I do not know that for sure, but it looks very likely that this setting is used to emphasize its similarity with other feldspars such as orthoclase which has monoclinic space group C2/m.

At least, I have seen the similar use of the non-standard settings for the lower symmetry phases in other cases. For example, the orthorhombic Aurivillius phases Bi2AB2O9 are usually described by the space group A21am instead of the standard Cmc21 in order to keep the same direction of the z axis as in the high-temperature tetragonal phases.

It is probably like Alexander indicates. Non-standard settings allow having a similar unit cell for structures of different space groups. Another example is use of a face centred tetragonal unit cell for somewhat distorted fcc metals like Indium. Then you have an axial ratio much closer to unity and the structure similarity becomes much more evident. In fact many programs cannot deal with non-standard settings. I good warning is if they simply want the space group number indicated. Many others can handle that, even the very old lazy pulverix. They translate space group symbols into explicit symmetry elements and process these.

@ A. Leineweber: I did not know that Lazy Pulverix generated the symmetry from the entered H-M symbol? Are you absolutely sure?

Comming back to the question: it does not surprize me that structures are described by  a non-standard setting. What surprizes me is that obviously ALL structure descriptions uses C-1. There is only one explanation: they all showed the similarity to orthoclase. I always assumed that if possible one should use standard settings, and only in exclusive cases another will be accepted. 

concerning lazy pulverix

perhaps I have to step back: I am not absolutely sure and at the moment I cannot acess the reference to the subroutine by Burzlaff et al. used by Yvon et al. But re-reading http://journals.iucr.org/j/issues/1977/01/00/a15322/a15322.pdf about lazy pulverix, for me it sounds really like the subroutine DERIVES the symmetry operations from the symbol.

"The

Hermann-Mauguin symbol for the space groups is used to

derive the general positions corresponding to the settings of

International Tables for X-ray Crystallography with a routine

written by Böhme, Burzlaff & Gomm (1975)." (which is from a supplement to Acta A which I cannot find at the moment at iucr).

But I also cannot fully exclude that the routine by Burzlaff et al (cited by Yvon et al) used an extensive listing including a lot of non-conventional settings to derive the postions etc.

I am quite sure that this is a tricky algorithms since from the H-M symbol you only know the alignment of symmetry elements but not their relative positions. It definitely works but there are moreover some simple definitions (declarations) and to press them all in a single concept is challenging. I did a similar work for PowderCell and I have to admit that the space group generation is amazingly systematic down to the definition of the special position, but if it would be that easy, why even the CIF file lists all symmetry-specific positions (in fact the symmetry elements)?

Anyway, many thanks for the temporary clarification.

I confirm the use of C-1 for albite by analogy with orthoclase C lattice. However it should not be difficult to obtain coordinates of albite in P-1. For example in solid state physics it is not rare to find the use of primitive cells only.

@ G. Ferraris: ...because their software does not accept centered lattices :-). Anyway, of course it is not difficult to transform the cell as well as the atomic coordinates, but why is seems to be general that albite is practically exclusively described ini C-1? I guess you are all right: they all used orthoclas for structure comparison. 

Unit cell parameters are important information for assessing the ordering state for feldspar minerals. For example, gamma angle in sanidine is constrained to 90 degree by symmetry. By using C-1 space group, the gamma angle is close to 90 degrees, and the deviation from 90 can be used to estimate the cooling rate of the host rock. And of course by using C-1, the coordinates of atoms are roughly the same in all feldspars.

@ S. Jin: These are in fact the same arguments for a comfortable use of C-1 instead of P-1. :-) Nevertheless, the international convention says that there is no reason to introduce a centering since the lattice can be described by shorter translation vectors without making problems regarding existing symmetry elements. The deviation from 90 degrees as estimation of the cooling rate is very like also correlatable (connected) with a certain atomic position within the structure. No doubt, this is much less comfortable than the angle but from my point of view the angle shift is only the result of some kind of  distortion within the atomic arrangement (crystal structure).

A convention is simply a convention an can be changed, but it needs to be clear that then all simplifications given by the convention are lost. And many (!) programs cannot deal with these settings so that any deviation from the international conventions involves the danger of misinterpretations and wrong results. It should be clear that these datasets cannot be used or have to be transformed into a description of P-1.    

I agree of the inconvenience of the unconventional setting. I guess this is some conversation in mineralogy. It's true that you'll never find an albite structure described in primitive cell. As I understand, unconventional setting of space group is quite common and more and more software are developed to adapt these settings.

Just curious, why do you care about the albite structure? What research are you doing on albite?

I confirm that the use of "uncoventional settings" is quite common for several reasons. But even more tricky can be cases where apparently the same setting is used but actually the origin of the seeting is different. In centrosymetric structures the origin is usually set at an inversion centre, but in a unit cell the always more than one inversion centre. In non centrosymmetric structures the choice of the origin is even more complex.

This is correct, but therefore it is even more important to use the standard settings in order to prevent any trouble in other software packages which are commonly black box systems were after years nobody anymore knows how an what has been implemented. And as Giovanni pointed out, the number of opportunities using another setup is quite numerous. On the other hand, a simply shift of the unit cell origin should not affect any physical properties, only a different alignment of basis vectors, e.g. the exchange of a, b and c.  Regarding a consideration of any possible settings in software packages I would not be that optimistic. There are many reasons, e.g. for each of this setting the fundamental sector (asymmetric sector) needs to be defined in a different way. This is a quite complex problem, especially if there is no general accepted way to define these settings (Hermann-Mauguin symbol etc.). As long as a crystallographer is doing this he/she should know how to deal with these problems. But even there I am not very optimistic and bet a wager that at least the half of them won't be able to transform a cell and the respective atomic coordinates. People, who usually write these software packages commonly do not have any crystallographic background which explains the bugs in very fundamental functions. Therefore I believe the best way is to use standard settings, and only in very specific cases (like albite) a discussion of the similarity should allow to display (but not define) the structure in e.g. C-1. The possibility to produce errors is simply too dangerous.

Why I am interested in albite? I was discussing the structure similarities of albite, anothite and orthoclas, and my opinion was that their EBSD patterns should be very similar. I did not checked this until now, but I guess the structure of the silicate or alumo-silicate framework will be comparable and only the cations will affect more or less dramatically the intensity of the visible bands. The band width  won't change that much because of the short wavelength of electrons. Only the lattice distortions will make a differentiation possible, but then one need to now very accurately the projection center. The current question is, how much one needs to know the projection center in order to distinguish non-equivalent directions of a quasi-monoclinic phase?        

Gert I suppose you know this site http://www.cryst.ehu.es/ likely there you can find some useful software

Yes, I know it under the name "Bilbao server" :-). If I remember correctly, Aroya and Wondratschek had quite close connections. But thanks again to post this link.

Best greetings! 

Well, according to your EBSD research, C-1 should serve better than a primitive cell setting. Because only in C-1 the Miller indices will be the same for albite and orthoclase. How do you expect to do the comparison if you index the albite in a P-1 setting?

I do not have access to the original work. Perhaps the problem is that it is the point symmetry of a position within the space group. If I triclinic space groups are P1 and P-1. Sorry I can not lack I clarify the original text.

Hi S. Jin, finally it does not matter which indexing a band has or not (at least from my point of view). Only for comparisons it can be beneficial. But also there the major question is, whether the indexing is important or the orientation description by Euler angles, i.e. which axis will rotate in which one. Is a parralel to X or c parallel to Z etc. For this specific example of Albite and orthoclase the definition  might match but I don't think it this is general. Crystallography defines standards but if there is a certain reason to use another description it makes sense to change to another basis vector definition which might result in another symmetry setup. A very nice example is magnetite and hematite. The space group of hematite is no subgroup of the space group of magnetite but there are strong structural correlation. For albite it is easier since there is no symmetry, and you can define the basis vectors as you like. If I would compare albite and orthoclase i would anyway always look for the match of the structure and not of the basis vectors.

I think you are a little confused here. Space group of hematite is not subgroup of magnetite no matter how you set it up. C-1 and P-1 are exactly the same space group, only the cell is changed, it doesn't do anything to the symmetry.

Oh, sorry, you totally misunderstood my remark. 

P-1 and C-1 are the same space group, or do you think Pmmm and Fmmm are the same space groups and the same symmetries? Symmetry is more than the rotations and rotoinversions. If you describe something with C-1 you introduce and absent reflections which are physically not existent but only the consequence of the bigger unit cell definition.

The example of magnetite and hematite you should have a look at the link. It might explain what I am talking about.

Conference Paper Characterisation of the topotactic transformation of hematit...

Pmmm and Fmmm are different because they have different symmetry elements related in different ways. And Pmmm is space group No 47. Fmmm is No 69. There are only 230 space groups and C-1 and P-1 are both No.2. I understand well how hematite and magnetite are related. And they certainly are not subgroup and supergroup.

Now I'm a little confused about your question. Are you simply don't understand the C-1 space group that seems doesn't exist in 230 space groups. Or are you simply complaining about the inconvenience it caused you? Because it doesn't really matter what you think is convenient or not, if you want to get your work published, you'll have to convert everything into C-1 for albite. This is just how it works. I believe your question is already perfectly answered. So please tell me what is it you still don't get?

if you compare the general positions of Pmmm and Fmmm you will see that there are no differences. This is also clear since the difference between both space-group types is in fact only the additional translations described by the generated selectors. That the drawing of the symmetry elements or the number of possible symmetry elements varies is again only the result of the additional translations. The same would by the case for C1 and P1, however, there is no necessity to define a C1 since you can simply transfer it without any real consequence into a P1 since you don't need to consider any symmetry since there is no. But it has consequences regarding the reflection conditions which are different and in so far C1 and P1 (or C-1 ans P-1) are different, also during generation of the content of the unit cell. The difference between Pmmm (47) and Cmmm (65) is comparable to P-1 and C-1: generation of one the content describing lattice point, and then add another lattice point. Why Pmmm and Cmmm and Fmmm have their own space-group type is that you cannot reduce Fmmm to Pmmm keeping the same symmetry density and the orthogonal basis vectors. For C-1 and P-1 you can do it since their are no requirements. There are also structures which are described by A-1 or F-1 because of structure correlations to similar phases. Without any limitation you can transfer them all into P-1 but the mathematical description of the group is different. This is also the only reason for my question. I don't want argue that  P-1 and C-1 need to be described by additional space-group types, but you cannot use a P-1 structure generation to generate a C-1 structure, and the reflection conditions are "wrong" as well. This is in principle trivial, and therefore we should stop this part of the discussion here. I only wanted point out that despite this triviality several programs have problems to deal with non-standard settings simple because they are using  the space-group number. And in that case it makes a difference whether you are using C-1 or P-1, or Pbcm (57) and Pmca (57), or Pbam (55) and Pmab (57). As consequence, the structure is wrongly generated, the expected intensities are wrong, the hkl generation is affected as well, and as consequence the inverse pole figure is wrongly defined as well and so the coloring of crystal orientations.

Anyway, I think we are anyway talking about that same and only using the same terms with a slightly different meaning. I think, the answer of my question is explained by some contributions. It has only comparable reasons. I am surprised that  ALL structure descriptions are using C-1, but this is obviously because they all wanted to display the similarity to orthoclase. 

Thanks for your information

I think I get what you are saying now, you can't simply add or reduce a centering condition (translation) to the symmetry. If you want to convert between P-1 and C-1, you need to do it with a matrix. C-1 cell is doubled volume of P-1 cell, because of the extra translation. Albite cell in P-1 cell is 7x7x7 and looks like this.

This is exactly the same structure as described in C-1, except you have to re-index everything since the axes are switched.

You can do this transformation easily with VESTA software, or any other structure visualization software, I suppose.