### Analyze 3D atomistic models

Atomes regroups the following physico-chemical analyses:

- Radial distribution functions g(r) (RDFs) [1] including:
- Structure factors S(q) [3] including:
- 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)

- 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 tetrahedral units
- Bond length 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

- 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*, as local atomic ordering symmetry identifiers [17]_{l}- Average
*Q*for each chemical species_{l} - Average
*Q*for a user specified structural unit_{l}

- Average
- 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 of the documentation to learn more about the physics and the chemistry behind these calculations.

For more about running calculation using * Atomes* see documentation chapter 4.

**References**

- M. P. Allen and D. J. Tildesley,
*Computer simulation of liquids*. Oxford science publications, 1987. - P. S. Salmon,
*J. Non-Cryst. Solids*, vol. 353, pp. 2959–2974, 2007. - M. T. Dove, M. G. Tucker, and D. A. Keen,
*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,
*Phys. Rev.*, vol. 159, no. 3, pp. 500–510, 1967. - N. W. Ashcroft and D. C. Langreth,
*Phys. Rev.*, vol. 166, no. 3, p. 934, 1968. - A. B. Bhatia and D. E. Thornton,
*Phys. Rev. B.*, vol. 2, no. 8, pp. 3004–3012, 1970. - S. V. King,
*Nat.*, vol. 213, p. 1112, 1967. - D. S. Franzblau,
*Phys. Rev. B.*, vol. 44, no. 10, pp. 4925–4930, 1991. - L. Guttman,
*J. Non-Cryst. Solids*, vol. 116, pp. 145–147, 1990. - K. Goetzke and H. J. Klein,
*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,
*Comp. Mat. Sci.*, vol. 49, pp. 70–83, 2010. - P. Steinhardt, D. R. Nelson, and M. Ronchetti,
*Phys. Rev. B.*, vol. 28, no. 2, pp. 784–805, 1983