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Numerical investigation of the validity of the Slater-Janak transition-state model in metallic systems
Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics. Linköping University, The Institute of Technology.
Condensed Matter Theory Group, Department of Physics, Uppsala University.
Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics. Linköping University, The Institute of Technology.
2005 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 72, no 13Article in journal (Refereed) Published
Abstract [en]

According to the so-called Janak’s theorem, the eigenstates of the Kohn-Sham Hamiltonian are given by the derivative of the total energy with respect to the occupation numbers of the corresponding one-electron states. The linear dependence of the Kohn-Sham eigenvalues on the occupation numbers is often assumed in order to use the Janak’s theorem in applications, for instance, in calculations of the core-level shifts in materials by means of the Slater-Janak transition state model. In this work first-principles density-functional theory calculations using noninteger occupation numbers for different core states in 24 different random alloy systems were carried out in order to verify the assumptions of linearity. It is found that, to a first approximation, the Kohn-Sham eigenvalues show a linear behavior as a function of the occupation numbers. However, it is also found that deviations from linearity have observable effects on the core-level shifts for some systems. A way to reduce the error with minimal increase of computational efforts is suggested.

Place, publisher, year, edition, pages
2005. Vol. 72, no 13
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:liu:diva-12559DOI: 10.1103/PhysRevB.72.134203OAI: oai:DiVA.org:liu-12559DiVA: diva2:1702
Note

Original publication: C. Göransson, W. Olovsson and I. A. Abrikosov, Numerical investigation of the validity of the Slater-Janak transition-state model in metallic systems, 2005, Physical Review B, (72), 134203. Copyright: The America Physical Society, http://prb.aps.org/

Available from: 2008-09-15 Created: 2008-09-15 Last updated: 2017-12-14
In thesis
1. Effects of disorder in metallic systems from First-Principles calculations
Open this publication in new window or tab >>Effects of disorder in metallic systems from First-Principles calculations
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis, quantum-mechanical calculations within density-functional theory on metallic systems are presented. The overarching goal has been to investigate effects of disorder. In particular, one of the properties investigated is the bindingenergy shifts for core electrons in binary alloys using different theoretical methods. These methods are compared with each other and with experimental results. One such method, the so-called Slater-Janak transition state method relies on the assumption that the single-particle eigenvalues within density-functional theory are linear functions of their respective occupation number. This assumption is investigated and it is found that while the eigenvalues to a first approximation show linear behavior, there are also nonlinearities which can influence the core-level binding energy shifts.

Another area of investigation has been iron based alloys at pressures corresponding to those in the Earth’s inner core. This has been done for the hexagonal close packed and face entered cubic structures. The effects of alloying iron with magnesium and nickel on the equation of state as well on the elastic properties have been investigated. The calculations have shown that the hexagonal close packed structure in FeNi is more isotropic than the face-centered cubic structure, and that adding Mg to Fe has a large impact on the elastic properties.

Finally, the effects of disorder due to thermal motion of the atoms have been investigated through ab-initio molecular dynamics simulations. Within the limits of this method and the setup, it is found that the face-centered cubic structure of molybdenum can be dynamically stabilized at high temperature, leading to a metastable structure, on the average. The dynamical stabilization of face-centered cubic molybdenum also rendered it possible to accurately calculate the lattice stability relative to the body-centered cubic phase. Inclusion of temperature effects for the lattice stability using ab-initio molecular dynamics simulations resolves the disagreement between ab-initio calculations and thermochemical methods.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2010. 126 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1299
Keyword
Iron, Nickel, Magnesium, Manganese, Molybdenum, Zirconium, Elastic Constants, High pressure, Earth's core, Density-functional theory, Ab-initio, First-Principles, Core-level shifts, Molecular Dynamics, Phonons, Dynamical Instability
National Category
Condensed Matter Physics Other Physics Topics
Identifiers
urn:nbn:se:liu:diva-53584 (URN)978-91-7393-445-9 (ISBN)
Public defence
2010-03-12, Planck, Fysikhuset, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2010-02-11 Created: 2010-01-25 Last updated: 2010-03-29Bibliographically approved
2. Spectroscopic and elastic properties in metallic systems from first-principles methods
Open this publication in new window or tab >>Spectroscopic and elastic properties in metallic systems from first-principles methods
2007 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis, ab initio calculations on metallic systems are presented. The overall aim is to probe properties that are often considered to be difficult to obtain within the framework of density-functional theory. The aim has also been to chose problems and systems that are of a wider interest and not only a testbed for calculations.

One of the properties investigated is the binding-energy shifts for core electrons in binary alloys of face-centered cubic structure using different theoretical methods. These methods are compared with each other and with experimental results. One of the methods, the so-called Slater-Jank transition state method has been investigated in more detail. This method relies on the assumption that the single-particle eigenvalues within density-functional theory are linear functions of their respective occupation number. This assumption is investigated , and it is found that while the eigenvalues to a first approximation show linear behaviour, the Slater-Jank transition state method can be improved by a first-order correction to the non-linearities.

Another area of investigation have been FeNi systems at high pressure. Calculations of elastic constants in this alloy at pressures corresponding to the Earth's core have been done for the hexagonal close packed and face centered cubic structures. These calculations show that, contrary to many other systems, the hexagonal close packed structure in FeNi is more isotropic than the face centered cubic structure.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet, 2007. 60 p.
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1314
Series
LIU-TEK-LIC, 23
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-37986 (URN)40827 (Local ID)978-91-85831-784 (ISBN)40827 (Archive number)40827 (OAI)
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2013-11-14

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Göransson Asker, ChristianAbrikosov, Igor A.

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