First Edition 19/ 09/ 2004
Second Edition 05/ 3/ 2014
in English/ in Esperanto/ in Portuguese
During crystal growth matter assembles in uniform mode according to one of the seven crystal systems. This uniform mode may occur without any modified orientation, developing a periodical repetition of a structural unit in a single crystal. One can imagine as every new unit cell with its respective origin fits into the crystal phase with the same orientation of any other previously assembled unit cell in the crystal at a distance defined by a whole number times the unit cell parameter along the unit cell referential, respectively. When this kind uniformity occurs from head to tail in the crystal it can be considered that nature built a single crystal, with or without the contribution of a laborer or experimentalist. Single crystals are rare objects. Frequently at common conditions, while assembilng the material on the solid and for some reason part of the material is assembled to the crystal into a new orientation related to a plane named twin plane. On the side of the plane where the new orientation occurs the new twin crystal will form the same chemical phase as the original part with the same density and with the same unit cells fitted now according the new orientation. A crystal object can de formed by several twin crystals each one sharing its structure with its neighbor twin crystal across the twin plane without any problem. On the other hand, when any biological body is shared by more complex living species then additional adaptation problems will demand solution. The chemical environment on the border of the twin plane is different from the bulk environment of any side of the twin plane.
A single crystal close to 0.3 mm of diameter will be selected under a microscope with suitable working distance for x-ray diffraction seeking structural information. As a general criterion, any cavity formed by crystal face planes will indicate a possible twin crystal and a search for another object will be necessary. Cell parameters refinement can be conducted by the data from powder method of x-ray diffraction. In this case twin crystals are acceptable. A secure indication of the existence of a single crystal occurrs when an anisotropic crystal displays a complete extinction when observed under a microscope with crossed polarizers.
The application above represents twin crystals after a click on buttons A, B or C and a single crystal of the same compound after a click on buttons D, E or F. The white circle on the left side of the figure represents the eyepeace view of the object without the analyzer of the crystallographic microscope. The black circle on the other side represents the eyepeace view of the object with crossed polarizers. All the images represent an equal magnification. The image obtained in A or D shows the object at the initial position. Images obtained after a click on buttons B or E shows the object after a rotation of 45o and images on C or D after a next turn of 45o on the circular rotating stage, as indicated by the numbers in red.
The birefringence of the samples on this page is 0.014. One of the objects
is thin, its thickness is 30 micrometers and the other has a thickness
of 50 micrometers.
Exercise
1) Find out and justify which of the samples is thinner: the twin or the single crystal?
2) What can be concluded about the direction of the ordinary ray and extraordinary ray of each sample component related to the rotation angle in red and in relation to the microscope polarizers?
3) Observe isotropic and anisotropic crystals and write a report.
Reference
Klein, C. and Dutrow, B.; Mineral Science, John Wiley & Sons, Inc., 2007.
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