Comparing RMC and RDM

ZnCl₂

A RMC study of glassy ZnCl₂ has already been published.

The same neutron data was used, as in this previous work.

Because in this early study, the model was small (324 atoms),
a much larger one was built here with 1950 atoms
in a cubic box with L = 39.906 Å.

Strategy

Strategy is quite important when using RMC, and the normal way for imposing a 4-connected three-dimensional network is :

first to fill randomly the box with Zn atoms, respecting a shortcut distance;
constraining a [ZnZn₄] fourfold coordination by a RMC run without diffraction data;
adding the Cl atoms at the Zn-Zn midpoints(ensuring corner sharing);
and finally running RMC with diffraction data.

Another approach was deliberately used here, in order to verify if a good fit would be obtained also when edge sharing could occur between [ZnCl₄] tetrahedra.

The model was built up by filling first the box with 650 Zn atoms, at random, but respecting a 3.1 Å shortest Zn-Zn distance.
Then, the chlorine atoms were added at random, with 1.9 Å and 3.0 Å respectively as shortest Zn-Cl and Cl-Cl interatomic distances.
The RMCA program was then run without diffraction data, in order to increase these shortest Zn-Zn, Zn-Cl and Cl-Cl distances to 3.4, 2.05 and 3.2 Å, respectively, adding the constraint that four Cl atoms should be found in the range 2.05-2.65 Å around a Zn atom.

Obtaining that all the Zn atoms form [ZnCl₄] tetrahedra was quite long (several days on a Pentium-II 333MHz).

Then, the RMCA program was run against the neutron diffraction data, obtaining finally an excellent agreement with Rp = 0.76 %.

Looking accurately to this model reveals that the systematic sharing of exactly two Zn atoms by Cl atom is far from being realized :

Repartition of neighbouring [ZnCl₄] tetrahedra in the final "classic" RMC model for ZnCl₂, starting from a pseudo random configuration.

N	0	1	2	3	4	5	6	7	8	9
NT	1	4	18	82	157	201	129	52	5	1

NT is the number of tetrahedra sharing N chlorine atoms with other tetrahedra. A perfect 4-connected 3D net would have corresponded to NT = 650 for N = 4.

One tetrahedron among 650 is isolated and clusters were built of which the biggest are 5 tetrahedra sharing each of their Cl atoms with 2 other tetrahedra (8 neighbours). One tetrahedron has even 9 other tetrahedra as next neighbours :

A central [ZnCl₄] tetrahedra sharing Cl atoms with 9 other tetrahedra : the biggest cluster built up by the "classic" RMC approach, but without [ClZn₂] coordination constraint :

A total of 37 tetrahedra share one edge and 2 tetrahedra share 2 edges. So that, the building conditions were unable to ensure the corner sharing exclusivity, if we expected it.

Nevertheless, the fit is almost perfect.

On the other hand, the ZnCl₂ RDM model (Rp = 2.40 %), built up from the d-ZnCl₂ structure, corresponds to a perfect 4-connected three-dimensional network.

Result from the ARITVE program :

That RDM model was expanded to 1728 atoms,
before to realize the RMC approach,
obtaining finally the expected low reliability value Rp = 1.09 %.

Projection of the RMC model for glassy ZnCl₂, starting from the d -ZnCl₂ RDM model.

The distorted triangular tunnels are finger print of the RDM starting model.