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Forms Involved in Titanite Crystal
  
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Josele




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PostPosted: Jan 20, 2022 10:52    Post subject: Forms Involved in Titanite Crystal  

I'm trying to understand this titanite crystal but I have more doubts than certainties. Maybe you can help? Thanks in advance.


P1050391.jpg
 Mineral: Titanite
 Locality:
Koksha Valley, Khash & Kuran Wa Munjan Districts, Badakhshan Province, Afghanistan
 Dimensions: 34 x 12 x 4 mm
 Description:
Sphene crystal with unusual flat elongated habit.
 Viewed:  2661 Time(s)

P1050391.jpg



P1250466_º.jpg
 Mineral: Titanite
 Locality:
Koksha Valley, Khash & Kuran Wa Munjan Districts, Badakhshan Province, Afghanistan
 Dimensions: 34 x 12 x 4 mm
 Description:
Backside.

Not sure if upper faces are a termination or a weird fracture.

Angles around the prism are about 60º and 120º.
 Viewed:  2662 Time(s)

P1250466_º.jpg



T2_edge.jpg
 Mineral: Titanite
 Locality:
Koksha Valley, Khash & Kuran Wa Munjan Districts, Badakhshan Province, Afghanistan
 Dimensions: 34 x 12 x 4 mm
 Description:
Lateral view from one side and from the opposite.

Front edge angle is about 60º in both cases.
 Viewed:  2662 Time(s)

T2_edge.jpg



T2_sideF.jpg
 Mineral: Titanite
 Locality:
Koksha Valley, Khash & Kuran Wa Munjan Districts, Badakhshan Province, Afghanistan
 Dimensions: 34 x 12 x 4 mm
 Description:
Diagonal views from one side …
 Viewed:  2660 Time(s)

T2_sideF.jpg



T2_sideR.jpg
 Mineral: Titanite
 Locality:
Koksha Valley, Khash & Kuran Wa Munjan Districts, Badakhshan Province, Afghanistan
 Dimensions: 34 x 12 x 4 mm
 Description:
… and from the other side.
 Viewed:  2659 Time(s)

T2_sideR.jpg



T2_top.jpg
 Mineral: Titanite
 Locality:
Koksha Valley, Khash & Kuran Wa Munjan Districts, Badakhshan Province, Afghanistan
 Dimensions: 34 x 12 x 4 mm
 Description:
Above: View from the elongated axis (b-axis?).
Note that left side seems thicker because it's closer, faces up and down are parallel.

Angle at right and left edges is about 60º.

Below: Seen perpendicular to the upper edge.
 Viewed:  2661 Time(s)

T2_top.jpg



T_11.jpg
 Description:
Sketch of a possible interpretation. Acute angles of prism would be 60.28º in accord with titanite ß celldata and with my measurements.
But I can’t find the way to draw “termination”* with simple Miller indices.

*between quotation marks because not sure if is a true termination.
 Viewed:  2661 Time(s)

T_11.jpg



T_14.jpg
 Description:
Sketch of another interpretation.
Here “termination” inclination fits titanite axes and angle between “termination” faces also fits but the acute angles of prism (about 60º) does not match any combination of indices (here (130)).
 Viewed:  2659 Time(s)

T_14.jpg


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Pete Richards
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PostPosted: Jan 20, 2022 13:20    Post subject: Re: Forms Involved in Titanite Crystal  

I think the notch visible in the top and one other photo indicates that this is a twin. Twinned titanites are very common. But if twinned it would certainly affect your interpretation of the morphology.

Dana's Textbook of Mineralogy states that twinning is common on (100), as does Mindat. However, the unit cell in Dana's Textbook has the a and c axial ratios switched relative to those of Mindat, and an acute beta angle about 60°. Mindat also quotes an "old cell" with the same unit cell as Dana except an obtuse beta of about 112°. Mindat's current cell data have an obtuse beta of about the same angle.

All three of these settings cannot be the same. But it is unclear which one(s) is wrong. My suspicion is that in the new cell given by Mindat, the twinning direction would be (001), and that the unit cell in Dana and the one favored by Mindat are essentiallly the same (possibly with a refined value of beta), and that the"old cell" given in Mindat is either mis-quoted or wrong at the source.

It is common for monoclinic minerals to have been described "in the old days" in a frame of reference in which the angle between the a and c axes (beta) was chosen as the acute angle between the two axes. More recently, the beta angle is usually taken to be the obtuse angle. In this setting, the old a axis becomes the c axis, the old c axis becomes the a axis, but with negative direction of c becoming the positive direction on a, and with new beta= 180-old beta. Indices (hkl) become (lk-h). So (100) becomes (00-1), but that is the same orietation as (001).

Sorry, I could not help myself.

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Josele




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PostPosted: Jan 20, 2022 14:53    Post subject: Re: Forms Involved in Titanite Crystal  

Do not apologize, that was a great help. I was not aware of these differences in titanite cell.

Then I must return to the start line. It took me quite long time elaborating my misleaded speculations, now must digest these data, adapt my "crystals tool" (Smorf draw) to currently accepted ß angle and start the game again.

Regarding twinning, as I knew titanite is often twinned, I looked for interpretations of my crystal as a twin but with the twin planes listed in Mindat and the Smorf data did not find any logic possibility.
Mayby with the new ß...
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Mark Holtkamp




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PostPosted: Jan 20, 2022 16:22    Post subject: Re: Forms Involved in Titanite Crystal  

Hi guys

The 'old' unit cell in Mindat is from Zachariasen (1930). For the full reference see the link on Mindat's titanite page to: Speer J A, Gibbs G V (1976) (below the crystal structure applet). This cell is used for Mindat's morphology descriptions and the Smorf drawings.

The conversion from Zachariasen to the Speer & Gibbs unit cell is (-101 / 010 / 100), so not just a switch of c- and a-axis, it's even worse :-) this also is the cause for the difference between the beta values (119 vz. 112).

Mindat's cell is probably the correct one,but Zachariasen's cell orientation is not necessarily wrong. All texts as far as I know use this cell as the base for morphology descriptions of titanite.
The trouble starts when you draw crystals using Mindat's cell and 'old' morphology descriptions. For instance (if I'm correct) the twinning on {100} in the 'old' cell becomes {-101} in Mindat's cell. As long as you use Zachariasens cell with the old morphology listings you should be ok.
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Bergur_E_Sigurdarson




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PostPosted: Jan 20, 2022 17:01    Post subject: Re: Forms Involved in Titanite Crystal  

While I am still an amateur collector and have limited knowledge on crystallography I do find this post very interesting.

I was fortunate enough to have some courses of geology in my highschool equivalent eduaction in Iceland... of which a considerable part was not just the geology of Iceland but also crystallogy.
I managed to get a 9,5/10 on my final test, but if anything was confusing, it was the cystallography.
I had similar issues in my maths... I got high scores on problems, but lacked in theory.
(in fact I was called to hte headmasters office after my final exam having scored perfectly on all the problems solved, but an absolute zero on theory... making them suspicious ...if I had cheated it surely would be the other way round!)

The fact that the crystallography uses all those references to numbered faces and this or that axis, that for me as a very visual person, I struggle with.

Calling things by alphabetical or greek alphabet names and not "vertical" "horizontal" etc have been difficult to me
...I absolutely accept that this is my problem in visualizing the terms used...
...and so... trying to better understand the terms and how they're used really helps me improve my understanding of the structures present in crystals

I love my minerals and I love being able to visually ID, even though I know that is just impossible at times.

I'm from Iceland, and currently live in Colombia... I recently bought a property here and am working on building a small house that will eventually house a small mineral museum.
Colombia may be mostly known for it's emeralds, but I know there is much more here and sadly the only national museum that has a decent mineral collection is closed due to the COVID... I hope that my contribution can at some later time become as important to Colombia as the MIM :-)
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Pete Richards
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PostPosted: Jan 20, 2022 19:22    Post subject: Re: Forms Involved in Titanite Crystal  

Thanks, Mark. Your comment is very helpful. Yes, things are more complex than I envisioned.

In the a-c plane perpendicular to the b-axis, with the beta angle close to 60° or 120°, there's a (third) alternative axis that completes the pseudo-hexagonal planar symmetry, which would have an axis every 120° (or an end of an axis every 60°). This transformation did not simply switch the a and c axes, it adopted the alternative axis as one of the two official ones.

With this kind of symmetry, the translations along a, c, and the third axis will be pretty similar. It's the kind of subtle distinction that can be made with x-ray crystal structure determination, and/or that follows from the accompanying rules about how you choose the unit cell. These are distinctions that were possible only to a more limited extent in the days of morphological determination of unit cells, or would not have been made because the cell that best describes the morphology is not always the best cell to describe the crystal structure and vise versa.

Mark makes the important point that there is not just one correct way to describe a unit cell, though conventions determine which of many is preferred. As long as the Miller indices are reported using the geometry defined by the unit cell, a crystal is properly characterized, and when drawn it will "look right". Mix Miller indices determined with one unit cell with the geometry of another unit cell, and the results can range from not so good to terrible.

Three unit cells for titanite (using axial ratios with b = 1)
(a : b : c beta angle)
0.7547 : 1 : 0.8543 60°17' Dana's System 6th ed. 1892, Dana's Textbook 1932
0.752 : 1 : 0.853 119°43' Dana's Manual 18th ed 1971, Barry & Mason Mineralogy 1959
0.812 : 1 : 0.754 113°93' Speer & Gibbs 1976, Dana's Mineralogy 8th ed 1997, Mindat, Handbook of Mineralogy (with minor variations)

Apologies to those who were interested but could not follow all of this thread. A lot of background is assumed here, and impossible to state here!

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Bob Carnein




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PostPosted: Jan 20, 2022 19:49    Post subject: Re: Forms Involved in Titanite Crystal  

The information on Mindat is itself confusing: i.e. "The morphological data is (sic) based on a choice of unit-cell parameters that differs from the one that is given in Mindat"...and then there are the rotating diagrams from Goldschmidt...It's unfortunate that orientations that, in some cases, have been accepted and used for a long time seem to morph into something "new", with the explanation for the change sometimes getting lost in the shuffle.
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Josele




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PostPosted: Jan 21, 2022 15:47    Post subject: Re: Forms Involved in Titanite Crystal  

Geometrical crystallography is fascinating, what I enjoy most about minerals. When I get an atypical crystal, the process to know what polyhedrons, forms or planes are involved, spinning round and round the crystal, is a real pleasure ...although not always resolved.

The problem of this crystal is that shape is too simple for titanite, even more if it's a twin.
I am puzzled with this angle ß of 113º, with ≈120º was much easier find possibilities.

Sirs, after your wise contributions and without having seen any interpretation of my crystal, either with the old or new data, I start to believe it's rarer than I thought.

Maybe I must consider a mistaken titanite identification?

Please, a little push, any clue, some indices, a scheme, albeit a risky hypothesis!
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PostPosted: Jan 21, 2022 18:25    Post subject: Re: Forms Involved in Titanite Crystal  

Joselle, have you been able to confirm that the physical properties (hardness, specific gravity, cleavage, etc.) are indeed those of titanite? Certainly, not all titanite crystals look the same.
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PostPosted: Jan 21, 2022 19:30    Post subject: Re: Forms Involved in Titanite Crystal  

Josele,

The most diagnostic angles on crystals, and the ones normally listed in textbooks, are interfacial angles - the angles between pairs of faces measured in a plane perpendicular to their mutual edge, not edge angles such as you show. And remember that the interfacial angle is measured as the angle between the lines perpendicular to the faces - so the interfacial angle between two adjacent faces of a cube is 90°, not 270°.

If you are comparing your measurements with published numbers, interfacial angles will work better.

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Josele




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PostPosted: Jan 21, 2022 21:35    Post subject: Re: Forms Involved in Titanite Crystal  

Bob, thanks for the push, I had not done any test until today.
I just checked hardness, it scratches fluorite easily and do not scratch pyrite, so it’s into titanite range.
I released the crystal from its base with a drop of alcohol and using a scale (accuracy=0.1g) and Archimedes method obtained a dry weight of 3.7g and a submerged weight of 1.0g which result a density of 3,7 that also can match titanite having in mind the low precision scale for this miniature, tap water, room temperature and the few inclusions.
Please see photos for fracture.
After all titanite remains as first option!

Pete, sorry, I was mistaken in a photo caption, about 60º in 2 edges and 150º in 4 edges are the interfacial angles around the prism properly measured with a goniometer in a plane perpendicular to the common edge.



P1250502.jpg
 Mineral: Titanite
 Locality:
Koksha Valley, Khash & Kuran Wa Munjan Districts, Badakhshan Province, Afghanistan
 Dimensions: FOV: 25 mm
 Description:
At the base, fracture is between conchoid and staggered.
 Viewed:  2394 Time(s)

P1250502.jpg



P1250504.jpg
 Mineral: Titanite
 Locality:
Koksha Valley, Khash & Kuran Wa Munjan Districts, Badakhshan Province, Afghanistan
 Dimensions: FOV: 20 mm
 Description:
Upper half part of fracture has created a “valley” with right slope at reflex and left side in the shadow.

Very poor signs of cleavage.

Anyway, a reconocible cleavage wouldn't have done me much good when I don't know how to relate it to the new parameters, different axes, indices and so.
 Viewed:  2392 Time(s)

P1250504.jpg


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Mark Holtkamp




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PostPosted: Jan 22, 2022 08:30    Post subject: Re: Forms Involved in Titanite Crystal  

Josele, you can just use the cell of Zachariasen (with beta=119°43'), where the best cleavage is {110} and the common twin plane {100}. If you have a textbook with the same cleavage en twin plane you know they refer to the same cell.
Did you look at the optical properties? Plechroism and the direction of extinction angles between crossed polarizers would be helpful.
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PostPosted: Jan 22, 2022 10:45    Post subject: Re: Forms Involved in Titanite Crystal  

I have developed drawings of two model prismatic titanite crystals, using what I think is the Zachariason unit cell (the source I used mentioned the correct cleavage but did not state the twin law). Both sets of drawings are presented with the prismatic axis vertical. In the first model, the prism is composed of faces of {110} and {100}; in the second the prism is composed of faces of {111} and {101}. There is a lot of superficial similarity. However, there is quite a lot of difference between the interfacial angles between faces of the prism. The interfacial angles shown are the crystallographic standard angles between face normals, and in parentheses the internal angle between the faces, probably a more familiar way of describing these angles for non-crystallographers. In the drawings with angles, the relevant faces are perpendicular to the page and so are seen as lines.

I also drew hypothetical twins with both models, in both cases leaving the bottom front-facing face out of the twin model (otherwise there is no notch). The first model has (100) as the twin plane. For the second model, the twin plane (100) would create a twin with a v-shape; in order to draw a twin similar to in the first model, one must use (101) as the twin plane. This twin plane is not reported, which makes this model less likely if indeed the crystal is twinned.

The difference in interfacial angles on the prism faces, together with the difference in the angle between the twinned individuals seen in the notch, should be adequate to determine which model better fits Josele's crystal. I suspect it will be the first one...



titanite 1.jpg
 Description:
Titanite crystal model 1; twin plane (100)
 Viewed:  2308 Time(s)

titanite 1.jpg



titanite 2.jpg
 Description:
Titanite model 2; twin plane (101)
 Viewed:  2302 Time(s)

titanite 2.jpg



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Josele




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PostPosted: Jan 23, 2022 08:18    Post subject: Re: Forms Involved in Titanite Crystal  

Well, I think we got it!

Mark, I have not Nicols to check extinction angles, but it is quite pleochroic. Following your advice everything falls into place.

Pete, your first scheme fits perfectly with the crystal, assuming that its "termination" is not a real face. Before seeing your last message, I measured again angles around the prism, this time very carefully and in different places to average, obtaining interfacial angles of 34º and 113.5º (or their supplementary 146º and 46.5º, at last I understood the concept of interfacial angle, measured in the exterior) which matches with your drawing.
My first wrong measurements of ≈30º and ≈120º (or ≈150º and ≈60º at interior) must have been influenced by the desire of fitting to the mistaken assumption of the prism along b-axis.
The supposed "termination" with a small spur must be a fracture with V shape due to symmetrical position of cleavage and parting in one and other half of the twin. This can also explain the "valley" in the fracture of the opposite side.

Measuring angles, I noted a narrow part of a {110} face close to the edge that confirms the twin. Not easily visible to me at naked eye but evident in amplified photo with proper light.

Thanks for your great support to reveal the nature of this not so simple crystal, without your help I never would have made it.



P1250511.jpg
 Mineral: Titanite
 Locality:
Koksha Valley, Khash & Kuran Wa Munjan Districts, Badakhshan Province, Afghanistan
 Dimensions: 34 x 12 x 4 mm
 Description:
A 0.3mm wide strip near the upper edge perfectly parallel to the rest of the face although a bit stepped, belongs to the other individual of the twin. Notice striation difference.
 Viewed:  2202 Time(s)

P1250511.jpg



T_2P.jpg
 Mineral: Titanite
 Locality:
Koksha Valley, Khash & Kuran Wa Munjan Districts, Badakhshan Province, Afghanistan
 Dimensions: 34 x 12 x 4 mm
 Description:
Conspicuously pleochroic.

In front of the polarized light of a computer screen in vertical and horizontal position.

Same camera setting.
 Viewed:  2196 Time(s)

T_2P.jpg


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Mark Holtkamp




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PostPosted: Jan 23, 2022 09:22    Post subject: Re: Forms Involved in Titanite Crystal  

Nice, I think this settles it and Pete's first scheme is the correct one. The plechroism also fits, if the polarisation of you screen is horizontal.
What colors do you see if you turn the crystal 90 degrees along the long axis? But maybe the crystal is too thick in this direction to get a good view of the colors.
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Josele




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PostPosted: Jan 23, 2022 11:08    Post subject: Re: Forms Involved in Titanite Crystal  

Mark Holtkamp wrote:
... What colors do you see if you turn the crystal 90 degrees along the long axis? But maybe the crystal is too thick in this direction to get a good view of the colors.

Yes, too thick, in c-axis direction it looks completely dark in any position.
Thanks for your help, pleochroism question was very useful!
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Josele




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PostPosted: Jan 26, 2022 09:03    Post subject: Re: Forms Involved in Titanite Crystal  

Mark Holtkamp wrote:
... the direction of extinction angles between crossed polarizers would be helpful.

I have not a petrographic microscope with nicols but I found two old "Polaroid" plastic glasses that can do the job:



T_nicols1.jpg
 Mineral: Titanite
 Locality:
Koksha Valley, Khash & Kuran Wa Munjan Districts, Badakhshan Province, Afghanistan
 Dimensions: 34 x 12 x 4 mm
 Description:
At left, extinction in vertical position. Also extinct when in horizontal position.

At right in most translucent position at 45º. It repeats translucence four times (every 90º) when rotating 360º.

That confirms it is biaxial? Sorry, I have my poor optics knowledge very oxidized.
 Viewed:  1959 Time(s)

T_nicols1.jpg



T_nicols2.jpg
 Mineral: Titanite
 Locality:
Koksha Valley, Khash & Kuran Wa Munjan Districts, Badakhshan Province, Afghanistan
 Dimensions: 34 x 12 x 4 mm
 Description:
Same result using the polarized light of a computer screen and only one polarizing filter: Extinction in vertical and horizontal positions and translucence at 45º.
 Viewed:  1959 Time(s)

T_nicols2.jpg



T_4ps.jpg
 Mineral: Titanite
 Locality:
Koksha Valley, Khash & Kuran Wa Munjan Districts, Badakhshan Province, Afghanistan
 Dimensions: 34 x 12 x 4 mm
 Description:
Here between crossed polarizers and the computer screen (polarized light), a nonsense?
Now most extincted position is at 45º. In vertical is somewhat more translucent and it looks brownish. When horizontal also more translucent but greenish.
I'm unable to interpret it ...
 Viewed:  1927 Time(s)

T_4ps.jpg


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Mark Holtkamp




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PostPosted: Jan 27, 2022 10:00    Post subject: Re: Forms Involved in Titanite Crystal  

Josele, the parallel extinction doesn't prove it is biaxial, it could still be uniaxial. But it is consistent with Pete's interpretation. If the photograps were taken along the b-axis, you would expect the extinction directions to make a large angle with the polarising directions.
I don't know what's going on in the last photograps but it looks like the polarisation directions of the sunglasses are not perpendicular?
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PostPosted: Jan 27, 2022 15:04    Post subject: Re: Forms Involved in Titanite Crystal  

Understood, thank you Mark.
Better we forget last image, these "polaroid" old glasses do very weird things when you turn one of them over facing the polarized computer light.
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PostPosted: Apr 22, 2022 14:58    Post subject: Re: Forms Involved in Titanite Crystal  

I have an untwinned single crystal of titanite from that area. I had it as from Mohmand Agency, Pakistan, not really near, but you know stones in these mountains walk with nomad peoples. It has many similarities with your crystal, color, elongation and is heavily included with actinolite-type mineral (looking white when inside, but looking black when outside of the titanite). Untwinned titanite crystal are very rare in hydrothermal veins, but common in volcanic miarolitic cavities, despite very small. The shape is simple and clear.


IMG_6945 (Mediano).JPG
 Mineral: Sphene
 Locality:
Mohmand District, Khyber Pakhtunkhwa Province, Pakistan
 Dimensions: 58 mm
 Description:
 Viewed:  395 Time(s)

IMG_6945 (Mediano).JPG



IMG_6946 (Mediano).JPG
 Mineral: Sphene
 Locality:
Mohmand District, Khyber Pakhtunkhwa Province, Pakistan
 Dimensions: 12 mm wide
 Description:
 Viewed:  394 Time(s)

IMG_6946 (Mediano).JPG


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