I purchased commercial Single crystalline Silicon wafer. company mentioned, it is plane oriented wafer.
When I am doing getting XRD peaks on 69.24, 65.84, 61.68, 33.
when i compare with JCPDS data, i found that 69.24 denote Si 400 plane. and other peaks are not mentioned. but company mentioned Si wafer.
Can any one tell, in single crystalline silicon case 400 and 100 and 001 peaks are same?
Because in literature i found 33.0 Si CuKalpha, 61.68 Si CuKbeta, 65.84 Si WLalpha, 69.24 Si CuKalpha.
Can you please explain what is the difference in 100, 200, 400, 004, 001 plane in single crystalline case?
Please send some literature and XRD reference data.
Thank you very much
1. For the cubic symmetry any permutation of the plane indices gives a symmetrically equivalent plane. For the powder diffraction experiment this means exactly the same peak position. If you scan the whole reciprocal space with a single crystal diffractometer 100 and 001 will be different directions.
2. 100, 200 etc correspond to the same orientation of the plane but different interplanar distances. So they appear all together (if allowed by symmetry), but at different 2Theta values.
3. For the space group Fd-3m only h=4n is allowed by symmetry (see International tables, vol. A). However, multiple diffraction can lead to the observation of the forbidden 200 peak. Of course, its intensity will be several orders of magnitude lower than that of 400. You can look through https://dx.doi.org/10.1107%2FS1600576715004732 and follow the references for more details.
4. Observation of CuKbeta and WLalpha satellites is absolutely normal for the high intensity peaks (obviously, the single crystalline wafer gives an extremely intense peak). The copper anode is deposited on tungsten substrate which produces its own radiation. And of course no type of filtering is 100% effective. However, if the intensity of these satellites becomes too large, you have to perform the corresponding maintenance of your diffractometer.
1. For the cubic symmetry any permutation of the plane indices gives a symmetrically equivalent plane. For the powder diffraction experiment this means exactly the same peak position. If you scan the whole reciprocal space with a single crystal diffractometer 100 and 001 will be different directions.
2. 100, 200 etc correspond to the same orientation of the plane but different interplanar distances. So they appear all together (if allowed by symmetry), but at different 2Theta values.
3. For the space group Fd-3m only h=4n is allowed by symmetry (see International tables, vol. A). However, multiple diffraction can lead to the observation of the forbidden 200 peak. Of course, its intensity will be several orders of magnitude lower than that of 400. You can look through https://dx.doi.org/10.1107%2FS1600576715004732 and follow the references for more details.
4. Observation of CuKbeta and WLalpha satellites is absolutely normal for the high intensity peaks (obviously, the single crystalline wafer gives an extremely intense peak). The copper anode is deposited on tungsten substrate which produces its own radiation. And of course no type of filtering is 100% effective. However, if the intensity of these satellites becomes too large, you have to perform the corresponding maintenance of your diffractometer.
Mr. Missyul' has given a very informative answer, that can be best understood if you are familiar with the various concepts of crystallography. Powder XRD presents a projection of the contributions of single crystals that take part in the diffraction process, and you only have to concentrate on angles or interplane distances. That means that lattice planes that yield the very same diffraction angle fall on the same place, collecting all equivalent planes (yielding a multiplicity factor in powder XRD). In order to distinguish between the two kinds of experiments, a certain kind of nomenclature has been established: Individual lattice planes are described by the symbols (hkl) and all equivalent ones collected as {hkl}.
Because of symmetry of a cubic system, there are 6 individual planes collected by {100}, namely the three you get by permutation -- (100), (010), (001) -- and another three by looking in the other direction (given by adding a minus sign to the non-zero figure). The same then goes for any orientation of {h00}. If in a face centred lattice (as here) you try to measure the intensities, you will of course find that all {h00} will have zero intensity when h is an odd number.
For the space group of the diamond structure, there are added restraints as commented on already (meaning that the intensity should be zero for {200}, were it not for the fact that not all electron density is situated at the atom centre but also between them to an appreciable extent in this type of covalent structure).
Because you work with a cubic substance you have mixed up directions and planes, a common error that occurs because the numbers describing the planes are the very same(!) as the numbers describing the orientations of the plane normals...
Collective orientations are described by , including all the permutations of the individual [uvw]. In the cubic case, the normals to the {h00} planes have 6 orientations. Because {100}, {200}, {300} et cetera are all parallel, they all have the same orientations of their plane normals. Therefore, the symbol collects all information concerning the 6 orientations concerning the faces of the unit cell cube. There is thus no plane! The symbol gives directions, in this case of the normals of the planes {h00} to illustrate their orientations. Since u=1, 2, 3.. all yield the same direction (irrespective of vector size), one chooses the easiest one, u= 1. The information is that the crystal face of the this silicon slab you have got is {100}, since the normal to it is .
For a non-cubic substance it is very obvious that one can never mix up (...) with [...] or {...} with , because the normals to the hkl-planes will carry other numbers u,v,w than the numbers h,k,l.
In a way it seems complicated, but a careful study of crystallography will make the situation crystal clear (pun...).
I only want add, that you have to distinguish between reflections hkl and diffracting lattice planes (hkl) or {hkl}. Following the Laue and Miller indexing hkl is the interference order of lattice plane {hkl}. hkl can have any size whereas {hkl} is defined by the first order so that h, k and l are relatively prime.
It is only very special for cubic that {hkl} has a perpendicular vector . For cubic it is even h=u, k=v and l=w. For all other lattice parameter ratios than 1:1:1 it might happen that the normals of some (hkl) are describable by a set of integral [uvw]. In general it is not true so that the lattice plane (hkl) is described by its normal vectors (hkl) which is the shortest vector hkl and parallel to the reciprocal lattice direction (hkl).
Therefore, a description of for a normal direction of a lattice plane (hkl) is misleading and should be prevented. (hkl) is described by its normal vector which a) is automatially perpendicular and b) delivers the the lattice plane distance by the 1/length of the vector...
This is all fundamental crystallography and well defined in International Tables for Crystallography. Companies often mix this up and irritate poeple, mainly because there are no crystallographers but materials scientists or physisists which mainly del with cubic phases, the majority of phases is however non-cubic! Thus, don't follow the rules for the only exceptional case!
Moreover, an orientation is never described by a single plane or direction. You always need two of them or a combination of both. In so far, the sample is cut parallel to (001) or it is aligned parallel to (001).
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