Practical Peaks and Structure Completion: an exercise

 

The following exercise with Peaks will step you through a suggested procession of steps to arrive at a plausible structure model. The example used in this exercise is the c(4x2) surface reconstruction on SrTiO3(001) published by N. Erdman, et al. (cf. Ref. 1). The files are located at /edm/fs98/Examples. One folder (STO4x2) contains the source data scanned in from the original diffraction patterns and the other (STO4x2_ran) contains a complete Direct Methods analysis with the final structure solution file (cf. the README files located in each folder for more information). It is suggested that you run the Direct Methods analysis yourself, and compare those results to the already run case.

 

After running the Direct Methods analysis, you find that there are several possible unique solutions. At this stage it may not be apparent which solution is the correct one to refine a model against. Therefore, the procedure outlined here may have to be iteratively carried out on several different genetic solutions. However, for the purpose of this exercise, the correct genetic solution is given to you and should look something like Figure 1. You can select this solution and begin the structure completion process by entering the Peaks interface (click on Analyze selected solution from the Analyze Feasible Sets Window).

 

Figure 1. Genetic algorithm solution for the STO c(4x2) surface.

 

An explanation of the utilities available in the Refine Solutions window can be found by following this link (Peaks). Before you begin the refinement make sure to select the Diagnostics button. This will allow you to follow your progress as you run the refinements. Also for the data set included, the reflections are structure factors not intensities, therefore the Use F’s box should be checked. Also checking the Overlay Atom Peaks will give you an idea of which atoms have been assigned to certain intensities by Peaks, through its initial cycle (upon loading).  The Refine Solutions window should look similar to that in Figure 2. Note: you should change the Peak Cutoff value, click on Change then Find Peaks and List Atoms to ensure that you have the three peaks shown in the example.

 

Figure 2.  Refine Solutions Window with the loaded Unique Solution for the (4x2) surface.

 

 

An initial Search Occupancy will produce a list of solutions in the Plausible Solutions window (Figure 3). The first Figure of Merit (FOM) that is being considered is the R-factor, and the solutions are listed in this window in order of increasing R-factor. By default Peaks uses the R-factor criterion; later, as appropriate the user can selected to refine against a Chi**2 factor. An explanation of how to use these other refinement factors is given in the Peaks Documentation.

 

Figure 3.  Plausible Solutions Window.

 

In the initial guess for the solution, Strontium atoms are assigned to the largest peak intensities. This produces a fairly good fit (FOM) using the first solution from the Search Occupancy; however, the structure of the Calculated Diffraction Pattern (DP) is not consistent with the Experimental Diffraction Pattern. To simulate the DP from the model, you need to Refine Positions. In practice, one must vary the type of atom sitting at a site to ensure the Calculated DP matches the Experimental DP.  Furthermore, additional atom sites might need to be added or removed from the model.  For example, when Peaks begins its first refinement, it attributes an Oxygen atom to the position at (0.1536, 0.0000). Since Peaks was developed to know very little about the problem it has been assigned, in particular that it is looking for atom positions, it believes that this site may be occupied by an atom. However, the intensity of this peak is too small (and weak) to be the result of scattering from an atom feature (at least at the surface). It may be a bulk position, however and may be considered in later refinements. For example, it is always possible to add or subtract a complete bulk layer to the model, in order to achieve an intensity compromise (in the Difference Map). By looking at the Difference Map, it is evident that this oxygen site should be omitted from the surface model (Figure 4).

 

Figure 4. Using the Difference Map helps determine whether or not atoms should be added or removed from a Model. For this case, the oxygen atoms sites should be removed from the model.

 

By changing the Strontium atom site to Titanium and removing the Oxygen from the surface, the Calculated Diffraction Pattern matches the Experimental much better (as seen through the Fourier Fit). In addition the Difference map is more neutral which suggests the correct scattering species have been determined (Figure 5).

 

Figure 5.  (left) Fourier Fit between Calculated and Experimental Diffraction Pattern; (right) Difference Map. The model only includes Titanium atoms.

 

In general, weakly scattering atoms are found through a combination of difference maps and chemical intuition.  In this particular example, the coordinating oxygen atoms were found by the presence of a difference peak.  By using the Show Difference Peaks option while viewing the Difference Map, it allows you to determine where there is an intensity discrepancy in the model. This can be refined by replacing these peaks with atoms. Since the intensity is relatively weak, and the sites provide possible coordination for the cations in the structure, it is probable that they are oxygen atoms. By selecting the peaks in the Atom Testing window, it is possible to change the species type; as well as to decide whether or not to include an atom in the model. While not all oxygen atoms appeared as difference peaks, the remain oxygen atom was found by requiring that the Titanium be satisfactorily coordinated. Here for example, after  a second structure completion iteration, the oxygen atoms have been chosen as shown in Figure 6. They are at the following positions: (0.000,0.000) and (0.2495,0.000). The task of finding these light scatters will depend on how good the data set is, and how much a priori information about the surface is know.

 

Figure 6.  (top) Genetic Solution with oxygen atoms added to satisfy coordination with the titanium atoms. (bottom) Difference Map of same model.

 

By performing another difference search, it is possible to find an oxygen atom at (0.5000,0000) position, which is consistent with TiO­­x units. Similarly the Ti at (0.3844,0.000) is under coordinated. After using the Iterate Entropy and Iterate Positivity functions and Refine Positions, with the Projection Functions, the map and model are updated with the current atom lists. The current genetic solution and Refine Solution window is shown in Figure 7.

 

Figure 7.  Refine Solutions Window.

 

The corresponding map, difference map and Fourier Fit (DP) are shown in Figure 8 for the current model. The model has an R1 factor of 0.2449. In the difference map (Figure 8b) there is a bright intensity localized at the position (0.160,0.195. However, due to the asymmetry in the intensity surrounding it, i.e. the dark crescent shape, this feature is attributed to atoms residing in the bulk (sub-surface layers), rather than those at the surface.

 

Figure 8.  (a) Current Map of the Model, (b) Difference Map, and (c) Fourier Fit of the Calculated and Experimental Diffraction Patterns.

 

At this point, it is worth mentioning, that it is helpful to consider how the surface will sit on the bulk material. Accordingly, different subsurface layers will restrict the possible structure solutions; therefore, it is useful to add bulk layers into the refinement and see whether or not the surface atoms are coordinated appropriately. This will enable you to further refine your structure, and sometimes, will match intensities much better. In this example a bulk layer of TiO has been added—Ti at (0.121,0.252) and O at (0.152,0.000)—and the following map result (Figure 9).

 

Figure 9.  Refined Map consisting of both the surface model and a bulk TiO underlayer.

 

To this end, the structure for the c(4x2) has been found, with final atom positions given in the FinalSols.ins file (Chi**2 = 2.1). It should be noted, that while this exercise is a general guide for performing a structure completion, there is no definite approach. You should not be discouraged though, the problem remains tractable, and in practice one should consider the following final remarks when performing a structure refinement:

  1. Several different genetic solutions will have to be investigated, as well as their Babinet solutions.
  2. Not all surface atoms will be represented in the scattering potential map; as a result of limited surface data, or a consequence of the scattering species.
  3. Different scatters should be varied at different sites (Peaks may not find all these sites initially) and the Calculated DP should be examined.
  4. Difference maps are helpful at finding weak scatters.
  5. Various subsurface layers should be considered to determine how a possible surface unit cell fits on the bulk (centered about various origins).
  6. Does my solution make chemical sense: coordination, bond distances, charge, etc.

 

Good luck!

REFERENCES

 

[1]  Surface Structures of SrTiO3 (001): A TiO2-rich Reconstruction with a c(4 × 2) Unit Cell, Erdman, N., Warschkow, O., Asta, M., Poeppelmeier, K.R., Ellis, D.E., and Marks, L.D. J. Am. Chem. Soc., 125, 33, 10050 - 10056, 2003, DOI: 10.1021/ja034933h