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James Catmur
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Posted: Sep 11, 2020 01:28 Post subject: Re: About cyclic twinning - (5) |
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The Natural History Museum of Denmark, in Copenhagen, has sent me a new and better photo of their Rutile cyclic twin. I suspect it is a 'dirty dimple' and not a hole, unlike the wooden model in the same display case.
See what you think.
Mineral: | Rutile |
Locality: | Magnet Cove, Hot Spring County, Arkansas, USA |  |
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Dimensions: | 6cm x 3cm x 4cm |
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LDMarks

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Posted: Aug 05, 2021 11:10 Post subject: Re: About cyclic twinning - (5) |
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I am looking for nice examples of fivelings, either images or references earlier than 1960 (in particular any in the 1800's). Any links very much appreciated.
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Bob Morgan
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Posted: Aug 05, 2021 11:42 Post subject: Re: About cyclic twinning - (5) |
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Although marcasite doesn't make an exact fiveling, there are drawings in Vol. VI of Goldschmidt's Atlas der Krystallformen on Tafel 6 no's. 87, 91-95. I believe the original reports might be available on the web. They are from the 1800's.
What other minerals form fivelings?
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Pete Richards
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Posted: Aug 06, 2021 10:19 Post subject: Re: About cyclic twinning - (5) |
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Several isometric minerals form fivelings, including diamond, copper, gold, and I think silver.
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LDMarks

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Posted: Aug 06, 2021 13:56 Post subject: Re: About cyclic twinning - (5) |
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If grown by, for instance, vapor deposition then every fcc metal can produce fivelings and also icosahedra -- not as naturally formed minerals though. From Goldschmidt's atlas I found naturally occuring As, Diagond, Gold, Copper, Chalcopyrite, Marcasite and silver. Pyrite forms icosahedra only, which is odd. There seem to be many nice images of these, but few to none of fivelings.
N.B., many of the early papers are not on the web, or at least I cannot find them.
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Peter Farquhar
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Posted: Aug 18, 2023 12:56 Post subject: Re: About cyclic twinning - (5) |
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Eleven years ago today, on August 18, 2012, Tracy Kimmel initiated this FMF thread with a question "About Cyclic Twinning." Since then, this thread has garnered more than a quarter million views and become an FMF Featured Column. In celebration of this anniversary, I want to share a tale of an "ugly duckling" recently found to be a rare specimen of scientific and historical significance.
Rutile Description
The photo below shows a blackish-grey rutile (PF-3126) in somewhat rough condition and with little aesthetic appeal. This odd-shaped specimen measures approximately 6.3 x 5.8 x 4.5 cm and weighs 371 grams.
The morphology of this specimen (PF-3126) reveals rather complex twinning with repeated layers of cyclic twinned rutile crystals. As noted with rutile specimen (PF-3349) posted at the beginning of this thread, rutile specimens exhibiting both cyclic and polysynthetic twinning are extremely rare. Not surprisingly, both of these rutile specimens come from the same locality in Brazil.
Locality in Brazil for Complex Rutile Twins
Later on, we will learn this rutile specimen (PF-3126) was discovered near the Rio des Almas in the foothills of the Pireneus Mountains, a short distance north from Pirenópolis in Goiás, Brazil.
From a mineralogical perspective, Jordi Fabre described this place as "a not widely reported Brazilian locality but that is well known for its complex rutile twins" (e.g., see the rutile ID RLA-6C3 posted on Mindat).
According to the Schortmann Minerals label, the locality for this rutile is "Meiaponte," which is an old name for this city. In 1890, the city's name Meia Ponte (or Meiaponte in German) was changed to Pirenópolis.
Meia Ponte was originally settled by a group of Portuguese prospectors in 1727 who discovered gold along the Rio des Almas and stayed to explore the nearby foothills for emeralds and other treasure. The name Meia Ponte means "half bridge" in Portuguese and refers to what remained after a flood swept away part of a primitive bridge over the Almas River many years ago.
The glory days of gold mining around the Rio des Almas near Meia Ponte lasted from the mid-1700s until the early 1800s. Because the village was located at the cross-roads of the region, it grew in size and eventually became an important trading hub. Many years later, the city evolved into a tourist destination with popular festivals, historic buildings, nearby waterfalls, hiking trails, and scenic vistas.
Recent Provenance from the 1900s
Researching the provenance of this rutile specimen has been an intriguing journey. As Michael Shaw once posted on FMF, "Sometimes the history or story associated with a specimen eclipses the specimen itself."
The first key to unlocking this rutile's provenance is to decode the numbers in the upper left-hand corner of the accompanying Schortmann label. Fortunately, Bill Smith's 1991 article in the Mineralogical Record (v. 22, no. 6, p. 438) holds the secret.
In particular, the numbers "2812-33-37" on the label indicate this rutile was specimen #2812 in the Lechner collection, and the 37th specimen unpacked in the 33rd parcel sent by the famous Austrian dealer Anton Berger to Schortmann Minerals around 1954.
Bill Smith's article describes the famed mineral collection of Mauritius (“Moritz”) Joachim Lechner (1850-1903) and his second son, Adolf Lechner (1882-1952), of Vienna, Austria, as "one of Europe's largest and finest private mineral collections." The article provides a history of the Lechner collection and notes that it was built primarily by acquiring many well-known European collections at the time.
The Austrian dealer Anton Berger acquired Moritz Lechner's collection from the son Adolf shortly before his death in 1952. Berger then sold a large portion of the collection to the US dealers Raymond and Alvin Schortmann of Easthampton, Massachusetts. Bill Smith's article notes, "The [Lechner] collection was stored and displayed in Ray's basement. If it ever entered their showroom, it was many years after its arrival in Massachusetts." Those who have visited Schortmann Minerals and seen the Lechner collection may wish to share their experiences here.
Collectors evidently overlooked the Lechner rutile #2812, because it remained with Schortmann Minerals from 1954 until 1971. At that time, the Schortmann's business and its entire inventory were sold to Connecticut dealer Ronald Bentley. The rutile remained with Ron Bentley from 1971 until 1978, when a well-known New York collector finally purchased it. I acquired this rutile and its labels in 2004 from the dealer who had just gotten it from this New York collector.
Earlier History from the 1800s
An important question to ask is, "How did Moritz Lechner of Vienna, Austria come to acquire this rutile from such a remote Brazilian locality in the 1800s?"
The key to answering this question is once again in Bill Smith's 1991 Mineralogical Record article, which lists those sources Moritz Lechner used to build his mineral collection. Of the sources listed, the obvious one to investigate first is "Dom Pedro de Alcantra (1825-1891), second and last Emperor of Brazil," whose mineral collection Moritz Lechner acquired in Paris around 1890.
But Dom Pedro II was not a field collector, and his collection reportedly focused more on gold, diamonds, emeralds, and other gemstones from Brazil. The few records available provide no mention of his traveling to distant Meia Ponte, nor of his acquiring rutile specimens for his collection.
The next person to investigate on the list of Lechner sources is Johann Pohl (1782-1834), who Bill Smith's article notes "was probably responsible for forming the bulk of the [Lechner] collection" (p. 434).
"Pohl was one of the leading scientists who guided Austrian Princess Leopoldina, wife of Crown Prince Dom Pedro of Brazil to Brazil and later traveled on various routes through [that] vast country, by chance collecting a lot of rocks, ores and minerals for the Imperial collection in Vienna (and most probably also for himself)" (quoted from Gerhard Niedermayr, 1990.)
Moritz Lechner acquired Johann Pohl's collection from his son Josef Pohl (1825-1900), who had inherited the elder Pohl's collection. Josef Pohl was a renowned professor and chemist specializing in photography at what is now the Technical University of Vienna in Austria.
Johann Pohl and the Austrian Expedition to Brazil in 1817
Johann Baptist Emanuel Pohl (1782-1834) was educated in Prague as a physician and later practiced medicine in Vienna, Austria. He devoted much of his attention to botany as well as mineralogy, entomology, and other branches of natural history.
In recognition of his diverse accomplishments and scientific publications in these fields, Johann Pohl was invited by the Austrian government to join other distinguished scientists on the Austrian Expedition to Brazil in 1817.
The Expedition to Brazil was part of the negotiation for Austrian Archduchess Dona Maria Leopoldina (1797-1826) to marry Dom Pedro I (1798-1834), the son of King John VI of Portugal, the future Emperor of Brazil, and later the father of Dom Pedro II (1825-1891). Dom Pedro I was part of Portugal's royal family, who had escaped to Brazil, a colony of Portugal, before Napoleon's army first invaded Portugal in 1807.
The purpose of the Austrian expedition was to conduct a comprehensive study of Brazil's natural resources. Johann Pohl was put in charge of mineralogy for the expedition, and later became responsible for botany, too. Pohl spent four years from 1817 to 1821 traveling to remote parts of Brazil; visiting hundreds of villages; accumulating thousands of plant and mineral specimens; exploring gold, diamond, and emerald deposits; and much more.
As Pohl's health suffered from his extensive travels throughout Brazil, he was forced to return home to Vienna in late 1821. Other Austrian scientists remained in Brazil and continued with the scientific expedition until it ended in 1835.
The Rutile Specimen from Meiaponte
The final key to unlocking the provenance of the Meiaponte rutile may be found in the detailed journal of Pohl's travels in Brazil (see below). In 1832, Pohl published his first volume numbering 448 pages of "Reise im Innern von Brasilien" ("Travels into the Interior of Brazil"); his second volume covered 641 pages and appeared posthumously in 1837.
Pohl's travel journal contained his detailed personal notes, scientific observations, and descriptions of the geological specimens he collected. Fortunately, a scanned copy of Johann Pohl's "Reise im Innern von Brasilien" is available from the digital libraries of Hathitrust.org.
According to his journal, Pohl traveled through Meiaponte several times enroute to various Brazilian sites of geological interest. He often stayed overnight at the Meiaponte cross-roads to rest and resupply, and to explore the surrounding area during the daytime.
In his report of February 24, 1819, Johann Pohl noted finding a rutile specimen loose in a gulley near the Rio des Almas just north of Meiaponte (see pages 306-307 of Volume 1 of "Reise im Innern von Brasilien"),
"... Up to Meiaponte the mountain type remained the same and only changes, either with respect to the color or the size of the mica, which contained garnets as well as rutile (footnote 32), were noticed. But I did not find the latter ingrown, but only loose in the gulleys.
"Meiaponte lies between two branches of the Serra dos Pyrenacos, separated by the Rio das Almas, running from east to west, and consisting of mica schist. Above this, on the northern mountain range, the quartz schist occurs in such an excellent form as I have not encountered anywhere else in this realm. Informed in advance, I went in a north-north-eastern direction away from Meiaponte for half an hour.
"Immediately before the crossing of the Rio das Almas, undulating mica schist with large, coarse garnets and hornblende occurs, alternating with clay slate on the other side. After this, the quartz schist becomes visible, which increases the further one follows the mountain towards the east, and finally it covers the whole slope of the mountain for a long way. ... " (DeepL translation from German to English, 2023).
Footnote 32: Rutile, blackish grey, partly crystallized, with petals slightly uncoiled [as in a whorl or rosette], No. 311.
Others may be able to improve on my initial translation of Pohl's Footnote 32. The original German from "Reise im Innern von Brasilien" reads,
Footnote 32: Rutil, blättriger, zum Theil krystallisirt; schwärzlichgrau, etwas abgerollt. Nr. 311.
Johann Pohl reportedly collected only one rutile specimen, namely No. 311, on the Austrian Expedition to Brazil. His brief description of this Meiaponte rutile specimen No. 311 appears to fit the rutile specimen (PF-3126). Pohl's description was no doubt influenced by his ready familiarity with terms from botany, and by the fact that more specific terms for describing cyclic twinned rutile specimens were simply not available until Gustav Rose's seminal 1862 publication, “Ueber eine neue kreisformige Verwachsung des Rutils,” Annalen der Physik und Chemie (Poggendorff), v. 115, pp. 643-649.
With the elimination of other possible sources, Pohl appears to be the only documented source to have contributed a specimen from this remote locality to Moritz Lechner's collection. Since Lechner often bought entire collections to acquire a few choice specimens, one might expect this Meiaponte rutile was included with any fine Brazilian golds, diamonds, tourmalines, emeralds, and gemstones that Johann Pohl may have set aside for his own collection.
Summary
This rutile (PF-3126) is a rare example of repeated cyclic twinning from Meiaponte, an old locality known today as Pirenópolis, Goiás, Brazil. It is famous to mineral collectors for its especially complex rutile twins.
The provenance of this specimen likely dates back to the Austrian Expedition to Brazil of 1817. Botanist and mineralogist Johann Pohl found this loose rutile specimen No. 311 in a gulley near the Rio des Almas a short distance north of Meiaponte in 1819. Upon his death in 1834, this rutile passed to his son, Josef Pohl, who lived and worked in Vienna, Austria. The younger Pohl kept his father's collection until shortly before his death in 1900, when it was sold to Moritz Lechner, also of Vienna, Austria.
Based upon the research evidence collected so far, I believe Johann Pohl's rutile No. 311 was included in the sale to Moritz Lechner, and thus became rutile specimen #2812 in his collection. In any event, the Meiaponte rutile #2812 remained in Moritz Lechner's collection until his death in 1903, when his second son, Adolf Lechner of Vienna, Austria, inherited his father's collection. Shortly before Adolf Lechner's death in 1952, he sold the collection (including the Meiaponte rutile #2812) to Anton Berger, a famous mineral dealer in Vienna, Austria.
Around 1954, Anton Berger shipped the Meiaponte rutile to US dealers Raymond and Alvin Schortmann. It remained unsold in the Schortmann inventory until 1971, when Ron Bentley acquired their business. The rutile remained with Ron Bentley from 1971 until 1978, when a well-known New York collector purchased it. I acquired this rutile in 2004 from the dealer who had just gotten it from this New York collector.
Although this Meiaponte rutile has been in my collection for almost 20 years, much of this history only came to light recently as I was preparing to post one more example of an unusual cyclic twinned rutile. Thanks, Tracy, for your inspiration and this thread.
Mineral: | Rutile (PF-3126) with repeated cyclic twins |
Locality: | Pirenópolis, Goiás, Central-West Region, Brazil |  |
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Dimensions: | 6.3 x 5.8 x 4.5cm, 341 grams |
Description: |
Rare complex twinning for rutile. Attributed to Johann Pohl (1782-1834), who found this rutile specimen in February 1819 in a gulley near the Rio des Almas, in the foothills north of Meiaponte (now Pirenopolis). Ex. Moritz Lechner (1850-1903) collection, No. 2812, Vienna, Austria. |
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Mineral: | Schortmann Minerals label (circa 1954) |
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Mineral: | Johann Baptist Emanuel Pohl (circa 1830) |
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Lithograph by Adolph Friedrich Kunike (1777-1838) of Johann Baptist Emanuel Pohl (circa 1830). In the public domain. |
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Mineral: | Travels to the Interior of Brazil, volume 1 (1832) |
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Cover page of Johann Pohl's travel log with his notes from the Austrian Expedition to Brazil 1817-1821. Volume 1 published in 1832. |
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Pete Richards
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Posted: Aug 24, 2023 10:53 Post subject: Re: About cyclic twinning - (5) |
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Thanks for a wonderfully careful search for the provenance of this unusual rutile twin. I am struck not only by your effort, but by the importance of the availability on line of literature such as Pohl's book on his journeys in Brazil – books which may be of great interest but certainly only to relatively few readers. In addition, excellent digital translators extend our reach into writings in languages that we (I at least) understand to a limited degree if at all. Imagine trying to make this research effort 50 years ago!
Still, there’s room for uncertainty in trying to understand a short description (footnote 32) written nearly 200 years ago in a to-us foreign language by a natural scientist who had access to a very different set of scientific ideas and perspectives than we have today. You correctly point to the influence of botanical ideas at the time – I believe Linnaeus originally included Minerals as a third Kingdom along with Plants and Animals.
I would lean toward a different interpretation of the word “blättrig” as meaning lamellar or layered, and describing the frequent horizontal striations and two contractions that run around the cyclic twin and suggest a repeated layering or stacking in the vertical direction. You seem to interpret this as repeated twinning – in one case with the term “polysynthetic” – in addition to the basic cyclic twinning structure.
I see no indications that this “layering” is anything more than a surface growth feature. I suspect that the six individuals that are twinned cyclically are each crystallographically single from top to bottom. If so, the crystallography of this twin is not particularly unusual, though the vertical elongation is different from classical cyclic “sixlings” like those from Chester County, Pennsylvania.
Thanks again for a very interesting report!
_________________ Collecting and studying crystals with interesting habits, twinning, and epitaxy |
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mmauthner
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Posted: Aug 24, 2023 15:22 Post subject: Re: About cyclic twinning - (5) |
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Thanks for researching such an intriguing story. I am a fan of that kind of digging and frequently find myself down some rabbit hole or another.
If I may, here is another translation of footnote 32:
Original as you wrote it:
"Footnote 32: Rutil, blättriger, zum Theil krystallisirt; schwärzlichgrau, etwas abgerollt. Nr. 311."
My translation:
Footnote 32: Rutile, lamellar (lit. "leaflike"), partly crystallized; very dark gray (lit. "blackish gray"), somewhat abraded (hint at alluvial or eluvial abrasion). Nr. 311.
Thanks for a wonderful history!
Mark
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Tony L. Potucek
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Posted: Aug 25, 2023 09:18 Post subject: Re: About cyclic twinning - (5) |
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I thoroughly enjoyed reading about your well researched historical rutile specimen. Thanks very much!
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Peter Farquhar
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Posted: Aug 25, 2023 09:49 Post subject: Re: About cyclic twinning - (5) |
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One of the best features of FMF is having experts like Pete Richards and Mark Mauthner sharing their insights. I am very grateful for their help with this research.
Pete Richards makes important observations about the crystallography of this Meiaponte rutile specimen, and makes some necessary distinctions to improve its description. He also notes the challenges in interpreting what Johann Pohl meant in his short description of this rutile specimen in Footnote 32.
Mark Mauthner then provides an indispensable translation of Footnote 32. His translation not only supersedes my initial effort, but it certainly clarifies our understanding of Footnote 32. The key for me was Mark's pointing out the German word "abgerollt" can mean "abraded" in this context. On the other hand, the common alternatives suggested by translators, such as DeepL and others, seemed confusing and off track.
Now with Mark Mauthner's translation of Footnote 32,
"Rutile, lamellar, partly crystallized, very dark gray, somewhat abraded. Nr. 311."
we see that the description of Pohl's rutile No. 311 matches the photo of the Meiaponte rutile PF-3126. Therefore, it appears that Johann Pohl's rutile No. 311 was indeed included in the sale of his collection to Moritz Lechner, and thus became his specimen #2812. The rest is history.
Eureka!
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Peter Farquhar
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Posted: Aug 26, 2023 13:41 Post subject: Re: About cyclic twinning - (5) |
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The rutile specimen below (PF-3651) is from Graves Mountain, Georgia, and was once in Rock Currier's collection #3085. This rutile is quite unusual, because it has six sides yet no central cavity.
I am interested in a discussion of whether this rutile specimen exhibits cyclic twinning. Is it appropriate to call this rutile a "sixling"?
Mineral: | Rutile |
Locality: | Graves Mountain, Lincoln County, Georgia, USA |  |
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Dimensions: | 1.4 x 1.0 x 0.8cm, 4 grams |
Description: |
Unusual six-sided rutile specimen without a central cavity (PF-3651). Ex Rock Currier collection #3085. |
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Mineral: | Rutile sixling (idealized drawing) from Graves Mountain, Georgia USA. |
Description: |
Drawing from G. H. Williams (1890), "Elements of Crystallography," Henry Holt Publishers (New York), p. 198, as reproduced in "Annual Report of the Geological Survey of Arkansas for 1890," vol. 2 (1891), p. 325. Note Williams' use of the term "sixling."
This idealized drawing originally appeared in Professor Gustav Rose's 1862 article, and was attributed to Graves Mountain, not Magnet Cove as Williams reported. |
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Pete Richards
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Posted: Aug 27, 2023 13:29 Post subject: Re: About cyclic twinning - (5) |
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I am confident that this is a twin, a hexagonal sixling like the drawing. The main difference is that the pits shown in the drawing have been filled in on the actual specimen.
I can imagine distortions to a single prismatic tetragonal crystal that would cause it to look vaguely like a hexagonal plate, but such distortions would seem highly unlikely to occur. For such distortions to produce such a perfect hexagonal plate, with all faces balanced, is beyond credibility.
It might be possible, with careful examination and use of different lighting directions, to make out the twin boundaries between adjacent individuals on the flat plate on top of the twin, on the basis of differences in reflectivity between the two individuals. This is often possible with Graves Mountain twins, especially if their faces are slightly etched, but may not be possible on such a lustrous surface. Use of polarizing filters might help.
The attached photo is of a simple rutile twin from Graves Mountain twinned according to the same law. The flat face corresponds to the hexagonal face in the specimen that is the subject of this post. The parts of the face belonging to the two individuals are illuminated quite differently, in spite of the fact that they are co-planar.
Mineral: | rutile |
Locality: | Graves Mountain, Lincoln County, Georgia, USA |  |
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Dimensions: | 2.5 cm wide |
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Bob Morgan
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Posted: Aug 28, 2023 06:38 Post subject: Re: About cyclic twinning - (5) |
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I too tried to figure how your rutile would be a single and couldn't find any way that worked. The dimpling indicates fairly strong dissolution. perhaps there was also some redeposition that filled in the center.
In the photo there appeared to be some differences near the outer edges which would also indicate twin boundaries.
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James Catmur
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Posted: Aug 28, 2023 12:51 Post subject: Re: About cyclic twinning - (5) |
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It may be me, but I see very faint marks that are where the dimple should be
Mineral: | Rutile |
Locality: | Graves Mountain, Lincoln County, Georgia, USA |  |
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Peter Farquhar
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Posted: Aug 29, 2023 14:31 Post subject: Re: About cyclic twinning - (5) |
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Based upon the helpful feedback, I carefully examined the top of the rutile specimen again. This time I experimented with different lighting sources, temperatures, and angles; polarizing filters; and 10x, 20x, and 40x stereo magnification. In the end, I could find no evidence of where a central cavity, pit, or dimple might have been.
Using a different camera, I did take another photo of this rutile specimen (PF-3651) in the same orientation. This photo shows a faint scratch not visible in the earlier photo, but otherwise nothing else is revealing. I wish I had capabilities for photographing magnified images of this specimen.
Thanks again for your comments.
Mineral: | Rutile |
Locality: | Graves Mountain, Lincoln County, Georgia, USA |  |
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Dimensions: | 1.4 x 1.0 x 0.8cm, 4 grams |
Description: |
Second photo of rutile specimen PF-3651 under different lighting conditions than the first photo above. |
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Bob Morgan
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Posted: Aug 29, 2023 16:40 Post subject: Re: About cyclic twinning - (5) |
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Examine the outer edges where two crystals meet, like the edge to the upper right. Cyclic twins of rutile often have places where one crystal overlaps the other in ways that don't have similar development on the edges of faces of single crystals.
How about the other side opposite the dimpled surface? If that is a contact surface, perhaps the dissolution would be more likely to fill in the center with redeposition.
Whatever, this is quite special. You and Rock have good taste.
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Pete Richards
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Posted: Aug 30, 2023 07:32 Post subject: Re: About cyclic twinning - (5) |
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Excellent point, Bob!
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Peter Farquhar
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Posted: Sep 08, 2023 09:38 Post subject: Re: About cyclic twinning - (5) |
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Rutile eightlings are found in several localities worldwide, but they are somewhat rare from Graves Mountain. Below is a photo of an unusual rutile eightling (PF-3645 ) on matrix from Graves Mountain, Georgia. This thumbnail specimen was acquired in a trade, and came originally from Neal Pfaff of "M. Phantom Minerals" many years ago.
After studying hundreds of rutile eightlings, I found they all share one distinguishing feature -- the “zig-zag” pattern of twinning (in German, “Zickzack”). The “zig-zag” pattern occurs ideally when the vertices on the rutile’s perimeter alternately lie in one of two parallel planes. I explain the reasoning and history behind this particular definition in a forthcoming paper that introduces a taxonomy for classifying different types of rutile eightlings.
Meanwhile, it is important to note that rutile eightlings are not defined here by the number of sides. In other words, it is possible for a rutile eightling to have more (or fewer) than eight sides (e.g., with aggregations of intergrown twinned crystals). Thus, it is the zig-zag twinning that defines a rutile eightling, not the number of sides per se.
For other examples of zig-zag twinning, see the photo of the rutile eightling (PF-2965) from Graves Mountain posted earlier in this thread, or the photos of any of the eightling rosettes from Magnet Cove also posted here.
Mineral: | Rutile eightling (PF-3645) |
Locality: | Graves Mountain, Lincoln County, Georgia, USA |  |
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Dimensions: | Overall 3.0 x 2.7 x 1.8cm. Main crystal 1.6 x 1.4 x 1.3cm. |
Description: |
Unusual rutile eightling from Graves Mountain. From Neal Pfaff of M. Phantom Minerals. |
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