Tilmann Hickel

Designing shape-memory Heusler alloys from first-principles

The phase diagrams of magnetic shape-memory Heusler alloys, in particular, ternary Ni-Mn-Z and quarternary (Pt, Ni)-Mn-Z alloys with Z = Ga, Sn, have been addressed by density functional theory and Monte Carlo simulations. Finite temperature free energy calculations show that the phonon contribution stabilizes the high-temperature austenite structure while at low temperatures magnetism and the band Jahn-Teller effect favor the modulated monoclinic 14M or the nonmodulated tetragonal structure. The substitution of Ni by Pt leads to a series of magnetic shape-memory alloys with very similar properties to Ni-Mn-Ga but with a maximal eigenstrain of 14%.

A comparison of atomistic and continuum theoretical approaches to determine electronic properties of GaN/AlN quantum dots

In this work we present a comparison of multiband k.p-models, the effective bond-orbital approach, and an empirical tight-binding model to calculate the electronic structure for the example of a truncated pyramidal GaN/AlN self-assembled quantum dot with a zincblende structure. For the system under consideration, we find a very good agreement between the results of the microscopic models and the 8-band k.p-formalism, in contrast to a 6+2-band k.p-model, where conduction band and valence band are assumed to be decoupled. This indicates a surprisingly strong coupling between conduction and valence band states for the wide band gap materials GaN and AlN. Special attention is paid to the possible influence of the weak spin-orbit coupling on the localized single-particle wave functions of the investigated structure.

Density functional theory in materials science

Materials science is a highly interdisciplinary field. It is devoted to the understanding of the relationship between (a) fundamental physical and chemical properties governing processes at the atomistic scale with (b) typically macroscopic properties required of materials in engineering applications. For many materials, this relationship is not only determined by chemical composition, but strongly governed by microstructure. The latter is a consequence of carefully selected process conditions (e.g., mechanical forming and annealing in metallurgy or epitaxial growth in semiconductor technology). A key task of computational materials science is to unravel the often hidden composition–structure–property relationships using computational techniques. The present paper does not aim to give a complete review of all aspects of materials science. Rather, we will present the key concepts underlying the computation of selected material properties and discuss the major classes of materials to which they are applied. Specifically, our focus will be on methods used to describe single or polycrystalline bulk materials of semiconductor, metal or ceramic form.

The Effect of Disorder on the Concentration-Dependence of Stacking Fault Energies in Fe1-xMnx – A First Principles Study

The stacking fault energy plays a significant role in defining the type of plasticity mechanism which prevails in high-Mn steels. Therefore, a detailed understanding and control over the physical mechanisms that influence the stacking fault energies is crucial for effective design and optimization of such steels. We present results of a first principle study on the influence of the chemical and magnetic ordering on the composition dependence of stacking fault energies in austenitic Fe1-xMnx alloys, which are prototypes for high-Mn steels. Our calculations show that chemical ordering has a significant influence on the intrinsic stacking faults. We have further demonstrated that, although FeMn-alloys have zero net magnetization, the internal magnetic structure significantly changes the properties of the stacking faults. Specifically, we have shown for chemically disordered structures that the dependence of the equilibrium volume and of the SFE on their composition is strongly changed if they are under paramagnetic instead of non-magnetic exposure. These results prove the importance of atomistic simulations for the determination of the SFE and clearly indicate that the magnetic interactions and the chemical ordering in this system must be accurately captured by the theory.

Ab initio study of thermodynamic, structural, and elastic properties of Mg-substituted crystalline calcite.

Arthropoda, which represent nearly 80% of all known animal species, are protected by an exoskeleton formed by their cuticle. The cuticle represents a hierarchically structured multifunctional biocomposite based on chitin and proteins. Some groups, such as Crustacea, reinforce the load-bearing parts of their cuticle with calcite. As the calcite sometimes contains Mg it was speculated that Mg may have a stiffening impact on the mechanical properties of the cuticle (Becker et al., Dalton Trans. (2005) 1814). Motivated by these facts, we present a theoretical parameter-free quantum-mechanical study of the phase stability and structural and elastic properties of Mg-substituted calcite crystals. The Mg-substitutions were chosen as examples of states that occur in complex chemical environments typical for biological systems in which calcite crystals contain impurities, the role of which is still the topic of debate. Density functional theory calculations of bulk (Ca,Mg)CO₃ were performed employing 30-atom supercells within the generalized gradient approximation as implemented in the Vienna Ab-initio Simulation Package. Based on the calculated thermodynamic results, low concentrations of Mg atoms are predicted to be stable in calcite crystals in agreement with experimental findings. Examining the structural characteristics, Mg additions nearly linearly reduce the volume of substituted crystals. The predicted elastic bulk modulus results reveal that the Mg substitution nearly linearly stiffens the calcite crystals. Due to the quite large size-mismatch of Mg and Ca atoms, Mg substitution results in local distortions such as off-planar tilting of the CO₃²⁻ group.

Polarization-induced charge carrier separation in polar and nonpolar grown GaN quantum dots

We have performed systematic studies of wurtzite GaN/AlN quantum dots grown on polar and nonpolar surfaces. For this purpose, experimentally observed quantum dot geometries have been employed within an eight-band k⋅p model. The spatial separation of electrons and holes due to polarization potentials is found to be much larger in nonpolar than in polar grown quantum dots. In order to improve the electron-hole overlap and thus the recombination rates, we have varied the shape, size, and the periodic arrangement of nonpolar quantum dots. We observed the strongest improvement of the charge carrier overlap in nonpolar quantum dots that have a reduced dimension. If the size is reduced below 60% of the dimensions reported recently in literature, this increase is clearly more pronounced than for the polar quantum dots, indicating much better recombination rates in smaller nonpolar quantum dots.

Plane-wave implementation of the real-space k⋅p formalism and continuum elasticity theory

Abstract In this work we demonstrate how second-order continuum elasticity theory and an eight-band k ⋅ p model can be implemented in an existing density functional theory (DFT) plane-wave code. The plane-wave formulation of these two formalisms allows for an accurate and efficient description of elastic and electronic properties of semiconductor nanostructures such as quantum dots, wires, and films. Gradient operators that are computationally expensive in a real-space formulation can be calculated much more efficiently in reciprocal space. The accuracy can be directly controlled by the plane-wave cutoff. Furthermore, minimization schemes typically available in plane-wave DFT codes can be applied straightforwardly with only a few modifications to a plane-wave formulation of these continuum models. As an example, the elastic and electronic properties of a III-nitride quantum dot system are calculated.

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.

Strong dipole coupling in nonpolar nitride quantum dots due to Coulomb effects

Optical properties of polar and nonpolar nitride quantum dots (QDs) are determined on the basis of a microscopic theory which combines a continuum elasticity approach to the polarization potential, a tight-binding model for the electronic energies and wavefunctions, and a many-body theory for the optical properties. For nonpolar nitride quantum dots, we find that optical absorption and emission spectra exhibit a weak ground-state oscillator strength in a single-particle calculation whereas the Coulomb configuration interaction strongly enhances the ground-state transitions. This finding sheds new light on existing discrepancies between previous theoretical and experimental results for these systems, as a weak ground state transition was predicted because of the spatial separation of the corresponding electron and hole state due to intrinsic fields whereas experimentally fast optical transitions have been observed.