Blazej Grabowski

Advancing density functional theory to finite temperatures: methods and applications in steel design

The performance of materials such as steels, their high strength and formability, is based on an impressive variety of competing mechanisms on the microscopic/atomic scale (e.g. dislocation gliding, solid solution hardening, mechanical twinning or structural phase transformations). Whereas many of the currently available concepts to describe these mechanisms are based on empirical and experimental data, it becomes more and more apparent that further improvement of materials needs to be based on a more fundamental level. Recent progress for methods based on density functional theory (DFT) now makes the exploration of chemical trends, the determination of parameters for phenomenological models and the identification of new routes for the optimization of steel properties feasible. A major challenge in applying these methods to a true materials design is, however, the inclusion of temperature-driven effects on the desired properties. Therefore, a large range of computational tools has been developed in order to improve the capability and accuracy of first-principles methods in determining free energies. These combine electronic, vibrational and magnetic effects as well as structural defects in an integrated approach. Based on these simulation tools, one is now able to successfully predict mechanical and thermodynamic properties of metals with a hitherto not achievable accuracy.

Structural stability and thermodynamics of CrN magnetic phases from ab initio calculations and experiment

The dynamical and thermodynamic phase stabilities of the stoichiometric compound CrN including different structural and magnetic configurations are comprehensively investigated using a first-principles density-functional-theory (DFT) plus U approach in conjunction with experimental measurements of the thermal expansion. Comparing DFT and DFT+U results with experimental data reveals that the treatment of electron correlations using methods beyond standard DFT is crucial. The non-magnetic face-centered cubic B1-CrN phase is both, elastically and dynamically unstable, even under high pressure, while CrN phases with non-zero local magnetic moments are predicted to be dynamically stable within the framework of the DFT+U scheme. Furthermore, the impact of different treatments for the exchange-correlation (xc)-functional is investigated by carrying out all computations employing the local density approximation and generalized gradient approximation. To address finite-temperature properties, both, magnetic and vibrational contributions to the free energy have been computed employing our recently developed spin-space averaging method. The calculated phase transition temperature between low-temperature antiferromagnetic and high-temperature paramagnetic (PM) CrN variants is in excellent agreement with experimental values and reveals the strong impact of the choice of the xc-functional. The temperature-dependent linear thermal expansion coefficient of CrN is experimentally determined by the wafer curvature method from a reactive magnetron sputter deposited single-phase B1-CrN thin film with dense film morphology. A good agreement is found between experimental and ab initio calculated linear thermal expansion coefficients of PM B1-CrN. Other thermodynamic properties, such as the specific heat capacity, have been computed as well and compared to previous experimental data.

Lattice Distortions in the FeCoNiCrMn High Entropy Alloy Studied by Theory and Experiment

Lattice distortions constitute one of the main features characterizing high entropy alloys. Local lattice distortions have, however, only rarely been investigated in these multi-component alloys. We, therefore, employ a combined theoretical electronic structure and experimental approach to study the atomistic distortions in the FeCoNiCrMn high entropy (Cantor) alloy by means of density-functional theory and extended X-ray absorption fine structure spectroscopy. Particular attention is paid to element-resolved distortions for each constituent. The individual mean distortions are small on average, <1%, but their fluctuations (i.e., standard deviations) are an order of magnitude larger, in particular for Cr and Mn. Good agreement between theory and experiment is found.

“Treasure maps” for magnetic high-entropy-alloys from theory and experiment

The critical temperature and saturation magnetization for four- and five-component FCC transition metal alloys are predicted using a formalism that combines density functional theory and a magnetic mean-field model. Our theoretical results are in excellent agreement with experimental data presented in both this work and in the literature. The generality and power of this approach allow us to computationally design alloys with well-defined magnetic properties. Among other alloys, the method is applied to CoCrFeNiPd alloys, which have attracted attention recently for potential magnetic applications. The computational framework is able to predict the experimentally measured TC and to explore the dominant mechanisms for alloying trends with Pd. A wide range of ferromagnetic properties and Curie temperatures near room temperature in hitherto unexplored alloys is predicted in which Pd is replaced in varying degrees by, e.g., Ag, Au, and Cu.

Deformation-Induced Martensite: A New Paradigm for Exceptional Steels

Martensite steel is induced from pearlitic steel by a newly discovered method, which is completely different from the traditional route of quenching austenitic steel. Both experimental and theoretical studies demonstrate that Fe-C martensite forms by severe deformation at room temperature. The new mechanism identified here opens a paths to material-design strategies based on deformation-driven nanoscale phase transformations.

Thermodynamic modeling of chromium: strong and weak magnetic coupling

As chromium is a decisive ingredient for stainless steels, a reliable understanding of its thermodynamic properties is indispensable. Parameter-free first-principles methods have nowadays evolved to a state allowing such thermodynamic predictions. For materials such as Cr, however, the inclusion of magnetic entropy and higher order contributions such as anharmonic entropy is still a formidable task. Employing state-of-the-art ab initio molecular dynamics simulations and statistical concepts, we compute a set of thermodynamic properties based on quasiharmonic, anharmonic, electronic and magnetic free energy contributions from first principles. The magnetic contribution is modeled by an effective nearest-neighbor Heisenberg model, which itself is solved numerically exactly by means of a quantum Monte Carlo method. We investigate two different scenarios: a weak magnetic coupling scenario for Cr, as usually presumed in empirical thermodynamic models, turns out to be in clear disagreement with experimental observations. We show that instead a mixed Hamiltonian including weak and strong magnetic coupling provides a consistent picture with good agreement to experimental thermodynamic data.

Steel Design from Fully Parameter-Free Ab Initio Computer Simulations

The high strength and formability of steels is based on a large number of competing mechanisms on the microscopic/atomistic scale. Among them are dislocation gliding, dynamic strain aging, mechanical twin formation and local martensitic phase transformations, for which stacking faults play a dominant role. Many of the underlying concepts are based on empirical and experimental data. For a deeper understanding, however, an atomistic simulation of those structural defects becomes more and more crucial. Recent advances in ab initio calculations have sparked a lot of interest in deriving this information from such completely parameter free methods. Employing ab initio methods allows exploring chemical trends, to deliver parameters for phenomenological models, and to identify new routes for the optimization of steel properties. A major challenge in applying these methods to the above questions is the inclusion of all relevant temperature effects on the desired properties. We have therefore developed a large range of computational tools to improve the capability and accuracy of first-principles methods in determining free energies. These combine electronic, vibrational, and magnetic effects in an integrated approach. Based on these simulation tools, we are able to successfully predict mechanical and thermodynamic properties of metals with hitherto not achievable accuracy.

Phonon broadening in high entropy alloys

Refractory high entropy alloys feature outstanding properties making them a promising materials class for next-generation high-temperature applications. At high temperatures, materials properties are strongly affected by lattice vibrations (phonons). Phonons critically influence thermal stability, thermodynamic and elastic properties, as well as thermal conductivity. In contrast to perfect crystals and ordered alloys, the inherently present mass and force constant fluctuations in multi-component random alloys (high entropy alloys) can induce significant phonon scattering and broadening. Despite their importance, phonon scattering and broadening have so far only scarcely been investigated for high entropy alloys. We tackle this challenge from a theoretical perspective and employ ab initio calculations to systematically study the impact of force constant and mass fluctuations on the phonon spectral functions of 12 body-centered cubic random alloys, from binaries up to 5-component high entropy alloys, addressing the key question of how chemical complexity impacts phonons. We find that it is crucial to include both mass and force constant fluctuations. If one or the other is neglected, qualitatively wrong results can be obtained such as artificial phonon band gaps. We analyze how the results obtained for the phonons translate into thermodynamically integrated quantities, specifically the vibrational entropy. Changes in the vibrational entropy with increasing the number of elements can be as large as changes in the configurational entropy and are thus important for phase stability considerations. The set of studied alloys includes MoTa, MoTaNb, MoTaNbW, MoTaNbWV, VW, VWNb, VWTa, VWNbTa, VTaNbTi, VWNbTaTi, HfZrNb, HfMoTaTiZr.High entropy alloys: Theoretical perspectives on phononsIn contrast to conventional alloys, high entropy alloys possess five or more equiatomic elemental species within a single lattice, resulting in some extraordinary physical properties. All these properties are linked to the lattice vibrations, i.e. phonons, indicating the importance of modelling of phonon excitations and their interactions. A team led by Fritz Körmann at Netherlands’ Delft University of Technology and Yuji Ikeda at Kyoto University in Japan performed first-principles calculations on 12 different refractory alloys to address the key question of how the chemical complexity impacts phonons. Results show that both atomic mass and force constants contribute to the phonon energies, and changes in the vibrational entropy with more elements could be comparable to the configurational entropy. Research into the computationally designed phonon broadening may open an avenue towards tailored high temperature high entropy alloys.

Computationally-driven engineering of sublattice ordering in a hexagonal AlHfScTiZr high entropy alloy

Multi-principle element alloys have enormous potential, but their exploration suffers from the tremendously large range of configurations. In the last decade such alloys have been designed with a focus on random solid solutions. Here we apply an experimentally verified, combined thermodynamic and first-principles design strategy to reverse the traditional approach and to generate a new type of hcp Al-Hf-Sc-Ti-Zr high entropy alloy with a hitherto unique structure. A phase diagram analysis narrows down the large compositional space to a well-defined set of candidates. First-principles calculations demonstrate the energetic preference of an ordered superstructure over the competing disordered solid solutions. The chief ingredient is the Al concentration, which can be tuned to achieve a D019 ordering on the hexagonal lattice. The computationally designed D019 superstructure is experimentally confirmed by transmission electron microscopy and X-ray studies. Our scheme enables the exploration of a new class of high entropy alloys.

Self-Healing Metals

Designing self-healing in metals is a challenging task. Self-healing concepts successfully applied in polymers cannot be directly transferred because of different energetics. This has detained the field of self-healing metals, as evidenced by absolute publication numbers. Yet, relative publication numbers indicate a rapidly increasing interest in recent years triggered by the potential economic impact of advanced metallic materials. This chapter reviews all currently available self-healing concepts in bulk metallic materials. We provide a classification into two conceptually distinct routes: (1) autonomous self-healing of nanovoids at the nanoscale, aiming at a prevention of large-scale damage and (2) non-autonomous self-healing of macrocracks by an external trigger such as heat. The general idea of each self-healing concept is comprehensibly introduced, relevant publications are reviewed, and the characteristics of the concepts are compared. Finally, we discuss current constraints and identify the most promising concepts.