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[WSS20]Design & Implementation of Data Structure of Crystalline Atomic Data

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POSTED BY: Claudio Chaib
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It should be emphasized that the data for the structure of pentadiamond are from an electronic structure calculation (reference above) for this theoretical carbon allotrope. Its properties are therefore predicted and yet to be confirmed experimentally.

Moreover, the data were not in the form of a CIF file and were compiled from information in the article and manually encoded as a CrystalLattice object in Wolfram Language. Additional coding was required to generate the 192 symmetry equivalent positions of the F m -3 m space group, which were critical for the construction of the theoretical crystalline network.

The central cavity of the structure shown in the third figure is composed of 24 5-membered rings and 6 8-membered rings, and has a total of 56 carbon atoms. Its point group symmetry is Oh. While the overall shape is spherical, it's best visualized as a cube with an 8-membered ring on each face (shown below), a triquinacene moiety at each vertex (shown below), and a pentalene moiety on each edge (shown below) of the cube. The diameter of the cavity is 6.50 Angstroms from pentalene to pentalene, and are large enough to contain a helium atom. These cavities are interconnected by cubic chambers composed solely of six 8-membered rings. The diameter of the chamber is 5.15 Angstroms.

Face view: enter image description here

Vertex view: enter image description here

Edge view: enter image description here
POSTED BY: Robert Nachbar

Update NEW CARBON ALLOTROPE

  • A new form of carbon allotrope was developed (30 June 2020 - link at the end of this post), harder and lighter than diamond; the pentadiamond! And I decided to update my work to demonstrate the use of the functions already developed, CrystalLattice, CrystalLatticeModify, CrystalLatticePlot3D.., for the visualization of this new crystal.

i1

  • First, the CrystalLattice object is created, and the symmetry group is checked:

An attached notebook contains the pentadiamond object!

1a

Then:

pentadiamond["SpaceGroupName"]
  • The symmetry group is the same as in the article (as expected!):

1b

There are only 3 unequal carbons in position:

2

  • Using CrystalLatticeModify with "UnitCellCopy" {0,0,0} we obtain the symmetries together:

    pentadiamondSymmetry = 
 CrystalLatticeModify[pentadiamond, {"UnitCellCopy", {0, 0, 0}}]

i3

  • Then CrystalLatticeModify is used again with the argument "UnitCellGather" to have the same display as the article of "pentadiamond":

    pentadiamondGather = 
  CrystalLatticeModify[pentadiamondSymmetry, "UnitCellGather"];
CrystalLatticePlot3D[pentadiamondGather]

i4

The article is: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.016001 from Yasumaru Fujii, Mina Maruyama, Nguyen Thanh Cuong, and Susumu Okada Phys. Rev. Lett. 125, 016001 – Published 30 June 2020

I would like to point out that Robert Nachbar (Wolfram), my mentor, who provided the fundamental pieces to obtain the coordinates of this allotrope. Thank you!

Thank you all!

Attachments:
pentadiamondObject.nb
POSTED BY: Claudio Chaib

No, the fractional lattice coordinates of the atoms and the symmetry elements of the space group are part of the input data in the CIF file. It could be adapted to tile 3D space with plesiohedra given the coordinates of their vertices, lists of vertices comprising the faces, and the elements of the corresponding space group.

For those not familiar with plesiohedra, see also the Wikipedia page.
POSTED BY: Robert Nachbar
Attachments:
2017341.pdf
Ewingite.cif
EwingiteNW.cif
POSTED BY: Claudio Chaib

Could this be used to make the plesiohedra?
POSTED BY: Ed Pegg

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