Theoretical modelling predicts very unusual structures and properties of materials at extreme pressure and temperature conditions(1,2). Hitherto, their synthesis and investigation above 200 gigapascals have been hindered both by the technical complexity of ultrahigh-pressure experiments and by the absence of relevant in situ methods of materials analysis. Here we report on a methodology developed to enable experiments at static compression in the terapascal regime with laser heating. We apply this method to realize pressures of about 600 and 900 gigapascals in a laser-heated double-stage diamond anvil cell(3), producing a rhenium-nitrogen alloy and achieving the synthesis of rhenium nitride Re7N3-which, as our theoretical analysis shows, is only stable under extreme compression. Full chemical and structural characterization of the materials, realized using synchrotron single-crystal X-ray diffraction on microcrystals in situ, demonstrates the capabilities of the methodology to extend high-pressure crystallography to the terapascal regime.

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.

We present a theoretical scheme to calculate the elastic constants of magnetic materials in the high-temperature paramagnetic state. Our approach is based on a combination of disordered local moments picture and ab initio molecular dynamics (DLM-MD). Moreover, we investigate a possibility to enhance the efficiency of the simulations of elastic properties using the recently introduced method: symmetry imposed force constant temperature-dependent effective potential (SIFC-TDEP). We have chosen cubic paramagnetic CrN as a model system. This is done due to its technological importance and its demonstrated strong coupling between magnetic and lattice degrees of freedom. We have studied the temperature-dependent single-crystal and polycrystalline elastic constants of paramagentic CrN up to 1200 K. The obtained results at T = 300 K agree well with the experimental values of polycrystalline elastic constants as well as the Poisson ratio at room temperature. We observe that the Young’s modulus is strongly dependent on temperature, decreasing by 14% from T = 300 K to 1200 K. In addition we have studied the elastic anisotropy of CrN as a function of temperature and we observe that CrN becomes substantially more isotropic as the temperature increases. We demonstrate that the use of Birch law may lead to substantial errors for calculations of temperature induced changes of elastic moduli. The proposed methodology can be used for accurate predictions of mechanical properties of magnetic materials at temperatures above their magnetic order-disorder phase transition.

Wurtzite aluminium nitride is a technologically important wide band gap semiconductor with an unusually high thermal conductivity, used in optical applications and as a heatsink substrate. Many of its properties depend on an accurate description of its lattice dynamics, which have thus far only been captured in the quasiharmonic approximation. In this work, we demonstrate that anharmonicity has a considerable impact on its phase stability and transport properties, since anharmonicity is much stronger in the rocksalt phase. We compute a pressure-temperature phase diagram of AlN, demonstrating that the rocksalt phase is stabilised by increasing temperature, with respect to the wurtzite phase. We demonstrate that including anharmonicity, we can recover the thermal conductivity of the wurtzite phase (320 Wm⁻¹K⁻¹ under ambient conditions), and compute the hitherto unknown thermal conductivity of the rocksalt phase (96 Wm⁻¹K⁻¹). We also show that the electronic band gap decreases with temperature. These findings provide further evidence that anharmonic effects cannot be ignored in high temperature applications.

We develop a method to accurately and efficiently determine the vibrational free energy as a function of temperature and volume for substitutional alloys from first principles. Taking Ti1-xAlxN alloy as a model system, we calculate the isostructural phase diagram by finding the global minimum of the free energy corresponding to the true equilibrium state of the system. We demonstrate that the vibrational contribution including anharmonicity and temperature dependence of the mixing enthalpy have a decisive impact on the calculated phase diagram of a Ti1-xAlxN alloy, lowering the maximum temperature for the miscibility gap from 6560 to 2860 K. Our local chemical composition measurements on thermally aged Ti0.5Al0.5N alloys agree with the calculated phase diagram.

We have developed a method to accurately and efficiently determine the vibrational free energy as a function of temperature and volume for substitutional alloys from first principles. Taking Ti1_−xAl_xN alloy as a model system, we calculate the isostructural phase diagram by finding the global minimum of the free energy, corresponding to the true equilibrium state of the system. We demonstrate that the anharmonic contribution and temperature dependence of the mixing enthalpy have a decisive impact on the calculated phase diagram of a Ti1_−xAl_xN alloy, lowering the maximum temperature for the miscibility gap from 6560 K to 2860 K. Our local chemical composition measurements on thermally aged Ti_0.5Al_0.5N alloys agree with the calculated phase diagram.

A recently discovered phase of orthorhombic iron carbide o-Fe7C3 [Prescher et al., Nat. Geosci. 8, 220 (2015)] is assessed as a potentially important phase for interpretation of the properties of the Earths core. In this paper, we carry out first-principles calculations on o-Fe7C3, finding properties to be in broad agreement with recent experiments, including a high Poissons ratio (0.38). Our enthalpy calculations suggest that o-Fe7C3 is more stable than Eckstrom-Adcock hexagonal iron carbide (h-Fe7C3) below approximately 100 GPa. However, at 150 GPa, the two phases are essentially degenerate in terms of Gibbs free energy, and further increasing the pressure towards Earths core conditions stabilizes h-Fe7C3 with respect to the orthorhombic phase. Increasing the temperature tends to stabilize the hexagonal phase at 360 GPa, but this trend may change beyond the limit of the quasiharmonic approximation.

We have developed a method to accurately and efficiently determine the vibrational free energy as a function of temperature and pressure for substitutional alloys from first principles. Taking the example of the technologically important hard coating alloy Ti1-xAlxN as an example, we investigate the effect on the vibrational free energy of substituting Ti for other group IV elements. By constructing the phase diagrams for these three alloys, we show why Zr_1-xAl_xN and Hf_1-xAl_xN are so difficult to experimentally synthesise in a metastable solid solution: both have solubility regions that span only a small low-AlN concentration range at temperatures above 1500 K. Moreover, Hf_1-xAl_xN is dynamically unstable at low temperatures and across most of the concentration range. We also show the chemical and thermal expansion effects dominate mass disorder in the Gibbs free energy of mixing.

Ti1_−xAl_xN is a technologically important alloy that undergoes a process of high temperature age-hardening that is strongly influenced by its elastic properties. We have performed first principles calculations of the elastic constants and anisotropy using the newly developed symmetry imposed force constant temperature dependent effective potential method, that include lattice vibrations and therefore the effects of temperature, including thermal expansion and intrinsic anharmonicity. These are compared with in situ high temperature x-ray diffraction measurements of the lattice parameter. We show that anharmonic effects are crucial to the recovery of finite temperature elasticity. The effects of thermal expansion and intrinsic anharmonicity on the elastic constants are of the same order, and cannot be considered separately. Furthermore, the effect of thermal expansion on elastic constants is such that the volume change induced by zero point motion has a significant effect. For TiAlN, the elastic constants soften non-uniformly with temperature: C₁₁ decreases substantially when the temperature increases for all compositions, resulting in an increased anisotropy. These findings suggest that an increased Al content and annealing at higher temperatures will result in a harder alloy.

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 Ti_1-xAl_xN. 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 Ti_1-xAl_xNs teoretiska löslighetslucka från 6560 K till 2860 K, i linje med de experiment som gjorts med atomsondstomografi. Genom att behandla legeringarna Zr_1-xAl_xN och Hf_1-xAl_xN 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 Hf_1-xAl_xN, 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 Ti_1-xAl_xN. 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.

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.

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.