Usually a translation lattice is invariant, i.e. one can describe it by different basis vectors, primitive or centered etc., but the arrangement of the lattice points won't change at all, only their indexing. If I have a high-symmetric lattice, and I shift a single atom out of a high symmetric position within the motif describing the lattice point, the symmetry of the point reduces to this low symmetry as well, although the lattice point positions do not change at all. This means, experimentally I have a high-symmetric lattice but a low crystal symmetry. Vice versa it is acceptable as well, that the lattice point has a higher symmetry than the lattice has.
Is it possible to change one or some of several atom positions in a way that the translation lattice changes?
I don't mean joining of lattice points, i.e. reducing the lattice point density by a simple systematic deleting of lattice points.
The term "lattice symmetry" only considers the arrangement of lattice points, i.e. in maximum 6 possibilities exists: -1, 2/m, mmm, 4/mmm, 6/mmm, and m-3m. It is only fixed by the experimentally detectable translation vectors, and their angles in between. And crystal symmetry you know by yourself. These are either point groups (for the definition of equivalent directions and planes) or space groups (for atomic positions).
consider, pls, the famous Bain transformation: 8 of 9 atoms are slightly shifted from initial positions to transform a "virtual" BCC elementary cell in real FCC lattice into actual BCC cell. However, this so trivial that I suspect you meant something other....
Thanks, but you are right. This is a "trivial" case. Also "joined" lattice points by oder/disorder effects (zinkblende - chalcopyrite) is clear. I wonder, wether there are more tricky cases available. Thanks A.A. :-)
Dear Sornadurai, thanks but I am not very sure that this is the final statement. I am still not absolutely sure, although I now believe, it is impossible since the translation lattice is the overall translation of all atomic positions. If this keeps unchanged for some atoms but changes for others the global translation lattice can be only a sublattice of both of them, i.e. a "joint" lattice point. The other option is described by A.A. Zisman where "all" atoms are allowed to change like during fcc-bcc transformation. If there is another solution let me know (this was actually the original question). Thanks!
Thanks for this extended description. My thought were related exclusively to the lattice as mathematic abstraction. Let me ask my question in another way: By which manipulation (I assume (!) on the atomic level) a lattice point arrangement which is not directly related to any atomic position can remarkably change (not only slightly shifted or deformed as described for perovskite)?
Coming back to your example:"Assume Cs at (0,0,0) position and Cl at (0.5 0.5 0.5) position. Imagine you slightly shifting Cs atom position as (0.9, 0.9, 0.9) and to keep the Cl at (0.5 0.5 0.5) position itself, in this case both the lattice symmetry and crystal symmetry did not change."
Your shift of Cs certainly does neither change the lattice symmetry nor the space group, but Cs has now a multiplicity of 8 instead of 1, i.e. you are changing remarkably the structure. The only chance you have is to change the crystal symmetry to triclinic.
A similar problem appears if you simply shift the Cl by 0.2. Then you have immediately 6 times more Cl in your unit cell, i.e. you have to co to triclinic with your crystal symmetry in order to keep the chemical composition constant, but your lattice point arrangement is (theoretically) still (pseudo)cubic.
Dear Sornadurai Dharmadoss, the symmetries of Bravais lattices are only seven: triclinic (P lattice), monoclinic (P and C lattices), orthorhombic (P, C, I, F), tetragonal (P, I), cubic (P, F, I), hexagonal (H) and rhombohedral (R). Total 14.
Dear Gert, cases where the metric symmetry of a lattice (e.g. orthorhombic) is higher than the crystal symmetry (e.g. triclinic, monoclinic) are well known. This is a source of the so called twinnning by metric merohedry. See, e.g., the following page http://www.crystallography.fr/mathcryst/twins.htm
Dear Gert
I went through your question, now rather old, and several answers to it. Since I find the question interesting let me add my bit of understanding, or misunderstanding to it.
Consider a cubic lattice without any atoms. Just, plain, pure, mathematical lattice of points. Then it is indeed a cubic lattice with a=b=c, alpha=beta=gamma=90 degree.
Now add atoms in the motif to get a crystal. The crystal will remain cubic, IF AND ONLY IF, the motif has the minimum cubic symmetry, i.e., four 3-fold axes, and these axes of the motif aligns with that of three-fold axes of the lattice so that these axes are preserved also in the crystal.
If above is not the case, the lattice WILL NOT BE CUBIC despite a=b=c, alpha=beta=gamma=90 degree.
In the extreme case of a completely arbitrary motif, such that the crystal looses all its point symmetry, the crystal, and hence the lattice will become triclinic. We will call this a triclinic lattice with accidental similarity of its lattice parameter to a cubic lattice. This will be better statement than calling it a "triclinic crystal with a cubic lattice."
regards
rajesh
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