My friend, pls. find attached a big file[ over 1KB] giving photocopies of the power point presentation as noted from internet. Hope you find this attachment useful.

Dear Sehgal, I have already read it.

Thanks dear all.

Regards.

Dear Dr Sertkol:

This question is very very interesting. I think that the concept of sublattice belongs to inorganic physical-chemistry. However, in general, when a text book of Inorganic Chemistry is consulted via INDEX appearst he word:  "structure", in the sequence "subgroup", after "super". Seems common the absence of sublattice. Also, seems that there is not a text dedicated to definitive concept. Then, a solid concept should be constructed from previous assumptions. In this sense, when is necessary the following assumptions can be used.  A priori, both concepts lattice and sublattice make sense only at crystal structures. If a lattice exist is mandatory the existence of a sublattice and vice-versa, mettalic lattice are particular cases. The terminology is as follow: in a general way, the chemical element that appears in several compounds that represents or are significant at a class of compounds receives the name sublattice. Ex.: oxygen in the oxides compose the sublattice. In this terminology, oxigen ions compose the sublattice of ZnO, CoO Co2O3, Fe2O3, Nb2O5. By consequence, cations Zn, Co, Fe Nb compose the lattice of these compounds. The sublattice defines the first coordination-sphera of a cation being that both lattice/sublattice are fundamental to derive the space group. From this point, the complements of question can be approched, the idea of long range order should be considered with some carefull. At almost simple compounds, both lattice and sublattice follow a long range order. However, one or another or both can be exhibits some kind of small desorder but that can be only a distortion based on slight departure of ion of a proper position at crystalline lattice. Such phenomena, migth be more realistic at complex crystalline structure with multiple occupation sites, with distict coordination polyhedra and/or multiplicity of unitary cells. From this point, an other concept emerges that is concept of desorder. In a broad sense, a cation is desordered when occupy two different sites in a crystalline structure, which is determined by the sublattice. As a whole, lattice and sublattice can be change in a major or minor extension, with no coupling in magnitude. From a practical view-point, when the sublattice undergoes further changing, are common changes in the crystal symmetry.  If only sublattice is taked in consideration, a particular case can be mentioned, that is the martensitic tranformation of the zirconia. In the transformation of the zirconia, several symmetries are reached by a kind of coordenate moving of oxygens (sulattice), depending on the temperature. Then, this exemple seems tto represent the case where the sublattice can be change the symmetry of compound, at least type oxide.

Kind regards.

Marcos Nobre (M. A. L. Nobre) 

Dear Dr. M.A.L. Nobre,

Thanks a lot for your valuable help.

I derived that both sublattice and lattice itself belong to a space group, and are able to change symmetry.

Long range order is not essential in some cases but mostly it is. Only the distortion that we observe in a small fraction of sample, can not be classified as sublattice. Are these true?

With my best wishes.

Murat

This is an old question but there is a problem with the answer.

It is not correct to call sublattice to the group of atoms of the same kind (related by space group symmetry operations such as rotations, roto-inversions, and translations) in a crystal. Al Na atoms in NaCl structure DO NOT form a sublattice. If you want to describe them all together maybe you should use substructure but for sure not sublattice.

A sublattice, correctly defined, is a group of translation operations that have a subgroup relation to another lattice. The group-subgroup relation implies that the number of operations in the subgroup have to be present in the group but the group has extra operations not present in the subgroup.

A lattice defined by the positions of all Na atoms in NaCl crystal is not a subgroup of the lattice of the whole structure. Indeed in this particular case the Na substructure shows exactly the same lattice of that of NaCl structure. I mean, in both cases the set of translation vectors that define the crystal lattice is the same as the set of translation vectors that generate all Na atoms from one of them.

There is a crystallographic term, not very much used, to define a substructure like this. When you refer to all atoms equivalent to one specific atom of the unit cell in the crystal this is called a CRYSTALLOGRAPHIC ORBIT.

This term is not very commonly used, but it is correct to say that all Na atoms belong to the same crystallographic orbit in NaCl, the same with all Cl atoms, but Na and Cl orbits are different. Unfortunately if you change crystallographic orbit with sublattice almost everyone will understand, but the choice of words is incorrect since sublattice refers to something different.

Indeed, there is no chance to have, by accident, a wrongly defined sublattice being a true sublattice of the crystal lattice. Since crystallographic orbits may define lattices with more vectors than the crystal lattice, the crystallographic orbits always form the same or a superlattice, never ever a sublattice.

I hope this helps.

any reference regarding this answerer please mention the DOI.

Article Lattice versus structure, dimensionality versus periodicity:...

this is one possible reference you may use.

The attached file given by Manohar Sehgal is clear. What point you are concerned about maybe is the lattice constants of the sublattices. Whether they're the same or not?

Lin Zhang This is a very old answer and the attached file given by Manohar Sehgal is not right.

A sublattice is a mathematical concept, equivalent to subgroup. A lattice in 3D space is defined by the set of three non-coplanar vectors that describe the positions of mathematical points ordered periodically in space. A lattice could be associated with a group of translations that fulfill the definition of a mathematical group. See IUCr Dictionary definition (https://dictionary.iucr.org/Lattice).

A sublattice is composed by a subset of the translations of a lattice. For a sublattice to be itself a lattice you need the subset to also fulfill the group axioms therefore it should contain less translations. This means, if it covers all the space, will have at least one of the three sublattice vectors longer than those of the lattice.

In the examples given in the document, all of the wrongly-called sub-lattices share the same translations, so they are the same lattice.

What Dr. Sehgal calls a sublattice could be called a substructure, because is a partial set of a crystal structure.

Indeed, a superlattice is also wrongly defined in the document. A superlattice of a lattice is itself lattice that contains all the vectors of the lattice and more. So a lattice is to a superlattice what a sublattice is to a lattice.

The superlattice of Dr. Sehgal is just the same lattice again. So, unfortunately, that explanation is wrong and the definitions are also wrong. At least considering what the International Union of Crystallography (that defines all aspects of crystal structures and diffraction experiments) suggest as definitions.

I hope this helps stop the spread of misleading information.