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Vibrational free energy and phase stability of paramagnetic and antiferromagnetic CrN from ab initio molecular dynamics
Linköping University, Department of Physics, Chemistry and Biology, Nanostructured Materials. Linköping University, The Institute of Technology.
Linköping University, Department of Physics, Chemistry and Biology, Thin Film Physics. Linköping University, The Institute of Technology.
Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics. Linköping University, The Institute of Technology.
Linköping University, Department of Physics, Chemistry and Biology, Computational Physics. Linköping University, The Institute of Technology.
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2014 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 89, no 17, 174108- p.Article in journal (Refereed) Published
Abstract [en]

We present a theoretical first-principles method to calculate the free energy of a magnetic system in its high-temperature paramagnetic phase, including vibrational, electronic, and magnetic contributions. The method for calculating free energies is based on ab initio molecular dynamics and combines a treatment of disordered magnetism using disordered local moments molecular dynamics with the temperature-dependent effective potential method to obtain the vibrational contribution to the free energy. We illustrate the applicability of the method by obtaining the anharmonic free energy for the paramagnetic cubic and the antiferromagnetic orthorhombic phases of chromium nitride. The influence of lattice dynamics on the transition between the two phases is demonstrated by constructing the temperature-pressure phase diagram.

Place, publisher, year, edition, pages
American Physical Society , 2014. Vol. 89, no 17, 174108- p.
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:liu:diva-110985DOI: 10.1103/PhysRevB.89.174108ISI: 000341308600001OAI: oai:DiVA.org:liu-110985DiVA: diva2:751584
Note

Funding Agencies|Erasmus Mundus Joint European Doctoral Programme DocMASE; SECO Tools AB; Swedish Research Council [621-2011-4426, 621-2011-4417]; Swedish Foundation for Strategic Research (SSF) programs SRL [10-0026]; project Designed Multicomponent Coatings (MultiFilms); Knut and Alice Wallenberg Foundation (KAW)

Available from: 2014-10-01 Created: 2014-10-01 Last updated: 2017-12-05Bibliographically approved
In thesis
1. Vibrations in solids: From first principles lattice dynamics to high temperature phase stability
Open this publication in new window or tab >>Vibrations in solids: From first principles lattice dynamics to high temperature phase stability
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis I introduce a new method for calculating the temperature dependent vibrational contribution to the free energy of a substitutionally disordered alloy that accounts for anharmonicity at high temperatures. This method exploits the underlying crystal symmetries in an alloy to make the calculations tractable. The validity of this approach is demonstrated by constructing the phase diagram via direct minimization of the Gibbs free energy of a notoriously awkward and technologically important system, Ti1-xAlxN. The vibrational entropy including anharmonic effects is shown to be large and comparable to the configurational entropy at high temperatures, and with its inclusion, the theoretical miscibility gap of Ti1-xAlxN is reduced from 6560 K to 2860 K, in line with atom probe experiments. A similar treatment of Zr1-xAlxN and Hf1-xAlxN alloys suggests that mass disorder has a minimal effect on phase stability compared with chemical ordering. My method is also capable of demonstrating that Hf1-xAlxN, which is dynamically unstable at room temperature, is stabilised at high temperatures. Moreover I develop a new method of computing temperature dependent elastic constants for alloys from their phonon spectra, and show that for Ti1-xAlxN, the elastic anisotropy is found to increase with temperature, helping to explain the spinodal decomposition.

The effects of lattice dynamics on phase stability, mechanical, magnetic and transport properties on other materials are also examined. Four specific systems are discussed in detail. Firstly, in the case of CrN, lattice vibrations are shown to decrease the antiferromagnetic to paramagnetic phase transition temperature from 500 K to 380 K, in line with experimental evidence. Secondly, a temperature/pressure induced phase transition in AlN becomes much more facile than in the quasiharmonic approximation, and the thermal conductivity of the rocksalt phase is shown to be much lower than that of the wurtzite phase, as a result of the increased anharmonicity in the rocksalt structure. Thirdly, the temperature dependence of elastic constants of TiN becomes more isotropic as the temperature increases. Finally, iron carbides are evaluated as potentially important phases at the Earth’s core; specifically, calculating the Gibbs free energy of a recently discovered orthorhombic phase of Fe7C3 demonstrates that it is not stable relative to the known hexagonal phase at extreme pressure and temperatures.

Abstract [sv]

I denna avhandling introducerar jag en ny metod för att beräkna de temperaturberoende vibrationernas bidrag till den fria energin för oordnade legeringar, vilket kan förklara anharmoniska effekter vid höga temperaturer. För att göra beräkningarna mer lätthanterliga utnyttjar den här metoden den inneboende strukturella symmetrin för kristaller i en legering. Hur lämpligt det här tillvägagångssättet är visas genom att konstruera ett fasdiagram genom en direkt minimering av Gibbs fria energi, vilket görs för ett notoriskt besvärligt (men teknologiskt viktigt) system, nämligen Ti1-xAlxN. Jag visar att vibrationsentropin, inkluderat de anharmoniska effekterna, är stor och jämförbar med konfigurationsentropin vid höga temperaturer. Vidare visar jag att man, genom att inkludera dem, kan reducera Ti1-xAlxNs teoretiska löslighetslucka från 6560 K till 2860 K, i linje med de experiment som gjorts med atomsondstomografi. Genom att behandla legeringarna Zr1-xAlxN och Hf1-xAlxN på samma sätt framstår det som troligt att en oordning i massan har en minimal effekt på fastemperaturen jämfört med en kemisk sammansättning. Min metod kan även visa att Hf1-xAlxN, som är instabil vid rumstemperatur, stabiliseras vid höga temperaturer. Dessutom har jag utvecklat en ny metod för att beräkna de temperaturberoende elastiska konstanterna för legeringar utifrån deras fononspektrum, och visar detta för Ti1-xAlxN. Den elastiska anisotropin visas öka avhängigt av temperaturen, vilket förklarar det spinodala sönderfallet.

Vidare undersöks gitterdynamikens effekt på andra materials fasstabilitet, samt deras mekaniska, magnetiska och transportegenskaper. Fyra specifika system diskuteras i detalj. Den här studien visar, för det första, att vibrationerna i gittret för CrN sänker övergångstemperaturen mellan den antiferromagnetiska och paramagnetiska fasen från 500 K till 380 K, vilket överensstämmer med existerande experimentella bevis. För det andra visar den att en fasövergång inducerad av temperatur eller tryck i AlN blir betydligt smidigare än i den kvasiharmoniska approximeringen, och att värmeledningsförmågan i bergsaltsfasen blir betydligt lägre som ett resultat av den ökade anharmoniciteten i bergsaltsstrukturen. För den tredje blir temperaturberoendet av TiNs elastiska konstanter mer isotropisk när temperaturen ökar. Slutligen utvärderas järnkarbider som potentiellt viktiga faser i jordkärnan; mer specifikt visas den, genom att beräkna Gibbs fria energi för en nyligen upptäckt ortorombisk fas av Fe7C3, inte vara stabil relativ till den redan kända hexagonala fasen vid tryck och temperatur på extrema nivåer.

Abstract [de]

In der vorliegenden Arbeit stelle ich eine neu entwickelte Methode zur Berechnung der temperaturabhängigen Vibrationsbeiträge zur freien Energie von ungeordneten Legierungen unter Berücksichtigung nicht- harmonischen Verhaltens bei hohen Temperaturen vor. Diese Methode nutzt bei der Berechnung die in der jeweiligen Legierung vorhandenen Kristallsymmetrien aus. Die Gültigkeit dieses Ansatzes wird durch die Konstruktion des Phasendiagrams des technologisch wichtigen komplexen Systems Ti1-xAlxN unter direkter Minimierung der freien Gibbs Energie gezeigt. Es zeigt sich, dass die Vibrationsentropie durch Berücksichtigung nicht-harmonischer Effekte in ihrer Größe vergleichbar der Konfigurationsentropie bei hohen Temperaturen ist, und dass durch ihre Miteinbeziehung die theoretische Mischungslücke von 6560 K auf 2860 K reduziert wird, in Einklang mit experimentellen Atomsonden Messungen. Vergleichbares Anwenden der Methode auf die Legierungen Zr1-xAlxN und Hf1-xAlxN zeigt, dass eine Unordnung der atomaren Masse im Vergleich zu chemischer Unordnung nur einen minimalen Effekt auf die Stabilität der Phase hat.

Die von mir entwickelte Methode ist des Weiteren im Stande zu zeigen, dass Hf1-xAlxN (dynamisch instabil bei Raumtemperatur) sich bei hohen Temperaturen stabilisiert. Weiterhin wurde eine neue Methode zur Berechnung von temperaturabhängigen elastischen Konstanten aus Phonon Spektren von Legierungen entwickelt und gezeigt, dass für Ti1-xAlxN die elastische Anisotropie mit der Temperatur ansteigt und so die spinodale Entmischung erklärt wird. Die Effekte von Gitterdynamik auf Phasenstabilität, mechanische-, magnetische- und Transport Eigenschaften werden zusätzlich für vier spezifische Systeme im Detail untersucht, und es wird gezeigt, dass

  • in Einklang mit experimentellen Ergebnissen die Gitterschwingungen in CrN die Temperatur des Phasenüberganges von antiferro- magnetischer- zu paramagnetischer Phase von 500 K auf 380 K reduziert;
  • mit der hier vorgestellten Methode ein Druck/Temperatur induzierter Phasenübergang in AlN müheloser beschrieben werden kann als in der quasiperiodischen Näherung. Weiterhin wird gezeigt dass die thermische Leitfähigkeit in AlN als Resultat aus erhöhter nicht-Harmonizität in der NaCl-artigen Gitterstruktur herabgesetzt wird;
  • die Temperaturabhängigkeit der elastischen Konstanten von TiN mit steigender Temperatur mehr und mehr isotrop wird;
  • die mit der vorgestellten Methode berechnete freie Gibbs Energie der kürzlich entdeckten orthorhombischen Phase Fe7C3 nahelegt, dass sie gegenüber der bekannten hexagonalen Phase nicht stabil ist.
Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2015. 94 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1718
National Category
Physical Sciences
Identifiers
urn:nbn:se:liu:diva-122949 (URN)10.3384/diss.diva-122949 (DOI)978-91-7685-911-7 (ISBN)
Public defence
2015-12-04, Schrödinger, Fysikhuset, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2015-11-30 Created: 2015-11-30 Last updated: 2015-12-01Bibliographically approved
2. Theoretical Description of the Electron-Lattice Interaction in Molecular and Magnetic Crystals
Open this publication in new window or tab >>Theoretical Description of the Electron-Lattice Interaction in Molecular and Magnetic Crystals
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Electron-lattice interactions are often considered not to play a major role in material's properties as they are assumed to be small, the second-order effects. However, this study shows the importance of taking these effects into account in the simulations. My results demonstrate the impact of the electron-lattice interaction on the physics of the material and our understanding from it. One way to study these effects is to add them as perturbations to the unperturbed Hamiltonians in numerical simulations. The main objective of this thesis is to study electron-lattice interactions in molecular and magnetic crystals. It is devoted to developing numerical techniques considering model Hamiltonians and first-principles calculations to include the effect of lattice vibrations in the simulations of the above mentioned classes of materials.

In particular, I study the effect of adding the non-local electron-phonon coupling on top of the Holstein Hamiltonian to study the polaron stability and polaron dynamics in molecular crystals. The numerical calculations are based on the semi-empirical Holstein-Peierls model in which both intra (Holstein) and inter (Peierls) molecular electron-phonon interactions are taken into account. I study the effect of different parameters including intra and intermolecular electron-phonon coupling strengths and their vibrational frequencies, the transfer integral and the electric field on polaron stability. I found that in an ordered two dimensional molecular lattice the polaron is stable for only a limited range of parameter sets with the polaron formation energies lying in the range between 50 to 100 meV. Using the stable polaron solutions, I applied an electric field to the system and I observed that the polaron is dynamically stable and mobile for only a limited set of parameters. Adding disorder to the system will result in even more restricted parameter set space for which the polaron is stable and moves adiabatically with a constant velocity. In order to study the effect of temperature on polaron dynamics, I include a random force in Newtonian equations of motion in a one dimensional molecular lattice. I found that there is a critical temperature above which the polaron destabilizes and becomes delocalized.

Moreover, I study the role of lattice vibrations coupled to magnetic degrees of freedom in finite temperature paramagnetic state of magnetic materials. Calculating the properties of paramagnetic materials at elevated temperatures is a cumbersome task. In this thesis, I present a new method which allows us to couple lattice vibrations and magnetic disorder above the magnetic transition temperature and treat them on the same footing. The method is based on the combination of disordered local moments model and ab initio molecular dynamics (DLM-MD). I employ the method to study different physical properties of some model systems such as CrN and NiO in which the interaction between the magnetic and lattice degrees of freedom is very strong making them very good candidates for such a study.

I calculate the formation energies and study the effect of nitrogen defects on the electronic structure of paramagnetic CrN at high temperatures. Using this method I also study the temperature dependent elastic properties of paramagnetic CrN. The results highlight the importance of taking into account the magnetic excitations and lattice vibrations in the studies of magnetic materials at finite temperatures. A combination of DLM-MD with another numerical technique namely temperature dependent effective potential (TDEP) method is used to study the vibrational free energy and phase stability of CrN. We found that the combination of magnetic and vibrational contributions to the free energy shifts down the phase boundary between the cubic paramagnetic and orthorhombic antiferromagnetic phases of CrN towards the experimental value.

I used the stress-strain relation to study the temperature-dependent elastic properties of paramagnetic materials within DLM-MD with CrN as my model system. The results from a combinimation of DLM-MD with another newly developed method, symmetry imposed force constants (SIFC) in conjunction with TDEP is also presented as comparison to DLM-MD results.I also apply DLM-MD method to study the electronic structure of NiO in its paramagnetic state at finite temperatures. I found that lattice vibrations have a prominent impact on the electronic structure of paramagnetic NiO at high temperatures and should be included for the proper description of the density of states.

In summary, I believe that the proposed techniques give reliable results and allow us to include the effects from electron-lattice interaction in simulations of materials.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2016. 85 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1766
Keyword
Molecular crystals, Charge transport, Polaron, Magnetic materials, Paramagnetic state, Molecular dynamics
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:liu:diva-130517 (URN)10.3384/diss.diva-130517 (DOI)9789176857625 (ISBN)
Public defence
2016-09-16, Plank, Fysikhuset, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2016-08-23 Created: 2016-08-11 Last updated: 2016-08-23Bibliographically approved

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Shulumba, NinaAlling, BjörnHellman, OlleMozafari, ElhamSteneteg, PeterOdén, MagnusAbrikosov, Igor

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