Many-Body Contribution to Self-Diffusion in Rare-Gas Solids

Burton, Justin

doi:10.1103/physrev.182.885

Cited by 31 publications

(3 citation statements)

References 38 publications

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“…Thus the cancellation is no longer complete except for Ne and this fact seems to be overlooked by Card and Jacobs [16]. These authors concluded that the relaxation energy is small and this fact is also supported by our calculation as may be seen from and Burton [14] also support these conclusions. For this reason the value of h + U calculated by us should differ by U ; + 2 U4+a from that calculated by Card and Jacobs [16].…”

Section: Resultssupporting

confidence: 90%

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Long‐range many‐body interaction and monovacancy heat of formation of rare‐gas crystals

Maity

Roy

Sengupta

1979

Physica Status Solidi (b)

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The heat of formation of rare gas crystals is calculated using a relatively simple approach. As the difference in the values of heat of formation and cohesive energy depend entirely upon the relaxation and many-body effects, the contribution of these terms to the heat of formation is examined critically. It is found that the relaxation effect is quite negligible. Though three-body interaction other than triple-dipole approximately cancels with the higher many-body effects in the case of cohesive energy, the cancellation is not at all complete in the case of heat of formation, and the many-body effects other than the triple-dipole is found t o contribute significantly to the difference between the energy of the perfect and imperfect crystal. The differences in the valuds of heat of formation and cohesive energy are calculated for the rare gas solids using a very simple approach and compared with experimental results and also with those obtained from more sophisticated calculation. The present calculation is found to reasonably reproduce the experimental results.It is emphasised that a n accurate determination of this difference is necessary as this serves as a direct test of the role of many-body forces in rare gas solids.Es wird die Bildungswarme von Edelgaskristallen mit einem relativ einfachen Verfahren berechnet. Da der Unterschied der Werte der Bildungswarme und der Kohiisionsenergie vollstandig von der Relaxation und den Vielkorpereffekten abhangt, werden die Beitrage dieser Terme zur Bildungswarme kritisch untersucht. E s wird gefunden, daB der RelaxationseinfluB vollstandig vernachlassigbar ist, obgloich die Dreikorperwechselwirkung, anders als die Tripel-Dipol-Wechselwirkung, sich naherungsweise mit den hoheren Vielkorpereffekten im Falle der Kohasionsenergie aufhebt, ist die Aufhebung im Falle der Bildungswarme nicht vollstandig, und es wird gefunden, daB die Vielkorper-Effekte im Gegensatz zum Tripel-Dipol betrachtlich zum Unterschied zwischen der Energie des perfekten und imperfekten Kristalls beitragen. Der Unterschied in den Werten der Bildungswarme und Kohasionsenergie werden fur die Edelgasfestkorper mit einem sehr einfachen Verfahren berechnet und mit den experimentellen Ergebnissen und mit Ergebnissen von aufwendigeren Rechnungen verglichen. Die dargestellte Berechnung reproduziert vernunftig die experimentellen Ergebnisse. Es wird hervorgehoben, daB eine sorgfiiltige Bestimmung dieser Differenz notwendig ist, da sie als direkte Priifung fur die Rolle der Vielkorperkrafte in festen Edelgasen dient.

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Section: Resultssupporting

confidence: 90%

“…Several authors [6,14,151 have considered the effect of many-body forces on the heat of formation of rare-gas solids. Recently Card and Jacobs [16] have performed a Monte Carlo calculation of the energy to form a vacancy in crystalline Au, Kr, and Xe using the latest accurate potentials.…”

Section: Introductionmentioning

confidence: 99%

Long‐range many‐body interaction and monovacancy heat of formation of rare‐gas crystals

Maity

Roy

Sengupta

1979

Physica Status Solidi (b)

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“…Assuming the experimental data to be correct, it is not yet possible to say whether the disagreement with theory is due to a large amount of "local melting" around the vacancy in the rare gas solid (as indicated earlier, this might be underestimated by the 'YIonte Carlo simulation 9 owing to its single-occupancy restriction), or to manybody forces. 13 The volumes of vacancy formation and motion are listed in columns four and five; both have been measured in gold by high-pressure experiments. 14 ,15 The Monte Carlo Lennard-Jones calculation,9 and also most static relaxation calculations using the Lennard-Jones or other potentials appropriate to rare gases, yield rather small displacements of the equilibrium positions of the neighbors of a vacancy, implying a volume of formation VI it' near unity for rare gas solids (however, see 16 for a suggestion that the volume of formation in Kr approaches 22' ncar the triple point).…”

Section: Comparison To Experimentsmentioning

confidence: 99%

Studies in Molecular Dynamics. IX. Vacancies in Hard Sphere Crystals

Bennett

Alder

1971

The Journal of Chemical Physics

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The concentration of monovacancies as well as their entropy and volume of formation have been determined in a face-centered hard sphere crystal at a series of densities. The results near the hard sphere melting density compare favorably with experiments on argon and metals. Although divacancies are shown to have an increasingly larger mobility relative to mono vacancies with increasing pressure, they do not contribute significantly to diffusion because their equilibrium concentration is too low. It is shown also that two monovacancies interact significantly when separated by many lattice spacings. The free energy of association of higher vacancy clusters is found to be approximately proportional to the number of vacancyvacancy contacts, so that compact clusters are stabilized relative to extended ones. This effect was found to be greatly enhanced for different shaped vacancy clusters in square-well particle systems, by an additional amount corresponding to the potential difference in particle-vacancy contacts.• The small number(s) behind an entry indicates the uncertainty in the last given number (s). b The first number stands for the number of particles in the system and the second number for the diffusing species (1 =monovacancy. 2 = divacancy, etc.).

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Thermodynamic Properties of Hypothetical Perfect and Real Krypton Crystals

Korpiun

Coufal

1971

Phys. Stat. Sol. (a)

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From measurements of the thermal expansivity and the isothermal compressibility at P = 0 of solid Kr using X‐ray diffraction and a dilatometer between 4 and 115 K some vacancy properties could be determined. We found h = (86 ± 9) meV for the formation enthalpy of monovacancies, for the entropy, and for the vacancy free volume of formation atomic volumes. Using these data, the thermal expansion coefficient, the compressibility, the isobaric and isochoric specific heat, the Grüneisen parameter, and the slope of the isochore for hypothetical perfect krypton have been deduced from the values measured in the bulk.

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Many-Body Contribution to Self-Diffusion in Rare-Gas Solids

Cited by 31 publications

References 38 publications

Long‐range many‐body interaction and monovacancy heat of formation of rare‐gas crystals

Long‐range many‐body interaction and monovacancy heat of formation of rare‐gas crystals

Studies in Molecular Dynamics. IX. Vacancies in Hard Sphere Crystals

Thermodynamic Properties of Hypothetical Perfect and Real Krypton Crystals

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