On Calculation of Lattice Energy in Spatially Confined Domains

On Calculation of Lattice Energy in Spatially Confined Domains Evaluation of internal energy and the inter-atomic or ionic interactions in a crystal lattice usually requires precise calculation of lattice sums. This in the case of small nano-particles (as space-limited domains) presents several challenges, as conventional methods are usually valid only for infinite lattices, tailored for a specific potential. In this work, a new method has been developed for calculation of atomic interactions based on the radial density function with the geometric probability approach, extended to arbitrary fixed lattices and potentials in a nano-particle. The derived radial density function (RDF) combines terms for a uniform particles distribution, for non-uniform spherical symmetry and the last one for an additional, angle-dependent term. The second term originates from Walfisz-like formula for lattice sums. The RDF with these three terms is explicitly integrated for spherical lattice domains resulting in the internal energy of the system with a prescribed interaction potential. The application of the method was demonstrated for Wigner model of electrons lattice interacting with compensating positive jelly in finite lattice sphere, which interacting energy between lattice and jelly was evaluated. The excess of this energy caused by space-limitation of the lattice was explicitly expressed in the terms of absolutely convergent lattice sums. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Materials Science and Applications World Academic Publishing Co.

On Calculation of Lattice Energy in Spatially Confined Domains

Loading next page...
 
/lp/world-academic-publishing-co/on-calculation-of-lattice-energy-in-spatially-confined-domains-MFvNDMVPt3
Publisher
THE WORLD ACADEMIC PUBLISHING CO. LIMITED
Copyright
Copyright © 2014, THE WORLD ACADEMIC PUBLISHING CO. LIMITED
ISSN
2306-9325
eISSN
2306-9317

Abstract

Evaluation of internal energy and the inter-atomic or ionic interactions in a crystal lattice usually requires precise calculation of lattice sums. This in the case of small nano-particles (as space-limited domains) presents several challenges, as conventional methods are usually valid only for infinite lattices, tailored for a specific potential. In this work, a new method has been developed for calculation of atomic interactions based on the radial density function with the geometric probability approach, extended to arbitrary fixed lattices and potentials in a nano-particle. The derived radial density function (RDF) combines terms for a uniform particles distribution, for non-uniform spherical symmetry and the last one for an additional, angle-dependent term. The second term originates from Walfisz-like formula for lattice sums. The RDF with these three terms is explicitly integrated for spherical lattice domains resulting in the internal energy of the system with a prescribed interaction potential. The application of the method was demonstrated for Wigner model of electrons lattice interacting with compensating positive jelly in finite lattice sphere, which interacting energy between lattice and jelly was evaluated. The excess of this energy caused by space-limitation of the lattice was explicitly expressed in the terms of absolutely convergent lattice sums.

Journal

Advances in Materials Science and ApplicationsWorld Academic Publishing Co.

Published: Dec 25, 2013

There are no references for this article.

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off