arXiv subjects

Paul H. Mayrhofer

Publications and source records attributed to Paul H. Mayrhofer.

At least 19 recordsLinked to original sources

arXiv2026

A correlation of structural changes with nanomechanical properties in TiN-AlN multilayer films

The present work investigates the changes in overall nanomechanical properties of reactively sputtered TiN-AlN multilayer films arising due to phase transformation in the AlN layers. Multilayered TiN-AlN films were sputter deposited with constant TiN layer thickness of 5 nm while the AlN layer thickness varied between 1-5 nm. The AlN underwent a phase transition from cubic rock salt to hexagonal wurtzite above 3 nm thickness due to the lattice strains. The hardness and indentation modulus of the multilayers decreased with increasing AlN film thickness, up to 3 nm, due to increased volume fraction of softer AlN layer and then stabilized for 4 nm and 5 nm thickness films. Micropillar compression of these multilayers showed a transition from columnar brittle to partially ductile failure associated with crack deflection with increasing AlN film thickness. Interestingly, nanoindentation scratch resistance of 3 nm AlN multilayer was observed to be superior compared to all other films. The crack propagation behavior in scratching showed increased microcracking tendency towards higher AlN film thickness. This shows that cubic to hexagonal transformation in AlN is beneficial for improving the damage tolerance of the multilayer system.

cond-mat.mtrl-sci↗

arXiv2025

Machine-Learning Potentials Predict Orientation- and Mode-Dependent Fracture in Refractory Diborides

Fracture toughness ($K_\mathrm{Ic}$) and fracture strength ($σ_\mathrm{f}$) are key criteria in the selection and design of reliable ceramics. However, their experimental characterization remains challenging -- especially for ceramic thin films, where size and interfacial effects hinder accurate and reproducible measurements. Here, machine-learning interatomic potentials (MLIPs) trained on \textit{ab initio} datasets of single crystal models deformed up to fracture are used to characterize transgranular cleavage in pre-cracked ceramic diboride TMB$_2$ (TM = Ti, Zr, Hf) lattices through stress intensity factor ($K$)-controlled loading. Mode-I simulations performed across distinct crack geometries show that fracture is primarily driven by straight crack extension along the original plane. The corresponding macroscale fracture-initiation properties ($K_\mathrm{Ic} \approx 1.7$-2.9 MPa$\cdot\sqrt{\text{m}}$, $σ_\mathrm{f} \approx 1.6$-2.4 GPa) are extrapolated using established scaling laws. Considering TiB$_2$ as a representative system, additional simulations explore loading conditions ranging from pure Mode-I (opening) to Mode-II (sliding). TiB$_2$ models containing prismatic cracks exhibit their lowest fracture resistance under mixed-mode conditions, where the crack deflects onto pyramidal planes--as confirmed by nanoindentation tests on TiB$_2$(0001) thin films. This study establishes $K$-controlled, MLIP-based simulations as predictive tools for orientation- and mode-dependent fracture in ceramics. The approach is readily extendable to finite temperatures for evaluating fracture behavior under conditions relevant to refractory applications.

cond-mat.mtrl-sci↗

arXiv2025

Realizing Scalable Chemical Vapour Deposition of Monolayer Graphene Films on Iron with Concurrent Surface Hardening by in situ Observations

Graphene has been suggested as an ultimately thin functional coating for metallurgical alloys such as steels. However, even on pure iron (Fe), the parent phase of steels, growth of high quality graphene films remains largely elusive to date. We here report scalable chemical vapour deposition (CVD) of high quality monolayer graphene films on Fe substrates. To achieve this, we here elucidate the mechanisms of graphene growth on Fe using complementary in situ X-ray diffractometry (XRD) and in situ near ambient pressure X-ray photoelectron spectroscopy (NAP XPS) during our scalable CVD conditions. As key factors that set Fe apart from other common graphene CVD catalyst supports such as Ni or Cu, we identify that for Fe (i) carbothermal reduction of persistent Fe-oxides and (ii) kinetic balancing of carbon uptake into the Fe during CVD near the Fe-C eutectoid because of the complex multi-phased Fe-C phase diagram are critical. Additionally, we establish that the carbon uptake into the Fe during graphene CVD is not only important in terms of growth mechanism but can also be advantageously utilized for concurrent surface hardening of the Fe during the graphene CVD process akin to carburization/case hardening. Our work thereby forms a framework for controlled and scalable high-quality monolayer graphene film CVD on Fe incl. the introduction of concurrent surface hardening during graphene CVD.

cond-mat.mtrl-sci↗

arXiv2025

Machine-learning potentials for structurally and chemically complex MAB phases: strain hardening and ripplocation-mediated plasticity

Though offering unprecedented pathways to molecular dynamics (MD) simulations of technologically-relevant materials and conditions, machine-learning interatomic potentials (MLIPs) are typically trained for ``simple'' materials and properties with minor size effects. Our study of MAB phases (MABs) - alternating transition metal boride (MB) and group A element layers - exemplifies that MLIPs for complex materials can be fitted and used in a high-throughput fashion: for predicting structural and mechanical properties across a large chemical/phase/temperature space. Considering group 4-6 transition metal based MABs, with A=Al and the 222, 212, and 314 type phases, three MLIPs are trained and tested, including lattice and elastic constants calculations at temperatures $T\in\{0,300,1200\}$ K, extrapolation grade and energy (force, stress) error analysis for $\approx{3\cdot10^6}$ ab initio MD snapshots. Subsequently, nanoscale tensile tests serve to quantify upper limits of strength and toughness attainable in single-crystal MABs at 300~K as well as their temperature evolution. In-plane tensile deformation is characterised by relatively high strength, {110}$\langle001\rangle$ type slipping, and failure by shear banding. The response to [001] loading is softer, triggers work hardening, and failure by kinking and layer delamination. Furthermore, W$_2$AlB$_2$ able to retard fracture via ripplocations and twinning from 300 up to 1200~K.

cond-mat.mtrl-sci↗

arXiv2024

Phase stability and mechanical property trends for MAB phases by high-throughput ab initio calculations

MAB phases (MABs) are atomically-thin laminates of ceramic/metallic-like layers, having made a breakthrough in the development of 2D materials. Though theoretically offering a vast chemical and phase space, relatively few MABs have yet been synthesised. To guide experiments, we perform a systematic high-throughput {\it{ab initio}} screening of MABs that combine group 4--7 transition metals (M); Al, Si, Ga, Ge, or In (A); and boron (B) focusing on their phase stability trends and mechanical properties. Considering the 1:1:1, 2:1:1, 2:1:2, 3:1:2, 3:1:3, and 3:1:4 M:A:B ratios and 10 phase prototypes, possible stabilisation of a single-phase compound for each elemental combination is assessed through formation energy spectra of the competing mechanically and dynamically stable MABs. Based on the volumetric proximity of energetically-close phases, we identify systems in which volume-changing deformations may facilitate transformation toughening. Subsequently, chemistry- and phase-structure-related trends in the elastic stiffness and ductility are predicted using elastic-constants-based descriptors. The analysis of directional Cauchy pressures and Young's moduli allows comparing mechanical response parallel and normal to M--B/A layers. Among the suggested most promising MABs are Nb$_3$AlB$_4$, Cr$_2$SiB$_2$, Mn$_2$SiB$_2$ or the already synthesised MoAlB.

cond-mat.mtrl-sci↗

arXiv2023

Machine-learning potentials for nanoscale simulations of deformation and fracture: example of TiB$_2$ ceramic

Machine-learning interatomic potentials (MLIPs) offer a powerful avenue for simulations beyond length and timescales of ab initio methods. Their development for investigation of mechanical properties and fracture, however, is far from trivial since extended defects -- governing plasticity and crack nucleation in most materials -- are too large to be included in the training set. Using TiB$_2$ as a model ceramic material, we propose a strategy for fitting MLIPs suitable to simulate mechanical response of monocrystals until fracture. Our MLIP accurately reproduces ab initio stresses and failure mechanisms during room-temperature uniaxial tensile deformation of TiB$_2$ at the atomic scale ($\approx{10}^3$ atoms). More realistic tensile tests (low strain rate, Poisson's contraction) at the nanoscale ($\approx{10}^4$--10$^6$ atoms) require MLIP up-fitting, i.e. learning from additional ab initio configurations. Consequently, we elucidate trends in theoretical strength, toughness, and crack initiation patterns under different loading directions. To identify useful environments for further up-fitting, i.e., making the MLIP applicable to a wider spectrum of simulations, we asses transferability to other deformation conditions and phases not explicitly trained on.

cond-mat.mtrl-sci↗

arXiv2023

On energetics of allotrope transformations in transition-metal diborides via plane-by-plane shearing

Transition metal diborides crystallise in the $α$, $γ$, or $ω$ type structure, in which pure transition metal layers alternate with pure boron layers stacked along the hexagonal [0001] axis. Here we view the prototypes as different stackings of the transition metal planes and suppose they can transform from one into another by a displacive transformation. Employing first-principles calculations, we simulate sliding of individual planes in the group IV-VII transition metal diborides along a transformation pathway connecting the $α$, $γ$, and $ω$ structure. Chemistry-related trends are predicted in terms of energetic and structural changes along a transformation pathway, together with the mechanical and dynamical stability of the different stackings. Our results suggest that MnB$_2$ and MoB$_2$ possess the overall lowest sliding barriers among the investigated TMB$_2$s. Furthermore, we discuss trends in strength and ductility indicators, including Young's modulus or Cauchy pressure, derived from elastic constants.

cond-mat.mtrl-sci↗

arXiv2019

Point-defect engineering of MoN/TaN superlattice films: A first-principles and experimental study

Superlattice architecture represents an effective strategy to improve performance of hard protective coatings. Our model system, MoN/TaN, combines materials well-known for their high ductility as well as a strong driving force for vacancies. In this work, we reveal and interpret peculiar structure-stability-elasticity relations for MoN/TaN combining modelling and experimental approaches. Chemistry of the most stable structural variants depending on various deposition conditions is predicted by Density Functional Theory calculations using the concept of chemical potential. Importantly, no stability region exists for the defect-free superlattice. The X-ray Diffraction and Energy-dispersive $\text{X-ray}$ Spectroscopy experiments show that MoN/TaN superlattices consist of distorted fcc building blocks and contain non-metallic vacancies in MoN layers, which perfectly agrees with our theoretical model for these particular deposition conditions. The vibrational spectra analysis together with the close overlap between the experimental indentation modulus and the calculated Young's modulus points towards MoN$_{0.5}$/TaN as the most likely chemistry of our coatings.

cond-mat.mtrl-sci↗

arXiv2018

High-entropy ceramic thin films; A case study on transition metal diborides

High-entropy materials often outperform their lower-entropy relatives in various aspects, such as thermal stability and fracture toughness. While there are extensive research activities in the field of high-entropy alloys, comparably little is performed for high-entropy ceramics, and especially for high-entropy diborides. Here we show, that not only the hardness of ZrB2 layers can be improved from 43.2 to 45.8 to 47.2 GPa through the formation of solid solution ternary diborides (Zr0.61Ti0.39B2) and high-entropy diborides (Zr0.23Ti0.20Hf0.19V0.14Ta0.24B2), respectively, but especially their thermal stability against structural rearrangements and decomposition towards the constituting binary diborides.

cond-mat.mtrl-sci↗

arXiv2017

Vacancy-driven extended stability of cubic metastable Ta-Al-N and Nb-Al-N phases

Quantum mechanical calculations had been previously applied to predict phase stability in many ternary and multinary nitride systems. While the predictions were very accurate for the Ti-Al-N system, some discrepancies between theory and experiment were obtained in the case of other systems. Namely, in the case of Ta-Al-N, the calculations tend to overestimate the minimum Al content necessary to obtain a metastable solid solution with a cubic structure. In this work, we present a comprehensive study of the impact of vacancies on the phase fields in quasi-binary TaN-AlN and NbN-AlN systems. Our calculations clearly show that presence of point defects strongly enlarges the cubic phase field in the TaN-AlN system, while the effect is less pronounced in the NbN-AlN case. The present phase stability predictions agree better with experimental observations of physical vapour deposited thin films reported in the literature than that based on perfect, non-defected structures. This study shows that a representative structural model is crucial for a meaningful comparison with experimental data.

cond-mat.mtrl-sci↗

arXiv2017

Stability and elasticity of metastable solid solutions and superlattices in the MoN-TaN system: a first-principles study

Employing ab initio calculations, we discuss chemical, mechanical, and dynamical stability of MoN-TaN solid solutions together with cubic-like MoN/TaN superlattices, as another materials design concept. Hexagonal-type structures based on low-energy modifications of MoN and TaN are the most stable ones over the whole composition range. Despite being metastable, disordered cubic polymorphs are energetically significantly preferred over their ordered counterparts. An in-depth analysis of atomic environments in terms of bond lengths and angles reveals that the chemical disorder results in (partially) broken symmetry, i.e., the disordered cubic structure relaxes towards a hexagonal NiAs-type phase, the ground state of MoN. Surprisingly, also the superlattice architecture is clearly favored over the ordered cubic solid solution. We show that the bi-axial coherency stresses in superlattices break the cubic symmetry beyond simple tetragonal distortions and lead to a new tetragonal $ζ$-phase (space group P4/nmm), which exhibits a more negative formation energy than the symmetry-stabilized cubic structures of MoN and TaN. Unlike cubic TaN, the $ζ\text{-TaN}$ is elastically and vibrationally stable, while $ζ$-MoN is stabilized only by the superlattice structure. To map compositional trends in elasticity, we establish mechanical stability of various Mo$_{1-x}$Ta$_x$N systems and find the closest high-symmetry approximants of the corresponding elastic tensors. According to the estimated polycrystalline moduli, the hexagonal polymorphs are predicted to be extremely hard, however, less ductile than the cubic phases and superlattices. The trends in stability based on energetics and elasticity are corroborated by density of electronic states.

cond-mat.mtrl-sci↗

arXiv2016

Point defects stabilise cubic Mo-N and Ta-N

We employ \textit{ab initio} calculations to investigate energetics of point defects in metastable rocksalt cubic Ta-N and Mo-N. Our results reveal a strong tendency to off-stoichiometry, i.e. defected structures are predicted to be more stable than perfect ones with 1:1 metal-to-nitrogen stoichiometry, in agreement with previous literature reports. While Ta-N significantly favours metal vacancies, Mo-N exhibits similar energies of formation regardless of the vacancy type ($V_\text{Mo}$, $V_\text{N}$) as long as their concentration is below $\approx15\,\text{at.\%}$. The overall lowest energy of formation were obtained for $\text{Ta}_{0.78}\text{N}$ and $\text{Mo}_{0.91}\text{N}$, which are hence predicted to be the most stable compositions. To account for various experimental condition during synthesis, we further evaluated the phase stability as a function of chemical potential of individual species. The proposed phase diagrams reveal four stable compositions, $\text{Mo}_{0.84}\text{N}$, $\text{Mo}_{0.91}\text{N}$, $\text{MoN}_{0.69}$ and $\text{MoN}_{0.44}$, in the case of Mo-N and nine stable compositions in the case of Ta-N indicating the crucial role of metal under-stoichiometry, since $\text{Ta}_{0.75}\text{N}$ and $\text{Ta}_{0.78}\text{N}$ significantly dominate the diagram. These results are important for understanding and designing experiments using non-equilibrium deposition techniques. Finally, we discuss a role of defects ordering and estimate a cubic lattice parameter as a function of a defect contents.

cond-mat.mtrl-sci↗

arXiv2015

Structural and mechanical properties of nitrogen-deficient cubic Cr-Mo-N and Cr-W-N systems

The tendency for nitrogen deficiency in cubic Cr-Mo-N and Cr-W-N solid solutions is predicted by a comprehensive evaluation of the lattice spacing, mixing thermodynamics, and elastic properties using first-principles calculations and experimentally confirmed by means of X-ray diffraction. A major conclusion is that these systems exhibit significant amount of N vacancies whose amount scales linearly with the TM content, hence making the Cr1-xTMxN1-0.5x chemical formula more precise and informative to describe the chemical composition of cubic Cr-Mo-N and Cr-W-N solid solutions as compared with the conventionally used Cr1-xTMxN. The cubic Cr1-xMoxN1-0.5x and Cr1-xWxN1-0.5x solid solutions exhibit large positive mixing enthalpies towards isostructural phase decomposition into cubic B1-CrN and γ-Mo2N or γ-W2N, respectively. Their ductility increases with increasing Mo or W content and both systems exhibit significantly direction-dependent Young's moduli over the entire composition range, even when using the approach to study their polycrystalline behavior. The excellent agreement between experimentally obtained lattice parameters, Mo- and W-dependent nitrogen content, elastic properties and their calculated values for our model descriptions, Cr1-xMoxN1-0.5x and Cr1-xWxN1-0.5x, allows to understand these complex material systems. Based on our results, we can conclude that their content of nitrogen vacancies scales with half of the alloying content Mo or W.

cond-mat.mtrl-sci↗

arXiv2014

Impact of point defects on the electronic structure of paramagnetic CrN

This paper presents first principles calculations of paramagnetic cubic CrN$_x$ with the aim to provide deeper insight into recently published transmission electron microscopy-based study on this material. Among several types of point defects which may result in N-deficient material, N vacancy is found to be energetically preferred to Cr interstitial and anti-sites. Electron Energy Loss Near Edge Structure of N K-edge transition is calculated for various concentrations of N vacancies in CrN$_x$, yielding the same trends as experimentally observed. Analysis of the electronic structure reveals decreased charge transfer from Cr sites with increased N vacancy content, hence increasing the metallic character of the defected material. Finally, the electronic structure is found to be strongly dependent on the local environment (i.e. presence of the N vacancies).

cond-mat.mtrl-sci↗

arXiv2014

Structural stability and thermodynamics of CrN magnetic phases from ab initio 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.

cond-mat.mtrl-sci↗

arXiv2014

Macroscopic Elastic Properties of Textured ZrN--AlN Polycrystalline Aggregates: From Ab initio Calculations to Grain-Scale Interactions

Despite the fast development of computational materials modelling, theoretical description of macroscopic elastic properties of textured polycrystalline aggregates starting from basic principles remains a challenging task. In this communication we use a supercell-based approach to obtain the elastic properties of random solid solution cubic ZrAlN system as a function of the metallic sublattice composition and texture descriptors. The employed special quasi-random structures are optimised not only with respect to short range order parameters, but also to make the three cubic directions $[1\,0\,0]$, $[0\,1\,0]$, and $[0\,0\,1]$ as similar as possible. In this way, only a small spread of elastic constants tensor components is achieved and an optimum trade-off between modelling of chemical disorder and computational limits regarding the supercell size is achieved. The single crystal elastic constants are shown to vary smoothly with composition, yielding $x\approx0.4$-0.5 an alloy constitution with an almost isotropic response. Consequently, polycrystals with this composition are suggested to have Young's modulus independent on the actual microstructure. This is indeed confirmed by explicit calculations of polycrystal elastic properties, both within the isotropic aggregate limit, as well as with fibre textures with various orientations and sharpness. It turns out, that for low AlN mole fractions, the spread of the possible Young's moduli data caused by the texture variation can be larger than 100 GPa. Consequently, our discussion of Young's modulus data of cubic ZrAlN contains also the evaluation of the texture typical for thin films.

cond-mat.mtrl-sci↗

arXiv2013

Alloying-related trends from first principles: An application to the Ti--Al--X--N system

Tailoring and improving material properties by alloying is a long-known and used concept. Recent research has demonstrated the potential of ab initio calculations in understanding the material properties at the nanoscale. Here we present a systematic overview of alloying trends when early-transition metals (Y, Zr, Nb, Hf, Ta) are added in the Ti$_{1-x}$Al$_x$N system, routinely used as a protective hard coating. The alloy lattice parameters tend to be larger than the corresponding linearised Vegard's estimation, with the largest deviation more than 2.5% obtained for Y$_{0.5}$Al$_{0.5}$N. The chemical strengthening is most pronounced for Ta and Nb, although also causing smallest elastic distortions of the lattice due to their atomic radii being comparable with Ti and Al. This is further supported by the analysis of the electronic density of states. Finally, mixing enthalpy as a measure of the driving force for decomposition into the stable constituents, is enhanced by adding Y, Zr and Nb, suggesting that the onset of spinodal decomposition will appear in these cases for lower thermal loads than for Hf and Ta alloyed Ti$_{1-x}$Al$_x$N.

cond-mat.mtrl-sci↗

arXiv2012

First-principles study of elastic properties of Cr-Al-N

The elastic properties of paramagnetic cubic B1 (c-) Cr1-xAlxN ternary alloys are studied using stress-strain and energy-strain methods within the framework of Density Functional Theory (DFT). A strong compositional dependence of the elastic properties is predicted. Young's modulus, E, and shear modulus, G, exhibit the same compositional trends as experimentally measured hardness values (i.e. increasing with Al content), while bulk modulus, B, remains almost constant. The isotropic elastic response in the c-Cr1-xAlxN is predicted for concentrations around x=0.50. Brittle behavior and directional bonding characteristics are predominant in the c-Cr1-xAlxN coatings in the whole composition range, and become more pronounced with increasing Al content.

cond-mat.mtrl-sci↗