Fritz Körmann

• Dr. rer. nat.
• Group Leader at Delft University of Technology, Max Planck Institute for Iron Research GmbH

Refractory medium/high-entropy alloys (M/HEAs) are emerging as promising alternative materials for hydrogen storage and hydrogen combustion engines due to their favorable thermodynamic and kinetic conditions for hydrogen accommodation (for the former) and promising high-temperature mechanical properties (for the latter). A better understanding of h...

The impact of magnetism on chemical ordering in face-centered cubic CrCoNi medium entropy alloy is studied by a combination of ab initio simulations, machine learning potentials, and Monte Carlo simulations. Large magnetic energies are revealed for some mixed L1 2 /L1 0 type ordered configurations, which are rooted in strong nearest-neighbor magnet...

Melting properties are critical for designing novel materials, especially for discovering high-performance, high-melting refractory materials. Experimental measurements of these properties are extremely challenging due to their high melting temperatures. Complementary theoretical predictions are, therefore, indispensable. One of the most accurate a...

Machine Learning-Enhanced Atomic Ordering Tomography In article number 2407564, Yue Li, Yilun Gong, Zhangwei Wang, Baptiste Gault, and co-workers introduce a machine learning-enhanced atom probe tomography technique that surpasses existing technological limitations. This method provides a comprehensive 3D view for investigating chemical short-rang...

Melting properties are critical for designing novel materials, especially for discovering high-performance, high-melting refractory materials. Experimental measurements of these properties are extremely challenging due to their high melting temperatures. Complementary theoretical predictions are, therefore, indispensable. The conventional free ener...

In solids, chemical short‐range order (CSRO) refers to the self‐organization of atoms of certain species occupying specific crystal sites. CSRO is increasingly being envisaged as a lever to tailor the mechanical and functional properties of materials. Yet quantitative relationships between properties and the morphology, number density, and atomic c...

We investigate the melting properties of the bcc refractory metals V and W, and the disordered equiatomic VW alloy from first principles. We show that thermal vibrations have a large impact on the electronic density of states (DOS) and thus considerably affect the electronic contribution to the free energy. For W, the impact of vibrations on the el...

The impact of magnetism on chemical ordering in face-centered cubic CrCoNi medium entropy alloy is studied by a combination of ab initio simulations, machine learning potentials, and Monte Carlo simulations. Large magnetic energies are revealed for some mixed L1 2 /L1 0 type ordered configurations, which are rooted in strong nearest-neighbor magnet...

This work aims to predict the microstructure of recrystallized medium and high-entropy alloys (MEAs and HEAs) with a face-centered cubic structure, in particular the density of annealing twins and their thickness. Eight MEAs and five HEAs from the Cr-Mn-Fe-Co-Ni system are considered, which have been cast, homogenized, cold-worked and recrystallize...

In multicomponent materials, short-range order (SRO) is the development of correlated arrangements of atoms at the nanometer scale. Its impact in compositionally complex materials has stimulated an intense debate within the materials science community. Understanding SRO is critical to control the properties of technologically relevant materials, fr...

Explicit anharmonicity, defined as the vibrational contribution beyond the quasiharmonic approximation, is qualitatively different between the group V and group VI bcc refractory elements. Group V elements show a small and mostly negative anharmonic entropy, whereas group VI elements have a large positive anharmonic entropy, strongly increasing wit...

Compositionally complex alloys or concentrated solid solutions are the latest frontier in catalyst design, but mixing different elements in one catalyst may result in surface segregation. Atomistic simulations can predict segregation patterns, but standard approaches based on mean-field models, cluster expansion, or classical interatomic potentials...

We present an analysis of temperature-dependent atomic short-range ordering and phase stability of the face-centered cubic CrCoNi medium-entropy alloy employing a combination of ab initio calculations and on-lattice machine learning interatomic potentials. Temperature-dependent properties are studied with canonical Monte Carlo simulations. At aroun...

High-entropy alloys are solid solutions of multiple principal elements that are capable of reaching composition and property regimes inaccessible for dilute materials. Discovering those with valuable properties, however, too often relies on serendipity, because thermodynamic alloy design rules alone often fail in high-dimensional composition spaces...

Multi-principal-component alloys have attracted great interest as a novel paradigm in alloy design, with often unique properties and a vast compositional space auspicious for materials discovery. High entropy alloys (HEAs) belong to this class and are being investigated for prospective nuclear applications with reported superior mechanical properti...

High-entropy alloys are solid solutions of multiple principal elements, capable of reaching composition and feature regimes inaccessible for dilute materials. Discovering those with valuable properties, however, relies on serendipity, as thermodynamic alloy design rules alone often fail in high-dimensional composition spaces. Here, we propose an ac...

Physical properties of ten single-phase FCC CrxMn20Fe20Co20Ni40-x high-entropy alloys (HEAs) were investigated for 0 ≤ x ≤ 26 at%. The lattice parameters of these alloys were nearly independent of composition while solidus temperatures increased linearly by ∼30 K as x increased from 0 to 26 at.%. For x ≥ 10 at.%, the alloys are not ferromagnetic be...

High- and medium-entropy alloys (HEAs and MEAs) possess high solid-solution strength. Numerous investigations have been conducted on its impact on yield strength, however, there are limited reports regarding the relation between solid-solution strengthening and strain-hardening rate. In addition, no attempt has been made to account for the dislocat...

Precipitation strengthening has been the basis of physical metallurgy since more than 100 years owing to its excellent strengthening effects. This approach generally employs coherent and nano-sized precipitates, as incoherent precipitates energetically become coarse due to their incompatibility with matrix and provide a negligible strengthening eff...

An active learning approach to train machine-learning interatomic potentials (moment tensor potentials) for multicomponent alloys to ab initio data is presented. Employing this approach, the disordered body-centered cubic (bcc) TiZrHfTax system with varying Ta concentration is investigated via molecular dynamics simulations. Our results show a stro...

Complex concentrated alloys (CCAs) are of growing interest due to their outstanding mechanical properties that exceed the property limits of conventional alloys. Whereas the superior properties is often attributed to severe lattice distortion, to date it is not clear what controls the lattice distortion and how it affects the mechanical properties...

Besides revealing excellent mechanical properties, compositionally complex alloys are also very promising candidates for applications in heterogeneous catalysis. The opportunity provided by the tremendously large composition phase space to explore new materials and tune the materials properties in the materials design cycle is, however, intrinsical...

Negative stacking fault energies (SFEs) are found in face-centered cubic high-entropy alloys with excellent mechanical properties, especially at low temperatures. Their roles remain elusive due to the lack of in situ observation of nanoscale deformation. Here, the polymorphism of Shockley partials is fully explored, assisted by a new method. We sho...

The phase stability of a bcc AlNbTiV high-entropy alloy at elevated temperatures is studied using a combination of machine-learning interatomic potentials, first-principles calculations, and Monte Carlo simulations. The simulations reveal a B2 ordering below about 1700 K, mainly caused by a strong site preference of Al and Ti. A much weaker site pr...

Multi-principal element alloys usually exhibit outstanding strength and toughness at cryogenic temperatures, especially in CrMnFeCoNi and CrCoNi alloys. These remarkable cryogenic properties are attributed to the occurrence of deformation twins, and it is envisaged that a reduced stacking fault energy (SFE) transforms the deformation mechanisms int...

Recent experiments show that the chemical composition of body-centered cubic (bcc) refractory high entropy alloys (HEAs) can be tuned to enable transformation-induced plasticity (TRIP), which significantly improves the ductility of these alloys. This calls for an accurate and efficient method to map the structural stability as a function of composi...

Concentrated solid solutions including the class of high entropy alloys (HEAs) have attracted enormous attention recently. Among these alloys a recently developed face-centered cubic (fcc) equiatomic VCoNi alloy revealed extraordinary high yield strength, exceeding previous high-strength fcc CrCoNi and FeCoNiCrMn alloys. Significant lattice distort...

Since its first emergence in 2004, the high-entropy alloy (HEA) concept has aimed at stabilizing single-or dual-phase multi-element solid solutions through high mixing entropy. Here, this strategy is changed and renders such massive solid solutions metastable, to trigger spinodal decomposition for improving the alloys' magnetic properties. The moti...

The field of atomistic simulations of multicomponent materials and high entropy alloys is progressing rapidly, with challenging problems stimulating new creative solutions. In this Perspective, we present three topics that emerged very recently and that we anticipate will determine the future direction of research of high entropy alloys: the usage...

The interface method is a well established approach for predicting melting points of materials using interatomic potentials. However, applying the interface method is tedious and involves significant human intervention. The whole procedure involves several successive tasks: estimate a rough melting point, set up the interface structure, run molecul...

The reactivity of the surface of multicomponent metals such as High Entropy Alloys (HEAs) is rapidly gaining importance for corrosion and catalytic applications, but the mechanisms of surface segregation in these complex materials are poorly understood. Here we investigate with ab initio calculations the segregation thermodynamics in the magnetic C...

We apply the efficient two-optimized references thermodynamic integration using Langevin dynamics method [Phys. Rev. B 96, 224202 (2017)] to calculate highly accurate melting properties of Al and magnetic Ni from first principles. For Ni we carefully investigate the impact of magnetism on the liquid and solid free energies including longitudinal sp...

High entropy alloys (HEAs) in the hexagonal close-packed (hcp) phase usually show poor mechanical properties. We demonstrate here, by use of ab initio simulations and detailed experimental investigations, that the mechanical properties can be improved by optimizing the microstructure. In particular we design a dual-phase HEA consisting of a body-ce...

We reveal the impact of magnetic ordering on stacking fault energy (SFE) and its influence on the deformation mechanisms and mechanical properties in a class of nonequiatomic quinary Mn-containing compositional complex alloys or high entropy alloys (HEAs). By combining ab initio simulation and experimental validation, we demonstrate magnetic orderi...

The lattice dynamics in magnetic materials, such as Fe depends on the degree of disorder of the atomic magnetic moments and the time scale of spin fluctuations. Using first-principles methods, we have studied this effect by determining the force constant matrix in two limits: (i) When spin fluctuations are much faster than the atom vibrations, thei...

Local lattice distortions in a series of body-centered cubic alloys, including refractory high-entropy alloys, are investigated by means of atomic volumes, atomic charges, and atomic stresses defined by the Bader charge analysis based on first-principles calculations. Analyzing the extensive data sets, we find large distributions of these atomic pr...

In conventional metallic materials, strength and ductility are mutually exclusive, referred to as strength-ductility trade-off. Here, we demonstrate an approach to improve the strength and ductility simultaneously by introducing micro-banding and the accumulation of a high density of dislocations in single-phase high-entropy alloys (HEAs). We prepa...

We combined experimental investigations and theoretical calculations to unveil an abnormal magnetic behavior caused by addition of the nonmagnetic element Cu in face-centered-cubic FeNiCoMn-based high-entropy alloys (HEAs). Upon Cu addition, the probed HEAs show an increase of both Curie temperature and saturation magnetization in as-cast and homog...

Density functional theory (DFT) calculations were performed on AlxCyCoFeMnNi multi-principal element alloys (MPEAs) to understand the influence of Al and C on the stacking-fault energy (SFE). C addition to CoFeMnNi resulted in increased SFE, while it decreased in Al-alloyed CoFeMnNi. For experimental verification, Al0.26CyCoFeMnNi with 0, 1.37 and...

Recently, high-entropy alloys (HEAs) have attracted wide attention due to their extraordinary materials properties. A main challenge in identifying new HEAs is the lack of efficient approaches for exploring their huge compositional space. Ab initio calculations have emerged as a powerful approach that complements experiment. However, for multicompo...

Interstitial alloying in CrMnFeCoNi-based high-entropy alloys is known to modify their mechanical properties. Specifically, strength can be increased due to interstitial solid-solution hardening, while simultaneously affecting ductility. In this paper, first-principles calculations are carried out to analyze the impact of interstitial C atoms on Cr...

Recent developments in electrical transportation and renewable energies have significantly increased the demand of hard magnetic materials with a reduced critical rare-earth content, but with properties comparable to (Nd,Dy)-Fe-B permanent magnets. Though promising alternative compositions have been identified in high-throughput screenings, the the...

To facilitate the understanding of Invar effects and design of FeNiCo-base Invar alloys characterized by low thermal expansion coefficient (TEC), we investigated the magnetic and thermal expansion behavior of an equiatomic prototype medium entropy alloy FeNiCo and a non-equiatomic (super Invar) Fe 63 Ni 32 Co 5 (at. %) reference alloy by means of e...

The unique and unanticipated properties of multiple principal component alloys have reinvigorated the field of alloy design and drawn strong interest across scientific disciplines. The vast compositional parameter space makes these alloys a unique area of exploration by means of computational design. However, as of now a method to compute efficient...

Quantitative and well-targeted design of modern alloys is extremely challenging due to their immense compositional space. When considering only 50 elements for compositional blending the number of possible alloys is practically infinite, as is the associated unexplored property realm. In this paper, we present a simple property-targeted quantitativ...

A density-functional-theory based approach to efficiently compute numerically exact vibrational free energies - including anharmonicity - for chemically complex multicomponent alloys is developed. It is based on a combination of thermodynamic integration and a machine-learning potential. We demonstrate the performance of the approach by computing t...

Multicomponent alloys with multiple principal elements including high entropy alloys (HEAs) and compositionally complex alloys (CCAs) are attracting rapidly growing attention. The endless possibilities to explore new alloys and the hope for better combinations of materials properties have stimulated a remarkable number of research works in the last...

Severe lattice distortion is a core effect in the design of multiprincipal element alloys with the aim to enhance yield strength, a key indicator in structural engineering. Yet, the yield strength values of medium‐ and high‐entropy alloys investigated so far do not substantially exceed those of conventional alloys owing to the insufficient utilizat...

The temperature-dependent intrinsic stacking fault Gibbs energy is computed based on highly converged density-functional-theory (DFT) calculations for the three prototype face-centered cubic metals Al, Cu, and Ni. All relevant temperature-dependent contributions are considered including electronic, vibrational, magnetic, and explicit anharmonic Gib...

Recently, high-entropy alloys (HEAs) attracted wide attention due to their extraordinary materials properties. A main challenge in identifying new HEAs is the lack of efficient approaches for exploring their huge compositional space. Ab initio calculations have emerged as a powerful approach that complements experiment. However, for multicomponent...

Medium and high entropy alloys (MEAs and HEAs) based on 3d transition metals, such as face-centered cubic (fcc) CrCoNi and CrMnFeCoNi alloys, reveal remarkable mechanical properties. The stacking fault energy (SFE) is one of the key ingredients that controls the underlying deformation mechanism and hence the mechanical performance of materials. Pre...

Quantum-mechanical calculations are used to determine the temperature dependence of the Gibbs energy of vacancy formation in nickel. Existing data reveal a discrepancy between the high-temperature estimates from experiments and low-temperature approximations from density functional theory. Our finite-temperature calculations—which include the effec...

A first-principles-based method for computing phonons of magnetic random solid solutions including thermal magnetic fluctuations is developed. The method takes fluctuations of force constants (FCs) due to magnetic excitations as well as due to chemical disorder into account. The developed approach correctly predicts the experimentally observed unus...

We study the mutual coupling of spin fluctuations and lattice vibrations in paramagnetic CrN by combining atomistic spin dynamics and ab initio molecular dynamics. The two degrees of freedom are dynamically coupled leading to non-adiabatic effects. Those effects suppress the phonon life times at low temperature compared to an adiabatic approach. Th...

We study the mutual coupling of spin fluctuations and lattice vibrations in paramagnetic CrN by combining atomistic spin dynamics and ab initio molecular dynamics. The two degrees of freedom are dynamically coupled leading to non-adiabatic effects. Those effects suppress the phonon life times at low temperature compared to an adiabatic approach. Th...

Doping with Co and Fe is a promising strategy to enhance the performance of Ni-Mn-based magnetocaloric materials. We investigate here the impact of these two elements on the magnetic properties and the martensitic transformations in Mn-rich Ni-Mn-Al Heusler alloy. Based on ab initio ground-state energies, we explain the martensitic transformation t...

Synthetic pentlandite (Fe4.5Ni4.5S8) is a promising electrocatalyst for hydrogen evolution, demonstrating high current densities, low overpotential and remarkable stability in bulk form. The depletion of sulfur from the surface of this catalyst during the electrochemical reaction has been proposed to be beneficial for its catalytic performance, but...

We introduce a new class of high-entropy alloys (HEAs), i.e., quinary (five-component) dual-phase (DP) HEAs revealing transformation-induced plasticity (TRIP), designed by using a quantum mechanically based and experimentally validated approach. Ab initio simulations of thermodynamic phase stabilities of Co20Cr20Fe40-xMn20Nix (x = 0–20 at. %) HEAs...

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 th...

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 trad...

Free energies of bulk materials are nowadays routinely computed by density functional theory. In particular for metals, electronic excitations can significantly contribute to the free energy. For an ideal static lattice, this contribution can be obtained at low computational cost, e.g., from the electronic density of states derived at T=0 K or by u...

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 trad...

A first-principles-based method for computing phonons of magnetic random solid solutions including thermal magnetic fluctuations is developed. The method takes fluctuations of force constants (FCs) due to magnetic excitations as well as due to chemical disorder into account. The developed approach correctly predicts the experimentally observed unus...

Modernmaterials science increasingly advances via a knowledge-based development rather than a trial- and-error procedure. Gathering large amounts of data and getting deep understanding of non-trivial relationships between synthesis of materials, their structure and properties is experimentally a tedious work. Here, theoretical modeling plays a vita...

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 entr...

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 entr...

Refractory high entropy alloys (HEA), such as BCC NbMoTaW, represent a promising materials class for next-generation high-temperature applications, due to their extraordinary mechanical properties. A characteristic feature of HEAs is the formation of single-phase solid solutions. For BCC NbMoTaW, recent computational studies revealed, however, a B2...

We reveal that in a prototypical bcc high-entropy alloy NbMoTaW chemical interactions are long ranged and highly frustrated. We show that this is the reason that bcc solid solutions in NbMoTaW can persist to low temperatures. The ab initio-computed long-ranged interactions strongly impact characteristic thermodynamic properties and ordering tempera...

We study the impact of lattice vibrations on magnetic and electronic properties of paramagnetic bcc and fcc iron at finite temperature, employing the disordered local moments molecular dynamics (DLM-MD) method. Vibrations strongly affect the distribution of local magnetic moments at finite temperature, which in turn correlates with the local atomic...

The spin-space averaging formalism is applied to compute atomic forces and phonon spectra for magnetically excited states of fcc nickel. Transverse and longitudinal magnetic fluctuations are taken into account by a combination of magnetic special quasi random structures and constrained spin-density-functional theory. It turns out that for fcc Ni in...

Partitioning of Cr and Si between cementite and ferrite was investigated by first-principles thermodynamics taking into account vibrational, electronic, and magnetic Gibbs energy contributions. At finite temperatures, these contributions lower the partitioning Gibbs energy and compete with the configurational entropy, which favors impurity segregat...

The quaternary Q phase is an important precipitate phase in the Al-Cu-Mg-Si alloy system and its accurate thermodynamic description is crucial for further tailoring this material class for light-weight structural applications. In order to achieve an improved thermochemical parameter set of this phase, we used a combination of experimental measureme...

We investigate the thermodynamic properties of the prototype equi-atomic high entropy alloy (HEA) CoCrFeMnNi by using finite-temperature ab initio methods. All relevant free energy contributions are considered for the hcp, fcc, and bcc structures, including electronic, vibrational, and magnetic excitations. We predict the paramagnetic fcc phase to...

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 gener...

Within this article we highlight recent advances in the modeling of magnetic contributions to the finite temperature phase stability of structural materials. A key quantity in this context is the specific heat capacity , since it provides a sensitive link to thermophysical and calorimetric experiments and to established thermodynamic databases. For...

Aluminum-based alloys that contain Mg, Si and Cu belong to the most promising materials in automotive and aircraft engineering. To achieve their best mechanical characteristics via heat treatment, a precise knowledge of their precipitation properties is essential. The Q phase is a ubiquitous quaternary precipitate in these alloys. Despite its impor...

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 (DFT+U) approach in conjunction with experimental measurements of the thermal expansion. Comparing DFT and DF...

An ab initio based framework for quantitatively assessing the phonon contribution due to magnon-phonon interactions and lattice expansion is developed. The theoretical results for bcc Fe are in very good agreement with high-quality phonon frequency measurements. For some phonon branches, the magnon-phonon interaction is an order of magnitude larger...

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 resu...

Thermophysical properties, such as heat capacity, bulk modulus and thermal expansion, are of great importance for many technological applications and are traditionally determined experimentally. With the rapid development of computational methods, however, first-principles computed temperature-dependent data are nowadays accessible. We evaluate var...

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...

DOI:https://doi.org/10.1103/PhysRevB.89.179901

This paper provides a comprehensive overview of state-of-the-art computational techniques to thermodynamically model magnetic and chemical order–disorder transitions. Recent advances as well as limitations of various approaches to these so-called lambda transitions are examined in detail, focussing on calphad models and first-principles methods bas...

Four commonly used embedded atom method potentials for bcc-Fe by Ackland et al. (1997), Mendelev et al. (2003), Chiesa et al. (2009) and Malerba et al. (2010) are critically evaluated with respect to their description of the edge dislocation core structure and its dynamic behavior. Our results allow us to quantify the transferability of the various...