Searching for building units and the underlying net in the crystal structure of Cu5Zn8 


Algorithm:

1. Convert the file Cu5Zn8.cif into the ToposPro database gamma-brass. Open the database and compute the adjacency matrices using AutoCN method Solid Angles (MinOm = 1.5).

2. Having the Cu5Zn8 record active (do not select it with Insert tab), open the Nanoclustering window (Compound/Auto Determine/Nanoclustering) and specify the following options:



Max. Number of Clusters – maximum number of nanoclusters in the representation; choose 0 if the number is unlimited.
Max. Number of Shells – maximum number of shells in each nanocluster (0 - unlimited).
One-Atom Cluster – permits existence of 1-atom (trivial) nanoclusters. This option is required for structures where some equivalent atoms are interconnected.
Enumerate Layers – consider all possible sizes for multi-shell nanoclusters, otherwise maximal possible size (maximal number of shells) will be assumed for each nanocluster.
Save All Nets – automatically save underlying nets in the database database name_c when computing several structures (continuous mode).
Search by Cations – if there are cations (atoms with positive oxidation degree) in the list of atoms, the centers of nanoclusters can be chosen only among them (Only Cations), or these atoms will necessarily be taken as centers of nanoclusters and some other nanoclusters will be searched among other atoms (All Cations and Other Atoms). In this case ToposPro ignores the symmetry of cation positions so you may enforce ToposPro to consider some special sets of nanoclusters that do not fit the principles of the nanocluster method (see below).
Consider Empty Clusters – you may consider voids as centers of nanoclusters. ToposPro treats all unoccupied Wyckoff positions without variable parameters as possible centers of nanoclusters. In the output they are designated as ZA with Wyckoff position in parentheses. You may consider only representations containing such "empty" nanoclusters (Only With Empty Clusters) or all representations both with and without "empty" nanoclusters (With All Clusters). To find the composition of the "empty" nanoclusters ToposPro considers all the contacts between ZA and atoms that have solid angle of the corresponding face of the Voronoi-Dirichlet polyhedron of ZA no less than Min. Omega value.
Porous Structures – a special mode to search for representation of a porous structure (like zeolite) as a set of tiles (one-shell empty clusters) and/or rings. The structure should be represented together with its dual net (see Module 7). In this mode the Porous Structures Units options are valid that allow to consider as nanoclusters only tiles, only rings, or both tiles and rings.
Consider Solutions – output all solutions, or only those where every nanocluster has at least one atom in the outer shell belonging to this nanocluster only (Without Fused Clusters), or only those where nanoclusters have no common atoms (Only Packings).

The most general set of options (largest number of representations) is: One-Atom Cluster checked; With All Clusters; other options are default. But the One-Atom Cluster option should be checked only if no representations were found with this option unchecked. So it is recommended initially try With All Clusters and other options being default. Change other options if the computation is too long (use Cancel menu item to interrupt computation). If you want to check some non-standard set of nanoclusters you may specify for their centers positive oxidation degrees and use Search by Cations options.

3. Push Ok button and wait until the window with the list of representations appears. The representations are ordered by the number of clusters. In the Cu5Zn8 there are three representations, two of them consist of one-shell clusters; the one starting with ZA1 contain “empty” cluster with the center ZA1 in Wyckoff position 2a. Select the second representation and check the option Generate Nets if you want to obtain the underlying nets (nets whose nodes correspond to structural units; see Appendix 2 for details) for the representations. Press Ok button and wait until the calculation will be finished.



You will be asked about creating a new database that will contain the underlying net:



Answer Yes, enter the user code and you will get the database gamma-brass_c with the one record marked nanocluster net.

4. Open the file gamma-brass.txt that contains the output of the Nanoclustering procedure for the selected representation. The file looks like:





The detailed information of the second representation shows that the second nanocluster is “empty” (non-centered) with the inner core ZA1 located in 2a positions. The first shell of the nanocluster consist the 4 Zn1 atoms. All four Zn1 are 3-coordinated (3^4) within the shell and presented as a tetrahedron. The (4,6,4)(3^4) line summarize the information about the first shell of the primary nanocluster, it means that it has 4 vertices, 6 edges and 4 faces (4,6,4) and that the 4 vertices are 3-coordinated atoms. In the second shell all ten Cu1, Cu2 atoms are 6-coordinated and the 12 Zn2 are 3-coordinated. The shell is now a 22 vertex polyhedron with 48 edges and 28 faces. To define the general type of the shells of nanoclusters we use the signature v,e,f where v, e and f atoms are projected to vertices, edges or faces of the previous shell or the inner core. Thus the four Cu1 6-coordinated atoms are of the type “f” [4 Cu1(6^4)(4f)], six 6-coordinated Cu2 atoms and twelve 3-coordinated Zn2 atoms have the “e” and “v”, respectively [6 Cu2(6^6)(6e) / 12 Zn2(3^12)(12v) ], (for the colour see below).
The numbering of atoms corresponds to the initial Cu5Zn8 structure and allows you to easily construct the nanoclusters with IsoCryst.

5. Turn to the database gamma-brass and run IsoCryst for the Cu5Zn8 record. Draw the picture () and specify Name&Index mode for the legend view.



Using the legend select all Zn1 atoms.



Leave only one tetrahedral core of Zn1 atoms () and press one time the Growth button () to obtain the second shell of the 0@4@22 nanocluster. Select the inner 0@4 core by yellow () and use the corresponding signature colours for the type 4 “f”, 6 “e” and 12 “v” atoms.



As shown in the two views above, we have the nanocluster model based on the inner tetrahedral core 0@4 (yellow) and the second shell contains 22 atoms. The “onion” 0@4@22 nanocluster is fully equivalent to the common description of γ-brasses in terms of nested polyhedra as a sequence of IT+OT+OH+CO, where IT, OT, OH, CO are Inner Tetrahedron, Outer Tetrahedron, Octahedron and Cuboctahedron, respectively (see Pankova A.A., Blatov V.A., Ilyushin G.D., Proserpio D.M. “γ-Brass polyhedral core in intermetallics: the nanocluster model” manuscript in preparation).

6. Close the IsoCryst window and run ADS for the record from the database gamma-brass_c in the Classification mode (you can always click on Default to set to Classification). You will find that the nanoclusters form a packing with the body-centered cubic with extended coordination: 14-c bcu-x underlying net topology.





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