Termodynamiska och elektroniska egenskaper för niob vid finita temperaturer

Niobium (Nb) is a fascinating element, that when it is in a solid state has remarkable properties. This is believed to be a result of its electronic configuration that has partially filled 4d and 5s sub-shells. Nb has a melting temperature of 2750 K, a high strength at high temperature, and a good wear resistance. Because of these properties, Nb is used as material for components of rockets and jet engines, and for strengthening steel. In the phonon dispersion relations, Kohn anomalies are experimentally observed to weaken with increased temperature, which is related to the superconducting properties of Nb. I include anharmonicity when I calculate the thermodynamic properties of Nb and relate this to the electronic structure. In this thesis I show that anharmonicity can not be neglected when considering thermodynamic properties of Nb. I observe broadening in the electronic band structure with increasing temperature, correlated with the gradual weakening of the Kohn anomalies in the phonon dispersion relations. Kohn anomaly in the phonon dispersion relation can be observed at 300 K and is completely absent at 1200 K. The observation of the Kohn anomaly's disappearance in the calculations is of great importance because it cannot be repeated by approaches that do not include anharmonic effects, meaning that properties that are directly related to phonon dispersion, like elastic constants, can be calculated more accurately with this approach

Lattice dynamics : From fundamental research to practical applications

The reason to perform calculations in material science usually falls into one of two categories: to predict or explain the origin of material properties. This thesis covers first-principle calculations for solids at extreme conditions, from both of the two mentioned categories. I primarily have studied the effects of high-pressure and high-temperature on lattice dynamics, mechanical and electronic properties. To treat the effects of temperature, ab initio molecular dynamics (AIMD) simulations and self-consistent phonon calculations, based on density functional theory, have been utilised. These approaches account for the temperature effects by considering thermally excited supercells as samples of a statistical ensemble. To extract properties from this representation, I have used methods which maps the supercell data to a unit cell representation or fits it to a simple model Hamiltonian. The small displacement method was used to analyse the dynamical stability for nitrides and polymorphs of silica, synthesised at high-pressure in a diamond anvil cell. The nitride compounds consist of a high amount of nitrogen either as chains, forming a porous framework together with transition metal atoms or as dinitrogen molecules, occupying the channels of the framework. The nitrogen chains consist of single- or double-bonded nitrogen atoms, making these compounds highly energetic. Polymorphs of silica can be used to model deep Earth liquids. These new polymorphs, named coesite-IV and coesite-V, consist of four-, five-, and six-oriented silicon. Some of the octahedra of the six-oriented silicon atoms, of these new phases, are sharing faces, which according to Pauling's third rule would make them highly unstable. My phonon calculations indicate these phases to be dynamically stable. Furthermore, my calculations predict higher compressibility for these new phases compared to the competing ones. By modelling silicate melts with coesite-IV and coesite-V, a more complex and compressible structure is expected, affecting the predicted seismic behaviour. I studied Kohn anomalies for body-centered cubic niobium by simulating this material with self-consistent phonon calculations. The electronic structure was studied by using a band unfolding technique, for which I obtained an effective unit cell representation of the electronic structure at elevated temperatures. Temperature primarily smeared the electronic states but did not induce significant shifts of the bands. In parallel, the anharmonicity of this system was studied using the temperature dependent effective potential method. Even close to the melting temperature, this element is remarkably harmonic. The experimentally observed disappearance of the Kohn anomalies with increased temperature is predominantly dependent, according to my calculations, on the temperature-induced smearing of the electronic states. Using stress-strain relations, accurate high-temperature elastic properties were predicted for Ti0.5Al0.5N. The simulations were performed with AIMD. The stresses were fitted using the least-squares method to a linear expression from which the elastic constants were derived. The results were compared with previously performed calculations that employed additional approximations. The results of the symmetry imposed force constant temperature dependent effective potential (SIFC-TDEP) method agrees well with our results. I also compared my results with TiN calculations that employed a similar methodology. My and the SIFC-TDEP results are reporting lower values for the polycrystalline moduli than the calculations for TiN. The data I generated were also used for a machine learned interatomic potential method, where moment tensor potentials were trained and evaluated, using this data.Den här avhandlingen handlar om beräkningar för material. När materialberäkningar utförs är det antingen för att förutsäga eller förklara egenskaper. De beräkningar som jag har gjort i denna avhandling är baserade på fundamentala fysiska lagar. Detta betyder att de är rent baserade på teori, och inte har anpassats efter resultat av experiment. Jag har i mitt arbete använt mig mycket utav en teori som kallas gitter dynamik. Den är definierad för periodiska material, det vill säga att atomerna i dessa material upprepas i periodiska mönster. Vi kan då anta att det finns en jämviktspunkt för alla atomerna, som de vibrerar omkring. Dessa vibrationer kan beskrivas som om atomerna påverkar varandra med fiktiva fjädrar. Genom att beräkna styrkan för dessa fjädrar kan vi beskriva vibrationerna av atomerna. Dessa vibrationer i sin tur är avgörande för materialets egenskaper. För att beskriva ett material vid en specifik temperatur har jag använt mig utav olika metoder för att simulera det. En simulering kan ses som ett “dator experiment”. Problemet är dock hur vi ska mäta egenskaperna i simuleringen. Ju större och mera komplex en simulering är, desto svårare blir det att beräkna egenskaperna av det simulerade materialet. Vi hamnar i en situation likt den vi skulle befinna oss om vi hade gjort ett experiment i verkligheten, och tvingas använda förenklade modeler för att kunna tolka resultatet. Jag har därför använt mig utav metoder för att utvinna vibrationer av atomer, elektrontillstånd eller elastiska egenskaper, specifikt utvecklade för att användas på denna typ utav simuleringar. Mitt arbete har kretsat kring hur dessa egenskaper påverkas av extrema temperaturer och tryck. De beräkningar jag har utfört vid höga tryck har varit för nyupptäckta nitrider och faser av kiseldioxid. Nitriderna är porösa material som innehåller en stor mängd kväve. Det höga kväveinehållet gör så att det lagras en stor mängd kemisk energi i enkel- och dubbelbindningar mellan kväveatomerna. De nya faserna av kiseldioxid har en betydelse för vår förståelse av jordens inre. Deras existens öppnar upp för att det kan finnas mera komplexa och ihoptryckbara flytande material, under jordens nedre mantel, än vad tidigare har varit antaget. Mina beräkningar har bekräftat strukturerna för dessa nyupptäckta material. Vid höga temperaturer har jag studerat för metallen niob hur vibrationerna av atomerna är relaterade till olika elektrontillstånd. För specifika vibrationer ökar frekvensen med ökad temperatur. Detta är något ovanligt eftersom vibrationernas frekvenser vanligtvis brukar minska med ökad temperatur. Mina simulering för denna metal överensstämmer med resultat från experiment. Orsaken till varför visa vibrationers frekvenser ökar kan jag förklara med att elektrontillståndens enskilda energier varierar över tid på grund av den ökade temperaturen. Jag har även använt mig av simuleringar för att beräkna elastiska egenskaper av legeringen Ti0.5Al0.5N. Ti1−xAlxN legeringar används som beläggningar på skärverktyg som används för metall. För att öka effektiviteten av beläggningen, behövs det detaljerad kunskap av dess mekaniska egenskaper för den temperatur som de används vid. Jag beräknade därför så noggrant som möjligt de elastiska egenskaperna för Ti0.5Al0.5N. Dessa beräkningar är avsedda för att användas som en referens för andra beräkningsmässigt billigare metoder. Datan som genererades från mina simuleringar användes även för en sådan metod, baserad på maskininlärning.

Accurate prediction of high-temperature elastic constants of Ti0.5Al0.5N random alloy

Using highly accurate ab initio molecular dynamic simulations we calculate elastic constants of Ti0.5Al0.5N as a function of temperature up to 1500 K and compare the results with those obtained for TiN. We analyze the variation of the materials elastic anisotropy with temperature by calculating directional Youngs moduli and Poisson ratios on the (100), (110) and (111) crystallographic planes. We show that though the elastic moduli of Ti0.5Al0.5N strongly decrease upon heating, the elastic anisotropy increases with temperature unlike in TiN. Since several approximate approaches have recently been utilized to predict elastic constants of Ti0.5Al0.5N at elevated temperature we compare our results with published data and benchmark the different approximate schemes. Giving the fact that Ti(1-x)AlxN is a prototypical system for hard coating applications, we conclude that the recently developed symmetry imposed force constants approach combined with the temperature dependent effective potential method is accurate and computationally cost-effective for this material class.Funding Agencies|Knut and Alice Wallenberg Foundation (Wallenberg Scholar Grant) [KAW-2018.0194]; Swedish Government Strategic Research Areas in Materials Science on Functional Materials at Linkodping University (Faculty Grant SFO-Mat-LiU) [2009 00971]; SeRCAgency for Science Technology &amp; Research (ASTAR); Swedish Research Council (VR)Swedish Research Council [2019-05600]; VINN Excellence Center Functional Nanoscale Materials (FunMat-2) [2016-05156]; Swedish Research CouncilSwedish Research CouncilEuropean Commission [2016-07213]</p

The Use of PD Patterns to Evaluate the Wear-Resistance and Manufacturing Quality to Estimate Expected Lifetime of Ignition Coils

Partial discharges (PDs) are localized flashovers that occur within electrical insulation, when the electric field exceeds its dielectric strength. The electrical insulation, which covers the distance between conductive parts is also referred to as the di electricum. In ignition coils, typically two different insulation materials are used: epoxy and transformer oil. Epoxy has the advantage of making the construction independent of positioning but its dielectric strength is sensitive to the potting process. Using oil as electrical insulation is less process sensitive than epoxy but the construction becomes more challenging as it must encap sulate its insulation material. An additional disadvantage is that an oil-insulated ignition coil can generally only be operated in certain positions, but it gains the advantage of being self-healing after dielectric breakdowns within the oil. Epoxy-insulated ignition coils lack this property as electrical trees are created within the insulation. These trees are gas-filled cavities that grow in size with the number of occurred PDs. In high performance ignition coil design, the maximum field strength should not exceed the dielectric strength of the insulation material. However, impurities locally decrease the dielectric strength and increase the electric field level. Thus, PDs are initiated at these impurities or defects and with time, the electric trees will continue to grow until the ignition coil breaks due to insulation breakdown. In epoxy insulated ignition coils, a defect can be introduced as a crack due to internal forces caused by differences in thermal expansion coefficients of the insulation system materials, even at normal operational temperatures. Therefore, measuring how homogeneous, free from impurities like gas bubbles, cracks and charred com30pounds, the epoxy is after the potting process could be a vital tool for monitoring manufacturing quality. An important aspect for an ignition coils performance is how temperature-wear-resistant, the resistance to cracking induced by a set of temperature cycles, it is. By measuring PDs, there is a possibility to quantify these quantities at a great resolution

Efficient prediction of elastic properties of Ti0.5Al0.5N at elevated temperature using machine learning interatomic potential

High-temperature thermal stability, elastic moduli and anisotropy are among the key properties, which are used in selecting materials for cutting and machining applications. The high computational demand of ab initio molecular dynamics (AIMD) simulations in calculating elastic constants of alloys promotes the development of alternative approaches. Machine learning concept grasped as hybride classical molecular dynamics and static first principles calculations have several orders less computational costs. Here we prove the applicability of the concept considering the recently developed moment tensor potentials (MTP), where moment tensors are used as materials descriptors which can be trained to predict the elastic constants of the prototypical hard coating alloy, Ti0.5Al0.5N at 900 K. We demonstrate excellent agreement between classical molecular dynamics simulations with MTPs and AIMD simulations. Moreover, we show that using MTPs one overcomes the inaccuracy issues present in approximate AIMD simulations of elastic constants of alloys.Funding Agencies|Knut and Alice Wallenberg Foundation (Wallenberg Scholar Grant) [KAW-2018.0194]; Swedish Government Strategic Research Areas in Materials Science on Functional Materials at Linkoping University [2009 00971]; SeRCAgency for Science Technology &amp; Research (ASTAR); Swedish Research Council (VR)Swedish Research Council [2019-05600]; VINN Excellence Center Functional Nanoscale Materials (FunMat-2) Grant [2016-05156]; RFBRRussian Foundation for Basic Research (RFBR) [20-53-12012]; Swedish Research CouncilSwedish Research CouncilEuropean Commission [2016-07213]</p

Temperature dependence of the Kohn anomaly in bcc Nb from first-principles self-consistent phonon calculations

Using ab initio calculations, we have analyzed the influence of anharmonic effects on the electronic structure and the phonon-dispersion relations of body-centered-cubic (bcc) niobium (Nb) and investigated the temperature dependence of the Kohn anomaly in this metal. A comparison of the results obtained in the framework of the temperature-dependent effective potential method with those derived within the quasiharmonic approximation demonstrates the importance of the explicit treatment of the finite-temperature effects upon the theoretical description of bcc Nb lattice dynamics. In agreement with experimental results, the inclusion of anharmonic vibrations in our calculations leads to the disappearance of the Kohn anomaly for the acoustic mode in a vicinity of the Gamma point with increasing temperature. Moreover, the calculated phonon self-energy indicates that the origin of the temperature dependence is related to the change of the electronic structure. We have calculated the temperature dependence of the electronic spectral function and analyzed the Fermi surface of Nb. A significant temperature-induced smearing of the electronic states has been identified as the origin of the disappearance of the Kohn anomaly in Nb at elevated temperature.Funding Agencies|Swedish Research Council (VR)Swedish Research Council [2015-04391, 2019-05551]; Swedish Government Strategic Research Areas in Materials Science on Functional Materials at Linkoping University (Faculty Grant SFO-Mat-LiU) [2009-00971]; Knut and Alice Wallenberg Foundation (Wallenberg Scholar Grant) [KAW-2018.0194]; Swedish Foundation for Strategic Research (SSF)Swedish Foundation for Strategic Research [EM16-0004]; Russian Science FoundationRussian Science Foundation (RSF) [18-12-00492]</p

The Influence of Ignition Control Parameters on Combustion Stability and Spark plug Wear in a Large Bore Gas Engine

The paper presents novel studies on the impact of different ignition control parameters on combustion stability and spark plug wear. First, experimental results from a 32.4-liter biogas fueled large bore single cylinder spark ignition engine are discussed. Two different ignition systems were considered in the experiment: a DC inductive and an AC capacitive. The spark plugs used in the experiment were of dual-iridium standard J-gap design of different electrode gaps. Test results show the importance of different degrees of freedom to control a spark. A robust ignition is found to be achieved by using a very short spark duration, which in turn reduces total energy discharge at the gap. Further observations reveal that once a stable and self-propagating flame kernel is developed, it becomes independent of the spark energy further added to the gap. Finally, results from the spark plug wear tests using a pressurized rig chamber are discussed. It is found that an excessive spark energy discharge at the gap contributes to high erosion of spark plug electrodes, which is not desirable. However, spark energy is not the only factor affecting spark plug erosion. It is also the type of spark discharge (DC/AC) that governs the electrode wear over time. Therefore, the advantage of an AC spark discharge over a DC spark has been well established through the experimental results. The inherent property of an AC spark is found to be significantly slowing down electrode wear over time, hence increasing the service life of a spark plug

High-pressure synthesis of a nitrogen-rich inclusion compound ReN8⋅xN2ReN_{8}·xN_{2} with conjugated polymeric nitrogen chains

A nitrogen‐rich compound, $ReN_{8}·xN_{2}$, was synthesized by a direct reaction between rhenium and nitrogen at high pressure and high temperature in a laser‐heated diamond anvil cell. Single‐crystal X‐ray diffraction revealed that the crystal structure, which is based on the ReN8 framework, has rectangular‐shaped channels that accommodate nitrogen molecules. Thus, despite a very high synthesis pressure, exceeding 100 GPa, $ReN_{8}·xN_{2}$ is an inclusion compound. The amount of trapped nitrogen (x) depends on the synthesis conditions. The polydiazenediyl chains [−N=N−]$_∞$ that constitute the framework have not been previously observed in any compound. Ab initio calculations on $ReN_{8}·xN_{2}$ provide strong support for the experimental results and conclusions

High-Pressure Synthesis of a Nitrogen-Rich Inclusion Compound ReN8·xN2 with Conjugated Polymeric Nitrogen Chains

A nitrogen-rich compound, ReN(8)xN(2), was synthesized by a direct reaction between rhenium and nitrogen at high pressure and high temperature in a laser-heated diamond anvil cell. Single-crystal X-ray diffraction revealed that the crystal structure, which is based on the ReN8 framework, has rectangular-shaped channels that accommodate nitrogen molecules. Thus, despite a very high synthesis pressure, exceeding 100GPa, ReN(8)xN(2) is an inclusion compound. The amount of trapped nitrogen (x) depends on the synthesis conditions. The polydiazenediyl chains [-N=N-] that constitute the framework have not been previously observed in any compound. Abinitio calculations on ReN(8)xN(2) provide strong support for the experimental results and conclusions.Funding Agencies|German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) [DU 954-8/1, DU 954-11/1]; Federal Ministry of Education and Research, Germany (BMBF) [5K16WC1]; DFG [FOR2125, FOR 2440]; Ministry of Education and Science of the Russian Federation [14.Y26.31.0005, K2-2017-080]; Swedish Research Council (VR) [2015-04391]; Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linkoping University (Faculty Grant SFO-Mat-LiU) [2009-00971]; VINN Excellence Center Functional Nanoscale Materials (FunMat-2) Grant [2016-05156]</p

High-Pressure Synthesis of a Nitrogen-Rich Inclusion Compound ReN8⋅xN2\mathrm{ReN_{8} ⋅ x N_{2}} with Conjugated Polymeric Nitrogen Chains

A nitrogen‐rich compound, $\mathrm{ReN_{8} ⋅ x N_{2}}$, was synthesized by a direct reaction between rhenium and nitrogen at high pressure and high temperature in a laser‐heated diamond anvil cell. Single‐crystal X‐ray diffraction revealed that the crystal structure, which is based on the ReN8 framework, has rectangular‐shaped channels that accommodate nitrogen molecules. Thus, despite a very high synthesis pressure, exceeding 100 GPa, $\mathrm{ReN_{8} ⋅ x N_{2}}$ is an inclusion compound. The amount of trapped nitrogen (x) depends on the synthesis conditions. The polydiazenediyl chains $\mathrm{[−N=N−]_∞}$ that constitute the framework have not been previously observed in any compound. Ab initio calculations on $\mathrm{ReN_{8} ⋅ x N_{2}}$ provide strong support for the experimental results and conclusions