### Using the R.I.N.G.S. code you can compute:

- Radial distribution functions
- Simulated neutron and X-rays structure factors
- Mean Square Displacement
- Bond angles and dihedral angles distribution
- Bond properties
- Structural environments distribution
- Voids distribution
**Very detailed ring statistics analysis**- Various inputs files for 3D visualization using OpenDX

More details on the calculations that you can perform using the R.I.N.G.S. code are given bellow:

**R**adial**D**istribution**F**unctions**RDF**

- Total RDF:
**g**(r) and**G**(r) - Partial RDFs:
**g**_{αβ}(r) and**G**_{αβ}(r) - Bhatia-Thornton RDFs [a]

- Total RDF:

- Simulated neutron and X-rays structure factors
^{*}

- Neutron and X-rays weighted distribution functions

- Total S(q)
- Partials S(q)
- Faber-Ziman [b] partials S(q)
- Ashcroft-Langreth [c, d, e] partials S(q)
- Bhatia-Thornton [f] partials S(q)

- Neutron and X-rays weighted distribution functions

^{*} Computations can be performed either using the fast Fourier transform of the RDFs or by computing the correlations between the atomic positions and a sampling of vectors from the reciprocal space.

*New in version 1.2.5: the Q point dependency is now implemented for the X-rays structure factors calculation in reciprocal space, see [n] for details.*

**M**ean**S**quare**D**isplacement**MSD**^{**}

- Atomic species MSD
- Directional MSD (x, y, z, xy, xz, yz)
- Drift of the center of mass
- Diffusion constant
- MSD for each single atom

^{**} Computations can be performed either with or without applying a self-correlation on the results.

**Very detailed ring statistics analysis**- Choice of the chemical species used to initiate the search
- All atoms can be used
- Only the species of highest coordination can be used (network forming nodes)
- Only the species of lowest coordination can be used (network modificating nodes)

- Choice to look only for ABAB rings
- Homopolar bonds are ignored when creating the nearest neighbors table
- Allows to look for primitive ABAB rings
- Allow to look for ABAB rings in systems with more than 2 chemical species

- Choice on the nature of the rings to look for:
- Search for all closed paths in the box
- Search for King's shortest paths rings [g, h] either with or without homopolar bond(s)
- Search for Guttman's shortest paths rings [i] either with or without homopolar bond(s)
- Search for primitive rings [j, k, l].
- Search for strong rings [k].

- Advanced use of the results of the ring statistics:
- Analysis of the "trajectories" of the barycenters of the rings using the OpenDX visualization software
- Evaluation of standard properties for atoms involved in rings:
- Advanced properties of the barycenters of the rings:

- Advanced properties of the atoms involved in rings:
- Average neutron structure factors of a ring with
*n*nodes^{****}

- Choice of the chemical species used to initiate the search

^{***} Computations can be performed using the Faber-Ziman [b], as well as the Ashcroft-Langreth [c, d, e] formalisms.^{****} Computations can be performed using the Faber-Ziman [b], the Ashcroft-Langreth [c, d, e] as well as the Bhatia-Thornton [f] formalisms.

- Various inputs files for 3D visualization using OpenDX
- Choice of the color map to be used in OpenDX (Atomic mass, radius, connectivity factor [m] and others ...)
- Possibility to add the results of the voids distribution analysis to the visualization interface
- Possibility to add the coordination tetrahedras to the visualization interface
- Visualization of the trajectories of the particles of highest Mean Square Displacement

- Several chemical standard properties are outputted in a global output file:
- Resume of the calculation(s) performed
- Direct and reciprocal lattice parameters
- Number density and real density
- Empirical formula

### => More informations on the radial distribution functions

### => More informations on the simulation of neutrons scattering

**=> More informations on ring statistics in the R.I.N.G.S. code**

**=> More informations on ring statistics**

**=> More informations on the mean square displacement**

- a
- P. Salmon.
*J. Non-Cryst. Solids..*,**353**:2959-2974, (2007). - b
- T. E. Faber and Ziman J. M.
*Phil. Mag.*,**11**(109):153-173 (1965). - c
- N. W. Ashcroft and D. C. Langreth.
*Phys. Rev.*,**156**(3):685-692 (1967). - d
- N. W. Ashcroft and D. C. Langreth.
*Phys. Rev.*,**159**(3):500-510 (1967). - e
- N. W. Ashcroft and D. C. Langreth.
*Phys. Rev.*,**166**(3):934 (1968). - f
- A. B. Bhatia and D. E. Thornton.
*Phys. Rev. B*,**2**(8):3004-3012 (1970). - g
- S. V. King.
*Nature*,**213**:1112 (1967). - h
- D. S. Franzblau.
*Phys. Rev. B*,**44**(10):4925-4930 (1991). - i
- L. Guttman.
*J. Non-Cryst. Solids.*,**116**:145-147 (1990). - j
- K. Goetzke and H. J. Klein.
*J. Non-Cryst. Solids.*,**127**:215-220 (1991). - k
- X. Yuan and A. N. Cormack.
*Comp. Mat. Sci.*,**24**:343-360 (2002). - l
- F. Wooten.
*Acta Cryst. A*,**58**(4):346-351 (2002). - m
- S. Le Roux.
*Ph.D. thesis*(2008). - n
- D. T. Cromer and J. B. Mann
*Acta. Cryst.*,**A24**:321 (1968).

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