Are there additional factors beside of general and special reflection conditions which may cause the absence of a reflection, e.g. the occupation factor of a position, or the substitution by different elements?
Yes and no. Yes there is another kind of extinction which is dependend on the perfectness of the crystal. No, occupancy and occupation will not cause an extinction but nevertheless influence the reflex intensities because of the form factor of the atoms.
But if the occupancy affects the reflex intensity, it might go so far that the final intensity is zero and the reflex becomes invisible. Is this no extinction?
Its a matter of definition: extinction is caused by destructive interference of the X-ray beams. But the form factor is about how much of the incoming beam is scattered.
Well, how do you explain the diffractogram of (K_0.8,Na_0.2)Cl, i.e. K will be substituted by 20% of Na? The intensity of the 111 is zero. OK, the intensity of the 111 is already close to be zero for KCl since K+ and Cl- have both 18 electrons, but using a solid solution one can reduce the size of the structure factore even more. I wonder if one can do the same with occupations, e.g. vacancies.
Thinking of it, the question is actually double-edged! Changing the atom type on a site completely to another one or vacancy may result in a different space-group and that in turn different reflection conditions. But with a solid solution, thats not the case. Also the atom/ion radius is important for scattering.
However, if you have atoms with similar form factors, you may get pseudosymmetry, but i am not able to answer about that.
No change of symmetry, i.e. only statistical substitution is permitted! Otherwise you are right: the symmetry would change to a subgroup (if the position would not vary).
Beside the given KCl, another practical example would be gamma' in nickel-based superalloys. One could change the composition that the already weak 100 would completely disappear.
How practically relevant the occupation influence is...I also don't know. However, mathematically obviously it work as well, i.e. if not all positions are occupied. As gedanken experiment you could describe Cu3Au as Cu3Cu (simulating an atom at the Au position with the same scattering power) and then you reduce the occupation of one of the independent Cu atoms in the asymmetric unit. Immediately the zero-predicted reflections are displayed by a non-zero value.
...interesting...
No, I don't know this paper but it already looks like the "effect" I am talking about. How they call this?
How do you would call the absence of the 222 reflection in Si? Special extinctions? How do you call the disappearing superstructure reflex in Ni-based superalloys?
I know that for 227 cell choice 1 for special position 8a the reflection condition is h+k+l=4n which is not fulfilled for 222. My question is how do you call this "extinction". Are we talking in crystallography about "extinction laws", or is this only a wrong use of the french expression extinction (like the German term (Ausloeschung)), and explains the reverse effect of the english term "reflection conditions"?
Nevertheless, disappearing intensities as result of effective atomic scattering factors are not covered by the general or special reflection conditions defined in International Tables for Crystallography (vol A).
One more thought on pseudosymmetry: if the mixed occupied Na+/K+ positions look to the xrd like Cl- , the extinction condition of the F-centered lattice would be perfectly fulfilled for 111: h+k=2n, k+l=2n, h+l=2n. And this would explain also, why the reflex is already very low for KCl, because it is almost fulfilled there.
True, sorry, its not right to say extinction condition. To get back to the original question, the occupancy/occupation contributes to the extinction not besides but because of the reflection condition.
Just to be clear about the term extinction, it only applies to dynamical diffraction theory. In kinematic diffraction there is no such concept as extinction.
As far as not seeing reflections that are allowed by symmetry due to changes in occupancy, I find it hard to believe that this is possible. Yes it could make the peak extremely weak and beyond your limit of detection, but not zero. If there is ordering in the occupancy then this is a different story, but that will cause a change in symmetry. Of course there can also be magnetic ordering, but that should lead to a forbidden peak appearing.
Lawrence, do you believe it is impossible or practically unlikely? I agree that mathematically you are perhaps right but if you cannot measure experimentally under common conditions a reflection who tells you that this reflection is absent or simply too weak to discover?
I believe it is theoretically impossible. Of course I haven't crunched the numbers to see if some random occupancy could actually bring a structure factor to zero, but it seems to be mathematically impossible when i consider it. With the flux density currently available at synchrotron sources and free electron lasers, even extremely weak peaks can be measured (for example magnetic ordering peaks) that would be undetectable above noise with laboratory sources. I would be eager to hear if anyone knows of a case where this is not true. I have not heard or read of anything in the literature, but if I am mistaken I would love to know how this could occur. Again I must make the caveat that I am talking about kinematical scattering. Dynamical effects can cause extinction, but I don't believe that was what your questions was referring to.
The example given for (K,Na)Cl is of course also more theoretically but should explain at least one idea. In general it describes the case when atomic scattering factors for two different positions are identiacl. This should result in an absent reflection. You don't think so?
(Well, with "common equipment and conditions" I did not mean a synchrotron but a common X-ray diffractometer. With a synchrotron you certainly have better opportunities to find even small intensities.
BTW: I believe that I've read long time ago a paper where they showed extinction effects measured with XRD at a semiconductor material (GaAs) in order to differenciate between (111) and (-1-1-1) planes. Am I wrong?
extinction effects are dynamical, and can be predicted by dynamical theory.
As far as the (K,Na)Cl example, atomic scattering factors are always independent of position, so I'm not sure what you are referring to.
A month ago I described the following thought experiment:
... how do you explain the diffractogram of (K_0.8,Na_0.2)Cl, i.e. K will be substituted by 20% of Na? The intensity of the 111 is zero. OK, the intensity of the 111 is already close to be zero for KCl since K+ and Cl- have both 18 electrons, but using a solid solution one can reduce the size of the structure factore even more. I wonder if one can do the same with occupations, e.g. vacancies....
regarding extinction effects: Do we don't have them if we don't have mosiac crystals, i.e. in the case of perfect crystals like semiconductors?
extinction effects occur in very perfect crystals (Si for example). A mosaic crystal would not show distinction. Also as the x-ray energy increase this effect becomes more stringent on crystallinity and you will need larger crystals to get the dynamical effects.
When you are talking about the absence of the 222 reflection in an FCC structure it is not called extinction (that is only used when dynamical theory must be used to explain the absence). These are referred to as forbidden reflections. I hope that clears up some of the confusion caused by using the word extinction with different meanings.
Lawrence, you are right. However, it is new for me that 222 is a forbidden reflection for fcc. Are the condition not: either all h,k,l even or all are odd?
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