We use cookies to show content based on your preferences. If you continue to browse you accept their use and installation. More information. >

FMF - Friends of Minerals Forum, discussion and message board
The place to share your mineralogical experiences

FMF English Forum is moderated by John S. White and Peter Megaw
 

Spanish message board






Newest topics and users posts
25 Apr-20:56:54 The mizunaka collection - rhodochrosite with pyrite (Am Mizunaka)
25 Apr-14:20:07 Re: new generation for picture - ploum (Ploum)
25 Apr-12:07:16 Re: agates in sicily (Alanbartlett)
25 Apr-11:53:31 Re: the mizunaka collection (Am Mizunaka)
25 Apr-11:35:15 Re: collection of michael shaw (Crosstimber)
25 Apr-11:16:01 Re: agates in sicily (Marco Campos-venuti)
25 Apr-11:09:18 Re: agates in sicily (James)
25 Apr-10:59:28 Re: agates in sicily (Alanbartlett)
25 Apr-10:52:28 Re: agates in sicily (James)
25 Apr-10:35:57 Re: how to start a new topic (Alanbartlett)
25 Apr-10:35:01 Agates in sicily (Alanbartlett)
25 Apr-10:02:13 Re: how to start a new topic (James)
25 Apr-09:56:36 Re: how to start a new topic (Alanbartlett)
25 Apr-09:31:08 Re: colourful crystals plus colourless crystals (Bashka)
25 Apr-04:58:11 Re: the collection of pierre and riana joubert (Pierre Joubert)
25 Apr-04:48:28 Re: collection of fiebre verde - peñas blancas (#682) (Fiebre Verde)
25 Apr-04:48:02 Re: the mizunaka collection (Pierre Joubert)
24 Apr-21:36:07 Re: chinese realgar (Rubytime)
24 Apr-16:56:48 Re: tourmaline included smokey quartz specimen real or fake? (Striker.Svr)
24 Apr-15:54:16 The mizunaka collection - rhodochrosite (Am Mizunaka)
24 Apr-14:30:17 Re: colourful crystals plus colourless crystals (Bob Carnein)
24 Apr-12:42:26 Re: colourful crystals plus colourless crystals (Bob Harman)
24 Apr-12:15:27 Re: colourful crystals plus colourless crystals (Bashka)
24 Apr-12:04:13 Colourful crystals plus colourless crystals (Bashka)
24 Apr-08:18:54 Re: help identifying this conglomerate (Joshtw)

For lists of newest topics and postings click here


RSS RSS

View unanswered posts

Why and how to register

Index Index
 FAQFAQ RegisterRegister  Log inLog in
 {Forgotten your password?}Forgotten your password?  

Like
42120


The time now is Apr 26, 2018 00:33

Search for a textSearch for a text   

A general guide for using the Forum with some rules and tips
Tetrahedron [111] penetration twin
  
  Index -> The Ten Thousand Club
Like
10


View previous topic :: View next topic  
Author Message

Josele




Joined: 10 Apr 2012
Posts: 292
Location: Tarifa, Spain


Access to the FMF Gallery title=

View user's profile

Send private message

PostPosted: Aug 13, 2013 16:35    Post subject: Tetrahedron [111] penetration twin  

I am following with great interest the thread Spinel Twins and also the thread Maclas in Spanish FMF.
Relating to tetrahedron [111] penetration twin, there is something I can not understand, perhaps you can help me to clarify this matter:



tetratwin.jpg
 Description:
Mineral: Tetrahedrite
Description: Penetration twin on [111]
Location: Cavnic (Kapnik), Romania
Author: C. Palache, H. Berman, C. Frondel, The system of mineralogy. Vol I, 7th edition, John Wiley & Sons, New York, 1944.
System: Cubic, point group: 43m
Cell: a: 1, b: 1, c: 1, alpha: 90, beta: 90, gamma: 90
image & data © Smorf

The twin operation is a 60º rotation around [111] plus a symetry in (111) plane, or, simpler, a 90º rotation around any of the crystallographic axes. But this 90º rotation will move the structure to an equivalent position. Both individuals have the crystal lattice in the same position, sharing a common volume. Then, where is the twin? Is not the same that occurs in two parallel grow crystals not considered as a twin?

Very thanks for your help!
 Viewed:  24766 Time(s)

tetratwin.jpg



_________________
Josele
Back to top
Reply to topic Reply with quote
Like
1
   

Gerhard Niklasch




Joined: 27 Mar 2009
Posts: 131
Location: Munich


Access to the FMF Gallery title=

View user's profile

Send private message

PostPosted: Aug 14, 2013 12:05    Post subject: Re: Tetrahedron  

Hello Josele,

no, a 90° rotation about any coordinate axis does not move the crystal structure of Tetrahedrite to a position that could also be obtained by a parallel translation without rotation. The structure really has tetrahedral symmetry.

Performing (say) a 90° rotation around the z axis followed by a reflection in the xy plane will map the structure into itself: this rotation-inversion is a symmetry of the tetrahedron inscribed into the obvious cube.

The space group is I-43m: You may contemplate the diagram which can be found e.g. here,
http://img.chem.ucl.ac.uk/sgp/large/217az1.htm
(link normalized by FMF)

You can find a crystal structure model on the Webmineral page linked from Mindat Tetrahedrite´s page

Enjoy,
Gerhard
Back to top
Reply to topic Reply with quote
Like
1
   

Josele




Joined: 10 Apr 2012
Posts: 292
Location: Tarifa, Spain


Access to the FMF Gallery title=

View user's profile

Send private message

PostPosted: Aug 14, 2013 19:40    Post subject: Re: Tetrahedron [111] penetration twin  

Gerhard, thanks for your help and patience.
OK, now I understand (I think!), the matter is: tetrahedrite crystal lattice have not holohedral symmetry, crystallographic axes are just binary axes then a 90º rotation around the crystallographic axes do NOT lets the structure as it was in the original position, in oposition to that I said before.

Another question:
Why the previous twin is called Penetration twin on [111]?
If the twin operation is a 90º rotation around any of the crystallographic axes,
Would not be better to call it Penetration twin on [100]?



Penetration twin on [111].jpg
 Description:
Mineral: Tetrahedrite
Description: Penetration twin on [111]
Location: Cavnic (Kapnik), Romania
Author: C. Palache, H. Berman, C. Frondel, The system of mineralogy. Vol I, 7th edition, John Wiley & Sons, New York, 1944.
System: Cubic, point group: 43m
Cell: a: 1, b: 1, c: 1, alpha: 90, beta: 90, gamma: 90
image & data © Smorf

This one is clearly a Penetration twin on [111], with 60º rotation around [111] as a twin operation.
Why the previous twin have the same name?
 Viewed:  24603 Time(s)

Penetration twin on [111].jpg



_________________
Josele
Back to top
Reply to topic Reply with quote
Like
1
   

Gerhard Niklasch




Joined: 27 Mar 2009
Posts: 131
Location: Munich


Access to the FMF Gallery title=

View user's profile

Send private message

PostPosted: Aug 19, 2013 12:25    Post subject: Re: Tetrahedron  

Hello Josele,

This latter shape, as I understand it, is the most common form of twinning in Tetrahedrite: As the Handbook of Mineralogy puts it, "on {111} around [111] as twin axis; contact and penetration twins, commonly repeated." That is, the individuals have a plane equivalent to (111) in common, and are related by rotation around an axis orthogonal to this plane. This axis (a 3-fold rotation axis of the tetrahedron) is polar, unlike the situation for Spinel, and the polarity is preserved under this twinning operation. (The other three 3-fold axes are moved to new positions.) Twinning may be repeated, via a different plane and axis, resulting in rather complicated shapes.

Examples can be found via mindat's photo search by asking for the species and for the keyword "twin" in the description. A nice one is: http://www.mindat.org/photo-330485.html

Returning to your first star shape: Inversion through the coordinate origin would be the simplest way to describe it, without singling out any coordinate axis or rotation axis. But given how common twinning via the [111] rotation is in Tetrahedrite, the shape could also arise from repeated twinning, once via this rotation, and once via a reflection in the same (111) plane. In that case, one would expect the reflection twinning to occur on its own, too. I am not sure whether it does. A quick search found no examples and no mention of it.

In Spinel and other holohedral isometric crystals, the rotation and the reflection are indistinguishable, and the second operation would simply undo the first. Here they are not: The reflection reverses the polarity of the 3-fold axis orthogonal to the mirror plane. And thus the composition of the two operations also reverses it, and indeed it reverses all four 3-fold axes, resulting in something new that's at least logically possible as a twin of a tetrahedral crystal.

Cheers, Gerhard

P.S. Now I've found an example of the first star shape, but cheating a little: This is Helvine, not Tetrahedrite. It does confirm that such things happen in nature, though!
http://www.mindat.org/photo-186519.html
Back to top
Reply to topic Reply with quote
Like
   

Ru Smith




Joined: 13 Oct 2012
Posts: 362


Access to the FMF Gallery title=

View user's profile

Send private message

PostPosted: Aug 22, 2013 20:43    Post subject: Re: Tetrahedron  

Greetings,

Here's an example (I think) of the [111] twin in a Romanian tetrahedrite.



Tetrahedrite twin 1.jpg
 Description:
Tetrahedrite on calcite.
Cavnic, Baia Mare, Marahures, Romania.
1 cm crystal on 8 cm matrix.
 Viewed:  24374 Time(s)

Tetrahedrite twin 1.jpg



Tetrahedrite twin 2.jpg
 Description:
Tetrahedrite on calcite.
Cavnic, Baia Mare, Marahures, Romania.
1 cm crystal on 8 cm matrix.
 Viewed:  24364 Time(s)

Tetrahedrite twin 2.jpg


Back to top
Reply to topic Reply with quote
Like
1
   

Josele




Joined: 10 Apr 2012
Posts: 292
Location: Tarifa, Spain


Access to the FMF Gallery title=

View user's profile

Send private message

PostPosted: Aug 23, 2013 14:53    Post subject: Re: Tetrahedron [111] penetration twin  

Gerhard, thanks for the detailed explanation. As you said, in the first case the twin operation is simply an inversion by the origin of crystallographic axes, which is not a symmetry center for a single tetrahedron but yes for the twin.
But still I think is confusing use the same name for these two twins.

Ru, thanks for your input, is heartwarming to confirm that theory corresponds to reality, ...although I have to admit that I'm unable to recognize the twin in your pictures.

_________________
Josele
Back to top
Reply to topic Reply with quote
Like
   

Ru Smith




Joined: 13 Oct 2012
Posts: 362


Access to the FMF Gallery title=

View user's profile

Send private message

PostPosted: Aug 24, 2013 12:43    Post subject: Re: Tetrahedron  

See if these two photos help, Josele. One looking roughly down the twin axis and the other orientated approximately as in your smorf drawing. As usual, not quite the ideal, but not bad either.


Tetrahedrite twin 3.jpg
 Description:
Tetrahedrite on calcite with bournonite, sphalerite and pyrite.
Cavnic Mine (Kapnikbánya), Cavnic (Kapnic; Kapnik), Maramureș Co., Romania
1 cm crystal on 8 cm matrix.
 Viewed:  24214 Time(s)

Tetrahedrite twin 3.jpg



Tetrahedrite twin 4.jpg
 Description:
Tetrahedrite on calcite with bournonite, sphalerite and pyrite.
Cavnic Mine (Kapnikbánya), Cavnic (Kapnic; Kapnik), Maramureș Co., Romania
1 cm crystal on 8 cm matrix.
 Viewed:  24250 Time(s)

Tetrahedrite twin 4.jpg


Back to top
Reply to topic Reply with quote
Like
1
   

Josele




Joined: 10 Apr 2012
Posts: 292
Location: Tarifa, Spain


Access to the FMF Gallery title=

View user's profile

Send private message

PostPosted: Aug 24, 2013 15:49    Post subject: Re: Tetrahedron [111] penetration twin  

Ru, sorry in advance for abusing your patience, I know is a twin but I can't recognize it.

I suppose is due to crystal whim and photo deceiving...



tetratwin2.jpg
 Description:
If I have not misunderstood, in [111] tetrahedrite penetration twin (second version, as the last Smorf image) the angles between edges (here marked in yellow) should be 20º. Doesn't matter if there is some translational movement but the angles must stay constant. Is hard to see in photo but to me they seem bigger than 20º.

However, the angle of the negative edge seems to be near 120º as it must be...
 Viewed:  24208 Time(s)

tetratwin2.jpg



_________________
Josele
Back to top
Reply to topic Reply with quote
Like
1
   

Ru Smith




Joined: 13 Oct 2012
Posts: 362


Access to the FMF Gallery title=

View user's profile

Send private message

PostPosted: Aug 24, 2013 19:52    Post subject: Re: Tetrahedron  

You have very sharp eyes, Josele!

Here attached is a view of the base of the twin together with an idealized drawing of what I see. What is clear is that the twin elements are rotated 180 degrees relative to each other about the twinning axis and that there's a shared basal face (though the element forming the "fins" is a tiny step off being flush with the face of the dominant element).

However, the angle you refer to in the dominant member of the twin is indeed a little larger than 120 degrees and seems to result from the presence of tristetrahedral faces ({211}). I've drawn the equilateral triangle of a simple tetrahedron face in the dotted line on the diagram. It seems that some sides of each tetrahedron have tristetrahedral faces expressed and others not. Turning the crystal around reveals that on some sides all three tristetrahedral faces (for one side of the tetrahedron) are expressed and on others only two.

The basal face, shared by both elements of the twin, is a single smooth plane with no sign of tristetrahedral faces.

I'd love to see some more examples.



Tetrahedrite twin base drawing.jpg
 Description:
Tetrahedrite on calcite with bournonite, sphalerite and pyrite.
Cavnic Mine (Kapnikbánya), Cavnic (Kapnic; Kapnik), Maramureș Co., Romania
1 cm crystal on 8 cm matrix.
 Viewed:  24181 Time(s)

Tetrahedrite twin base drawing.jpg


Back to top
Reply to topic Reply with quote
Like
1
   

Josele




Joined: 10 Apr 2012
Posts: 292
Location: Tarifa, Spain


Access to the FMF Gallery title=

View user's profile

Send private message

PostPosted: Aug 25, 2013 19:02    Post subject: Re: Tetrahedron [111] penetration twin  

Thanks Ru, after your clue of tristetrahedron modifications, now I begin to understand. Is a complex crystal, hard to see in photos.


tetratwin4.jpg
 Description:
If I'm not mistaken, both large faces above belongs to tristetrahedron but in fact the third face of both triads which should be in contact with (111) are missing (marked in blue).

Is curious that the edges in red are more or less parallel when they should be divergent, but contrary to the divergence of the edges at right in picture. Face between red edges seems to belong to a tetrahedron, not modified.
 Viewed:  24106 Time(s)

tetratwin4.jpg



_________________
Josele
Back to top
Reply to topic Reply with quote
Like
1
   

Ru Smith




Joined: 13 Oct 2012
Posts: 362


Access to the FMF Gallery title=

View user's profile

Send private message

PostPosted: Aug 25, 2013 21:48    Post subject: Re: Tetrahedron  

Basically correct, Josele. Here's a sketch looking down the twinning axis from the pointy end. I've drawn over the actual faces and edges and then extrapolated where the crystal contacts the matrix. One member of the twin is shaded blue, the other green. The edges of each tetrahedron are shown in bold lines.

Looking at non-twinned tetrahedrite crystals from this locality I see that they also show very variable development of faces on each side - some are simply tetrahedron faces with striations whereas adjacent sides of the tetrahedron reveal tristetrahedron and other faces.



Tetrahedrite twin axis view drawing.jpg
 Description:
Tetrahedrite on calcite with bournonite, sphalerite and pyrite.
Cavnic Mine (Kapnikbánya), Cavnic (Kapnic; Kapnik), Maramureș Co., Romania
1 cm crystal on 8 cm matrix.
 Viewed:  24069 Time(s)

Tetrahedrite twin axis view drawing.jpg


Back to top
Reply to topic Reply with quote
Like
1
   

Mark Holtkamp




Joined: 26 Dec 2013
Posts: 12

View user's profile

Send private message

PostPosted: Dec 27, 2013 11:33    Post subject: Re: Tetrahedron [111] penetration twin  

Hi all,

Sorry for the confusion and the late reply. The drawings in the original post are from my website, after a bit of research I think the crystal in the first drawing is not a twin on [111] at all.

I based my drawing and the interpretation as a twin on [111] on a picture in Dana’s sytem of mineralogy, 7th edition, page 375. In my crystal drawing program I cannot recreate a twin on [111] that looks like the first drawing (when I made the original drawing a couple of years ago I had to create this twin another way for specific reasons).

I read a couple of old mineralogy handbooks, it seems there are 3 types of tetrahedrite twins:

1. penetration twins on [111] like in the second drawing. The two tetrahedrons share a common plane (when of equal size). 2. contact twins on [111] with {211} (or also {111}?) as composition plane. 3. penetration twins in which edges of both tetrahedrons make right angles. The twin element is {100}. I believe it could also be described as an inversion twin.

The twin in the first drawing clearly is of the third type. In my (recent) handbooks, and on the internet, I could not find a reference to this type of twin. Both Dana’s manual of mineralogy, 7th ed., and Klockmanns Lehrbuch der Mineralogie have a crystal drawing like this and refer to this as a twin om [111], which is wrong in my opinion.

Interestingly The System of Mineralogy of James Dwight Dana, 6th edition, has the following text, describing the tetrahedrite twin on {100}: “Twins (1) twinning plane o (o refers to the terahedron (MH)), contact twins with the composition face either parallel or perpendicular to the twinning plane, and penetration-twins, both common, twinning often repeated; also rarely twins (2) with axes parallel and symmetrical with reference to a cubic plane.”

The last twin described by Dana is the twin from the first drawing in the original post.
I wonder why in recent literature this twin law is no longer mentioned. Or did I miss something?

cheers, Mark.
Back to top
Reply to topic Reply with quote
Like
   

Mark Holtkamp




Joined: 26 Dec 2013
Posts: 12

View user's profile

Send private message

PostPosted: Dec 27, 2013 17:15    Post subject: Re: Tetrahedron [111] penetration twin  

After more reading I now believe that the tetrahedrite {100} twin doesn't occur in recent literature because it doesn't exist. The images in Strunz and Dana probably were copied from old references and falsly interpreted as twins on [111]. See the article by Sadebeck from 1872 which is online (A. Sadebeck, Über Fahlerz und seine regelmässigen Verwachsungen. Zeitschrift der Deutschen Geologische Gesellschaft 24 Heft 3, p. 427-464 (1872).). Apparently I cannot post a url here so I will attach a piece of text in an image. If you google the title of the article you'll find it.

Mark.



sadebeck.jpg
 Description:
Fahlerz - tetrahedrite
N/A
N/A
 Viewed:  22115 Time(s)

sadebeck.jpg


Back to top
Reply to topic Reply with quote
Like
   

Josele




Joined: 10 Apr 2012
Posts: 292
Location: Tarifa, Spain


Access to the FMF Gallery title=

View user's profile

Send private message

PostPosted: Dec 27, 2013 19:02    Post subject: Re: Tetrahedron [111] penetration twin  

Mark, thank you doubly for your priceless web site (SMORF) and for your work as archaeologist of crystalography.
And again thanks for clarify this matter here.

_________________
Josele
Back to top
Reply to topic Reply with quote
Like
   

Mark Holtkamp




Joined: 26 Dec 2013
Posts: 12

View user's profile

Send private message

PostPosted: Dec 29, 2013 10:08    Post subject: Re: Tetrahedron [111] penetration twin  

Thank jou Josele also for spotting the error. You were right after all, it is a twin on [100] !

Mark.
Back to top
Reply to topic Reply with quote
Like
   

Rodney B Jackson




Joined: 13 Dec 2013
Posts: 12

View user's profile

Send private message

PostPosted: Dec 31, 2013 11:03    Post subject: Re: Tetrahedron [111] penetration twin  

Fantastic symmetry. The math is a bit deep for me though.
Back to top
Reply to topic Reply with quote
Like
   

chrisjacob




Joined: 08 Jan 2014
Posts: 1

View user's profile

Send private message

PostPosted: Jan 08, 2014 05:18    Post subject: Re: Re: Tetrahedron [111] penetration twin  

Your discussion about the Tetrahedron penetration twin was very helpful for a newbie like me. I felt some parts very difficult to understand still the graph you shared help me in a better way to understand what you meant.






_________________________________
CHris-
Back to top
Reply to topic Reply with quote
Like
   

Pete Richards
Site Admin



Joined: 29 Dec 2008
Posts: 588
Location: Northeast Ohio


Access to the FMF Gallery title=

View user's profile

Send private message

PostPosted: Jan 13, 2018 20:26    Post subject: Re: Tetrahedron [111] penetration twin  

The symmetry of tetrahedrite is a reduced isometric symmetry. The form {111}, for example, is a tetrahedron, not an octahedron. Thus a rotation of 90° about one of the axes introduces new symmetry elements and does not simply replicate the structure. I believe this is called twinning by merohedry.

Sorry, I now realize that I have missed a long and complex discussion....

_________________
Collecting and studying crystals with interesting habits, twinning, and epitaxy
Back to top
Reply to topic Reply with quote
Like
1
   
Display posts from previous:   
   Index -> The Ten Thousand Club   All times are GMT - 5 Hours
Page 1 of 1
    

 
Jump to:  
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum
You cannot attach files in this forum
You can download files in this forum


All pictures, text, design © Forum FMF 2006-2018


Powered by FMF