Is the average coordination number obtained by empirical relation is always correct or there are some other means to find it for an alloy?
e.g. for an alloy AxByCz the empirical relation used is Z=(xNA+yNB+ zNC)/(x+y+z)
Is it always valid?
The short answer is no. As can be seen from the attached reference (see the references herein, for instance that by Yoshio Waseda), rigorous calculation of the average coordination number requires calculation of the radial pair-distribution function of the atoms, which in turn requires molecular-dynamics simulation of the atomic coordinates; for this, one can use empirical potentials, but also first-principles methods -- see Chapter 12 of the book Atomic and Electronic Structure of Solids, by Efthimios Kaxiras (Cambridge University Press, 2003). See also: Phase Transitions and Self-Organization in Electronic and Molecular Networks, edited by J.C. Phillips, and M.F. Thorpe (Kluwer, New York, 2001).
https://en.wikipedia.org/wiki/Coordination_number
The short answer is no. As can be seen from the attached reference (see the references herein, for instance that by Yoshio Waseda), rigorous calculation of the average coordination number requires calculation of the radial pair-distribution function of the atoms, which in turn requires molecular-dynamics simulation of the atomic coordinates; for this, one can use empirical potentials, but also first-principles methods -- see Chapter 12 of the book Atomic and Electronic Structure of Solids, by Efthimios Kaxiras (Cambridge University Press, 2003). See also: Phase Transitions and Self-Organization in Electronic and Molecular Networks, edited by J.C. Phillips, and M.F. Thorpe (Kluwer, New York, 2001).
https://en.wikipedia.org/wiki/Coordination_number
In first approximation you can use it (as practically everybody does). But B. Farid is right. A closer look shows that in many materials the assumed statistic substitution is not really correct. Even in perfect homogenized materials locally self-ordering occur. The question is only, how much it dominates the entire process. And you need to make differences with respect to the actual interaction processes. For x-rays it is the electron shell, for backcattered electrons it is the core of the element. Nevertheless, I would use it if it works as first approximation. If remarkable deviations would appear I would start to think what might be the reason for the observed deviations Maybe this model.
Dear Prof. Behnam Farid
Dear colleague,
Please, Provide us with an electronic soft copy of these valuable references of both:
Atomic and Electronic Structure of Solids, by Efthimios Kaxiras (Cambridge University Press, 2003)
and
Phase Transitions and Self-Organization in Electronic and Molecular Networks, edited by J.C. Phillips, and M.F. Thorpe (Kluwer, New York, 2001)
Very thanks for your kind cooperation.
Yours,
Ahmed Saeed Hassanien
Dear Dr. Suresh Sharma
Have a nice day and happy time,
The average coordination number is determined somewhat differently for amorphous molecules than for crystals.
For the amorphous chalcogenide materials can be calculated from the mentioned equation: < Z >=(xNA+yNB+ zNC) / (x+y+z)
where, NA, NB, and NC are the numbers of valence electrons of the compositional elements of the chalcogenide system, and x,y and z are their respective concentrations in the amorphous chalcogenide system.
In case of crystalline materials, to determine the coordination number of an atom in a crystal, the crystal structure has first to be determined. This is achieved using X-ray, neutron or electron diffraction.
Good Luck
Yours,
Ahmed Saeed Hassanien
Dear Dr Hassanien, the books you are requesting are both copyright protected so that their electronic transfer is strictly prohibited. I would therefore recommend you to obtain copies of these from your local library. Some libraries also provide electronic copies of copyright-protected documents to their members for which they have permission from the publishers.
Yours sincerely,
Behnam Farid.
ps. I attach bellow the relevant links to the publishers. Google Books provides limited viewing of the book edited by Phillips and Thorpe, the link to which I also attach below.
http://www.cambridge.org/gb/academic/subjects/physics/condensed-matter-physics-nanoscience-and-mesoscopic-physics/atomic-and-electronic-structure-solids?format=PB&isbn=9780521523394
http://www.springer.com/gp/book/9780306465680
https://books.google.co.uk/books?id=DeZ7vUQIbYQC&source=gbs_book_other_versions
Dear Suresh Sharma Garu,
Generally, calculate the average coordination numer using that relation. we can calculate from Raman data.But exactly I donot know. I will give the mail id of that person. You can ask him.
Atul Khanna, Department of Physics, Guru Nanak Dev University , Punjab.
mail id: [email protected]
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