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Amir C. Akhavan's Photo Gallery

Relation between symmetry and crystallographic forms in quartz - Video 3

This is one of several videos that demonstrate how the symmetry of the trigonal trapezohedral class 32 determines which crystallographic forms are possible for quartz.

For a background on what this video shows, also read the caption of https://www.mindat.org/photo-864301.html

Description of Video 3

The video shows how the shape of a crystallographic form and the position of the faces on a quartz crystal change with the direction of the face pole. The pole is shown as a red vector pointing upwards, along the c axis, at the beginning of the video. During the video, the pole is rotated around the a2 axis (the blue axis pointing to the right).

According to the symmetry of class 32, two kinds of symmetry operations are applied to that vector:
a. twofold (180°) rotation around each of the three horizontal a axes (blue)
b. threefold (120°) rotation around the vertical c axis (red-orange)

While the vector rotates, the following crystallographic forms can be observed:
1. basal pinacoid
2. positive rhombohedron
3. hexagonal prism
4. negative rhombohedron
5. basal pinacoid

The video starts with the last of the 7 basic crystallographic forms, the basal pinacoid, on open form that will cut into the tips at the opposite ends of the crystal and that is only rarely found in nature. Flat rhombohedra follow and slowly grade into steeper rhombohedral forms and finally the hexagonal prism. As the vector proceeds downward the rhombohedral faces switch their positions and turn from positive to negative rhombohedra. A similar switch occurs when the vector passes through the c-axis direction.

For clarity the planes of the crystallographic form to the left have been confined to a cylindrical area - in theory the basal pinacoidal form would extend to infinity.

Copyright: © Amir Akhavan      Photo ID: 864334     Uploaded by: Amir C. Akhavan   View Count: 11   Approval status: User gallery    Type: Video - 0 min 44 sec - 1280 x 768 pixels (1.0 Mpix)

Relation between symmetry and crystallographic forms in quartz - Video 2

This is one of several videos that demonstrate how the symmetry of the trigonal trapezohedral class 32 determines which crystallographic forms are possible for quartz.

For a background on what this video shows, also read the caption of https://www.mindat.org/photo-864301.html

Description of Video 2
The video shows how the shape of a crystallographic form and the position of the faces on a quartz crystal change with the direction of the face pole. The pole is shown as a red vector pointing to the right, along the a2 axis, at the beginning of the video. During the video, the pole is rotated around the c axis, while maintaining its horizontal orientation.
According to the symmetry of class 32, two kinds of symmetry operations are applied to that vector:
a. twofold (180°) rotation around each of the three horizontal a axes (blue)
b. threefold (120°) rotation around the vertical c axis (red-orange)

The crystallographic form that is the result of the symmetry operation is shown to the left, it is a body with six faces.
While the vector rotates, the following crystallographic forms can be observed during the first 120°:
1. trigonal prism (2. order)
2. ditrigonal prism (2. order)
3. hexagonal prism
4. ditrigonal prism (1. order)
5. trigonal prism (1. order)
6. ditrigonal prism (1. order)
7. hexagonal prism
8. ditrigonal prism (2. order)

This pattern then repeats two more times before the vector arrives at its initial position.
The term order reflects the position of the forms relative to the axes (axis a1 points to the lower left, a2 to the right, and a3 backwards).
In addition to the forms shown in video 1, these three basic crystallographic forms can be observed:
4. trigonal prism
5. ditrigonal prism
6. hexagonal prism

The forms are "open forms", they will extend vertically to infinity. I have cut them open to show the geometry of their cross sections.
They are also all "special forms", as the vector is always perpendicular to the c axis. It is noteworth that there are only 2 trigonal prisms and only 1 hexagonal prism (the only form in class 32 with hexagonal symmetry). The ditrigonal prism does apparently not occur on quartz. Judging from some photos on Mindat, the ditrigonal prism seems to occur on selenium.
Copyright: © Amir Akhavan      Photo ID: 864304     Uploaded by: Amir C. Akhavan   View Count: 13   Approval status: User gallery    Type: Video - 0 min 44 sec - 1280 x 768 pixels (1.0 Mpix)

Relation between symmetry and crystallographic forms in quartz - Video 1

This is one of several videos that demonstrate how the symmetry of the trigonal trapezohedral class 32 determines which crystallographic forms are possible for quartz.

Crystal Faces and Crystallographic Forms
Crystal faces correspond to planes that cut through the crystal lattice in a specific direction. If the crystal lattice possesses certain symmetry elements (like mirror or rotational symmetry), there will be two or more equivalent planes that cut through the lattice in different directions.
A crystallographic form is a geometric body that is made of a set of equivalent crystal faces. To construct a crystallographic form, one starts with a single plane and applies the symmetry operations that characterize the lattice to it, for example, by reflecting it at a mirror plane or rotating it around an axis. The crystallographic form is then obtained by combining the resulting planes.

It is much easier to compute and visualize these symmetry operations when they are applied to the poles of the planes, which are vectors that point in a direction perpendicular to the plane.

Description of Video 1
The video shows how the shape of a crystallographic form and the position of the faces on a quartz crystal change with the direction of the face pole. The pole is shown as a red vector pointing to the upper right at the beginning of the video. During the video, the pole is rotated around the c axis.
According to the symmetry of class 32, two kinds of symmetry operations are applied to that vector:
a. twofold (180°) rotation around each of the three horizontal a axes (blue)
b. threefold (120°) rotation around the vertical c axis (red-orange)

The crystallographic form that is the result of the symmetry operation is shown to the left, it is a body with six faces.
While the vector rotates, the following crystallographic forms can be observed during the first 120°:
1. trigonal bipyramid (2. order)
2. right negative trigonal trapezohedron
3. negative rhombohedron
4. left negative trigonal trapezohedron
5. trigonal bipyramid (1. order)
6. right positive trigonal trapezohedron
7. positive rhombohedron
8. left positive trigonal trapezohedron

This pattern then repeats two more times before the vector arrives at its initial position.
The terms left, right, positive, negative and order reflect the position of the forms relative to the axes (axis a1 points to the lower left, a2 to the right, and a3 backwards).
Three basic crystallographic forms can be observed:
1. trigonal bipyramid
2. rhombohedron
3. trigonal trapezohedron
The trigonal bipyramid and rhomboderon are called "special forms" and occur only when the component of the pole vector coincides with or points perpendicular to a symmetry axis. In all other cases a trigonal trapezohedron is observed, which is the "general form" of the trigonal trapezohedral crystal class. In total 7 basic types of forms can be distinguished in this class.
Copyright: © Amir Akhavan      Photo ID: 864301     Uploaded by: Amir C. Akhavan   View Count: 13   Approval status: User gallery    Type: Video - 0 min 44 sec - 1280 x 768 pixels (1.0 Mpix)

Y93-W41Samsonite : Ag4MnSb2S6

Samson Mine, St Andreasberg, St Andreasberg District, Harz, Lower Saxony, Germany

Dimensions: 50 mm

Large samsonite specimen from Grube Samson, St. Andreasberg. Collection Mineralogical Museum University Bonn.
Width of the specimen is approximately 5 cm. Photographed at Mineralien Hamburg 2015.
Copyright: © Amir Akhavan      Photo ID: 864017     Uploaded by: Amir C. Akhavan   View Count: 29   Approval status: Public galleries    Type: Photo - 6688 x 5120 pixels (34.2 Mpix)

Blue John art objects

Blue John Mine, Castleton, Derbyshire, England, UK

Various goblets, bowls and an egg made of Blue John.
Collection of Elizabeth and David Hacker.
Photo done at a special exhibition at Mineralien Hamburg 2014.
Copyright: © Amir Akhavan      Photo ID: 863568     Uploaded by: Amir C. Akhavan   View Count: 21   Approval status: User gallery    Type: Photo - 4928 x 5760 pixels (28.4 Mpix)

WQU-9KVCrocoite : PbCrO4

Callenberg, Glauchau, Saxony, Germany

Dimensions: 200 mm x 150 mm

Crocoite from Callenberg (probably Callenberg-Nord 1).
Size of the specimen about 200x150mm.
Ex. collection Leonhardt.
Photo taken at the Mineralien Hamburg show 2015.
Copyright: © Amir Akhavan      Photo ID: 863538     Uploaded by: Amir C. Akhavan   View Count: 23   Approval status: Public galleries    Type: Photo - 7072 x 5152 pixels (36.4 Mpix)

T3G-UCJWavellite : Al3(PO4)2(OH)3·5H2O

Altmannsgrün, Plauen, Vogtland, Saxony, Germany

Dimensions: 120 mm

Radially grown wavellite from Altmannsgrün.
Size of the specimen about 100-150mm.
Collection Hartmut Zimmer.
Photo taken at the Mineralien Hamburg show 2015.

Copyright: © Amir Akhavan      Photo ID: 863536     Uploaded by: Amir C. Akhavan   View Count: 19   Approval status: Public galleries    Type: Photo - 6752 x 4928 pixels (33.3 Mpix)

QL4-8A4Halite : NaCl

Menzengraben, Stadtlengsfeld, Thuringian Forest, Thuringia, Germany

Dimensions: 150 mm x 150 mm

Halite cubes with dark blue patches.
Size of the specimen about 15 by 15 cm.
Collection TU Bergakademie Freiberg.
Photo taken at the Mineralien Hamburg show 2015.
Copyright: © Amir Akhavan      Photo ID: 863535     Uploaded by: Amir C. Akhavan   View Count: 14   Approval status: Public galleries    Type: Photo - 5376 x 5376 pixels (28.9 Mpix)

AG2-5G3Natrolite : Na2(Si3Al2)O10·2H2O

Zeilberg Quarry, Maroldsweisach, Franconia, Bavaria, Germany

Dimensions: 100 mm x 150 mm

Balls of acicular natrolite from the Zeilberg quarry.
Height of the specimen about 15cm.
Collection Klaus Hielscher.
Photo taken at the Mineralien Hamburg show 2015.
Copyright: © Amir Akhavan      Photo ID: 863534     Uploaded by: Amir C. Akhavan   View Count: 12   Approval status: Public galleries    Type: Photo - 4928 x 6688 pixels (33.0 Mpix)

8G9-91MGalena : PbS

Himmelfahrt Mine, Freiberg, Freiberg District, Erzgebirge, Saxony, Germany

Dimensions: 150 mm

Galena from the Grube Himmelfahrt in Freiberg.
Size of the specimen about 15cm.
Collection TU Bergakademie Freiberg.
Photo taken at the Mineralien Hamburg show 2015.
Copyright: © Amir Akhavan      Photo ID: 863522     Uploaded by: Amir C. Akhavan   View Count: 17   Approval status: Public galleries    Type: Photo - 6496 x 5152 pixels (33.5 Mpix)
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