Dear Colleagues,
I would like to compute the coherency strain energy between Fe (BCC) and
TiO (NaCl). I have created a lat.in (attachment), a 2x2x2 BCC cell, and
decorated the atomic sites such that I get BCC Fe and NaCl-type TiO.
The 2x2x2 BCC Fe cell has a lattice parameter of 5.73A. But lattice
parameter of TiO is only 4.18A. Can I use the csfit for this case,
considering the large misfit of about 27%?
csfit can handle large misfit (the function for the elastic energy is allowed to be nonharmonic). You may have to manually increase these options beyond the default values:
-np=[int] Number of points in stretching mesh in the direction perpendicular to the k-vector(default 5)
-nl=[int] Number of points in stretching mesh in the direction parallel to the k-vector (default 3)
-ml=[real] Maximum parallel stretching (default 0.05)
However, you have to wonder if, in a real system, such epitaxial conditions will even happen…
Thanks Dr. Axel for the mail.
I am trying to compute the coherency strain energy between Fe and TiO for the following
reason. The Oxide Dispersion Strengthened (ODS) steel is a class of steel with outstanding
mechanical properties which are considered to come from the homogeneous dispersion of a
large density of oxide nano-crystals in the ferrite matrix. These oxide particles are also shown
to remain stable up to about melting point of the steel, without any coarsening.
Nature Materials Vol.10 December 2011, pp.922-926 concludes that the nano particles have
a defective NaCl structure like TiO. This article refers several times to high lattice coherency between the nano-clusters and Fe matrix. (For example, caption to Fig.5). But formation
enthalpies of the TiO-based defective NaCl-type nano-clusters (with some Ti substituted by Y/Fe) are computed to be higher than that of pure TiO, indicating that this model is less stable than stoichiometric Y2Ti2O7 or Y2TiO5 or TiO.
I am considering whether the Fe-TiO coherency strain energy combined with formation energy of
defective TiO can make the nano-clusters relatively more stable than pure TiO (or Y2Ti2O7 or
Y2TiO5).
Phys. Rev. Lett. 109 (2012) 125506 (Olson-Northwestern Univ) has considered interface between
Fe and TiC, which also has a large lattice constants mismatch.
It will be helpful if you could verify my reading of the above reference and my calculation plan.
Ok, this seems like a good project.
As a first step, I would just try to do calculation at various imposed fixed volumes (or even fixed cell shape) to simulate the strain imposed by the matrix. No need to simulate the interface before the bulk contributions have been determined.
I would expect that enlarging the volume would stabilize O vacancy formation (as those typically have a positive formation volume change in an oxide).
Dear Dr. Axel,
Thanks for your comments and suggestions on Fe-TiO strain energy calculations. The graph below gives the total energy of TiO at fixed volumes. The volume range covers from the experimental value of Ti4O4 (NaCl-type) to that of 16 atom BCC Fe supercell.
[attachment deleted]
Please give your advice for calculating the bulk contribution to the strain energy.
I have also proceeded with the calculation of coherence strain. The results are shown in the following graph.
[attachment deleted]
The top graph was obtained with csfit -d. In this calculation, csfit has generated 75 structures in both 0 and 1. For this calculation, csfit was printing "Warning: instability detected" a 58 times. The middle graph was obtained with np=8, nl=4, ml=0.1. This generated 160 structures. 142 "Warning: instability detected". Bottom graph is obtained with -np=10, -nl=6, -ml=0.1. This generated 300 structures. Only 2 "Warning: instability detected".
Please give a look at the graphs and give your comments and suggestions. The coherency strain is given in eV/atom. Is this correct?
I would like to see (establish) if the coherent-formation energy (Like in Eq.5 of Phys. Rev. B86, 144202) of the TiO,
DH^{coh}(TiO)=DH^{incoh}(TiO)-DH^{cs}(Fe-TiO), (D=Delta)
is more negative than that of incoherent TiO.
Although I have run csfit, I don’t know how to get DH^{cs}(Fe-TiO) to use with the above relation. Please help me with this. After completing the work I would like to write for a publication. ATAT is very useful for my research. I would be benefited to have your participation as a co-author in this work.
Best regards,
Sorry for the delay in responding - I have a lot on my plate!
The "instability detected" message indicates that, when trying to find a minimum of energy, the code noticed that the function has a negative curvature, so that the true minimum is even lower than the one found over the range where the function is known.
In the case of csfit, the solution (I think) would be to increase the -ml parameter from the default of 0.05.