scholarly journals An Effective Strategy to Maintain the CALPHAD Atomic Mobility Database of Multicomponent Systems and Its Application to Hcp Mg–Al–Zn–Sn Alloys

Materials ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 283
Author(s):  
Ting Cheng ◽  
Jing Zhong ◽  
Lijun Zhang

In this paper, a general and effective strategy was first developed to maintain the CALPHAD atomic mobility database of multicomponent systems, based on the pragmatic numerical method and freely accessible HitDIC software, and then applied to update the atomic mobility descriptions of the hcp Mg–Al–Zn, Mg–Al–Sn, and Mg–Al–Zn–Sn systems. A set of the self-consistent atomic mobility database of the hcp Mg–Al–Zn–Sn system was established following the new strategy presented. A comprehensive comparison between the model-predicted composition–distance profiles/inter-diffusivities in the hcp Mg–Al–Zn, Mg–Al–Sn, and Mg–Al–Zn–Sn systems from the presently updated atomic mobilities and those from the previous ones that used the traditional method indicated that significant improvement can be achieved utilizing the new strategy, especially in the cases with sufficient experimental composition–distance profiles and/or in higher-order systems. Furthermore, it is anticipated that the proposed strategy can serve as a standard for maintaining the CALPHAD atomic mobility database in different multicomponent systems.

1—The method of the self-consistent field for determining the wave functions and energy levels of an atom with many electrons was developed by Hartree, and later derived from a variation principle and modified to take account of exchange and of Pauli’s exclusion principle by Slater* and Fock. No attempt was made to consider relativity effects, and the use of “ spin ” wave functions was purely formal. Since, in the solution of Dirac’s equation for a hydrogen-like atom of nuclear charge Z, the difference of the radial wave functions from the solutions of Schrodinger’s equation depends on the ratio Z/137, it appears that for heavy atoms the relativity correction will be of importance; in fact, it may in some cases be of more importance as a modification of Hartree’s original self-nsistent field equation than “ exchange ” effects. The relativistic self-consistent field equation neglecting “ exchange ” terms can be formed from Dirac’s equation by a method completely analogous to Hartree’s original derivation of the non-relativistic self-consistent field equation from Schrodinger’s equation. Here we are concerned with including both relativity and “ exchange ” effects and we show how Slater’s varia-tional method may be extended for this purpose. A difficulty arises in considering the relativistic theory of any problem concerning more than one electron since the correct wave equation for such a system is not known. Formulae have been given for the inter-action energy of two electrons, taking account of magnetic interactions and retardation, by Gaunt, Breit, and others. Since, however, none of these is to be regarded as exact, in the present paper the crude electrostatic expression for the potential energy will be used. The neglect of the magnetic interactions is not likely to lead to any great error for an atom consisting mainly of closed groups, since the magnetic field of a closed group vanishes. Also, since the self-consistent field type of approximation is concerned with the interaction of average distributions of electrons in one-electron wave functions, it seems probable that retardation does not play an important part. These effects are in any case likely to be of less importance than the improvement in the grouping of the wave functions which arises from using a wave equation which involves the spins implicitly.


2011 ◽  
Vol 66-68 ◽  
pp. 933-936
Author(s):  
Xian Jie Meng

A one degree of freedom nonlinear dynamics model of self-excited vibration induced by dry-friction was built firstly, the numerical method was taken to study the impacts of structure parameters on self-excited vibration. The calculation result shows that the variation of stiffness can change the vibration amplitude and frequency of the self-excited vibration, but can not eliminate it, Along with the increase of system damping the self-excite vibration has the weakened trend and there a ritical damping, when damping is greater than it the self-excite vibration will be disappeared.


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