Abstract
We have developed an N-body interatomic potential, based on the second moment approximation of the tight-binding scheme, by fitting its four adjustable parameters to the cohesive energy, atomic volume, and elastic constants of hcp-Zr. We then showed that various properties of this potential compare favorably with those of zirconium in both the low temperatures hcp phase and the high temperature bcc phase. Such is the case in particular for the elastic constants, the phonon dispersion curves, the thermal expansion, and the melting temperature. We reproduced by molecular dynamics (MD) simulations on this potential the hcp/bcc phase transformation in both ways. It indeed occurs following the mechanism predicted by Burgers. We find a vibrational entropy of transformation equal to 0.13 k{sub B}. Our calculations suggest that in real zirconium the electronic contribution to the transformation entropy is important. We show that some interatomic potential lead to a higher value of the vibrational entropy in the hcp phase than in the bcc phase. We specified the dynamics of the vacancy migration in the bcc phase. The atomic jumps are almost exclusively nearest neighbour ones. The walk of the vacancy becomes strongly correlated at high temperatures. The vacancy jump frequency is very large
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Citation Formats
Willaime, F.
Dynamics of the HCP/BCC phase transition and of the diffusion in zirconium: a model based on a tight-binding potential; Dynamique de la transition {alpha}/{beta} et de la diffusion dans le zirconium: modelisation par un potentiel de liaisons fortes.
France: N. p.,
1991.
Web.
Willaime, F.
Dynamics of the HCP/BCC phase transition and of the diffusion in zirconium: a model based on a tight-binding potential; Dynamique de la transition {alpha}/{beta} et de la diffusion dans le zirconium: modelisation par un potentiel de liaisons fortes.
France.
Willaime, F.
1991.
"Dynamics of the HCP/BCC phase transition and of the diffusion in zirconium: a model based on a tight-binding potential; Dynamique de la transition {alpha}/{beta} et de la diffusion dans le zirconium: modelisation par un potentiel de liaisons fortes."
France.
@misc{etde_10125765,
title = {Dynamics of the HCP/BCC phase transition and of the diffusion in zirconium: a model based on a tight-binding potential; Dynamique de la transition {alpha}/{beta} et de la diffusion dans le zirconium: modelisation par un potentiel de liaisons fortes}
author = {Willaime, F}
abstractNote = {We have developed an N-body interatomic potential, based on the second moment approximation of the tight-binding scheme, by fitting its four adjustable parameters to the cohesive energy, atomic volume, and elastic constants of hcp-Zr. We then showed that various properties of this potential compare favorably with those of zirconium in both the low temperatures hcp phase and the high temperature bcc phase. Such is the case in particular for the elastic constants, the phonon dispersion curves, the thermal expansion, and the melting temperature. We reproduced by molecular dynamics (MD) simulations on this potential the hcp/bcc phase transformation in both ways. It indeed occurs following the mechanism predicted by Burgers. We find a vibrational entropy of transformation equal to 0.13 k{sub B}. Our calculations suggest that in real zirconium the electronic contribution to the transformation entropy is important. We show that some interatomic potential lead to a higher value of the vibrational entropy in the hcp phase than in the bcc phase. We specified the dynamics of the vacancy migration in the bcc phase. The atomic jumps are almost exclusively nearest neighbour ones. The walk of the vacancy becomes strongly correlated at high temperatures. The vacancy jump frequency is very large and has a perfectly arrhenian behaviour. There is no evicence of a dynamical lowering of the vacancy migration barrier: the static and dynamic values of the vacancy migration energy are almost equal, both being unusually small (0.3 eV). The self diffusion coefficent of our model for the vacancy mechanism reproduces an anomalous fast diffusion close to that measured experimentally in bcc-Zr. In our model at high temperatures the time interval between successive jumps is almost equal to the time of flight. The migration events will therefore influence the formation of the vacancies.}
place = {France}
year = {1991}
month = {Sep}
}
title = {Dynamics of the HCP/BCC phase transition and of the diffusion in zirconium: a model based on a tight-binding potential; Dynamique de la transition {alpha}/{beta} et de la diffusion dans le zirconium: modelisation par un potentiel de liaisons fortes}
author = {Willaime, F}
abstractNote = {We have developed an N-body interatomic potential, based on the second moment approximation of the tight-binding scheme, by fitting its four adjustable parameters to the cohesive energy, atomic volume, and elastic constants of hcp-Zr. We then showed that various properties of this potential compare favorably with those of zirconium in both the low temperatures hcp phase and the high temperature bcc phase. Such is the case in particular for the elastic constants, the phonon dispersion curves, the thermal expansion, and the melting temperature. We reproduced by molecular dynamics (MD) simulations on this potential the hcp/bcc phase transformation in both ways. It indeed occurs following the mechanism predicted by Burgers. We find a vibrational entropy of transformation equal to 0.13 k{sub B}. Our calculations suggest that in real zirconium the electronic contribution to the transformation entropy is important. We show that some interatomic potential lead to a higher value of the vibrational entropy in the hcp phase than in the bcc phase. We specified the dynamics of the vacancy migration in the bcc phase. The atomic jumps are almost exclusively nearest neighbour ones. The walk of the vacancy becomes strongly correlated at high temperatures. The vacancy jump frequency is very large and has a perfectly arrhenian behaviour. There is no evicence of a dynamical lowering of the vacancy migration barrier: the static and dynamic values of the vacancy migration energy are almost equal, both being unusually small (0.3 eV). The self diffusion coefficent of our model for the vacancy mechanism reproduces an anomalous fast diffusion close to that measured experimentally in bcc-Zr. In our model at high temperatures the time interval between successive jumps is almost equal to the time of flight. The migration events will therefore influence the formation of the vacancies.}
place = {France}
year = {1991}
month = {Sep}
}