Influence of Short-Range Three-Ion Interactions on Polymorphism and Elastic Constants of Simple Solids. I. Alkali Halide Crystals

Lombardi, E.; Jansen, L.; Ritter, R.

doi:10.1103/physrev.185.1150

Cited by 33 publications

(3 citation statements)

References 20 publications

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“…We shall have to include three-body interaction from both the first-order and the second-order exchange energy for this purpose. Calculations of Lambardi et al [12] on the relative stability of alkali halides using both these effects seem to confirm this conclusion.…”

Section: ') ( 2 2 )supporting

confidence: 76%

Short‐Range Three‐Body Potential in the First‐Order Exchange Energy and the Relative Stability of Alkali Halide Crystals

Paul¹,

Sarkar²,

Sengupta³

1972

Physica Status Solidi (b)

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Using the Heitler-London approach a simple expression for the first-order exchange energy between a system of interacting atoms or ions is obtained in the S2 approximation. It is shown that this expression leads t o two-body, three-body, and four-body interactions only. A specific expression for the three-body interaction is evaluated using several different approximations. Assumptions which lead to the expression previously obtained by Lundqvist are discussed. It is found that these expressions vanish for neutral particles.Some modification in the assumption is made and an expression for three-body interaction for neutral particles is obtained. Numerical calculations are made for argon, xenon, and helium and the results compared with those obtained by others. The three-body interaction is also applied to study the relative stability of different alkali halide structures. It is found that this three-body potential has a strong preference for CsCl structure.Mit der Heitler-London-Methode wird ein einfacher Ausdruck fur die Austauschenergie erster Ordnung zwischen einem System wechselwirkender Atome oder Ionen in der S2-Naherung erhalten. Es wird gezeigt, daB dieser Ausdruck nur zu Zwei-Teilchen-, DreiTeilchen-und Vier-Teilchen-Wechselwirkungen fuhrt. Fur Drei-Teilchen-Wechselwirkung wird mit verschiedenen Naherungen ein spezifischer Ausdruck abgeleitet. Annahmen, die zu dem kurzlich von Lundquist erhaltenen Ausdruck fiihren, werden diskutiert. Es wird gefunden, daB diese Ausdriicke fur neutrale Teilchen verschwinden. Numerische Berechnungen werden fur Argon, Xenon und Helium durchgefiihrt und die Ergebnisse mit denen anderer Autoren verglichen. Die Drei-Teilchen-Wechselwirkung wird auch zur Untersuchung der relativen Stabilitat verschiedener Alkalihalogenidstrukturen benutzt. Es wird gefunden, daB dieses Drei-Teilchen-Potential eine starke Bevorzugung der CsC1-Struktur ergibt.

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Section: ') ( 2 2 )supporting

confidence: 76%

Short‐Range Three‐Body Potential in the First‐Order Exchange Energy and the Relative Stability of Alkali Halide Crystals

Paul¹,

Sarkar²,

Sengupta³

1972

Physica Status Solidi (b)

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“…c That is, the barrier along the Bain path [32] between the BCC and FCC phase. [42,43]. As can be seen from table 3, our model finds all of these relations to be true, although our value of T m is slightly lower than 0.1E c /k, about 0.05E c /k for titanium and 0.08E c /k for iron.…”

Section: Physical Propertiessupporting

confidence: 57%

Simple pair-wise interactions for hybrid Monte Carlo–molecular dynamics simulations of titania/yttria-doped iron

Hammond

Voigt

Marus

et al. 2013

J. Phys.: Condens. Matter

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We present pair-wise, charge-neutral model potentials for an iron-titanium-yttrium-oxygen system. These simple models are designed to provide a tractable method of simulating nanostructured ferritic alloys (NFAs) using off-lattice Monte Carlo and molecular dynamics techniques without deviating significantly from the formalism employed in existing Monte Carlo simulations. The model is fitted to diamagnetic density functional theory (DFT) calculations of the various species over a range of densities and concentrations. The resulting model potentials provide reasonable and in some cases even excellent mechanical and thermodynamic properties for the pure metals. The model replicates the qualitative trends in formation energy predicted by DFT, though the energies of formation do not agree as well for dilute systems as they do for more concentrated systems. We find that on-lattice models will consistently favor tetrahedral oxygen interstitial sites over octahedral interstitial sites, while relaxed systems typically favor octahedral sites. This emphasizes the need for the off-lattice simulations for which this potential was designed.

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“…tion is about 0.6%. As Lombardi et al [8] have not calculated the individual elastic constants, no comparison is possible in those cases.…”

Section: A Model Potential For the Alkali Halidesmentioning

confidence: 98%

A Model Potential for Alkali Halide Crystals Including a Short Range Three‐Body Interaction

Sarkar¹,

Sengupta

1973

Physica Status Solidi (b)

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The model potential including a short range three-body interaction which was used by Sarkar and Sengupta [I, 21 to calculate various static properties of some alkali halide crystals has been extended to include overlap interaction between next nearest neighbours. This has been used to calculate the cohesive energy, harmonic elastic constants, phase transition pressure, and transitionvolume for transition from sodium chloride to the cesium chloride structure in the case of potassium and rubidium halides. The results have been compared with experimental values and with the theoretical calculations done on other models. It is found that the inclusion of overlap interaction between next nearest neighbours considerably improves the overall agreement between theoretical and experimental results.Das Modellpotential mit kurzreichweitiger Dreiteilchen-Wechselwirkung, das von Sarkar und Sengupta [l, 21 benutzt wurde, um verschiedene statische Eigenschaften einiger Alkalihalogenidkristalle zu berechnen, wird erweitert und schlieSt Uberlappungswechselwirkung zwischen uberniichsten Nachbarn ein. Es wird benutzt, um die Kohasionsenergie, die harmonischen elastischen Konstanten, Phasenubergangsdruck und tfbergangsvolumen fur den Ubergang von der Natriumchloridstruktur zur Ciisiumchloridstruktur fiir den Fall von Kalium-und Rubidiumhalogenid zu berechnen. Die Ergebnisse werden mit experimentellen Werten und mit theoretischen Berechnungen a n anderen Modellen verglichen. Es wird gefunden, daS die Einbeziehung der tfberlappungswechselwirkung zwischen iibernachsten Nachbarn betrschtlich die Gesamtubereinstimmung zwischen theoretischen und experimentellen Ergebnissen verbessert.

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Influence of Short-Range Three-Ion Interactions on Polymorphism and Elastic Constants of Simple Solids. I. Alkali Halide Crystals

Cited by 33 publications

References 20 publications

Short‐Range Three‐Body Potential in the First‐Order Exchange Energy and the Relative Stability of Alkali Halide Crystals

Short‐Range Three‐Body Potential in the First‐Order Exchange Energy and the Relative Stability of Alkali Halide Crystals

Simple pair-wise interactions for hybrid Monte Carlo–molecular dynamics simulations of titania/yttria-doped iron

A Model Potential for Alkali Halide Crystals Including a Short Range Three‐Body Interaction

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