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A Simple Theory of the Invar Effect in Iron-Nickel Alloys
Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics . Linköping University, The Institute of Technology.
Scottish Universities Physics Alliance (SUPA), Shool of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, U.K..
(English)Manuscript (Other academic)
Abstract [en]

Certain alloys of iron and nickel (so-called ‘Invar’ alloys) exhibit almost no thermal expansion over a wide range of temperature. It is clear that this is the result of an anomalous contraction upon heating which counteracts the normal thermal expansion arising from the anharmonicity of lattice variations. This anomalous contraction seems to be related to the alloys’ magnetic properties, since the effect vanishes at a temperature close to the Curie temperature. However, despite many years of intensive research, a widely accepted microscopic theory of the Invar effect in face-centered-cubic Fe-Ni alloys is still lacking. Here we present a simple theory of the Invar effect in these alloys based on Ising magnetism, ab initio total energy calculations, and the Debye-Grüneisen model. We show that this theory accurately reproduces several well known properties of these materials, including Guilaume’s famous plot of the thermal expansion coefficient as a function of the concentration of nickel. Within the same framework, we are able to account in the straightforward way for experimentally observed deviations from Vegard’s law. Our approach supports the idea that the lattice constant is governed by a few parameters, including the fraction of iron-iron nearest-neighbour pairs.

National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:liu:diva-17432OAI: oai:DiVA.org:liu-17432DiVA: diva2:209318
Available from: 2009-03-24 Created: 2009-03-24 Last updated: 2010-01-14Bibliographically approved
In thesis
1. Thermal Expansion and Local Environment Effects in Ferromagnetic Iron-Based Alloys: A Theoretical Study
Open this publication in new window or tab >>Thermal Expansion and Local Environment Effects in Ferromagnetic Iron-Based Alloys: A Theoretical Study
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The Nobel Prize for Physics 1920 was awarded to C.-E. Guillaume for his discovery of properties of nickel steels. He had previously observed that certain iron-nickel alloys exhibit the Invar effect i.e. an extremely low thermal expansion coefficient over a wide range of temperature. The decades since then have seen the observation of similar phenomena in other iron-based materials such as iron-platinum and iron-palladium. Moreover, there has been a great deal of theoretical work on the mechanism behind the Invar anomaly in the above-mentioned systems. However, despite many years of intensive research, a widely accepted microscopic theory of the effects is still lacking.

The present thesis aims at providing an insight into the physical nature of the thermal expansion of ferromagnetic random face-centered cubic iron-nickel, ironplatinum and iron-palladium bulk solids.

First, the thermal expansion coefficient is modeled as a function of temperature. The theory relies on the disordered local moment (DLM) formalism. However, contrary to all the previous models, the mapping between equilibrium states and partially disordered local moment (PDLM) states involves the probability that an iron-iron nearest-neighbour pair shows anti-parallel local magnetic moments, and the average lattice constant of the system at a finite temperature is calculated by minimization of an energy. The approach is applied to iron-nickel alloys. The model qualitatively reproduces several experimentally observed properties of disordered fcc iron-nickel solids. This includes Guillaume’s famous plot of the thermal expansion coefficient at room temperature as a function of concentration.

Second, for the purpose of studying the origin of the anomalous expansion, the anomalous and normal contributions to the thermal expansion coefficient are defined, then evaluated for iron-nickel alloys. The results support the idea that the peculiar behaviour of the expansivity, , originates solely from the anomalous contribution,αa.

Subsequently, the anomalous contribution is modeled for iron-nickel systems. In formulating the model, the following observation is taken into account; the average lattice spacing of an Fe100−xNix alloy at temperature T in a partially disordered local moment state is strongly negatively correlated with the probability that a nearest-neighbour pair has each of its two sites occupied by an iron atom and exhibits anti-ferromagnetically aligned magnetic moments (XFFAP). The quantity αa(x, T ) is estimated for several couples of values of the parameters x and T . Model results are found to agree qualitatively and quantitatively well with data obtained from the definition of αa. Thus, the model can successfully explain the basic process leading to the anomalous thermal expansion. It is consistent with the theory that the coefficient αa is controlled by the temperature derivative of XFFAP. Finally, the anomalous contribution to the thermal expansion coefficient of Fe72Pt28 and Fe66Pd34 solids is modeled as that of Fe65Ni35. A good agreement between the model results and experimental data for the expansivity as a function of temperature is noted. In conclusion, the Invar effects in disordered fcc iron-nickel, iron-platinum and iron-palladium alloys may have a common origin.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2009. 49 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1245
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-17433 (URN)978-91-7393-682-8 (ISBN)
Public defence
2009-04-03, Planck, Fysikhuset, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2009-03-24 Created: 2009-03-24 Last updated: 2009-03-24Bibliographically approved

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