1' could be made.
In 1843 Mitscherlich introduced a high precision goniometer with a vertical circle and a telescope that was firmly attached to the base of the instrument; a variety of Mitscherlich-type goniometers of increasing complexity were produced over the years.
In the Virtual Museum Wollaston- and Mitscherlich-type goniometers are classified under the grouping "vertical circle goniometers".

In 1839 Babinet introduced a new type of goniometer equipped with two telescopes, one serving as a collimator for the light source and the other containing the reference. The Babinet goniometer could therefore be used in any orientation.
The instrument became known as the "horizontal circle goniometer". Horizontal circle instruments typically attained an accuracy of 30". This kind of instruments was put on the market by firms like Fuess (Berlin) and Troughton and Simms (London).
An advantage of the horizontal circle was an improved attachment of the crystal. In vertical circle instruments heavy crystals could easily move from their position and spoil the measurement.

The main drawback of single circle instruments was that they could only measure the faces of one zone at a time. To measure the faces of another zone, the crystal had to be detached, remounted and measured again and this process had to be repeated several times in order to obtain a complete measurement of the whole crystal.
The English crystallographer W.H. Miller was the first, in 1874, to use a goniometer with two circles and thus overcoming the problem of remounting the crystal over and over again. The original posthumous publication of 1882 apparently attracted little attention and his method was rediscovered independently by Fedorov (1889), Goldschmidt (1893) and Czapski (1893). The principle of these instruments was that the crystal was mounted on an axis that was at his turn mounted on another axis perpendicular to the first one. As such the position of several crystal faces could be measured one after the other and the angular positions (phi and rho) plotted on a Wulff net. These instruments were called "two-circle goniometers", "theodolite goniometers", "Goldschmidt goniometers".

To overcome certain indexing problems three circle instruments were developed at the end of the 19th century. Because they were very expensive and complicated to adjust, they only found very limited use.
In 1896, Goldschmidt also invented a two-circle contact goniometer. This instrument was suited to measure larger crystals than with the equivalent optical goniometer.

After 1900 the development of the goniometer slowed down, mainly because x-ray-diffraction made his entrée in crystallography. In the first half of the 20th century some major improvements to goniometers were still made by Terpstra in the Netherlands and Codd and Moore in England. Today goniometers are definitively moved to the gallery of historical instruments as witnesses of the historical development of mineralogy and crystallography. Therefore the Virtual Museum also holds some of these 20th century instruments in its collection.


References
  • Burchard, U. (1998) History and Development of the Crystallographic Goniometer, The Mineralogical Record, 29, 517-583.
  • Leiss, C. (1899) Die optischen Instrumente der Firma R. Fuess, Leipzig
  • Medenbach, O., Mirwald, P.W. and Kubath, P. (1995) Rho und Phi, Omega und Delta – Die Winkelmessung in der Mineralogie, Mineralien Welt, 6 (5), 16-25.
  • Stoe & Cie. (1929) Mineralogische Instrumente, Heidelberg
  • Terpstra, P. and Codd, L.W. (1961) Crystallometry, Groningen
  • Tutton, A.E.H. (1911) Crystallography and Practical Crystal Measurement, London