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Temperature dependence of TiN elastic constants from ab initio molecular dynamics simulations
Linköping University, Department of Physics, Chemistry and Biology, Theoretical 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, Theoretical Physics. Linköping University, The Institute of Technology.
Linköping University, Department of Physics, Chemistry and Biology. Linköping University, The Institute of Technology.
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2013 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 87, no 9Article in journal (Refereed) Published
Abstract [en]

Elastic properties of cubic TiN are studied theoretically in a wide temperature interval. First-principles simulations are based on ab initio molecular dynamics (AIMD). Computational efficiency of the method is greatly enhanced by a careful preparation of the initial state of the simulation cell that minimizes or completely removes a need for equilibration and therefore allows for parallel AIMD calculations. Elastic constants C11, C12, and C44 are calculated. A strong dependence on the temperature is predicted, with C11 decreasing by more than 29% at 1800 K as compared to its value obtained at T=0 K. Furthermore, we analyze the effect of temperature on the elastic properties of polycrystalline TiN in terms of the bulk and shear moduli, the Young's modulus and Poisson ratio. We construct sound velocity anisotropy maps, investigate the temperature dependence of elastic anisotropy of TiN, and observe that the material becomes substantially more isotropic at high temperatures. Our results unambiguously demonstrate the importance of taking into account finite temperature effects in theoretical calculations of elastic properties of materials intended for high-temperature applications.

Place, publisher, year, edition, pages
American Physical Society , 2013. Vol. 87, no 9
National Category
Natural Sciences Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-78754DOI: 10.1103/PhysRevB.87.094114ISI: 000316791600001OAI: oai:DiVA.org:liu-78754DiVA: diva2:535567
Note

Funding Agencies|Swedish Research Council|621-2008-5535621-2011-4426|Swedish Foundation for Strategic Research (SSF) programs|10-0026|project Designed Multicomponent Coatings (MultiFilms)||Erasmus Mundus doctoral program DocMase||Ministry of Education and Science of the Russian Federation within the framework of Program Research and Pedagogical Personnel for Innovative Russia|14.B37.21.089010.09.2012|

Available from: 2012-06-20 Created: 2012-06-20 Last updated: 2017-12-07Bibliographically approved
In thesis
1. Thermal properties of materials from first principles
Open this publication in new window or tab >>Thermal properties of materials from first principles
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In the search of clean and efficient energy sources intermediate temperature solid oxide fuel cells are among the prime candidates. What sets the limit of their efficiency is the solid electrolyte. A promising material for the electrolyte is ceria. This thesis aims to improve the characteristics of these electrolytes and help provide thorough physical understanding of the processes involved. This is realised using first principles calculations.

The class of methods based on density functional theory generally ignores temperature effects. To accurately describe the intermediate temperature characteristics I have made adjustments to existing frameworks and developed a qualitatively new method. The new technique, the high temperature effective potential method, is a general theory. The validity is proven on a number of model systems.

Other subprojects include low-dimensional segregation effects, adjustments to defect concentration formalism and optimisations of ionic conductivity.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2012. 62 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1453
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-78755 (URN)978-91-7519-884-2 (ISBN)
Public defence
2012-06-15, Planck, Fysikhuset, Campus Valla, Linköpings universitet, Linköping, 14:00 (English)
Opponent
Supervisors
Available from: 2012-06-20 Created: 2012-06-20 Last updated: 2012-06-20Bibliographically approved
2. Development of molecular dynamics methodology for simulations of hard materials
Open this publication in new window or tab >>Development of molecular dynamics methodology for simulations of hard materials
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is focused on molecular dynamics simulations, both classical and ab initio. It is devoted to development of new methods and applications of molecular dynamics based techniques to a series of materials, all of which have the common property of being hard.

I first study grain boundaries in diamond and apply a novel method to better explore the configurational phase space. Using this method several new grain boundary structures are found. The lowest energy grain boundary structure has 20% lower energy then the one obtained with a conventional approach.

Another area is the development of efficient methods for first principles Born-Oppenheimer molecular dynamics. Here a fundamental shortcoming of the method that limits efficiency and introduces drift in the total energy of the system, is addressed and a solution to the problem is presented. Special attention is directed towards methods based on plane waves. The new molecular dynamics simulation method is shown to be more efficient and conserves the total energy orders of magnitude better then previous methods.

The calculation of properties for paramagnetic materials at elevated temperature is a complex task. Here a new method is presented that combines the disordered local moments model and ab initio molecular dynamics. The method is applied to calculate the equation of state for CrN were the connection between magnetic state and atomic structure is very strong. The bulk modulus is found to be very similar for the paramagnetic cubic and the antiferromagnetic orthorhombic phase.

TiN has many applications as a hard material. The effects of temperature on the elastic constants of TiN are studied using ab initio molecular dynamics. A significant dependence on temperature is seen for all elastic constants, which decrease linearly with temperature.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2012. 69 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1454
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-78823 (URN)978-91-7519-883-5 (ISBN)
Public defence
2012-06-08, Planck, Fysikhuset, Campus Valla, Linköpings universitet, Linköping, 10:00 (English)
Opponent
Supervisors
Available from: 2012-06-21 Created: 2012-06-21 Last updated: 2012-06-21Bibliographically approved
3. Influence of stresses and impurities on thermodynamic and elastic properties of metals and alloys from ab initio theory
Open this publication in new window or tab >>Influence of stresses and impurities on thermodynamic and elastic properties of metals and alloys from ab initio theory
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Stresses and impurities may influence elastic properties, phase stability and magnetic behavior of metals and their alloys. A physical understanding of this influence is of great importance to both fundamental science and technological applications. The diverse methods used in this work allowed us to shed light on the various aspects of the problem. In particular, in this work the thermodynamic, magnetic and elastic properties of Fe and Fe-Ni alloys at Earth’s inner core conditions were investigated by means of the ab initio theory. The main features of these calculations are on one side the extreme pressure-temperature conditions; on the other side the strong-correlation effects, which at these conditions may play an unexpected role. That is why I used different approaches, ranging from molecular dynamics to the dynamical mean field theory.

Interesting possibility for the effect of non-hydrostatic stresses on the stability of the body-centered cubic (bcc) phase of iron was observed. If detected, it could allow for an explanation of striking contradictions in high-pressure experiments. The influence of the alloying with Ni on the stability of Fe was studied. It was shown that the observed reverse of the stability trend under pressure is associated with the suppression of ferromagnetism at conditions of Earth’s inner core.

The strong correlation effects were observed in Fe3Ni by means of the dynamical mean field theory, revealing that the local environment of iron atoms is crucial for the strength of the on-site electronic correlations.

There is also an exciting experimental finding of our colleagues indicating that magnetism in pure nickel survives at very high pressures up to 260 GPa, i.e. up to the highest pressure at which magnetism in any material has ever been observed. Our calculations of the pressure dependence of the effective exchange interaction parameter and the hyperfine field support the picture of the ordered ferromagnetic state in Ni at multimegabar pressures.

Further, hydrogen is believed to be an important light impurity in Earth’s core. Thereupon the hydrogen containing FeOOH was also investigated. The prediction of the effect of symmetrization of the hydrogen bond under pressure was made.

The universality of applied methods allowed us to study the elastic constants of TiN, which is of high relevance to the industry of cutting tools. The importance of taking into account the finite temperature effects in the calculations of the elastic properties was demonstrated. Another case of practical interest is the Fe-Cr system, a prototype of many industrial steels. For instance, it is used in cooling pipes of pressure vessel reactors. We studied the effect of hydrostatic pressure on the phase stability of Fe-Cr alloys and revealed intriguing differences in the ordering tendencies depending on the Cr concentration and magnetic state of the alloy. We showed how variation of the ordering tendency between the Fe and Cr atoms emerges due to suppression of the local magnetic moment on the Cr atoms.

Noteworthy, hydrogen is not only the basic material playing fundamental role on and in the Earth, it is also a very promising source of fuel, which does not pollute the environment. In this sense the problem of hydrogen storage in Pd is of separate but related interest and it was theoretically investigated in the present work. The effect of vacancies on the energetically preferable position of hydrogen in the Pd cell was addressed. My theoretical results supported the experimental suggestion of multiple occupation of Pd vacancies by hydrogen.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2013. 85 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1531
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:liu:diva-97383 (URN)9789175195575 (ISBN)
Public defence
2013-09-19, Planck, Fysikhuset, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2013-09-11 Created: 2013-09-11 Last updated: 2017-12-14Bibliographically approved
4. 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

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