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[marco campos-venuti]

The photo shows a 13.6 cm Japan twin quartz from Minas Gerais, Brazil.
Japan twin quartz crystals are considered typical contact twins. By definition, in a contact twin, the two individuals meet on a plane, unlike interpenetration twins, in which the two individuals occupy a common space. Japan twin quartz crystals usually exhibit a butterfly shape, but only when they are standing upright on the matrix. In the case of floater crystals where the quartz is double-terminated, the twin's shape forms an X and therefore should be better described as interpenetration. I have read that the twin boundary between the two individuals in a Japan twin is actually undulating (Lenart et al., 2012), which is strange for a contact twin.
I found an article by Sunagawa on the subject in which he claims that X-shaped twins are the result of a combination of two Y-shaped forms (not V-shaped). Since I couldn't find the article online, I don't understand this statement taken from the abstract. What do you think?

Lenart, A., Samardžija, Z., Godec, M., Mirtič, B., & Šturm, S. (2012). Twin-boundary formation in Japan-law twinned quartz crystals. European Journal of Mineralogy, 24(3), 509-517.
Sunagawa, I., Imai, H., Takada, M., & Hoshino, Y. (2004). Morphogenesis of quartz crystals twinned after Japan Law. European Journal of Mineralogy, 16(1), 91-97.

[Bob Morgan]

The specimen in the photo does not appear to be a Japan Law twin. There should be parallel prism faces toward the camera that are in the same plane.
Japan Law contact surfaces are still a mystery. I have examined 'ears' or half Quartz twins where the contact surface is exposed, and complexity is revealed.
Even more a mystery is their origin. How would two crystals develop a relationship on a plane that quartz doesn't produce as a face?
You might be interested in:
Momma, Koichi et al, (2015) Growth history and textures of quartz twinned in accordance with Japan law, European Journal of Mineralogy, 27, 71-80.

[Bob Carnein]

At first, I thought it might be a grieserntal twin, but it appears that the angle between the two crystals on the left is near 90 degrees while the angle between the crystals on the right is more than 90 degrees. Can you accurately measure the angles or the angles between the front-facing edges?

[Roger Warin]

Hello,
I was surprised to see this question asked.
Marco's double X crystal is indeed a twin from Japan, on a single multiple crystal lattice by contact on the Xi plane (11-22).
Although sometimes observed on a crystal (as a face), its presence is rare because neighboring forms quickly engulf it.
However, it is the only plane that allows the initial unit cell to develop a larger cell (called a multiple cell), allowing the twin to graft itself onto it.
This new crystal lattice is a coherent extension of the initial lattice.
However, this transition requires energy because it causes atoms to move within the new lattice. It is therefore normal for this phenomenon to occur only once.
When it was formed, the crystal seed randomly chose an optical direction. Fortunately, this seed was not in geophysical conditions similar to those found in the Alps. There, for any reason whatsoever, the vertical axes can be reversed without requiring energy. There is no displacement of atoms. Only the bonds between atoms are mutated. This is the cause of the formation of mosaic quartz, which is more “ecological” in nature.

In the case of Japanese twin crystals, the initial germ undergoes the selection of its chirality and then, in most cases, does not vary any further. The twin crystal is therefore formed on the germ, and the two individuals then follow their own destinies.
The twin plane is therefore formed at birth. But as is often the case, situations are not perfect, and crystals are not necessarily very regular. The example shown by Marco will not be included in the MIM in Beirut.

Fortunately, Marco oriented his Japanese twin for the photo.
Previously, by eye, without any manipulation, I estimated the position of the c-axes in the photo. This gave me an X. All that remained was to measure the angle.
Rather than trembling in front of the screen, I manipulated Marco's photo to make one c-axis horizontal. It wasn't essential, but I preferred it that way.
I then pasted a goniometric template, actually a protractor, onto the photo.
I'll let you do the reading... It looks like 83°, and I was surprised myself by this relative accuracy. The true value is 84°33'.

For thermodynamic reasons, don't look for any other quartz twinning laws than the following three:
1) By contact, Japan.
2) From the Dauphiné region, primarily called La Gardette, but there are very few of this origin (a “pure” habit).
3) From Brazil.

[marco campos-venuti]

Thanks to both Bobs. I actually rushed it too quickly, and it's obviously not a Japan twin. I measured an angle close to 78 degrees, so I assume it could be a Grieserntal twin (76.26). I'm happy with my mistake, in fact, it's a much rarer twin.
The effect of the angle appearing close to 90 is due to the fact that the prisms faces are inclined, and therefore the apparent angle seen on the prism faces is greater. To measure the correct angle, I traced the two imaginary c-axes and measured the angle at the intersection. For that reason, the measured angle is a bit approximate.
I read the interesting paper by Momma et al. I was aware of the role of twin reentrant angle as a self-perpetuating step source, but it seems the reality is much more complex.

[marco campos-venuti]

Back side

[marco campos-venuti]

Lateral view

[Bob Morgan]

When I saw your first photo I thought immediately of an R-G twin, but the angle didn't match up due to, as I understand, the angle of the photo. With square on prism faces meeting in the middle of the notch, it certainly resembles an R-G twin.
To measure the angle more accurately use the prism striations of the two crystals. They are less likely to wander than the prism edges. The angle between the outer pairs of them would be the complementary angle or 104 degrees to the pair of the other.
The 'x' pattern is from overgrowth around one side of the crystal of origin the one that was attached to matrix. Japan Law twins do that on occasion
On the front side the axis toward the matrix is offset from the one above the intersecting twin. On the back side the edge connecting both sectors wanders to make the connection. This is probably because of exaggerated growth in the 76 degree twin notches, both to the upper left and to the lower right in your original photo.
Some might question whether or not this is a true twin since the two crystals did not start from a common origin. This is twinning by oriented attachment on an already established crystal.
It's interesting that the attached crystal is almost the same size as its host. They have faster growth to the side in the 76 degree twin notches, which would have continued until it matched its host's width. The extension of the attached crystal is a result of both the widening and the greater notch effect on the attached crystal.
For more information see my article in the 2022 December-November Mineralogical Record Vol. 53, 739-754

[marco campos-venuti]

Thank Bob. I used the prism striations and I get 76.
Can you share your article? I found online only the preview of the first page.