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EducationPositive vs. negative rhombohedra

24th Nov 2016 15:46 UTCEd Clopton 🌟 Expert

In the crystallography of various minerals (quartz and calcite, for example) there are "positive rhombohedron" and "negative rhombohedron" forms. I understand that one is rotated 120° about its c-axis with respect to the other (or is it 180° about one of its a-axes?) and that the intersection of the two forms generates the classic six-faced termination of a quartz crystal, usually with three larger faces of one rhombohedron alternating with three smaller faces of the other.

My question is this: How does one decide which rhombohedron form on a given specimen is positive and which is negative? Is it just a matter of calling the dominant rhombohedron on that specimen "positive", thereby making the other one "negative" by default, or are there objective characteristics that make one positive and the other negative?

24th Nov 2016 19:01 UTCRonald J. Pellar Expert

The negative and positive rhombohedron have a rotation angle of 60 degrees around the c-axis. It is my understanding that the positive rhomb is usually the larger of the two. However, when they are the same size, I have no idea but when that does occure with the absence of the prism faces it is called pseudo-cubic.

Example:

and

Pseudocubic Quartz

Pégut, La Chapelle-sur-Usson, Issoire, Puy-de-Dôme, Auvergne-Rhône-Alpes, France

24th Nov 2016 23:03 UTCAmir C. Akhavan Expert

Positive rhombohedron and negative rhombohedron are just naming conventions reflecting the orientation of the rhombohedra relative to the crystallographic axes.

One rhombohedron is rotated about the c-axis by 60° relative to the other (120° rotation would just bring the rhombohedron back into the same position).

The name has nothing to do with the sizes of the faces.

On the mineral page of quartz http://www.mindat.org/min-3337.html , on Fig.4, you can see computer renderings of the basic crystallographic forms of quartz of a right-handed crystal.

A pseudocubic quartz habit is the result of a single rhombohedral form dominating the shape, not two. If you combine positive and negative rhombohedra and leave out the prism faces, you get a Cumberland habit.

For common habits see Fig.6 on the mineral page of quartz http://www.mindat.org/min-3337.html

25th Nov 2016 12:51 UTCAlfred L. Ostrander

Ed

If a quartz crystal shows the trigonal trapezohedron and/or trigonal dipyramid the positive rhombohedral form can be determined. Properly orient the trapezohedron or dipyramid and the positive rhombohedron will be the forward orientated face. As Amir said, this is all by convention but convention is based on observation and theory. So, by chosen convention based on solid science you can orient the positive and negative rhombohedron.

Taking a step further, differences in the growth rate of the positive and negative rhombohedrons in quartz has indeed been noted. I think that observation has indicated a trend toward the larger faces being the positive rhombohedron. It sure would be nice to always have at least a trapezohedron or dipyramid to verify this. This does lead me to ask or at least wonder if any study has verified the trend that that the trapezohedron or dipyramid do point to the larger face, when present, of the positive rhombohedron. Needless to say, convention does seem to indicate if you can clearly see one set of rhombohedral faces is larger than the other then the larger is considered the positive rhombohedron. Keep in mind that this may only be a convention of convenience.

With very equal development of the two rhombohedrons and no other evidence I think the best that can be said is the two faces are developed in equalibrium. But then watch out for the beta quartz paramorph. That is another story for another day. Just take a look at the quartz crystals from the Huanggang Mine in Inner Mongolia. It has been said that these are beta quartz paramorphs.

Best Regards,

Al O

Best Regards,

Al O

25th Nov 2016 18:44 UTCRonald J. Pellar Expert

Thanks Amir for the clarification on pseudo-cubic quartz. I was wrong on that one, must be old age! :-D

25th Nov 2016 23:54 UTCAmir C. Akhavan Expert

The caption explains one way to distinguish positive and negative rhombohedra. The negative rhombohedron is the bigger one on this crystal. Unfortunately, more often than not, the s face is dull or shows no striation. and then you are out of luck.

With positive trapezohedral faces there's usually no problem, they don't sit in the middle between the faces but more under the r face (as shown on Fig.5 on the quartz page) and negative trapezohedra that occupy the mirror positions are very rare and still sit under the r face. So if you see a trapezohedral face on an untwinned crystal, the positive rhombohedron is above it. For Dauphiné law twins the distinction between positive and negative rhombohedral faces may be pointless as the faces can be composites.

Even if an evently developed crystal would show larger r faces under certain environmental conditions - most crystals are somewhat distorted, and the size of the rhombohedral faces goes with the overall shape. Extreme example: Dauphiné habit.

You can try to identify faces by surface features (pits, growth hillocks) - frankly I would not be able to do that without looking it up in a book or article, and there's a good chance that the one surface feature you notice on the crystal is not in the book.

As a side note, I have never seen beta quartz that grew in a cavity that has a "Cumberland habit". Such beta quartz crystals are usually prismatic and tapered and may even be extremely elongated like whiskers. The Huanggang Mine specimens have switched their mode of growth from one with fast growing rhombohedral faces (slender crystals) to one with fast growing m prism faces (Cumberland habit). Some specimens show scars of dissolved calcite blades, that doesn't make sense unless the temperature during growth was well below 500°C.

26th Nov 2016 15:54 UTCAlfred L. Ostrander

Amir,

As to the crystals from the Huanggang, I was referring to the stacked crystals that do not seem to show any prism faces and some are more or less sceptered on the top of crude prismatic crystals. Many of these crystals are colored green by inclusions of what is often considered hedenbergite. I should have been clear on the type I was referring to. A very large amount of them in the Mindat photo galleries for the Huanggang mines are captioned as beta quartz. If this is not the case should the captions be edited? Please check them out as I value your insights.

As you indicated in the caption of your photo, the r face is often larger but that is not always reliable. Isn't that what the general case is all about? When crystals are heavily distorted either form can show the single largest face. The trick is to look at both sets of faces and see which set dominates. Again, not always reliable, particularly if any one face is quite enlarged and almost totally dominates the termination of a crystal. And the photo you presented demonstrates why I brought up the role the presence of the s face is important. That is a reliable objective characteristic that Ed inquired about.

But to the point of Ed's original question, the general case, lacking any other evidence or special cases, has been accepted by many. This convention was handed down to me by my mineralogy professor and optical mineralogy professor when I was in university. Maybe the real reason was what else are you going to do with a wooden model on your crystallography exam? It was expected you name it something. It was expected that a proper stereo net was produced. I applied the convention that the larger or dominant set of faces was the positive rhombohedron. Twice, with two different professors. Was given full credit for the correct answer. Twice. I also got the trapezohedral and dipyramidal faces right on those models. I know this because I still have those test results in my crystallography notebook. When I tutored and taught mineralogy I would have been obliged to give Ed full credit if he cited the general case and applied it properly. You are correct to point out special cases and I appreciate your insights. I asked the same question Ed asked when I was a student. And I am still wondering if a statistical analyses of alpha quartz (trigonal trapezohedral, class 32) all special cases aside would show the trend of the general rule has any validity. By virtue of several five gallon buckets full of self collected Arkansas quartz crystals and a rather large number of Herks I do know there are an extremely large number of quartz crystals that may very well fit in the general case and that is why it was presented to me as a student. Ed, I hope you got an answer and enjoyed this discussion with Amir as much as I have.

Best Regards,

Al O

26th Nov 2016 18:54 UTCAmir C. Akhavan Expert

> I was referring to the stacked crystals that do not seem to show any prism faces and some are more or less sceptered on the top of crude prismatic crystals.

Yes, I was talking about those.

> And the photo you presented demonstrates why I brought up the role the presence of the s face is important. That is a reliable objective characteristic that Ed inquired about.

Trapezohedral faces are reliable indicators for r and z faces.

Bipyramidal faces are reliable only ifthey show striation, for the geometrical reasons given above. Otherwise they are completely useless for determining the nature of the rhombohedral faces.

If the s face on the photo had no striation, the guess based on the general case would have been the right face is r, which is wrong.

I haven't done statistics and I can't recall one having done one, but on quartz crystals with trapezohedral faces they seem to sit under the larger rhomobohedral face more often.

For Herkimers that seems to be correct, too, which can be tested because most have a striation on their s faces.

> This convention was handed down to me by my mineralogy professor and optical mineralogy professor when I was in university. ...

I've looked it up: The naming convention for negative and positive rhombohedra is based on the way these forms are plotted in a stereographic projection.

Accordingly the terms positive and negative are used for quite a few "blablahedrons".

Other minerals of symmetry classes -32/m, 32, -3 and 3 will all have positive and negative rhombohedra in the same relative positions to the crystallographic axes.

I'm not into stereographic projections, so a crystallographer might shed some light on it.

Anyway, the size of the faces has nothing to do with the names.

27th Nov 2016 14:58 UTCAlfred L. Ostrander

Amir,

As a crystallographer I am trying to shed some light.

Good grief, another fake crystal form: the blablahedrons. Great crystallography there.

With the "blablahedrons" I am stepping out of this. I no longer consider it a useful discussion.

Best Regards,

Al O

27th Nov 2016 15:31 UTCAmir C. Akhavan Expert

So be it.

I have noticed that I made a mistake earlier that I need to correct:

"... and negative trapezohedra that occupy the mirror positions are very rare ..."

That's nonsense - they are rotated with respect to each other, negative ones sit under z. So trapezohedrons as such are also not 100% reliable for distinguishing positive ad negative rhombohedra.

28th Nov 2016 07:38 UTCEd Clopton 🌟 Expert

Useful or not, I've learned some things from this discussion. Thanks to everyone who has contributed (and who may contribute further).

28th Nov 2016 14:01 UTCMark Holtkamp

Positive and negative rhombohedra are correlate forms, these a forms with a specific morphological relationship.

I couldn't find decent explanations in English on the internet, but several in German (search on 'Korrelate Formen').

Like Amir said the terms 'positive' and 'negative' are conventions as (I guess) is the choice of which rhombohedron is the positive one.

But 'positive' and 'negative' always relate to the orientation of the rhombohedra with respect to the symmetry elements of the point group.

Size has nothing to do with it. All rhombohedra, also steeper ones that occur on quartz, are positive rhombohedra if they lie in the same section as the base positive rhombohedron. Even if the correlate negative rhombohedron happens to be the 'dominant' one on quartz.

These are objective mathematical criteria and not general rules. Perhaps the fact that the basic positive rhombohedron on quartz almost always is dominant has caused some confusion.

Mark.

30th Nov 2016 12:15 UTCAlfred L. Ostrander

Hello All,

I thought I would leave this alone but I did find a very good web site I could reference in regards to Ed's original question about the convention of referring to the positive r face as generally the larger face and the negative z face as the smaller face.

For general discussions on many aspects of quartz see www.quartzpage.de

For some specifics check these two links.

www.quartzpage.de/crs_intro.html

In the discussion of Fig 2: Common Quartz Crystal Faces the following description occours.

r: three larger, often roughly triangular faces at the crystal's tips. In well developed crystals these faces are always present.

z: three smaller, usually triangular faces also at the crystal's tips.

www.quartzpage.de/crs_habits.html

In the discussion of the trigonal habit of quartz the following statement is made.

The rhombohedral z faces generally tend to be smaller than the r faces.

Both topics refer to the generally larger r faces and the generally smaller z faces. I think this does indicate size has something to do with the issue. Maybe I am wrong but I think larger and smaller does refer to size.

I did some double checking on my old college lecture notes. I have no reference to cite for this. That's not uncommon for lecture notes. To the point, some older crystallographers referred to the major or dominant form as the R form as compared to the minor form or r form. I take this dominant to indicate larger and minor to indicate smaller. Perhaps more fully developed and lesser developed indicates the same thing. Also note the use of capitol R and lower case r. Today, the R form correlates directly to what is now called the positive form and is usually labeled r. The old r form correlates to the the negative rhombohedron now referred to as z. I am of the thinking that the use of the upper and lower case is not coincidence.

I think that was what this has been about. You decide for yourself if larger face and smaller face has anything to do with answering Ed's original question.

Amir, I think this indicates how simple the answer to Ed's question should have been. You could have very easily referred Ed to the quartz page web site. Correct me if I am wrong but I think the quartz page web site is written by one Amir C Akhavan. Is that you? If so, my compliments.

Bet Regards,

Al O

30th Nov 2016 12:38 UTCAlfredo Petrov Manager

Yes, that indeed is our very own Amir... who is probably just too modest to refer people to his own website. ;-)

30th Nov 2016 13:52 UTCAmir C. Akhavan Expert

Thanks to pointing out this error on my website, sloppy description of Fig.2, it could be interpreted as r faces being generally larger - which is nonsense - they only tend to be larger.

I will have to correct it to match what I have said earlier here.

Ed's question was this:

"How does one decide which rhombohedron form on a given specimen is positive and which is negative? Is it just a matter of calling the dominant rhombohedron on that specimen "positive", thereby making the other one "negative" by default, or are there objective characteristics that make one positive and the other negative?"

The answer to Ed's question was as simple as I could do without getting too inaccurate, but I'll repeat it in a simple summary:

You can determine positive and negative faces with some confidence by

a) surface features (etch pits etc.) if present

b) position of positive trapezohedra

c) position of bipyramids, if and only if they are striated

Combinations of a b and c will give you very good confidence.

You cannot rely on the size of the faces (an example pghotograph has been shown, I will upload another example soon), and that is also not the reason for naming them positive and negative.

The objective characteristics are the relative orientation of both forms to the crystallographic axes.

30th Nov 2016 21:26 UTCRonald J. Pellar Expert

The general observation that the r faces are usually larger than the z faces would be consistent with a faster growth rate in the z direction. Since quartz is in the trigonal system, the difference in growth rate is not unreasonable and would account for the general difference in size and make same size r & z faces very rare indeed. In a trigonal xtal the growth rate along an a axis can certainly be different than in the direction between a axes. If this reasoning is correct than assigning the r face to larger rhombohedral faces ties the larger faces to the slower growing xtal direction consistently and precisely. There should be no confusion on assignment of the r & z faces with only the one exception of their being of same size, which brings up the question of "beta" quartz pseudomorphs. :-D

30th Nov 2016 21:59 UTCAmir C. Akhavan Expert

> If this reasoning is correct than assigning the r face to larger rhombohedral faces ties the larger faces to the slower growing xtal direction consistently and precisely.

No.

Your reasoning says "usually", your conclusion says "always".

1st Dec 2016 18:38 UTCRonald J. Pellar Expert

That is correct and intentional Amir. However, the "always" conclusion was not explicit and it was tempered by my comment on the rare occurrence of equally developed r and z faces and reference to "beta pseudomorphs" with a tongue-in-cheek emoticon. Which, by the way, is a perfectly logical reason for the equal development of the r and z faces absent any evidence that growth conditions were not conducive to beta quartz.

The growth conditions in a pocket can influence the relative growth rates of faces and even alter or distort the xtal forms. But the differential growth rate between two forms will still influence the relative sizes of the faces themselves. An example of unusual growth that still maintains this relation ship is:

By going through all of the photos of this specimen you can see that the r face is consistently bigger than the z face. If growth conditions are right the faster growth rate of the z face can result in its disappearance completely, as in the photo posted previously in this thread.

1st Dec 2016 22:20 UTCAmir C. Akhavan Expert

1. Nobody doubts that in most cases r faces are larger than z. And of course there is a physical reason behind this.

2. Sometimes the z face is larger, I have presented an example of such a specimen.

Conclusion: Size is not a reliable property for distinguishing r and z faces.

In other words: "Bigger rhombohedral faces are r faces" is an erroneous conclusion.

I have presented various methods of identification that are more suitable.

How do you know which are r and which z faces on your gwindel specimen?

2nd Dec 2016 00:09 UTCRonald J. Pellar Expert

I seemed to have missed your example and your rational for proving the larger face is a z face!

2nd Dec 2016 01:08 UTCAmir C. Akhavan Expert

Another example.

Where is the r face?

2nd Dec 2016 05:18 UTCSteve Hardinger 🌟 Expert

A positive rhomb sees the glass as half full whereas the negative rhomb sees it as half empty...?

2nd Dec 2016 14:05 UTCJosé Zendrera 🌟 Manager

Striation in the s-face suggest that r-face is the smaller at center.

Is this rule always reliable?

2nd Dec 2016 17:15 UTCAlfred L. Ostrander

Jose,

You are correct, this suggests the r face is the physically smaller face. So does the smoothness of the probable r face and the roughness (striations) of what would then be the adjacent z faces.

However, the original question Ed proposed and the answer I then gave is based on the presence of three forms, and only these three forms, a prism m, the positive r face and the negative z face. Objective information beyond just those three faces can be used to determine which face is the r and which is the z. Maybe I didn't make that clear enough in my first reply or any subsequent reply. Maybe, maybe not. However, with no other information and I repeat, no other information, the larger physical rhombohedral face is customarily designated as the positive r rhombohedron. This is a long standing custom. Go look at the drawings on many many pages showing the forms of crystal faces. Even the chart on the Mindat quartz page follows this custom. If you look, note the larger green faces r vs the smaller pink faces z. As another source, view the crystal projections and text of quartz in Manual of Mineralogy after J D Dana 20th Edition, page 440. So everyone, I am holding out and standing for Dana. And the convention is not always reliable but it is not an erroneuos conclusion. It is convention and is pragmatic. And Amir, your better solutions are great but they go beyond the paramaters of the general convention. This is not a case of either/or, it is a case where appropriate information makes a better answer. And it does not make the lesser case "erroneous". If that case is so erroneous, how come so many texts and crystallographers use it? Look up the Dana citation I presented. It is a special case and as such is not erroneous. That is why it appears, even in Dana.

The second photo case Amir has presented contains two additional pieces of information, the striations on the s face and the striations on the z faces. The additional pieces of information (and either one would generally suffice) would negate the general rule. It appears Amir is posting what ever he can to prove the r face is not always the largest. (See the first picture he posted.) Lots of cases exist when more complete evidence beyond the three forms listed exist. And in those cases the r form may be smaller. Amir is posting great points, arguments and photos. In my opinion, they are not the basic answer to the original question. Great stuff, but not the answer to the original question. I think Amir is trying to point out what I also presented. Objective information does exist but often goes beyond the three faces of the general rule. Actually, any additional information immediately takes one beyond the general rule. And your comment that the striations on the s face are necessary, I present the opinion that the simple presence of an s face, striated or not may take the general rule out of play. You are again faced with the question of which rhombohedron is which. But no one said any of this will always be easy or that general positions are always reliable.You keep gathering information and do the best you can.

Best Regards,

Al O

2nd Dec 2016 20:05 UTCMark Holtkamp

Hi Alfred,

Maybe I am missing your point, but isn't it the other way around? The positive and negative rhombohedron are different crystal forms, with different properties. Most of the time the positive rhombohedron is the larger one on quartz crystals. That's a property of quartz, so you would expect to see that reflected in crystal drawings.

If you have a crystal with only m r z faces, and no other information.. yes you can make an educated guess and assume that the larger rhombohedron is the positive one.

My answer to Ed would be that is is not a matter of decision. Without additional information you don't know for certain which rhombohedron is positive or negative. But it likely would be the dominant one :-)

I tried to find more information on the striatons of the s face, but all authors I read simply state that the striations run parallel to the s-r edge, without further references or explanation. I hope Amir can tell us more.

Mark.

3rd Dec 2016 01:05 UTCAlfred L. Ostrander

Mark,

I think what I have been saying is exactly what you said. You can make an educated guess and assume the larger rhombohedron is the positive one if you have a crystal with only the m, r, and z faces. I have been saying that it has been a long standing convention to do just that. And the convention or general rule is arbitraty but it is not erroneous. And that rule makes the decision for you. You stay with convention and consider the larger form the major or positive rhombohedron. The smaller form has to become the minor or negative rhombohedron. Please re-read the second paragraph in my response to Jose. And to quote Dana:

In some crystals one rhombohedron predominates or occours alone. It is chosen as r{10-11}.

My response to Jose was in regards to the additional information provided that pointed to the small smooth rhombohedron being the positive one. Also check back to Amir's list referring to the possibility that the negative rhombohedron may not have smooth faces. In the second photo I believe you can clearly see the smooth frontal face and the faces on each side of it are not smooth. I referred to that as an indication (along with other evidence) that those faces were most probably two faces of the negative rhombohedron. As you said, "most" of the time the positive rhombohedron is the larger one on quartz crystals. But that word most leaves the door open and Amir has clearly shown that several times. I will add this caveat. I always like to have the crystal in question in my own hands so I can rotate them and see every face. ID from photos isn't always ideal. That said I think that Amir did a good job with the photos.

In the cases of the two photos Amir has posted, additional information indicates the smaller face may indeed be the positive rhombohedron. That is where the additional informatiom comes into play. And that is why I said in my first posting that additional information can be objectively used to determine which rhombohedron is which.

I think the photos Amir and the points he made demonstrate quite well the position of the striae on the involved faces and their implications. Striations are oscillations between two faces trying to occupy the same space. Amir's explanation above is solid.

Positive and negative forms of rhombohedrons and other positive and negative forms found in other systems and classes have a special relationship. Each is different as indicated by the Miller indices for each form. However, point theory indicates a rotation and an inversion occours from the positive to the negative form. If you have a calcite crystal, orient it in the position of the positive rhombohedron. Rotate it and then flip it. Faces should now be in the position of the negative rhombohedron. That should demonstrate the special relationsip quite nicely. I am not sure what you mean by different properties.

Best Regards,

Al O

3rd Dec 2016 20:33 UTCRonald J. Pellar Expert

Amir,

I am having a problem with the two photos you present in this thread. In both photos the striated face is bounded by a r, a z, and two m faces yet the outline of the face is rhomb in one case and a kite in the other. It seems to me that they both cannot be the s face, so which faces are they? These outlines are fixed by the appropriate miller indices and one should be able to derive their correct designations therefor determine which rhombohedron is 4 and which is z.

3rd Dec 2016 22:02 UTCAmir C. Akhavan Expert

> It seems to me that they both cannot be the s face, so which faces are they?

Just read the captions of both photos.

(Mark, Alfred, sorry for not responding to your posts first, I'll do that later when I have more time)

3rd Dec 2016 23:25 UTCMark Holtkamp

Alfred,

With properties I mean physical properties, like solubility and size/shape of etch pits (see Rykarts Quartz Monographie or this link
link fig. 19 and 20), piezoelectical properties, hardness (http://www.quartzpage.de/gen_phys.html), growth rate etc.

Because r and z faces have different properties, I still have problems with statements like that of Dana, in my opinion this only leads to confusion (e.g. etch pitch geometries that belong to the z face in the the conventional unit cell orientation, become r face etch pits if another rhombohedron is chosen as the positive one).

I can't quite follow you calcite example. If you want to transform the positive rhombohedron to the negative rhombohedron all you need is a rotation around 60 degrees. No inversion required. It should be clear that this is not a symmetry operation in the calcite and quarz point group, and there are no symmetry operations in these pointgroups that transform positive forms to correlate negative forms.

Mark.

4th Dec 2016 14:45 UTCAlfred L. Ostrander

Mark,

Mark, I brought up a practical exercise to rotate a positive rhombohedron and indicate how it fits into the physical position of the negative rhombohedron. That is all. It works when you are playing around trying to orient a crystal. Maybe I should have more clearly separated the other comment about checking out the positive and negative rhombohedrons following point theory. Look at both, but separate examples, as useful to show the geometric relationship. That geometric relationship is why they are separated out as the positive and negative forms. If I hand you two rhombodral calcite crystals of very similar size and shape, how do you tell them apart? You can orient both of them in the positive or the negative position on a crytallographic set of axes. So what do you do when they are in combination in a calcite crystal? You do the same as the classical crystallographers did with quartz. For general purposes you orient the big form in the positive position and the small form in the negative position. There was no intent to imply I was attempting to rotate a face of positive rhombohedron into the face of a negative rhombohedron. And the relationship between other positive and negative forms in other systems and classes is pretty much the same. Look at the physical shape and the positions each form occupies. Great exercise to learn how to sort them out when dealing with specimens. As a suggested exercise, look at zunyite as an example from another class and system. Look at the combination of the positive and negative forms and their relative positions. And what form do you have when the two forms have developed in equilibrium? These are examples where the classical crystallographers set up general or conventional solutions as guidance. You can always argue convention until it becomes trivialized. That still does not make those conventions erroneous or useless. We might as well argue why the elements silicon and oxygen bear those names and why a particular combination of those two elements are called quartz. Why don't we toss out that convention and call it silica or silicon oxide, or maybe silicon dioxide?

This brings me to the point that following some forms is difficult. Back to quartz. Many crystallographers accept the idea that forms with simpler Miller Bravais indices are the most commonly seen. Other faces like the trigonal trapezohedrons are far less common. So what do you do when the general form of the class is not often seen and not fully developed? You most likely do what so many crystallographers did. You punt. You set up a convention. And that is why you see so many projections of the prism and rhombohedrons presented as they are. I know I am repeating myself. I am hoping this concept sinks in. Like it or not, that is what they did. To expand on an earlier comment, it sure would be nice to have trigonal pyramids and well developed trigonal trapezohedrons, striations aside, to properly orient quartz crystals. Or, as you indicated, all the different characteristics of the positive and negative rhombohedrons of calcite available to determine which is which. And if a trigonal pyramid shows only one face in the left handed position, regardless of striations, I'll orient that face into its proper position on the axes regardless of the size of any rhombohedral face. Remember, if the left hand form and the right hand form appear, the crystal is a Dauphine twin. that is real good evidence for me to choose that orientation. I would be following the case that both forms do not present themselves in the same single crystal. Note the word single, indicating no twinning is present. For more on that, go read Dana again, same edition and page I cited earlier. Comments on the value of the trapezohedron as the true and best indicator of the class symmetry are also there. You don't have to take my word on this.

As to Dana and many many other crystallographers, this became the convention. Be it arbitrary, confusing, disagreeable or whatever, there you have it

What I have been presenting through this thread are some concepts readily double checked in many textbooks and some practical or hands on things I have learned from many years of experience and many many specimens I have worked with through over 45 years. You are allowed to agree or disagree. You are all allowed to put into practice the things you have learned just as I have. I will state again, I will follow the convention of Dana and many other accomplished crystallographers in their treatment of the three basic forms found in many quartz crystals. If for no other reason, it is out of respect for the incredible work they did. That goes for Naumann, Penfield, Goldschmidt, Tutton and others. I am always amazed at just how right they got almost every last bit of it.

Best Regards,

Al O

4th Dec 2016 17:51 UTCEd Clopton 🌟 Expert

As the one who opened this can of worms, allow me to say that my original question has been answered to my satisfaction: yes, there is an objective difference between the positive and negative rhomohedon forms; and yes, although there is a way to tell which is which by eye, it's not always possible to do so with certainty since other key faces often are missing, but in quartz, at least, the larger faces usually (with all the qualifications that have been threshed out above) belong to the positive (r) rhombohedron. Thanks!

4th Dec 2016 18:24 UTCJosé Zendrera 🌟 Manager

I have understood that a x-face, when present, is always under a r-face. Then, what happens when there are two x-faces below adjacent rhombohedral faces? That means one of them is of the negative trapezohedron? Anyway in this case seems that x-faces don't help to discern between r and z faces.

4th Dec 2016 21:51 UTCAlfred L. Ostrander

Jose,

The trigonal trapezohedra are the general form of the class and when observed reveal the true symmetry. Hurray for the general form! That gives them priority. Properly place them and everything else has to follow. See Dana as previously cited. The trapezohedron in the upper left corner of the frontal prism face would be considered the negative trapezohedron 'X and the upper right trapezohedron is the positive trapezohedron X' . Most likely these are the (61-51) and (51-61) faces respectively. Using this orientation the trazohedrons sit at the lower corners of the positive rhombohedron. That is the position the positive rhombohedron must occupy according to the indices (10-11) made necessary by the position the trapezohedrons having been placed in and their proper place according to their indices.

Looking at the photo, I think I have the faces in the proper places. The left face is sitting lower than the right face. It appears the positive rhombohedron on this crystal isn't all that large. But this is a case where more information is present and the trapezohedrons are the indicators of the proper orientation.

I chose the orientation I did but I have no idea if any pyramidal or trapzohedral faces appear on the back side of the crystal. Anything on the back may or may not change anything. I did the best I could with the information presented. Nice crystal.Thanks for sharing!

Best Regards,

Al O

4th Dec 2016 22:13 UTCMark Holtkamp

Alfred,

Yes I think I see now what you were saying with your previous calcite example, in other words: you can transform a positive calcite rombohedron to a negative rhombohedron, using a symmetry element that is not part of the calcite point group, but is part of the point group with the highest symmetry in the same crystal system. If that is what you meant, I agree, this is the definition of what correlate forms are.

What would I do with a calcite crystal that is a combination of a positive and a negative rhombohedron? With calcite the problem can readily be answered by looking for cleavage planes. But without these, I would accept that I wouldn't be able to properly identify the forms. I would never publish a drawing implying that the bigger one is the positive rhombohedron. Of course, compared with the times of Goldschmidt, my drawing would have little scientific value anyway. I also have great respect for the crystallographers of old and I understand that without the data and tools we have nowadays, they had to make certain assumptions in their publications. I f these are the conventions you mean I'll go along with that.

Regards, Mark

4th Dec 2016 22:28 UTCMark Holtkamp

Jose,

I would say this is a right-handed Dauphiné twin, likely with the trapezohedron {51.1} as the general form.

Mark.

4th Dec 2016 22:36 UTCMark Holtkamp

Alfred,

Assuming you mean {6-1-51}, would that not result in a crystal with both right and left correlate (and enantiomorphic) trapezohedron on the same crystal? I would have no problem with that but conventions say that this must be a Brazil twin.

Mark.

Edit: changed negative / positive to left / right

5th Dec 2016 00:22 UTCAmir C. Akhavan Expert

José Zendrera Wrote:

-------------------------------------------------------

> Striation in the s-face suggest that r-face is the smaller at center.

> Is this rule always reliable?

Quite reliable, if striation is present. There can also be elongated growth hillocks and dissolution pits running in the same direction. I would not claim 100% certainty.

It's like the striation on the prism faces, which runs perpendicular to the c axis, regardless of how fine, wavy, coarse, regular etc. it looks. It can be absent, but it won't run parallel to the c axis - there's only one exception I'm aware of: on industrial quartz grown in alkaline solutions the growth hillocks may be oriented obliquely, but there is no striation like the one seen on natural crystals. If you want artificial crystals to show the same striation as the natural ones, you need to grow them in a sodium chloride solution, in which they grow rather slowly.

José Zendrera Wrote:

-------------------------------------------------------

> I have understood that a x-face, when present, is

> always under a r-face. Then, what happens when

> there are two x-faces below adjacent rhombohedral

> faces? That means one of them is of the negative

> trapezohedron? ...

No, that's simply a Dauphiné law twin, quite common, in your case it's right-handed, as Mark said.

No negative trapezohedron is present on the crystal. These would sit at a different position, anyway, simply right of the x faces, on the neighboring prism face, just around the corner, so to say, and not on the other side of the same prism (that would be a Brazil law twin). Simple sketches of these twins are on Mindat's quartz mineral page (figs. 7 and 8).

I'm not going any deeper into all this. I'm currently preparing two Mindat articles on quartz crystal forms and quartz crystal habits, to go more into detail than I could do on Mindat's quartz mineral page. This will take some time (months).

"Usually"

Luckily this is not a mushroom site where people ask for advice on how to distinguish a toxic from an edible species. "... but if these features are missing, the edible ones are usually larger".

It's a bit like calling a tourmaline a schorl just because it's the most common tourmaline. There's really no justification for labeling species or anything else purely on "statistical grounds". If you don't know what something is then you don't know it, so what, nothing to be ashamed of. Dreaming up certainty or accuracy where is none is not exactly "scientific".

5th Dec 2016 02:56 UTCAlfred L. Ostrander

Hello All,

I almost passed on the crystal Jose posted as it is hard for me to tell exactly where the faces on the left side actually line up. If that face sits higher up and shifted to the right I understand looking at it as a twin. That is why I commented on what can be seen and not seen. At least by me.

And Mark, I think we are on the same page with the calcite. As to posting a drawing with a large rhombohedron and a small modifying rhombohedron it appears that the convention of calling the larger positve and smaller negative is the same as for quartz. Looking for other evidence is good. Sometimes it just isn't there.

And Amir, I will say it again. Thids is not erroneous or dreaming stuff up. It is a convention. What part of this do you not understand? Consider this a rhetorical question. I think we have both said about all there is to say on the matter. I will repeat, I am sticking with Dana. Ignore Dana if you wish.

Best Regards,

Al O

5th Dec 2016 12:25 UTCJosé Zendrera 🌟 Manager

Mark, Amir, Alfred, thanks so much for your comments.

Amir, I'm already looking forward to read your new articles! Your Quartz Page is for me, and I imagine for many others also, the quartz bible. Thank you for publishing all these information.

Mark, my gratitude for Smorf page too. I use it very often.

It's a treat to have you here.

5th Dec 2016 21:12 UTCMark Holtkamp

Thank you José

@Alfred, interpreting crystals from photographs is tricky, I used the link to the video of José 's crystal on
youtube

Mark

5th Dec 2016 22:16 UTCRobert (Bob) Morgan

I seek further answers. If z faces develop and grow faster than r faces, is there any explanation for this? Is there any structural description of the differences in their surfaces? Has anyone investigated why the striations on s faces are built to point toward the r faces? Do z faces always etch more readily, or might there be more rapid etching of r faces by certain solutions? What are the differences in etch pits on r vs. z faces? Is selective deposition of other minerals on just one form a product of a rougher surface of that form, or is something else happening? Does anyone have references to research on these matters?

6th Dec 2016 00:24 UTCAlfred L. Ostrander

Mark,

Thanks. I did finally figure that out. Did a bit of a duh moment. Sometimes interpreting a crystal in your hand is tricky. And I am due for new glasses. Appoinment coming up in January. Don't get old.

Jose, I think by now you have it sorted out this is a twin and I still think it is a nice specimen.

Robert, there are some good sources on line. I'm looking for a good source describing striations and so is Mark. If I find something good I'll post it.

And Amir, I do think your blablahedrons and poison mushroom stories are rather disingenuous. Do they really help here?

Best Regards,

Al O

8th Dec 2016 17:01 UTCAlfred L. Ostrander

Mark and Bob,

I have had this guideline in my notes regarding striations on the trigonal pyramid faces since college days. It is short on indices but long on reality.

Striations (when present) on the trigonal pyramid s always point to the z face.

I knew I had seen an article on this somewhere. See Rocks and minerals Vol 64 Nov/Dec 1989 p. 455. This is in the letters section and is a correction to an article in vol 63. The idealized line drawings were executed by Steven C. Chamberlain. They clearly show the differing directions striations can take on the s faces in numerous situations. Sometimes, the different directions on a face can be confusing. These drawings say it all. Steven rotated the position of some drawings to clearly show the relationship of the s, r and z forms. Just watch which face is labeled z or r.

Best Regards,

Al O

10th Dec 2016 12:50 UTCMark Holtkamp

Hi Al,

I don't have access to Rocks and Minerals, what do these drawings say?

According to this article striations on the s-face can be parallel to r-x, r-r, s-z, or s-m

Mark.

10th Dec 2016 16:55 UTCAlfred L. Ostrander

Taylor and Francis Online Journals

Mark, try this link - it should take you to an article about striations on trigonal pyramids. It makes the statement I had in my notes striations on the trigonal pyramid always point to the Z face. That's how I found it; I used that sentence and that's how I found it online!

Al O

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