15.10. Handling dopants

15.10.1. Overview

This section is adapted from the answer to a Frequently Asked Question at the IFEFFIT Wiki.

ATOMS is, except in extremely contrived situations, not capable of writing a proper feff.inp file for a doped material. This is not a programming shortcoming of ATOMS (or its author!), but a number theoretic limitation imposed by the physical model used by FEFF.

In the feff.inp file, there is a big list of atomic coordinates. The reason that people like using ATOMS is because, without ATOMS, it is a pain in the ass to generate that list. The virtue of ATOMS is that it automates that annoying task for a certain class of matter, i.e. crystals.

FEFF expects a point in space to be either unoccupied or occupied by a specific atom. A given point may be occupied neither by a fraction of an atom nor by two different kinds of atoms.

Let's use a very simple example – gold doped into FCC copper. In FCC copper, there are 12 atoms in the first shell. If the level of doping was, say, 25 percent , then ATOMS could reasonably select 3 of the 12 nearest neighbors at random and replace them with gold atoms. However, what should ATOMS do with the second shell, which contains 6 atoms? 25 percent of 6 is 1.5. FEFF does not allow a site to be half occupied by an atomic species, thus ATOMS would have to decide either to over-dope or under-dope the second shell.

This problem only gets worse if the doping fraction is not a rational fraction, if the material is non-isotropic, or if the material has multiple sites that the dopant might want to go to.

Because ATOMS cannot solve this problem correctly except in the most contrived of situations, its author decided that ATOMS would not attempt to solve it in any situation. If you specify dopants in ATOMS' input data, the list in the feff.inp file will be be made as if there are no dopants.

This leads to two big questions:

  1. Why would dopants be allowed in ATOMS in any capacity?
  2. How does one deal with XAS of a doped sample?

The first question is the easy one. At the programming level in DEMETER, ATOMS can do other things besides generating feff.inp files. Calculations involving tables of absorption coefficients, simulations of powder diffraction, and simulations of DAFS spectra could all effectively use of the dopant information. In ARTEMIS you will notice that there is not even a column for specifying occupancy -- in ARTEMIS occupancy can only be 1.

The second question is the tricky one and the answer is somewhat different for EXAFS as for XANES. The bottom line is that you need to be creative and willing to run FEFF more than once.

The best approach to simulating a XANES spectrum on a doped material that I am aware of also involves running FEFF many times. One problem a colleague of mine asked me about some time ago was the situation of oxygen vacancies in Au2O3. After some discussion, the solution we came up with was to use ATOMS to generate the feff.inp for the pure material. This fellow then wrote a little computer program that would read in the feff.inp file, randomly remove oxygen atoms from the list, write the feff.inp file back out with the missing oxygens, and run FEFF. He would do this repeatedly, each time replacing a different set of randomly selected atoms and each time saving the result. This set of computed spectra was then averaged. New calculations were made and added to the running average until the result stopped changing. If I remember, it took about 10 calculations to converge.

This random substitution approach would work just as well for dopants as for vacancies.

15.10.2. Crystal data with partial occupancy

A structure for the mineral zirconolite, CaZrTi2O7, was published as

  • H. J. Rossell. Zirconolite — a fluorite-related superstructure. Nature, 283(5744):282–283, Jan 1980. doi:10.1038/283282a0.

In that paper, significant site swapping was found between the site occupied by Zr and one of the Ti sites. Consequently, the CIF file is published with partial occupancies for those tow sites. Here is the CIF file.

When this CIF file is imported into ARTEMIS, you see this error message:

../_images/feff_atoms_partical_occupancy.png

Fig. 15.34 Atoms responds with an error message for crystal data with partial occupancy.

To use this crystal data in ARTEMIS, you need to edit the CIF file before importing it to remove the examples of partial occupancy. Change the last loop from this:

loop_
_atom_site_label
_atom_site_fract_x
_atom_site_fract_y
_atom_site_fract_z
_atom_site_occupancy
CaM1 0.37180 0.12450 0.49520 1.00000
ZrM2 0.12250 0.12220 -0.02580 0.93000
TiM2 0.12250 0.12220 -0.02580 0.07000
TiM3 0.24980 0.12230 0.74650 1.00000
TiM4 0.50000 0.05500 0.25000 0.86000
ZrM4 0.50000 0.05500 0.25000 0.14000
TiM5 0.00000 0.12700 0.25000 1.00000
O1 0.31000 0.13300 0.27500 1.00000
O2 0.47000 0.14600 0.10200 1.00000
O3 0.19700 0.08300 0.57300 1.00000
O4 0.40300 0.17400 0.71900 1.00000
O5 0.70200 0.16900 0.59000 1.00000
O6 -0.00100 0.11100 0.41400 1.00000
O7 0.11900 0.05500 0.78800 1.00000

to this:

loop_
_atom_site_label
_atom_site_fract_x
_atom_site_fract_y
_atom_site_fract_z
_atom_site_occupancy
CaM1 0.37180 0.12450 0.49520 1.00000
ZrM2 0.12250 0.12220 -0.02580 1.00000
TiM3 0.24980 0.12230 0.74650 1.00000
TiM4 0.50000 0.05500 0.25000 1.00000
TiM5 0.00000 0.12700 0.25000 1.00000
O1 0.31000 0.13300 0.27500 1.00000
O2 0.47000 0.14600 0.10200 1.00000
O3 0.19700 0.08300 0.57300 1.00000
O4 0.40300 0.17400 0.71900 1.00000
O5 0.70200 0.16900 0.59000 1.00000
O6 -0.00100 0.11100 0.41400 1.00000
O7 0.11900 0.05500 0.78800 1.00000

To analyze your data while considering the partical occupancy, try one of the techniques discussed in the following section.

15.10.3. Doped crystal and alloys

This section is adapted from text posted by Scott Calvin to the IFEFFIT Wiki and retains his voice.

For samples which are doped crystals, there are a couple of methods people have used. For purposes of this article, I'll consider cases where the dopant is substitutional as opposed to interstitial.

As an example of two methods, let's consider FeS2 substitutionally doped with molybdenum. (I have no idea if such a material is possible...I'm using it because FeS2 is included as an example in the DEMETER distrribution.)

15.10.3.1. Method 1

Run atoms for FeS2.

Now look at the feff.inp file that is generated. Under POTENTIALS, it says the following:

POTENTIALS
*    ipot   Z  element
       0   26   Fe
       1   26   Fe
       2   16   S

Add another line for the Mo, which is atomic number 42 (the atomic number is required):

POTENTIALS
*    ipot   Z  element
       0   26   Fe
       1   26   Fe
       2   16   S
       3   42   Mo

Important: Do not skip numbers in the ipot column, and make sure 0 is the absorber!

Next, take the list following the word ATOMS in the feff.inp file, and arbitrarily change roughly the right number of iron atoms to molybdenum atoms. Make sure to change the ipot column to match...it's the part FEFF will actually use:

ATOMS                          * this list contains 71 atoms
*   x          y          z      ipot  tag              distance
   0.00000    0.00000    0.00000  0    Fe1              0.00000
   2.07514    0.62686    0.62686  2    S1_1             2.25657
   0.62686   -2.07514    0.62686  2    S1_1             2.25657
  -0.62686    0.62686    2.07514  2    S1_1             2.25657
  -0.62686    2.07514   -0.62686  2    S1_1             2.25657
  -2.07514   -0.62686   -0.62686  2    S1_1             2.25657
   0.62686   -0.62686   -2.07514  2    S1_1             2.25657
  -3.32886    0.62686    0.62686  2    S1_2             3.44488
   0.62686    3.32886    0.62686  2    S1_2             3.44488
   0.62686   -0.62686    3.32886  2    S1_2             3.44488
   3.32886   -0.62686   -0.62686  2    S1_2             3.44488
  -0.62686   -3.32886   -0.62686  2    S1_2             3.44488
  -0.62686    0.62686   -3.32886  2    S1_2             3.44488
  -2.07514   -2.07514    2.07514  2    S1_3             3.59425
   2.07514    2.07514   -2.07514  2    S1_3             3.59425
   2.70200    2.70200    0.00000  1    Fe1_1            3.82121
  -2.70200    2.70200    0.00000  3    Mo1_1            3.82121
   2.70200   -2.70200    0.00000  1    Fe1_1            3.82121
  -2.70200   -2.70200    0.00000  1    Fe1_1            3.82121
   2.70200    0.00000    2.70200  1    Fe1_1            3.82121
  -2.70200    0.00000    2.70200  3    Mo1_1            3.82121
   0.00000    2.70200    2.70200  1    Fe1_1            3.82121
   0.00000   -2.70200    2.70200  1    Fe1_1            3.82121
   2.70200    0.00000   -2.70200  1    Fe1_1            3.82121
  -2.70200    0.00000   -2.70200  3    Mo1_1            3.82121
   0.00000    2.70200   -2.70200  1    Fe1_1            3.82121
   0.00000   -2.70200   -2.70200  1    Fe1_1            3.82121
  -2.07514    3.32886    2.07514  2    S1_4             4.43776

In this case, I changed 3 of the 12 nearest iron neighbors into molybdenum ... reasonable if I have about 25 percent doping.

If you are doing a FEFF calculation for the molybdenum absorber, then also change the very first iron to molybdenum, and change potential 0 in the ipot list to molybdenum with ipot 0.

POTENTIALS
*    ipot   Z  element
       0   42   Mo
       1   26   Fe
       2   16   S
       3   43   Mo

ATOMS                          * this list contains 71 atoms
*   x          y          z      ipot  tag              distance
   0.00000    0.00000    0.00000  0    Mo1              0.00000
   2.07514    0.62686    0.62686  2    S1_1             2.25657
   0.62686   -2.07514    0.62686  2    S1_1             2.25657
  -0.62686    0.62686    2.07514  2    S1_1             2.25657
  -0.62686    2.07514   -0.62686  2    S1_1             2.25657

If you are doing the calculation for the iron edge, leave the first iron alone, since it is still the absorber.

Now run FEFF, and you'll get the iron scattering paths listed separately from the molybdenum scattering paths.

One more step ... correcting for the actual doping fraction. Suppose there is actual 20 percent molybdenum and not 25 percent, as we implied. We couldn't have handled that just through FEFF, because we can't change exactly 20 percent of 12 atoms...we have to change 2, which is 17 percent, or 3, which is 25 percent.

The fix for this is to change the S20 in the molybdenum and sulfur scattering paths to account for this. You could, for example, use the following GDS parameters:

set: MolyPercent = 0.20
def: IronPercent = 1-MolyPercent

Then go to the individual path representing the scattering from the nearest neighbor molybdenum atom, and assign it an S20 of

amp*MolyPercent/(3/12)

That way, if the MolyPercent is 20 percent, it will reduce the amplitude of those paths by 20/25 percent, as is proper.

Of course, the iron scatterer would get an S20 of

amp*IronPercent/(9/12)

That's more or less it!

You could, of course, guess the MolyPercent instead of setting it, if for some reason it was unknown in your sample.

15.10.3.2. Method 2

Suppose we want to analyze the iron edge.

Run atoms for FeS2 and then run FEFF.

Then make a new ATOMS page, type or read in the FeS2 file, and just change the Fe to Mo. Run ATOMS again.

If you're doing the iron edge, then change the absorber to iron in the feff.inp file (this requires changing the potential list; see the description under “Method 1” for how to do this.) Run FEFF.

(If you want to analyze the molybdenum edge, then of course you change the feff.inp file in the first calculation to molybdenum and leave it as molybdenum in the second.)

You now have two sets of FEFF files associated with one data set.

Make GDS parameters:

set: MolyPercent = 0.20
def: IronPercent = 1-MolyPercent

Now make the S20 for all paths calculated with the original ATOMS file:

amp*IronPercent

and for all paths calculatged with the new ATOMS file:

amp*MolyPercent

Again, you can guess the MolyPercent if it's unknown.

15.10.3.3. Discussion of these two methods

Which method you use is largely a matter of taste. The first method is easier to screw up, since there's a lot of counting involved. On the other hand, it generates many fewer paths, and thus makes for smaller files and may fit faster (you're not wasting time and effort counting sulfur paths twice, for example). The first method also gives you the potential of finding a few multiple scattering paths that involve both iron and molybdenum (in this example) that you can't probe at all by the second method. This is most likely to be true when the dopant is in low concentrations but is high-Z ... it's possible that there may be a molybdenum-iron multiple-scattering path that is significant, and it's not going to be modeled so well by the weighted average of iron-iron and molybdenum-molybdenum paths used in method 2. But the price for this is that properly incorporating multiple-scattering paths via method 1 requires an annoying amount of counting and thinking.



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