Dear Gert,

Do you know the book by Jean Sivardière, a colleague of mine.

La Symétrie en Mathématiques, Physique et Chimie., Collection Grenoble Sciences Editions de Physique - Sciences - (1995) 880 p.

But.... in french...!!!

pp 422 and more particularly pp 441 etc there is a discussion on apparent higher symmetry, in relation with the G. Friedel rules and twin occurence...

If you have no access to this book Is can propose scan a few pages.

Kind regards

Daniel

Dear Daniel,

I have to admit that I do not understand french at all :-(. But any thanks fr your offer. It is very kind!

Best greetings

Gert

I have look ahead for more information on the Ti3Ga(Al)5 structure but I have got not more data...

I will visit the Lv'iv crystallographiers next week and I will ask for.!!!

I will provide you with a few ten pages in french...

Kind regards...

Gert the following article, but even more literature there quoted, might help you

http://www.degruyter.com/view/j/zkri.2011.226.issue-2/zkri.2011.1321/zkri.2011.1321.xml

Dear Gert,

do you know the paper of Michael Ruck from Dresden?

Kristallographische Konsequenzen von Pseudosymmetrie

in Kristallstrukturen, Z. Kristallogr. 215 (2000) 148 - 156.

Best regards

Guido

Thanks a lot. No, I don't.

I will see whether I am able to get it. (I don't get it...in German. How this happened? )

Guido, do you still have some similar surprizes? :-)

Dear Gert, I attract your attention on the attached paper.

Many thanks, Giovanni!

Dear Gert,

                            I'm not able to enter in  theoretical considerations concerning the relationships between crystal symmetry and pseudosymmetry. Really, this is time consuming for me and probably is too complicated as well. 

Nevertheless, I recently faced an interesting case: the hydroxyapatite (HAp) crystal. In the past , pure HAp crystals have been attributed to the hexagonal system, with a large choice of S.G. ( P63, P63/m, und so weiter...). Structural crystallographers, as you know, have a great imagination: as a matter of fact, it is quite surprising that the dipole moments associated to the OH- groups can alternate (without systematic and important repulsion...)  in a up-down position, along the channels parallel to the z axis, in order to respect a symmetry 0001 plane !

At the end of Seventies  a new polymorph of pure HAp was discovered, monoclinic, with a0 practically coincident with c0 and  beta close to 120°.  It ensued that monoclinic HAp is pseudosymmetric with respect to the hexagonal phase.

We crystallized HAp crystals (mild hydrotermal growth) and found that single crystals are perfectly monoclinic, especially when their growth morphology  is investigated by SEM, where the polarity of the crystal forms are put in evidence by the areas of the single faces (and hence by the overall morphology). But, multiple twins of the monoclinic phase (very common) look as perfectly hexagonal: we are sure of that, because the SEM images are not ambiguous in distinguishing a twin frm a single crystal.  

Summing up, pure HAp crystals are monoclinic (when single crystals precipitate) and look as hexagonal when twinning occurs. This is very easy to happen, due to the very low twin energy for HAp.  Finaslly, we are induced to suppose that the hexagonal HAp phase cannot exist and that the "sogenante"  pseudo-symmetry is nothing else than the consequence of the XRD methods  which average the bulk structure and neglect the crystal surfaces... with their non ambiguous features.

This is my own contribution to your interesting question...

All the best

Dino

Well, we are all learning :-). It is a nice example. Practiacally all domain-containing structures are of similar properties. And here we are only talking about commensurable conditions...not imaging how many materials are concerned by weak incommensurate effects. From my very personal point of view... I wonder, how much these small deviations finally will affect the materials properties? In fact, all our experimental equipment is detecting them. If they are "practically" not existing, does it practically matters that we are looking for such small deviations? I guess the real impact is not that HAp is actually monoclinic but that we have some ideas how these images in SEM can be meaningfully explained. 

This is also related to the question: When pseudosymmetry becomes important? The other part is, how pseudosymmetry can be used to a) predict structure relationships, or b) derive them for a probably better usable or suitable (?) classification of structures?

Have very simple question:  is the term pseudosymmetry primarily used in inorganic chemistry?   In organic chemistry, we use the term chiral to identify compounds that have mirror image structures and the term "pro-chiral" to identify as potentially chiral or not quite there yet chiral. .    .

No, pseudosymmetry is a general term. Chiral or (left right) or possibly prochiral are special terms and denote a small part of pseudosymmetries. The latter one can concern the translation lattice only, or a small shift of single atom which destroys the symmety of the structure but not mandatory of the translation lattice.

Thanks!   You added to my knowledge in Materialforschung.  So,  in effect, pseudosymmetry is the smallest molecular perturbation that will show up destroying symmetry but not the structure of the translational lattice.

This is one (very unlikely) case since if you destroy the symmetry by a change of bondings this should affect the translation lattice as well. The question is only whether you will be able to measure it if it is very small. In databases you can find triclinic phases described by a "cubic" translation lattice. I have no idea how accurate these descriptions are, but it is not forbidden since trinclinic means that there are no conditions regarding the lattice parameters. Thus, they can look like cubic. Vice versa it is not possible.

Endosulfan exists as an alpha and a beta isomer and they have hugely different melting points.   Our lab using NMR confirmed in solution the alpha isomer was a mixture of two asymmetric isomer.  For about 30 years chemist thought the average of two asymmetrical isomers was instead a symmetrical isomer.   Grew some excellent crystals of the alpha isomer and had an excellent Xray crystallographer who confirmed we were correct.    Endosulfan has a seven membered ring and the beta isomer has two CH2 groups with one H in each pointing down from the ring. Earlier literature had it that the alpha isomer had on H in each pointing up.   Incorrrect.  Half the alpha isomers had one H pointing up and the other down; the other half had one pointing down, the other pointing up..   In this case, when one heat the beta-isomer above the alpha-isomer melting point, the beta becomes alpha:  two symmetrical isomers form one each of the  two alpha-isomer forms.   Reviewer believed the Xray results.   Glad there are highly competent Xray crystallographers.

This sounds really unbelievable...:-). How do you explain the hugely different melting point? When I understand everything correctly, the different in structure as well as all bonds are nearly identical? What causes this difference in stored energy. Or are my models/rules too simple?  

Three decent publications on this are:

J. Molec. Str. 2017  1139: 43-51

J. Ag. Food Chem.  2014  62:2023-2-30

J. Ag. Food Chem.  2001  49: 5372-5376

Really interesting how things integrate so precisely together.

The key is Chemical Physics part is that  Bochian calculated the vibrational modes of a seven membered ring and found the most stable form to be asymmetrical.

Have appointment in 15 minutes, but sure, if you have any questions after looking at any one of the articles, would be pleased to continue this conversation.

Dear Gert,

                           I agree with your precise information about the term "pseudo-symmetry". I would like to give my personal contribution concerning the effect of the pseudosymmetry on two  properties: the growth shape and the equilibrium shape of a well known crystal, the Hydroxyapatite. I'm sending you a paper we recently published about the ambiguities arising  when both the theoretical and experimental crystal shapes are assigned to the hexagonal symmetry instead of to the monoclinic one.

Thanks for your attention

Dino

Very cool the inorganic chemistry of chirality and pseudo-symmetry.  My recent research has been on cis polyunsaturated fatty acid lipid structure: one end has a carbonyl, the other has a methyl group, and in biochemistry there are one, two, three, four, five, and six double bonds in between [each is CH2-(H-C=C-H)-CH2 redundancy].  If one' thumb is facing towards the carbonyl site, clearly, one can have a right handed curvature or left handed curvature, even though the hand being held is almost flat.  Some PUFA structure is a U shape, other are a C shape.  Only possible if curvature (handedness) sequentially is self-consistent over a sequence of double bonds.  When up and down are not identical and front and back are not identical, any curvature disrupts symmetry and precludes a left handed glove fitting a right handed structure.

Normally, one does not think of a flat hand as chiral. .    .

I recently had a discussion with a friend of mine which came in contact with a very interesting problem: Crystal class 23 is one of the enantiomorphic classes. The puzzling thing is that a 21 cannot cause a left or a right-handed crystal structure. Why is it the called enantiomorphic? If you look for phases crystallizing in this group (e.g. FeSi) it is not easy to see that even this structure really forms handed structure. However, only one. In case there is an "inverted" phase, does it has to be described as new phase (like right- and left-handed quartz)?)