# Analyzing models using Atomes

* Atomes* can compute the following structural characteristics of a 3D structure model:

Radial distribution functions g(r) (RDFs) [1] including \(^{\circ}\):

Total RDFs for neutrons and X-rays.

Partial RDFs.

Bhatia-Thornton RDFs [2]

\(^{\circ}\) Radial distribution functions can be computed by i) direct real space calculation and/or ii) Fourier transforming of the structure factor calculated using the Debye formalism [3]

Structure factors S(q) [3] including \(^{\circ\circ}\):

Total structure factors S(q) for neutrons and X-rays.

Total Q(q) [3], [4] for neutrons and X-rays.

Partial S(q):

Faber-Ziman [5] partial S(q)

Ashcroft-Langreth [6], [7], [8] partial S(q)

Bhatia-Thornton [9] partial S(q)

\(^{\circ\circ}\) Structure factors can be computed by i) Fourier transforming of the radial distribution functions and/or ii) using the Debye formalism [3]

Interatomic bond properties

Coordination numbers

Atomic near neighbor distribution

Fraction of links between tetrahedra

Fraction of tetrahedral units

Bond lengths distribution for the first coordination sphere

Distribution of Bond angles

Distribution of Dihedral angles

Ring statistics, according to several definitions:

All closed paths (no rules)

King's rings [10], [11]

Guttman's rings [12]

Primitive rings [13], [14] (or Irreducible [15])

Strong rings [13], [14]

And including options to:

search only for ABAB rings

exclude rings with homopolar bonds (A-A or B-B) from the analysis

Ring statistics is presented according to the R.I.N.G.S. method [16].

Chain statistics, including options to:

search only for AAAA chains

search only for ABAB chains

exclude chains with homopolar bonds (A-A or B-B) from the analysis

search only for 1-(2)\(_n\)-1 chains

Spherical harmonics invariant, \(Q_l\), as local atomic ordering symmetry identifiers [17]

Average Q\(_l\) for each chemical species

Average Q\(_l\) for a user specified structural unit

Mean Square Displacement of atoms (MSD)

Atomic species MSD

Directional MSD (x, y, z, xy, xz, yz)

Drift of the center of mass

See appendix 5 to learn more about the physics and the chemistry behind these calculations.

The calculations presented in this list can only be performed on the * active* project, ie. the project which name appears in the title bar of the

*program main window, in bold font in the*

**Atomes***workspace tree and in green bold font in the workspace information dialog [Fig. 1.1].*

**Atomes**For more about running calculation using

*see chapter 4.*

**Atomes**- M. P. Allen and D. J. Tildesley,
*Computer simulation of liquids*. Oxford science publications, 1987. - P. S. Salmon,
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*Eur. Jour. Mat.*, vol. 14, pp. 331–348, 2002. - B. Thijsse,
*J. App. Cryst.*, vol. 17, pp. 61–76, 1984. - T. E. Faber and Z. J. M.,
*Phil. Mag.*, vol. 11, no. 109, pp. 153–173, 1965. - N. W. Ashcroft and D. C. Langreth,
*Phys. Rev.*, vol. 156, no. 3, pp. 685–692, 1967. - N. W. Ashcroft and D. C. Langreth,
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*Nat.*, vol. 213, p. 1112, 1967. - D. S. Franzblau,
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*J. Non-Cryst. Solids*, vol. 127, pp. 215–220, 1991. - X. Yuan and A. N. Cormack,
*Comp. Mat. Sci.*, vol. 24, pp. 343–360, 2002. - F. Wooten,
*Act. Cryst. A*, vol. 58, no. 4, pp. 346–351, 2002. - S. Le Roux and P. Jund,
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*Phys. Rev. B.*, vol. 28, no. 2, pp. 784–805, 1983.