Dr. Yujiao Li
Center for Interface-Dominated High Performance Materials (ZGH)
- Atomic scale understanding of phase stability and decomposition of a nanocrystalline CrMnFeCoNi Cantor alloy
Li, Y.J. and Savan, A. and Ludwig, A.
Applied Physics Letters 119 (2021)High entropy alloys (HEAs) provide superior mechanical and functional properties. However, these advantages may disappear when a metastable single-phase solid solution decomposes at low temperatures upon long-term annealing. Therefore, understanding the underlying phase separation mechanisms is important for the design of new HEAs with controlled properties. In the current work, the thermal stability of a nanocrystalline CrMnFeCoNi HEA was investigated at different annealing conditions using a combinatorial processing platform, involving fast and parallel synthesis of nanocrystalline thin films, short annealing time for a rapid phase evolution, and direct characterization by atom probe tomography. The microstructural features of the decomposed CrMnFeCoNi alloy as well as its decomposition process were analyzed in terms of elemental distributions at the near-atomic scale. The results show that the segregation of Ni and Mn to grain boundaries in the initial single-phase alloy is a prerequisite and is observed to be the only occurring physical process at the early stage of phase decomposition. When the concentrations of Ni and Mn reach a certain value, phase decomposition starts and a MnNi-rich phase forms at grain boundaries. Next, two Cr-rich phases form at the interface between the MnNi-rich phase and the matrix. Meanwhile, a FeCo-rich phase forms in the grain interior. Based on these observations, the underlying mechanisms involving nucleation, diffusivity as well as thermodynamic considerations were discussed. © 2021 Author(s).
view abstract 10.1063/5.0069107
- Chemical Vapor Deposition of Cobalt and Nickel Ferrite Thin Films: Investigation of Structure and Pseudocapacitive Properties
Zywitzki, D. and Schaper, R. and Ciftyürek, E. and Wree, J.-L. and Taffa, D.H. and Baier, D.M. and Rogalla, D. and Li, Y. and Meischein, M. and Ludwig, A. and Li, Z. and Schierbaum, K. and Wark, M. and Devi, A.
Advanced Materials Interfaces 8 (2021)Transition metal ferrites, such as CoFe2O4 (CFO) and NiFe2O4 (NFO), have gained increasing attention as potential materials for supercapacitors. Since chemical vapor deposition (CVD) offers advantages like interface quality to the underlying substrates and the possibility for coverage of 3D substrates, two CVD processes are reported for CFO and NFO. Growth rates amount to 150 to 200 nm h−1 and yield uniform, dense, and phase pure spinel ferrite films according to X-ray diffraction (XRD), Raman spectroscopy, Rutherford backscattering spectrometry and nuclear reaction analysis (RBS/NRA) and scanning electron microscopy (SEM). Atom probe tomography (APT) and synchrotron X-ray photoelectron spectroscopy (XPS) give insights into the vertical homogeneity and oxidation states in the CFO films. Cation disorder of CFO is analyzed for the first time from synchrotron-based XPS. NFO is analyzed via lab-based XPS. Depositions on conducting Ni and Ti substrates result in electrodes with pseudocapacitive behavior, as evidenced by cyclovoltammetry (CV) experiments. The interfacial capacitances of the electrodes are up to 185 µF cm−2. © 2021 The Authors. Advanced Materials Interfaces published by Wiley-VCH GmbH
view abstract 10.1002/admi.202100949
- Complex-Solid-Solution Electrocatalyst Discovery by Computational Prediction and High-Throughput Experimentation**
Batchelor, T.A.A. and Löffler, T. and Xiao, B. and Krysiak, O.A. and Strotkötter, V. and Pedersen, J.K. and Clausen, C.M. and Savan, A. and Li, Y. and Schuhmann, W. and Rossmeisl, J. and Ludwig, Al.
Angewandte Chemie - International Edition (2021)Complex solid solutions (“high entropy alloys”), comprising five or more principal elements, promise a paradigm change in electrocatalysis due to the availability of millions of different active sites with unique arrangements of multiple elements directly neighbouring a binding site. Thus, strong electronic and geometric effects are induced, which are known as effective tools to tune activity. With the example of the oxygen reduction reaction, we show that by utilising a data-driven discovery cycle, the multidimensionality challenge raised by this catalyst class can be mastered. Iteratively refined computational models predict activity trends around which continuous composition-spread thin-film libraries are synthesised. High-throughput characterisation datasets are then used as input for refinement of the model. The refined model correctly predicts activity maxima of the exemplary model system Ag-Ir-Pd-Pt-Ru. The method can identify optimal complex-solid-solution materials for electrocatalytic reactions in an unprecedented manner. © 2021 The Authors. Angewandte Chemie International Edition published by Wiley-VCH GmbH
view abstract 10.1002/anie.202014374
- Correlation between grain size and carbon content in white etching areas in bearings
Mayweg, D. and Morsdorf, L. and Li, Y. and Herbig, M.
Acta Materialia 215 (2021)Premature failure of bearings during rolling contact fatigue is often associated with the formation of white etching cracks (WECs). Crack surface rubbing of WECs transforms the original bainitic/martensitic microstructure into white etching areas (WEAs), comprised of nanocrystalline ferrite. The grain size and carbon content vary within the WEA. Here, we show by atom probe tomography and scanning electron microscopy, that there is an inversely proportional relationship between grain size and carbon content in WEAs formed in 100Cr6 bearings that failed by WECs in service. We explain this phenomenon by the reduction of grain boundary energy through carbon segregation. Depending on the carbon content, this reduces the driving force for recrystallization and grain coarsening, thereby stabilizing the nanocrystalline microstructure. No such effect is observed for the substitutional element chromium. The smallest grain size (< 10 nm) is found directly next to decomposing cementite precipitates, which act as carbon sources, leading to carbon contents as high as ~9.5 at% in ferrite. Correspondingly, the WEA segments with the lowest carbon contents exhibit the largest grain sizes. Increasing carbon contents in sub regions of WEAs do not only lead to smaller grain sizes but also to higher average carbon contents at the grain boundaries as well as in the grain interior. Our results show that the mechanisms of ferrite microstructure stabilization through carbon grain boundary segregation shown in model experiments are also valid for the microstructure alterations associated with WEC failure occurring in practical bearing applications of the technical alloy 100Cr6. © 2021
view abstract 10.1016/j.actamat.2021.117048
- Effect of cooling rate on the microstructure and mechanical properties of a low-carbon low-alloyed steel
Wang, H. and Cao, L. and Li, Y. and Schneider, M. and Detemple, E. and Eggeler, G.
Journal of Materials Science 56 (2021)Heavy plate steels with bainitic microstructures are widely used in industry due to their good combination of strength and toughness. However, obtaining optimal mechanical properties is often challenging due to the complex bainitic microstructures and multiple phase constitutions caused by different cooling rates through the plate thickness. Here, both conventional and advanced microstructural characterization techniques which bridge the meso- and atomic-scales were applied to investigate how microstructure/mechanical property-relationships of a low-carbon low-alloyed steel are affected by phase transformations during continuous cooling. Mechanical tests show that the yield strength increases monotonically when cooling rates increase up to 90 K/s. The present study shows that this is associated with a decrease in the volume fraction of polygonal ferrite (PF) and a refinement of the substructure of degenerated upper bainite (DUB). The fine DUB substructures feature C-rich retained austenite/martensite-austenite (RA/M-A) constitutes which decorate the elongated micrograin boundaries in ferrite. A further increase in strength is observed when needle-shaped cementite precipitates form during water quenching within elongated micrograins. Pure martensite islands on the elongated micrograin boundaries lead to a decreased ductility. The implications for thick section plate processing are discussed based on the findings of the present work. © 2021, The Author(s).
view abstract 10.1007/s10853-021-05974-3
- Investigation of an atomic-layer-deposited Al2O3 diffusion barrier between Pt and Si for the use in atomic scale atom probe tomography studies on a combinatorial processing platform
Li, Y. and Zanders, D. and Meischein, M. and Devi, A. and Ludwig, A.
Surface and Interface Analysis 53 (2021)In order to enable the application of atomic probe tomography combinatorial processing platforms for atomic-scale investigations of phase evolution at elevated temperatures, the pre-sharpened Si tip of 10–20 nm in diameter must be protected against interdiffusion and reaction of the reactive Si with a film of interest by a conformal coating on the Si tip. It is shown that unwanted reactions can be suppressed by introducing a 20-nm-thick intermediate Al2O3 layer grown by atomic layer deposition (ALD). As a representative case, Pt is chosen as a film of interest, as it easily forms silicides. Whereas without the ALD coating diffusion/reactions occur, with the protective film, this is prevented for temperatures up to at least 600°C. The effectiveness of the Al2O3 layer serving as a diffusion barrier is not limited to a sharpened Si tip but works generally for all cases where a Si substrate is used. © 2021 The Authors. Surface and Interface Analysis published by John Wiley & Sons Ltd.
view abstract 10.1002/sia.6955
- Correlative chemical and structural investigations of accelerated phase evolution in a nanocrystalline high entropy alloy
Li, Y.J. and Kostka, A. and Savan, A. and Ludwig, Al.
Scripta Materialia 183 (2020)Based on our recently-developed combinatorial processing platforms for accelerated investigations of phase evolution in multinary alloys, a novel correlative atom probe tomography and transmission electron microscopy approach is proposed to study phase stability in a nanocrystalline CrMnFeCoNi alloy. We observed that the material can decompose at 250 °C for 5 h or 300 °C for 1 h, having the same decomposed products as in its coarse-grained counterpart after annealing at 500 °C for 500 days. A low apparent activation energy for the diffusion of Ni in the nanocrystalline alloy is derived and explains the fast kinetics of phase decomposition in nanocrystalline alloys. © 2020 Acta Materialia Inc.
view abstract 10.1016/j.scriptamat.2020.03.016
- Generalized stability criterion for exploiting optimized mechanical properties by a general correlation between phase transformations and plastic deformations
Huang, L. and Lin, W. and Zhang, Y. and Feng, D. and Li, Y. and Chen, X. and Niu, K. and Liu, F.
Acta Materialia 201 (2020)Designing structured materials with optimized mechanical properties generally focuses on engineering microstructures, which are closely determined by the processing routes, such as phase transformations. However, the direct connection between phase transformations and mechanical properties remains largely unexplored. Here, we propose a new concept of generalized stability (GS) to correlate phase transformations with plastic deformations in terms of the trade-off relationship that exists between thermodynamics and kinetics. We then suggest that, to achieve structured materials with excellent strength–plasticity combinations, phase transformations and/or plastic deformations with high GS, thermodynamic driving force (ΔG), and kinetic activation energy (Q), are highly expected. We verify the GS concept against a phase transformation-modulated nanostructured Fe alloy, for which an ultrahigh yield strength of 2.61 GPa and an ultimate compressive strength of 3.32 GPa while having a total strain to failure of 35% are achieved via multiple strengthening and hardening mechanisms. A theoretical analysis, in combination with microstructural characterization, indicates that the desired thermo-kinetic parameter triplets (i.e., high GS-high ΔG-high Q) could be inherited from the phase transformation to the plastic deformation, which ultimately yields good mechanical performance. The proposed concept can be regarded as the first theoretical criterion or a general rule that correlates phase transformation with plastic deformation, and can assist in the rapid selection of phase transformations to facilitate superior mechanical properties. © 2020
view abstract 10.1016/j.actamat.2020.10.005
- High temperature creep resistance of a thermally stable nanocrystalline Fe-5 at.% Zr steel
Shan, G.B. and Chen, Y.Z. and Li, Y.J. and Zhang, C.Y. and Dong, H. and Cong, Y.B. and Zhang, W.X. and Huang, L.K. and Suo, T. and Liu, F.
Scripta Materialia 179 (2020)The application of nanocrystalline (NC) materials at high temperatures is challenging due to their poor thermal stability or low creep resistance. Here we report that a thermally stable NC Fe-5 at.% Zr steel produced by High-Pressure-Thermal-Compression sintering exhibits an excellent creep resistance (with a creep rate of 3.92 × 10−8 s−1 at 923 K and under the applied stress of 250 MPa). The excellent creep resistance is ascribed to its highly stable NC structure stabilized by nano-sized precipitates. Mechanical testing suggests that the creep of the NC Fe-5 at.% Zr steel is controlled by dislocation activities rather than diffusion dominated mechanisms. © 2019
view abstract 10.1016/j.scriptamat.2019.12.036
- Mechanism of collective interstitial ordering in Fe–C alloys
Zhang, X. and Wang, H. and Hickel, T. and Rogal, J. and Li, Y. and Neugebauer, J.
Nature Materials 19 (2020)Collective interstitial ordering is at the core of martensite formation in Fe–C-based alloys, laying the foundation for high-strength steels. Even though this ordering has been studied extensively for more than a century, some fundamental mechanisms remain elusive. Here, we show the unexpected effects of two correlated phenomena on the ordering mechanism: anharmonicity and segregation. The local anharmonicity in the strain fields induced by interstitials substantially reduces the critical concentration for interstitial ordering, up to a factor of three. Further, the competition between interstitial ordering and segregation results in an effective decrease of interstitial segregation into extended defects for high interstitial concentrations. The mechanism and corresponding impact on interstitial ordering identified here enrich the theory of phase transitions in materials and constitute a crucial step in the design of ultra-high-performance alloys. © 2020, The Author(s), under exclusive licence to Springer Nature Limited.
view abstract 10.1038/s41563-020-0677-9
- Moving cracks form white etching areas during rolling contact fatigue in bearings
Morsdorf, L. and Mayweg, D. and Li, Y. and Diederichs, A. and Raabe, D. and Herbig, M.
Materials Science and Engineering A 771 (2020)White etching cracks (WECs) and the associated white etching areas (WEAs) are responsible for failure of widely spread engineering applications such as bearings and railways. Although the phenomenon is known for more than 100 years, the underlying mechanisms are still a matter of debate. In this work, we thoroughly investigate a 100Cr6 wind turbine gearbox bearing after failure in service operation. Based on our findings from detailed microstructure characterization on multiple length scales we formulate a new consistent explanation for the formation of WEAs during rolling contact fatigue. We propose a mechanism of moving WECs - not only in terms of conventional crack propagation but also as a movement of the crack normal to its plane. During cyclic loading the crack continuously changes its position and leaves behind a severely plastically deformed area consisting of ferritic nano-grains, i.e. the WEAs. The atomic-scale delocalization of the crack plane in a single loading cycle adds up to micron-sized WEAs during repetitive loading/unloading. After the initial formation of a fatigue crack around inclusions, crack face rubbing occurs during compressive loading cycles. This leads to the formation of WEA by local severe plastic deformation. It also leads to partial cohesion of the abutting crack faces and material transport between them. As a result, the WEC opens at a slightly shifted position with respect to its former location during unloading. © 2019 Elsevier B.V.
view abstract 10.1016/j.msea.2019.138659
- Phase decomposition in a nanocrystalline CrCoNi alloy
Li, Y.J. and Kostka, A. and Savan, A. and Ludwig, Al.
Scripta Materialia 188 (2020)Phase stability of a nanocrystalline CrCoNi alloy is investigated using the combinatorial processing platform approach, which enables synthesis, processing and direct atomic-scale characterizations of alloys by atom probe tomography and transmission electron microscopy. Phase decomposition with formation of CoNi-rich phase occurs faster in the smaller (10 nm) grain-sized region than the larger one (20 nm), both being present in the same sample. Chemical analyses indicate that diffusion of Co and Cr plays an important role in phase decomposition. Comparison of phase stability between CrMnFeCoNi and CrCoNi implies that elemental segregation may promote phase decomposition by providing an additional chemical driving force for it. © 2020 Acta Materialia Inc.
view abstract 10.1016/j.scriptamat.2020.07.054
- Revealing the two-step nucleation and growth mechanism of vanadium carbonitrides in microalloyed steels
Wang, H. and Li, Y. and Detemple, E. and Eggeler, G.
Scripta Materialia 187 (2020)Combining high-resolution transmission electron microscopy (HR-TEM) and 3-dimensional atom probe tomography (3D-APT), the early stages of nucleation and growth of vanadium carbonitrides (VCN) were revealed. VCN nucleation starts with locally distorted body-centered cubic (bcc) lattices due to a substitution of Fe atoms by V atoms, which results in the formation of an intermediate coherent crystal structure within the ferrite matrix. Misfit strain self-accommodation leads to twining within the VCN particles. As the particles grow, the precipitates gradually lose coherency and grow into discs or plates. Simultaneously, the intermediate crystal structure of the nucleus transforms into the equilibrium VCN-structure. © 2020
view abstract 10.1016/j.scriptamat.2020.06.041
- Solute hydrogen and deuterium observed at the near atomic scale in high-strength steel
Breen, A.J. and Stephenson, L.T. and Sun, B. and Li, Y. and Kasian, O. and Raabe, D. and Herbig, M. and Gault, B.
Acta Materialia 188 (2020)Observing solute hydrogen (H) in matter is a formidable challenge, yet, enabling quantitative imaging of H at the atomic-scale is critical to understand its deleterious influence on the mechanical strength of many metallic alloys that has resulted in many catastrophic failures of engineering parts and structures. Here, we report on the APT analysis of hydrogen (H) and deuterium (D) within the nanostructure of an ultra-high strength steel with high resistance to hydrogen embrittlement. Cold drawn, severely deformed pearlitic steel wires (Fe–0.98C–0.31Mn–0.20Si–0.20Cr–0.01Cu–0.006P–0.007S wt%, ε=3.1) contains cementite decomposed during the pre-deformation of the alloy and ferrite. We find H and D within the decomposed cementite, and at some interfaces with the surrounding ferrite. To ascertain the origin of the H/D signal obtained in APT, we explored a series of experimental workflows including cryogenic specimen preparation and cryogenic-vacuum transfer from the preparation into a state-of-the-art atom probe. Our study points to the critical role of the preparation, i.e. the possible saturation of H-trapping sites during electrochemical polishing, how these can be alleviated by the use of an outgassing treatment, cryogenic preparation and transfer prior to charging. Accommodation of large amounts of H in the under-stoichiometric carbide likely explains the resistance of pearlite against hydrogen embrittlement. © 2020 Acta Materialia Inc.
view abstract 10.1016/j.actamat.2020.02.004
- Effect of Nb on improving the impact toughness of Mo-containing low-alloyed steels
Wang, H.C. and Somsen, C. and Li, Y.J. and Fries, S.G. and Detemple, E. and Eggeler, G.
Journal of Materials Science 54 (2019)The microalloying of low-alloyed steels with Nb can improve the strength-to-toughness balance. Such an effect of Nb is usually ascribed to the refinement of the grain structure occurring in the austenite regime during hot forming. In the present work, we report that Nb enhances the impact toughness of a low-alloyed Cr–Mo steel by a mechanism which has not been appreciated so far. The lower impact toughness in the Nb-free Cr–Mo steel is due to segregation of Mo to boundaries, which facilitates the formation of fine Mo-rich ξ-phase carbides lining up along the boundaries. This further promotes the nucleation and propagation of microcracks. The addition of Nb leads to the formation of Mo-enriched NbC particles. The interfaces between these particles and the matrix supply new preferential sites for precipitation of Mo-rich ξ-phase carbides upon subsequent tempering. In this way, Nb additions result in a decrease of Mo segregation to boundaries, significantly reducing the precipitation of ξ-phase carbides on grain boundaries, thus leading to improved impact toughness. In addition to the classical microstructural explanation (grain size effect), this chemical role of Nb sheds new light on the design strategies of advanced low-alloyed steels with optimized strength-to-toughness ratios. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.
view abstract 10.1007/s10853-019-03374-2
- Photocurrent Recombination through Surface Segregation in Al-Cr-Fe-O Photocathodes
Stein, H.S. and Zhang, S. and Li, Y. and Scheu, C. and Ludwig, Al.
Zeitschrift fur Physikalische Chemie (2019)Chemical surface segregation is a design variable in the optimization of phocathodes but has largely been investigated through surface passivation or decoration. In this study a long charge carrier lifetime material, Al-Cr-Fe-O, exhibiting strong photocurrent recombination is investigated for its atomic scale crystallographic and chemical inhomogeneity. Combined scanning transmission electron microscopy and atom probe tomography unveils that insulating Al- and Cr-rich surface layers form during processing. These are discussed to be the primary reason for experimentally observed charge carrier recombination. This study highlights the importance of processing in the design, discovery and optimization of new light absorber materials for photoelectrochemical water splitting. ©2019 Walter de Gruyter GmbH, Berlin/Boston.
view abstract 10.1515/zpch-2019-1459
- Accelerated atomic-scale exploration of phase evolution in compositionally complex materials
Li, Y.J. and Savan, A. and Kostka, A. and Stein, H.S. and Ludwig, Al.
Materials Horizons 5 (2018)Combining nanoscale-tip arrays with combinatorial thin film deposition and processing as well as direct atomic-scale characterization (APT and TEM) enables accelerated exploration of the temperature- and environment-dependent phase evolution in multinary materials systems. Results from nanocrystalline CrMnFeCoNi show that this alloy is unstable and already decomposes after 1 h at low temperatures of around 300 °C. The combinatorial processing platform approach is extendible to explore oxidation and corrosion in complex structural and functional materials on the atomic scale. © 2018 The Royal Society of Chemistry.
view abstract 10.1039/c7mh00486a
- Atomic-scale investigation of fast oxidation kinetics of nanocrystalline CrMnFeCoNi thin films
Li, Y.J. and Kostka, A. and Savan, A. and Ludwig, Al.
Journal of Alloys and Compounds 766 (2018)Atom probe tomography was combined with transmission electron microscopy to characterize in atomic detail the structure of nanocrystalline high entropy alloy CrMnFeCoNi thin films before and after exposure to air at 500 °C for 5 min. Mn and Cr oxide scales were observed on the surface of the sample. These results on the nanoscale for short experimental time agree with literature reports on bulk counterparts after oxidation at 900 °C for 100 h, which means that the oxidation performance of complex materials can be tested in an accelerated way. Moreover, oxidation-related sub-surface depletion of Mn and Cr together with partial decomposition of the initial Cantor phase yield a FeCo-B2 sub-surface phase. In comparison to coarse-grained bulk material, the faster oxidation of the nanocrystalline material was attributed to an enhanced outwards diffusion of Cr and Mn along grain boundaries and within the newly formed B2 phase. © 2018 Elsevier B.V.
view abstract 10.1016/j.jallcom.2018.07.048
- Grain boundary-constrained reverse austenite transformation in nanostructured Fe alloy: Model and application
Huang, L. and Lin, W. and Wang, K. and Song, S. and Guo, C. and Chen, Y. and Li, Y. and Liu, F.
Acta Materialia 154 (2018)Reverse austenite transformation (RAT) is critical for designing advanced high-strength steels (AHSS), which, however, has not been sufficiently studied in nanostructured (NS) steels or Fe alloys, and hence not fully understood yet. Herein, the RAT (e.g. ferrite to austenite) kinetics in the NS Fe alloy upon continuous heating was experimentally and theoretically investigated, where, the ultrafine austenite characterized by a sluggish growth velocity and a high thermal stability, and additionally, an appreciable solute partitioning detected using atom probe microscopy, indicate the diffusion-controlled mechanism of RAT. The double-edged role of grain boundaries (GBs) in the NS alloy is elucidated, i.e. enhancing the diffusivity due to the type-A kinetics, and simultaneously, facilitating the formation of constrained diffusion field mainly due to the segmented effect of GB nucleation. On this basis, a modified diffusion model incorporating the effect of GBs is implemented to understand the GB-constrained austenite growth and the associated partitioning behavior, and further complemented with Cahn model, an austenite growth model is applied to predict the overall kinetics of RAT in the NS Fe alloy. It then follows that a strategy by combination of diffusion-controlled growth model and microstructure model could serve as a framework to predict the kinetics of RAT in the NS alloys. Regarding the RAT kinetics in the NS alloys, the present work uncovers the ‘GB-constrained’ mechanism, which is expected to offer the potential application for nanostructure manipulation in the development of AHSS. © 2018 Acta Materialia Inc.
view abstract 10.1016/j.actamat.2018.05.021
- Multiscale Characterization of Microstructure in Near-Surface Regions of a 16MnCr5 Gear Wheel After Cyclic Loading
Medghalchi, S. and Jamebozorgi, V. and Bala Krishnan, A. and Vincent, S. and Salomon, S. and Basir Parsa, A. and Pfetzing, J. and Kostka, A. and Li, Y. and Eggeler, G. and Li, T.
JOM (2018)The dependence of the microstructure on the degree of deformation in near-surface regions of a 16MnCr5 gear wheel after 2.1 × 106 loading cycles has been investigated by x-ray diffraction analysis, transmission electron microscopy, and atom probe tomography. Retained austenite and large martensite plates, along with elongated lamella-like cementite, were present in a less deformed region. Comparatively, the heavily deformed region consisted of a nanocrystalline structure with carbon segregation up to 2 at.% at grain boundaries. Spheroid-shaped cementite, formed at the grain boundaries and triple junctions of the nanosized grains, was enriched with Cr and Mn but depleted with Si. Such partitioning of Cr, Mn, and Si was not observed in the elongated cementite formed in the less deformed zone. This implies that rolling contact loading induced severe plastic deformation as well as a pronounced annealing effect in the active contact region of the toothed gear during cyclic loading. © 2018 The Minerals, Metals & Materials Society
view abstract 10.1007/s11837-018-2931-z
- On the detection of multiple events in atom probe tomography
Peng, Z. and Vurpillot, F. and Choi, P.-P. and Li, Y. and Raabe, D. and Gault, B.
Ultramicroscopy 189 (2018)In atom probe tomography (APT), multiple events can arise as a consequence of e.g. correlated field evaporation and molecular ion dissociation. They represent challenging cases for single-particle detectors and can cause compositional as well as spatial inaccuracies. Here, two state-of-the-art atom probe microscopes (Cameca LEAP 5000 XS and 5000 XR) were used to investigate cemented tungsten carbide, which exhibits high amounts of multiple events. By advanced data analysis methods, the natural character of the multiple events, as well as the performance of the APT detectors, are assessed. Accordingly, possible signal loss mechanisms are discussed. © 2018 Elsevier B.V.
view abstract 10.1016/j.ultramic.2018.03.018
- On the origin of the improvement of shape memory effect by precipitating VC in Fe–Mn–Si-based shape memory alloys
Lai, M.J. and Li, Y.J. and Lillpopp, L. and Ponge, D. and Will, S. and Raabe, D.
Acta Materialia 155 (2018)We studied the role of VC precipitation in improving the shape memory effect (SME) of the as-solution treated Fe–Mn–Si-based shape memory alloys by examining the microstructures developed during aging and deformation using transmission electron microscopy and electron channeling contrast imaging. Our results suggest that VC particles are not the only product of aging. Upon aging at 650 °C, the precipitation of VC particles is accompanied by the formation of profuse dislocations (2.26 ± 0.098 × 1013 m−2). In this case, the SME is not improved compared to the as-solution treated reference state. Upon aging at high temperatures (700–900 °C), a number of stacking faults are formed accompanying the VC precipitation and the SME is significantly improved, where the recovery ratios reach almost twice that of the as-solution treated state (<50%). For these high-temperature aged states, in situ straining experiments reveal that the stacking faults rather than the VC particles play an important role in the stress-induced martensitic transformation, leading to the formation of very thin (<3 nm) martensite plates with a single crystallographic variant within each grain. These martensite plates are in contrast to the very thick (from tens to hundreds of nanometers) and multi-variant martensite plates that prevail in the as-solution treated state. By comparing the characteristics of the martensite plates between the as-solution treated and the high-temperature aged states, the reasons for the improvement of SME by precipitating VC were discussed. © 2018 Acta Materialia Inc.
view abstract 10.1016/j.actamat.2018.06.008
- Atomic scale characterization of white etching area and its adjacent matrix in a martensitic 100Cr6 bearing steel
Li, Y.J. and Herbig, M. and Goto, S. and Raabe, D.
Materials Characterization 123 (2017)Atom probe tomography was employed to characterize the microstructure and C distribution in the white etching area (WEA) of a martensitic 100Cr6 bearing steel subjected to rolling contact fatigue. Different from its surrounding matrix where a plate-like martensitic structure prevails, the WEA exhibits equiaxed grains with a uniform grain size of about 10 nm. Significant C grain boundary enrichment (>7.5at.%) and an overall higher C concentration than the nominal value are observed in the WEA. These results suggest that the formation of WEA results from severe local plastic deformation that causes dissolution of carbides and the redistribution of C. © 2016 Elsevier Inc.
view abstract 10.1016/j.matchar.2016.12.002
- Multiscale characterization of White Etching Cracks (WEC) in a 100Cr6 bearing from a thrust bearing test rig
Danielsen, H.K. and Guzmán, F.G. and Dahl, K.V. and Li, Y.J. and Wu, J. and Jacobs, G. and Burghardt, G. and Fæster, S. and Alimadadi, H. and Goto, S. and Raabe, D. and Petrov, R.
Wear 370-371 (2017)A common cause for premature bearing failures in wind turbine gearboxes are the so-called White Etching Cracks (WEC). These undirected, three-dimensional cracks are bordered by regions of altered microstructure and ultimately lead to a cracking or spalling of the raceway. An accelerated WEC test was carried out on a FE8 test rig using cylindrical roller thrust bearings made of martensitic 100Cr6 steel. The resulting WECs were investigated with several characterisation techniques. Ultrasonic measurements showed the WEC were mainly located in the region of the overrolled surface in which negative slip occurs, which agrees with hypotheses based on an energetic approach for a prognosis. SEM orientation contrast imaging of the area around WEC revealed an inhomogeneous structure with varied grain sizes and a large amount of defects. Microstructure characterization around the WEA using EBSD showed significant grain refinement. Atom probe tomography showed the microstructure in the undamaged zone has a plate-like martensitic structure with carbides, while no carbides were detected in the WEA where the microstructure consisted of equiaxed 10 nm grains. A three dimensional characterisation of WEC network was successfully demonstrated with X-ray computerized tomography, showing crack interaction with unidentified inclusion-like particles. © 2016 Elsevier B.V.
view abstract 10.1016/j.wear.2016.11.016
- Defect Recovery in Severely Deformed Ferrite Lamellae During Annealing and Its Impact on the Softening of Cold-Drawn Pearlitic Steel Wires
Chen, Y.Z. and Csiszár, G. and Cizek, J. and Shi, X.H. and Borchers, C. and Li, Y.J. and Liu, F. and Kirchheim, R.
Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science 47 (2016)Cold-drawn pearlitic steel wires with a drawing true strain of 3 were annealed at temperatures (Tann) ranging from 423 K to 723 K (150 °C to 450 °C) with an interval of 50 K. Recovery of the lattice defects in the severely deformed ferrite lamellae were characterized by means of high-energy X-ray diffraction and positron annihilation techniques (including positron annihilation spectroscopy and coincidence Doppler broadening spectroscopy). Accordingly, the impact of defect recovery on the softening of the annealed wires was investigated. It is found that at low temperatures [Tann ≤ 523 K (250 °C)], the recovery of the lattice defects in ferrite lamellae is dominated by the agglomeration and annihilation of vacancy clusters, while at Tann > 523 K (250 °C), the recovery process is controlled by the annihilation of dislocations. Further analyses on the softening of the annealed wires indicate that the evolutions of dislocation density and concentration of vacancy clusters, and the strain age hardening in ferrite lamellae play important roles in changing the strength of the wires. The strain aging hardening leads to a maximum strength at 473 K (150 °C). Above 523 K (250 °C), the annihilations of vacancy clusters and dislocations in ferrite lamellae cause a continuous softening of the wires, where the decrease in dislocation density plays a major role. © 2015, The Minerals, Metals & Materials Society and ASM International.
view abstract 10.1007/s11661-015-3263-z
- Deformation-Induced Martensite: A New Paradigm for Exceptional Steels
Djaziri, S. and Li, Y. and Nematollahi, G.A. and Grabowski, B. and Goto, S. and Kirchlechner, C. and Kostka, A. and Doyle, S. and Neugebauer, J. and Raabe, D. and Dehm, G.
Advanced Materials 28 (2016)
view abstract 10.1002/adma.201601526
- Formation of nanosized grain structure in martensitic 100Cr6 bearing steels upon rolling contact loading studied by atom probe tomography
Li, Y.J. and Herbig, M. and Goto, S. and Raabe, D.
Materials Science and Technology (United Kingdom) 32 (2016)To understand the origin of white etching cracks (WECs), a systematic microstructural characterisation in the regions affected from the near-surface region down to the subsurface layers where WECs occur is necessary. As a starting point, we focus on the near-surface region of an axial thrust bearing, made of martensitic 100Cr6 steel, to study the influence of rolling contact loading on the microstructure and the resulting distributions of the major alloying elements C and Cr using atom probe tomography. We find that upon rolling contact loading the original plate-like martensitic structure evolves into a nanosized equiaxed grain structure with C segregation up to 5 at.-% at the grain boundaries. Cementite particles, located at grain boundaries and triple junctions, undergo spheroidisation. The originally homogeneously distributed Cr becomes enriched in spheroidised cementite particles. The microstructural changes give strong hints that rolling contact loading induces plastic deformation and an increased temperature on the near-surface region. This paper is part of a Themed Issue on Recent developments in bearing steels. © 2016 Institute of Materials, Minerals and Mining.
view abstract 10.1080/02670836.2015.1120458
- Ultra-strong and damage tolerant metallic bulk materials: A lesson from nanostructured pearlitic steel wires
Hohenwarter, A. and Völker, B. and Kapp, M.W. and Li, Y. and Goto, S. and Raabe, D. and Pippan, R.
Scientific Reports 6 (2016)Structural materials used for safety critical applications require high strength and simultaneously high resistance against crack growth, referred to as damage tolerance. However, the two properties typically exclude each other and research efforts towards ever stronger materials are hampered by drastic loss of fracture resistance. Therefore, future development of novel ultra-strong bulk materials requires a fundamental understanding of the toughness determining mechanisms. As model material we use today's strongest metallic bulk material, namely, a nanostructured pearlitic steel wire, and measured the fracture toughness on micron-sized specimens in different crack growth directions and found an unexpected strong anisotropy in the fracture resistance. Along the wire axis the material reveals ultra-high strength combined with so far unprecedented damage tolerance. We attribute this excellent property combination to the anisotropy in the fracture toughness inducing a high propensity for micro-crack formation parallel to the wire axis. This effect causes a local crack tip stress relaxation and enables the high fracture toughness without being detrimental to the material's strength. © 2016 The Author(s).
view abstract 10.1038/srep33228
- Atomic scale investigation of non-equilibrium segregation of boron in a quenched Mo-free martensitic steel
Li, Y.J. and Ponge, D. and Choi, P. and Raabe, D.
Ultramicroscopy 159 (2015)B-added low carbon steels exhibit excellent hardenability. The reason has been frequently attributed to B segregation at prior austenite grain boundaries, which prevents the austenite to ferrite transformation and favors the formation of martensite. The segregation behavior of B at prior austenite grain boundaries is strongly influenced by processing conditions such as austenitization temperatures and cooling rates and by alloying elements such as Mo, Cr, and Nb. Here an local electrode atom probe was employed to investigate the segregation behavior of B and other alloying elements (C, Mn, Si, and Cr) in a Cr-added Mo-free martensitic steel. Similar to our previous results on a Mo-added steel, we found that in both steels B is segregated at prior austenite grain boundaries with similar excess values, whereas B is neither detected in the martensitic matrix nor at martensite-martensite boundaries at the given cooling rate of 30 K/s. These results are in agreement with the literature reporting that Cr has the same effect on hardenability of steels as Mo in the case of high cooling rates. The absence of B at martensite-martensite boundaries suggests that B segregates to prior austenite grain boundaries via a non-equilibrium mechanism. Segregation of C at all boundaries such as prior austenite grain boundaries and martensite-martensite boundaries may occur by an equilibrium mechanism. © 2015 Elsevier B.V.
view abstract 10.1016/j.ultramic.2015.03.009
- Mechanisms of subgrain coarsening and its effect on the mechanical properties of carbon-supersaturated nanocrystalline hypereutectoid steel
Li, Y.J. and Kostka, A. and Choi, P. and Goto, S. and Ponge, D. and Kirchheim, R. and Raabe, D.
Acta Materialia 84 (2015)Carbon-supersaturated nanocrystalline hypereutectoid steels with a tensile strength of 6.35 GPa were produced from severely cold-drawn pearlite. The nanocrystalline material undergoes softening upon annealing at temperatures between 200 and 450°C. The ductility in terms of elongation to failure exhibits a non-monotonic dependence on temperature. Here, the microstructural mechanisms responsible for changes in the mechanical properties were studied using transmission electron microscopy (TEM), TEM-based automated scanning nanobeam diffraction and atom probe tomography (APT). TEM and APT investigations of the nanocrystalline hypereutectoid steel show subgrain coarsening upon annealing, which leads to strength reduction following a Hall-Petch law. APT analyzes of the Mn distribution near subgrain boundaries and in the cementite give strong evidence of capillary-driven subgrain coarsening occurring through subgrain boundary migration. The pronounced deterioration of ductility after annealing at temperatures above 350°C is attributed to the formation of cementite at subgrain boundaries. The overall segregation of carbon atoms at ferrite subgrain boundaries gives the nanocrystalline material excellent thermal stability upon annealing. © 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
view abstract 10.1016/j.actamat.2014.10.027
- Segregation of boron at prior austenite grain boundaries in a quenched martensitic steel studied by atom probe tomography
Li, Y.J. and Ponge, D. and Choi, P. and Raabe, D.
Scripta Materialia 96 (2015)The distribution of B and other alloying elements (C, Cr, Mo) at prior austenite grain boundaries (PAGBs) and in the matrix was quantified by atom probe tomography in a quenched martensitic steel. B and Mo were observed to be segregated only at PAGBs and to be absent at martensite-martensite boundaries. C is segregated both at PAGBs and at martensite-martensite boundaries, whereas Cr is homogeneously distributed in the probed volume. Our results indicate that B undergoes a non-equilibrium segregation. © 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
view abstract 10.1016/j.scriptamat.2014.09.031
- Atomic-scale quantification of grain boundary segregation in nanocrystalline material
Herbig, M. and Raabe, D. and Li, Y.J. and Choi, P. and Zaefferer, S. and Goto, S.
Physical Review Letters 112 (2014)Grain boundary segregation leads to nanoscale chemical variations that can alter a material's performance by orders of magnitude (e.g., embrittlement). To understand this phenomenon, a large number of grain boundaries must be characterized in terms of both their five crystallographic interface parameters and their atomic-scale chemical composition. We demonstrate how this can be achieved using an approach that combines the accuracy of structural characterization in transmission electron microscopy with the 3D chemical sensitivity of atom probe tomography. We find a linear trend between carbon segregation and the misorientation angle ω for low-angle grain boundaries in ferrite, which indicates that ω is the most influential crystallographic parameter in this regime. However, there are significant deviations from this linear trend indicating an additional strong influence of other crystallographic parameters (grain boundary plane, rotation axis). For high-angle grain boundaries, no general trend between carbon excess and ω is observed; i.e., the grain boundary plane and rotation axis have an even higher influence on the segregation behavior in this regime. Slight deviations from special grain boundary configurations are shown to lead to unexpectedly high levels of segregation. © 2014 American Physical Society.
view abstract 10.1103/PhysRevLett.112.126103
- Grain boundary segregation engineering in metallic alloys: A pathway to the design of interfaces
Raabe, D. and Herbig, M. and Sandlöbes, S. and Li, Y. and Tytko, D. and Kuzmina, M. and Ponge, D. and Choi, P.-P.
Current Opinion in Solid State and Materials Science 18 (2014)Grain boundaries influence mechanical, functional, and kinetic properties of metallic alloys. They can be manipulated via solute decoration enabling changes in energy, mobility, structure, and cohesion or even promoting local phase transformation. In the approach which we refer here to as 'segregation engineering' solute decoration is not regarded as an undesired phenomenon but is instead utilized to manipulate specific grain boundary structures, compositions and properties that enable useful material behavior. The underlying thermodynamics follow the adsorption isotherm. Hence, matrix-solute combinations suited for designing interfaces in metallic alloys can be identified by considering four main aspects, namely, the segregation coefficient of the decorating element; its effects on interface cohesion, energy, structure and mobility; its diffusion coefficient; and the free energies of competing bulk phases, precipitate phases or complexions. From a practical perspective, segregation engineering in alloys can be usually realized by a modest diffusion heat treatment, hence, making it available in large scale manufacturing. © 2014 Elsevier Ltd. All rights reserved.
view abstract 10.1016/j.cossms.2014.06.002
- Segregation stabilizes nanocrystalline bulk steel with near theoretical strength
Li, Y. and Raabe, D. and Herbig, M. and Choi, P.-P. and Goto, S. and Kostka, A. and Yarita, H. and Borchers, C. and Kirchheim, R.
Physical Review Letters 113 (2014)Grain refinement through severe plastic deformation enables synthesis of ultrahigh-strength nanostructured materials. Two challenges exist in that context: First, deformation-driven grain refinement is limited by dynamic dislocation recovery and crystal coarsening due to capillary driving forces; second, grain boundary sliding and hence softening occur when the grain size approaches several nanometers. Here, both challenges have been overcome by severe drawing of a pearlitic steel wire (pearlite: lamellar structure of alternating iron and iron carbide layers). First, at large strains the carbide phase dissolves via mechanical alloying, rendering the initially two-phase pearlite structure into a carbon-supersaturated iron phase. This carbon-rich iron phase evolves into a columnar nanoscaled subgrain structure which topologically prevents grain boundary sliding. Second, Gibbs segregation of the supersaturated carbon to the iron subgrain boundaries reduces their interface energy, hence reducing the driving force for dynamic recovery and crystal coarsening. Thus, a stable cross-sectional subgrain size <10nm is achieved. These two effects lead to a stable columnar nanosized grain structure that impedes dislocation motion and enables an extreme tensile strength of 7 GPa, making this alloy the strongest ductile bulk material known. © 2014 American Physical Society.
view abstract 10.1103/PhysRevLett.113.106104
- Atomic scale investigation of redistribution of alloying elements in pearlitic steel wires upon cold-drawing and annealing
Li, Y.J. and Choi, P. and Goto, S. and Borchers, C. and Raabe, D. and Kirchheim, R.
Ultramicroscopy 132 (2013)A local electrode atom probe has been employed to analyze the redistribution of alloying elements including Si, Mn, and Cr in pearlitic steel wires upon cold-drawing and subsequent annealing. It has been found that the three elements undergo mechanical mixing upon cold-drawing at large strains, where Mn and Cr exhibit a nearly homogeneous distribution throughout both ferrite and cementite, whereas Si only dissolves slightly in cementite. Annealing at elevated temperatures leads to a reversion of the mechanical alloying. Si atoms mainly segregate at well-defined ferrite (sub)grain boundaries formed during annealing. Cr and Mn are strongly concentrated in cementite adjacent to the ferrite/cementite interface due to their lower diffusivities in cementite than in ferrite. © 2012.
view abstract 10.1016/j.ultramic.2012.10.010
- Influence of supersaturated carbon on the diffusion of Ni in ferrite determined by atom probe tomography
Kresse, T. and Li, Y.J. and Boll, T. and Borchers, C. and Choi, P. and Al-Kassab, T. and Raabe, D. and Kirchheim, R.
Scripta Materialia 69 (2013)In patented and cold-drawn pearlitic steel wires dissociation of cementite occurs during mechanical deformation. In this study the influence of the carbon decomposition on the diffusion of nickel in ferrite is investigated by means of atom probe tomography. In the temperature range 423-523 K we observed a much smaller activation energy of Ni diffusion than for self-diffusion in body-centered cubic iron, indicating an increased vacancy density owing to enhanced formation of vacancy-carbon complexes. © 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
view abstract 10.1016/j.scriptamat.2013.05.039
- Nanocrystalline Fe-C alloys produced by ball milling of iron and graphite
Chen, Y.Z. and Herz, A. and Li, Y.J. and Borchers, C. and Choi, P. and Raabe, D. and Kirchheim, R.
Acta Materialia 61 (2013)A series of nanocrystalline Fe-C alloys with different carbon concentrations (xtot) up to 19.4 at.% (4.90 wt.%) are prepared by ball milling. The microstructures of these alloys are characterized by transmission electron microscopy and X-ray diffraction, and partitioning of carbon between grain boundaries and grain interiors is determined by atom probe tomography. It is found that the segregation of carbon to grain boundaries of α-ferrite can significantly reduce its grain size to a few nanometers. When the grain boundaries of ferrite are saturated with carbon, a metastable thermodynamic equilibrium between the matrix and the grain boundaries is approached, inducing a decreasing grain size with increasing xtot. Eventually the size reaches a lower limit of about 6 nm in alloys with x tot > 6.19 at.% (1.40 wt.%); a further increase in xtot leads to the precipitation of carbon as Fe3C. The observed presence of an amorphous structure in 19.4 at.% C (4.90 wt.%) alloy is ascribed to a deformation-driven amorphization of Fe3C by severe plastic deformation. By measuring the temperature dependence of the grain size for an alloy with 1.77 at.% C additional evidence is provided for a metastable equilibrium reached in the nanocrystalline alloy. © 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
view abstract 10.1016/j.actamat.2013.02.006
- Evolution of strength and microstructure during annealing of heavily cold-drawn 6.3 GPa hypereutectoid pearlitic steel wire
Li, Y.J. and Choi, P. and Goto, S. and Borchers, C. and Raabe, D. and Kirchheim, R.
Acta Materialia 60 (2012)Hypereutectoid steel wires with 6.35 GPa tensile strength after a cold-drawing true strain of 6.02 were annealed between 300 and 723 K. The ultrahigh strength remained upon annealing for 30 min up to a temperature of 423 K but dramatically decreased with further increasing temperature. The reduction of tensile strength mainly occurred within the first 2-3 min of annealing. Atom probe tomography and transmission electron microscopy reveal that the lamellar structure remains up to 523 K. After annealing at 673 K for 30 min, coarse hexagonal ferrite (sub)grains with spheroidized cementite, preferentially located at triple junctions, were observed in transverse cross-sections. C and Si segregated at the (sub)grain boundaries, while Mn and Cr enriched at the ferrite/cementite phase boundaries due to their low mobility in cementite. No evidence of recrystallization was found even after annealing at 723 K for 30 min. The stability of the tensile strength for low-temperature annealing (<473 K) and its dramatic drop upon high-temperature annealing (>473 K) are discussed based on the nanostructural observations. © 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
view abstract 10.1016/j.actamat.2012.03.006
- Atomic-scale mechanisms of deformation-induced cementite decomposition in pearlite
Li, Y.J. and Choi, P. and Borchers, C. and Westerkamp, S. and Goto, S. and Raabe, D. and Kirchheim, R.
Acta Materialia 59 (2011)Pearlitic steel can exhibit tensile strengths higher than 5 GPa after severe plastic deformation, where the deformation promotes a refinement of the lamellar structure and cementite decomposition. However, a convincing correlation between deformation and cementite decomposition in pearlite is still absent. In the present work, a local electrode atom probe was used to characterize the microstructural evolution of pearlitic steel, cold-drawn with progressive strains up to 5.4. Transmission electron microscopy was also employed to perform complementary analyses of the microstructure. Both methods yielded consistent results. The overall carbon content in the detected volumes as well as the carbon concentrations in ferrite and cementite were measured by atom probe. In addition, the thickness of the cementite filaments was determined. In ferrite, we found a correlation of carbon concentration with the strain, and in cementite, we found a correlation of carbon concentration with the lamella thickness. Direct evidence for the formation of cell/subgrain boundaries in ferrite and segregation of carbon atoms at these defects was found. Based on these findings, the mechanisms of cementite decomposition are discussed in terms of carbon-dislocation interaction. © 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
view abstract 10.1016/j.actamat.2011.03.022
- Deformation resistance in the transition from coarse-grained to ultrafine-grained Cu by severe plastic deformation up to 24 passes of ECAP
Blum, W. and Li, Y.J. and Zhang, Y. and Wang, J.T.
Materials Science and Engineering A 528 (2011)Pure Cu was subjected to severe plastic predeformation by p=1, 2, 4, 8, 16 and 24 passes of equal channel angular pressing (ECAP) on route BC at ambient temperature and subsequently tested in uniaxial compression parallel to the extrusion direction at constant rate or constant stress and temperatures from ambient temperature up to 418K. The maximum compressive strength of the ECAPed Cu varies in a systematic fashion with p, until a steady state is finally reached between p=8 and 16 where the rate sensitivity of flow stress is maximal. The results are quantitatively interpreted in terms of the boundary structure, considering the superposition of hardening due to refinement of low-angle boundaries and softening due to enhanced thermal recovery at high-angle boundaries. Beyond the maximum the compressive strength declines with strain for relatively low rate and/or elevated temperature of compression. This is explained by dynamic grain coarsening towards the new steady state developing in compression. © 2011 Elsevier B.V.
view abstract 10.1016/j.msea.2011.08.010
atom probe tomography