On Mar 10, 2010, at 10:35 AM, mohnish pandey wrote:
> Dear users,
> I want to get the results for surface reconstructions
> computationally, but the problem is as we have specify the "ibrav" i.e
> symmetry of the system the relax calculation only optimizes the structure
> within the given symmetry. Can anybody suggest a way to model reconstructions
> .
> Thanks in advance,
> MOHNISH
>
> --
> Mohnish Pandey
> Y6927262,4th Year dual degree student,
> Department of Chemical Engineering,
> IIT KANPUR
> 09235721300
>
Well, I think that a "very general" answer is difficult to give (maybe someone
more expert could try). What one usually does in studying surfaces, is try to
identify,
step by step, possible reconstructions and look at the lower energy ones.
In practice, for a given surface direction (e.g. the silicon 100 surface) you
first identify the "minimal" unit cell (size and symmetry) in the plane
parallel to the surface. Then, you must decide
the number of atomic planes that you want to include in your calculation (this
will fix the lattice constant in the direction orthogonal to the surface). This
will represent a so-called 1x1 model, meaning that your "surface unit cell" is
made by just one unit cell. Possible reconstruction (which means atomic
rearrangement of the atoms with respect to the ideal positions) will be, of
course, the same in all surface unit cells.
More complicated reconstructions might arise because:
i) there can be a surface atomic displacement different in neighbor unit cells
(for example, in the case of the cited Si surface two Si atoms in different 1x1
cells approach to each other to form a dimer, this gives you a 2x1
reconstruction; then two neighbor dimers can show different tilt with respect
to the surface plane, this gives a 2x2 reconstruction, etc.); to include
this effect in your calculation you replicate your surface unit cell (building
a "supercell") in one or both directions parallel to the surface, so as to
build 1x2, 2x1, 2x2, 1x4, etc. models. Of course one should
be driven by either already known results, experimental evidences, etc. or by
physically/chemically meaningful guesses. In this case one should also be
careful to break possible symmetries that would prevent from reaching the
energy minimum. Again, in the case of the Si(100) surface, if you just
replicate the 1x1 unit cell along one surface direction, to build the 2x1
model, the code will just give you
a structure identical to the 1x1 model, with an energy 2 times larger; so, what
you do is to move (even by a small amount) the atoms you expect will move,
namely, the two Si atoms which dimerize. Alternatively, you can randomize the
position of some/all atoms, just to break the symmetry.
ii) there can be a reconstruction where there are more/less atoms than you
would expect in the "ideal" surface, a typical example is the case of O
vacancies in oxide surfaces.
Because the plane-wave calculation, as you probably already know, is by
construction periodic in all directions, you must be sure to include, along the
direction orthogonal to the surface a
"vacuum space" (that means to increase the corresponding lattice parameter) to
prevent two consecutive slabs from interacting. Convergence must be checked
against the vacuum space.
Also, if you want to retrieve the "bulk surface" properties, the thickness of
your slab should be larger enough (this is controlled by the number of atomic
planes included in the unit cell) to prevent
opposite sides of a given slab from interacting with each other.
Another issue is that the "optimal" surface unit cell might show a completely
different "symmetry" than the bulk one. For example, in the case of Au/Pt/etc.
(111) surfaces, the bulk crystal is a cubic
fcc lattice, whereas the minimal surface unit cell can be represented using an
hexagonal lattice.
Hope this helps,
Giovanni
--
Giovanni Cantele, PhD
CNR-SPIN and Dipartimento di Scienze Fisiche
Universita' di Napoli "Federico II"
Complesso Universitario M. S. Angelo - Ed. 6
Via Cintia, I-80126, Napoli, Italy
Phone: +39 081 676910 - Fax: +39 081 676346
Skype contact: giocan74
ResearcherID: http://www.researcherid.com/rid/A-1951-2009
Web page: http://people.na.infn.it/~cantele
http://www.nanomat.unina.it
