Computing dual net and determining migration paths of cations in the α-KAlO2 crystal structure 


1. Open the database KAlO2, the record KAlO2/alpha and compute the adjacency matrix in the Domains mode with MinOm=5 (to consider only strong bonds).

2. Open an ADS window and check Topology/Edit matrix and Tiling/Dual Nets flags. Run ADS.

3. In the Choose Atoms to Delete Bonds window select potassium atoms to build the tiling for the framework only, ignoring mobile cations.

In the Choose Central Atoms window select all atoms.

4. Run IsoCryst for the record in the resulting KAlO2# database and be sure that the nodes of the dual net (ZA) almost coincide with the positions of potassium cations. For this purpose, specify the radius of potassium atoms 1.2Å (that is equal to the default radius of ZA atoms) using IsoCryst options, Atoms tab, Radii button, then click the K button, specify the requited value and click the Apply and Ok buttons.

The result looks like as follows.

5. Close the IsoCryst window, open the Crystal Data window. The dual net is formed by two types of voids, ZA1 and ZA2. Analyze the channel radii (distances from the edges of the dual net to the oxygen atoms). Break the narrowest channels, where such distances do not exceed 2.2Å. In following Figure example of removing the connection ZA1-ZA2 (for which oxygen is too close) is showed.

After breaking the narrowest channels the voids ZA1 and ZA2 have CN 2 and 3, respectively.
Save the changes.

6. Check with IsoCryst and ADS that the resulting migration map of potassium atoms is two-dimensional (010). Try to draw a picture like as follows.

Exercise: analyze in the same way the migration map of β-KAlO2 (the record KAlO2/beta). What are the channel radii, migration map dimensionality and topology? Which KAlO2 modification should possess higher ionic conductivity?

Answer: The net of structure β-KAlO2 (the record KAlO2/beta) is formed by one type of voids ZA1.

The average channel radius is 2.972 Å. The migration map of potassium cation is three-dimensional.

The topology of dual net is dia (check with ADS). The β-KAlO2 should possess higher ionic conductivity, because his system of migration paths extended into three dimensions.

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