The current study reports in situ TEM observations of the growth of bainitic ferrite in an Fe-0.3C-3Mn-1.5Si-0.15Mo steel held isothermally at 300 °C with a higher spatio-temporal resolution than in previous studies. Significant variations were found in the lengthening rate, with the highest being in excess of 30,000 nm.s⁻¹ while more common lengthening rates of 10–1000 nm.s⁻¹ provided the highest quality observations. Both sheaves with visible sub units and individual laths were observed during growth with the lengthening behaviour of sheaves found to be discontinuous - in the most favourably oriented sheave this could be linked to sub unit behaviour. The transformation behaviour was comparable to that of HT-LSCM observations of bainitic ferrite growth for the most comparable steel compositions and to ‘textbook’ descriptions of the formation of bainite sheaves. In addition, other relevant phenomena were recorded, including the generation and movement of dislocations in the austenite during transformation, the interaction of laths with twin boundaries and the initially slow growth of bainitic ferrite laths.

The influence of carbon concentration variations on pearlite formation (20 h at 600 °C) in a case-carburized steel is investigated. The resultant microstructure shows three distinct regions: carburized case, a transition region, and the original core. The microstructural transition from the case to the core regions is observed to be relatively sharp. The investigated region of the carburized case (0.9 wt.% C) contains two types of pearlite: ferrite + cementite and ferrite + M₂₃C₆, where the pearlitic aggregate with M₂₃C₆ shows faster formation kinetics. The kinetics of pearlite formation in the transition region (0.3 wt.% C) is very slow and is observed with only M₂₃C₆ carbide. Only around 40% austenite decomposes into pearlite in the transition region, which, in comparison to the carburized case region of 0.9 wt.% C is a fraction that is lower by a factor of two. Pearlite is absent in the investigated core region (0.16 wt.% C). The microstructure in this region is predominantly martensite and pro-eutectoid ferrite, with a fraction of ferrite well below the equilibrium fraction. Ferrite formation in this region is limited by the redistribution of mainly Ni, Mn, and Cr, and their resulting solute drag effect on the austenite/ferrite interface. A thermodynamic and kinetic argumentation of these observations is provided with the help of thermodynamic data, precipitation simulations, and a general mixed-mode Gibbs energy balance model.

Understanding the local strain enhancement and lattice distortion resulting from different microstructure features in metal alloys is crucial in many engineering processes. The development of heterogeneous strain not only plays an important role in the work hardening of the material but also in other processes such as recrystallization and damage inheritance and fracture. Isolating the contribution of precipitates to the development of heterogeneous strain can be challenging due to the presence of grain boundaries or other microstructure features that might cause ambiguous interpretation. In this work a statistical analysis of local strains measured by electron back scatter diffraction and crystal plasticity based simulations are combined to determine the effect of M₂₃C₆ carbides on the deformation of an annealed AISI 420 steel. Results suggest that carbides provide a more effective hardening at low plastic strain by a predominant long-range interaction mechanism than that of a pure ferritic microstructure. Carbides not only influence local strain directly by elastic incompatibilities with the ferritic matrix, but also the spatial interactions between ferrite grains. Carbides placed at the grain boundaries enhanced the development of strain near ferrite grain boundaries. However the positive effect of carbides and grain boundaries to develop high local strains is mitigated at regions with high density of carbides and ferrite grain boundaries.

The kinetic behaviour of austenite/ferrite interfaces in a low carbon – 0.5 mass% Mn containing steel during Cyclic Partial Phase Transformation (CPPT) experiments has been investigated using hot stage Transmission Electron Microscopy (TEM). Individual interfaces were observed to display behaviour typical of CPPT experiments as recorded in macroscopic dilatometry experiments and demonstrated i) the “normal”, ii) inverse transformations and iii) a stagnant stage in which the interface migrates at a very low velocity as a result of the interface passing through a Mn enriched zone due to the preceding transformation. The length of the stagnant stage determined from the TEM observations shows excellent agreement with that measured from dilatometry and kinetic modelling, whilst the distance migrated from the interface shows some disparities which are primarily attributed to differences in assumptions about grain geometry and nucleation. No special interface features were observed when the interface changed direction and passed through the previously Mn-enriched zones. General observations on the interaction of the transformation interface with microstructural features are also reported.

We present a local quasi-geoid (QG) model which combines a satellite-only global gravity model with local data sets using weighted least squares. The QG is computed for an area comprising the Netherlands, Belgium, and the southern North Sea. It uses a two-scale spherical radial basis function model complemented by bias parameters to account for systematic errors in the local gravity data sets. Variance factors are estimated for the noise covariance matrices of all involved data sets using variance component estimation. The standard deviation (SD) of the differences between the computed QG and GPS/leveling data is 0.95 and 1.52 cm for the Netherlands and Belgium, respectively. The fact that the SD of the control data is about 0.60 and 1.20 cm for the Netherlands and Belgium, respectively, points to a lower mean SD of the computed QG model of about 0.7 cm for the Netherlands and 1.0 cm for Belgium. The differences to a QG model computed with the remove-compute-restore technique range from −5.2 to 2.6 cm over the whole model domain and from −1.5 to 1.5 cm over the Netherlands and Belgium. A variogram analysis of the differences with respect to GPS/leveling data reveals a better performance of the computed QG model compared to a remove-compute-restore-based QG model for wavelengths >100 km for Belgium but not for the Netherlands. The latter is due to the fact that at the spatial scales resolved by the global gravity model, variance component estimation assigns significantly lower weights to the local data set in favor of the global gravity model.

Controlling the kinetics of austenite decomposition by controlled partitioning of alloying elements, in particular carbon and manganese, is the key factor for optimizing the microstructures of advanced high-strength steels. In this study, a systematic set of computational and experimental cyclic partial phase transformations in low to medium manganese steels revealed a critical manganese concentration range of 1.5–2.5 mass% at which designated manganese partitioning at moving austenite–ferrite interfaces can be used to locally increase the effective Mn concentration and temporarily suspend further transformation during subsequent cooling. Most interestingly, this critical concentration only becomes visible in cases of reversed partial transformations in the intercritical regime and is un-noticeable in continuous cooling or conventional isothermal treatments.

In this research, in situ high-temperature electron backscattered diffraction (EBSD) mapping is applied to record and analyze the migration of the α/3 interfaces during cyclic austenite-ferrite phase transformations in a medium manganese steel. The experimental study is supplemented with related 3D phase field (PF) simulations to better understand the 2D EBSD observations in the context of the 3D transformation events taking place below the surface. The in situ EBSD observations and PF simulations show an overall transformation behavior qualitatively similar to that measured in dilatometry. The behavior and kinetics of individual austenite-ferrite interfaces during the transformation is found to have a wide scatter around the average interface behavior deduced on the basis of the dilatometric measurements. The trajectories of selected characteristic interfaces are analyzed in detail and yield insight into the effect of local conditions in the vicinity of interfaces on their motion, as well as the misguiding effects of 2D observations of processes taking place in 3D.

Investigating the partitioning effect of substitutional and interstitial elements on the migration of transformation interfaces during austenite-ferrite phase transformation in steels with the conventional experimental method is extremely challenging due to interaction between the solute atoms and the transformation interfaces. Additionally, the simultaneous nucleation of new phases during phase transformations limits the accuracy of extracted growth rates from experimental kinetics measurements of phase fractions. In a novel experimental approach, the cyclic partial phase transformation concept is used to avoid the effect of nucleation on total kinetics of phase transformations. In this study, a Fe-0.5Mn alloy in the presence and absence of interstitial C and N additions is subjected to different cyclic transformation routes to examine the possible interaction between solute atoms and migrating interfaces. The experimental results are in semi-quantitative agreement with modelling predictions made by the local equilibrium approach and provide indirect evidence of Mn partitioning at austenite/ferrite interface in absence of any interstitial elements. It is also confirmed that the presence of interstitial elements promotes Mn interaction with the interface, whereas N promotes more Mn partitioning at transformation interface compared to C.

We present an efficient and flexible alternative method to connect islands and offshore tide gauges with the height system on land. The method uses a regional, high-resolution hydrodynamic model that provides total water levels. From the model, we obtain the differences in mean water level (MWL) between tide gauges at the mainland and at the islands or offshore platforms. Adding them to the MWL relative to the national height system at the mainland’s tide gauges realizes a connection of the island and offshore platforms with the height system on the mainland. Numerical results are presented for the connection of the Dutch Wadden islands with the national height system (Normaal Amsterdams Peil, NAP). Several choices of the period over which the MWLs are computed are tested and validated. The best results were obtained when we computed the MWL only over the summer months of our 19-year simulation period. Based on this strategy, the percentage of connections for which the absolute differences between the observation- and model-derived MWL differences are (Formula presented.) cm is about 34% (46 out of 135 possible leveling connections). In this case, for each Wadden island we can find several connections that allow the transfer of NAP with (sub-)centimeter accuracy.

The posed question arises for instance in regional gravity field modelling using weighted least-squares techniques if the gravity field functionals are synthesised from the spherical harmonic coefficients of a satellite-only global gravity model (GGM), and are used as one of the noisy datasets. The associated noise covariance matrix, appeared to be extremely ill-conditioned with a singular value spectrum that decayed gradually to zero without any noticeable gap. We analysed three methods to deal with the ill-conditioned noise covariance matrix: Tihonov regularisation of the noise covariance matrix in combination with the standard formula for the weighted least-squares estimator, a formula of the weighted least-squares estimator, which does not involve the inverse noise covariance matrix, and an estimator based on Rao’s unified theory of least-squares. Our analysis was based on a numerical experiment involving a set of height anomalies synthesised from the GGM GOCO05s, which is provided with a full noise covariance matrix. We showed that the three estimators perform similar, provided that the two regularisation parameters each method knows were chosen properly. As standard regularisation parameter choice rules do not apply here, we suggested a new parameter choice rule, and demonstrated its performance. Using this rule, we found that the differences between the three least-squares estimates were within noise. For the standard formulation of the weighted least-squares estimator with regularised noise covariance matrix, this required an exceptionally strong regularisation, much larger than one expected from the condition number of the noise covariance matrix. The preferred method is the inversion-free formulation of the weighted least-squares estimator, because of its simplicity with respect to the choice of the two regularisation parameters.

Predicting the effect of alloying elements on the degree of incomplete austenite to bainite transformation in low carbon steels is of great industrial importance. This study introduces an extended Gibbs energy balance model which makes use of an additive approach to calculate the coupled effect of Mn, Si and Mo on the fraction of bainitic ferrite after the incomplete transformation in multicomponent steels. The model predicts significant effects of Mn and Mo and the negligible effect of Si levels on the fraction of bainitic ferrite. This is attributed to the high value of dissipation of Gibbs energy caused by interfacial diffusion of Mn and Mo and low values caused by Si diffusion. The model predictions for quaternary Fe–C–Mn–Si system are comparable with the experimentally measured values of bainite fraction. For the Fe–C–Mn–Mo system, the agreement is less accurate and the accuracy decreases with increasing Mo content, which is attributed a substantial carbide formation but interaction effects between Mn and Mo or a temperature dependent binding energy cannot be ruled out.

The paper is about a methodology to combine a noisy satellite-only global gravity field model (GGM) with other noisy datasets to estimate a local quasi-geoid model using weighted least-squares techniques. In this way, we attempt to improve the quality of the estimated quasi-geoid model and to complement it with a full noise covariance matrix for quality control and further data processing. The methodology goes beyond the classical remove–compute–restore approach, which does not account for the noise in the satellite-only GGM. We suggest and analyse three different approaches of data combination. Two of them are based on a local single-scale spherical radial basis function (SRBF) model of the disturbing potential, and one is based on a two-scale SRBF model. Using numerical experiments, we show that a single-scale SRBF model does not fully exploit the information in the satellite-only GGM. We explain this by a lack of flexibility of a single-scale SRBF model to deal with datasets of significantly different bandwidths. The two-scale SRBF model performs well in this respect, provided that the model coefficients representing the two scales are estimated separately. The corresponding methodology is developed in this paper. Using the statistics of the least-squares residuals and the statistics of the errors in the estimated two-scale quasi-geoid model, we demonstrate that the developed methodology provides a two-scale quasi-geoid model, which exploits the information in all datasets.

Direct microscopic observation of the isothermal bainite evolution in terms of nucleation events, the location of the nuclei, as well as their growth is very valuable for the refinement of models predicting the kinetics of bainite transformation. To this aim, the microstructural evolution in a Fe-0.2C-1.5Mn-2.0Cr alloy during isothermal bainite formation at temperatures between 723 K and 923 K is monitored in situ using high temperature laser scanning confocal microscopy (LSCM). Both the nucleation and the growth kinetics of the bainitic plates are analyzed quantitatively. Bainitic plates are observed to nucleate on three different types of locations in the grain: at austenitic grain boundaries, on newly-formed bainite plates and at unspecific sites within the austenite grains. Grain boundary nucleation is observed to be the dominant nucleation mode at all transformation temperatures. The rate of nucleation is found to vary markedly between different austenite grains. The temperature dependence of the average bainite nucleation rate is in qualitative agreement with the classical nucleation theory. Analysis of plate growth reveals that also the lengthening rates of bainite plates differ strongly between different grains. However, the lengthening rates do not seem to be related to the type of nucleation site. Analysis of the temperature dependence of the growth rate shows that the lengthening rates at high temperatures are in line with a diffusional model when a growth barrier of 400 J mol^–1 is considered.

Formation of the microstructural ferrite/pearlite bands in medium Mn steels is an undesirable phenomenon commonly addressed through fast cooling treatments. In this study, a novel approach using the cyclic partial phase transformation concept is applied successfully to prevent microstructural band formation in a micro-chemically banded Fe-C-Mn-Si steel. The effectiveness of the new approach is assessed using the ASTM E1268-01 standard. The cyclic intercritical treatments lead to formation of isotropic microstructures even for cooling rates far below the critical one determined in conventional continuous cooling. In contrast, isothermal intercritical experiments have no effect on the critical cooling rate to suppress microstructural band formation. The origin of the suppression of band formation either by means of fast cooling or a cyclic partial phase transformation is investigated in detail. Theoretical modeling and microstructural observations confirm that band formation is suppressed only if the intercritical annealing treatment leads to partial reversion of the austenite-ferrite interfaces. The resulting interfacial Mn enrichment is responsible for suppression of the band formation upon final cooling at low cooling rates.

We assess the surface gravity data requirements for a 5-mm quasi-geoid model for the Netherlands mainland and continental shelf in terms of omission and commission errors. The omission error critically depends on the roughness of the topography and bathymetry. For the Netherlands continental shelf, Central and Northern Netherlands, the omission error is well described by the model 0.32d mm, where d is the data spacing in km. For the more hilly Southern Netherlands, the omission error model is 0.92d mm. The commission error depends on the kernel modification, the data spacing, and the data accuracy. When using the spheroidal Stokes kernel, it is well described by 0.277 d σ_Δg mm, where σ_Δg is the noise standard deviation of surface gravity data in mGal. An upper bound of the commission error of the state-of-the-art satellite-only gravity model GOCO05S over the Netherlands is e^{0.03676L–11.419} mm, where L is the maximum degree up to which this model is used. Only if this model is truncated at a sufficiently low degree, e.g., at degree 100, its contribution to the total commission error can be neglected. We determine the total error as the sum of commission and omission errors. Hence, to realize a 5-mm quasi-geoid model for the Netherlands mainland and continental shelf, a data spacing of 3.5 km is needed when assuming a noise standard deviation of 1.5 mGal for surface gravity data. The currently available land-based gravity data fulfill this requirement. This does not apply to the situation at sea, where the density of the shipboard gravity data and the accuracy of the radar altimeter-derived data do not allow the realization of a 5-mm quasi-geoid model.

GPS data collected by satellite gravity missions can be used for extracting the long-wavelength part of the Earth’s gravity field. We propose a new data processing method which makes use of the ‘average acceleration’ approach to gravity field modelling. In this method, satellite accelerations are directly derived from GPS carrier phase measurements with an epoch-differenced scheme. As a result, no ambiguity solutions are needed and the systematic errors that do not change much from epoch to epoch are largely eliminated. The GPS data collected by the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite mission are used to demonstrate the added value of the proposed method. An analysis of the residual accelerations shows that accelerations derived in this way are more precise, with noise being reduced by about 20 and 5% at the cross-track component and the other two components, respectively, as compared to those based on kinematic orbits. The accelerations obtained in this way allow the recovery of the gravity field to a slightly higher maximum degree compared to the solution based on kinematic orbits. Furthermore, the gravity field solution has an overall better performance. Errors in spherical harmonic coefficients are smaller, especially at low degrees. The cumulative geoid height error is reduced by about 15 and 5% up to degree 50 and 150, respectively. An analysis in the spatial domain shows that large errors along the geomagnetic equator, which are caused by a high electron density coupled with large short-term variations, are substantially reduced. Finally, the new method allows for a better observation of mass transport signals. In particular, sufficiently realistic signatures of regional mass anomalies in North America and south-west Africa are obtained.

We study the impact of an accurate computation and incorporation of coloured noise in radar altimeter data when computing a regional quasi-geoid model using least-squares techniques. Our test area comprises the Southern North Sea including the Netherlands, Belgium, and parts of France, Germany, and the UK. We perform the study by modelling the disturbing potential with spherical radial base functions. To that end, we use the traditional remove-compute-restore procedure with a recent GRACE/GOCE static gravity field model. Apart from radar altimeter data, we use terrestrial, airborne, and shipboard gravity data. Radar altimeter sea surface heights are corrected for the instantaneous dynamic topography and used in the form of along-track quasi-geoid height differences. Noise in these data are estimated using repeat-track and post-fit residual analysis techniques and then modelled as an auto regressive moving average process. Quasi-geoid models are computed with and without taking the modelled coloured noise into account. The difference between them is used as a measure of the impact of coloured noise in radar altimeter along-track quasi-geoid height differences on the estimated quasi-geoid model. The impact strongly depends on the availability of shipboard gravity data. If no such data are available, the impact may attain values exceeding 10 centimetres in particular areas. In case shipboard gravity data are used, the impact is reduced, though it still attains values of several centimetres. We use geometric quasi-geoid heights from GPS/levelling data at height markers as control data to analyse the quality of the quasi-geoid models. The quasi-geoid model computed using a model of the coloured noise in radar altimeter along-track quasi-geoid height differences shows in some areas a significant improvement over a model that assumes white noise in these data. However, the interpretation in other areas remains a challenge due to the limited quality of the control data.

We present an improved mascon approach to transform monthly spherical harmonic solutions based on GRACE satellite data into mass anomaly estimates in Greenland. The GRACE-based spherical harmonic coefficients are used to synthesize gravity anomalies at satellite altitude, which are then inverted into mass anomalies per mascon. The limited spectral content of the gravity anomalies is properly accounted for by applying a low-pass filter as part of the inversion procedure to make the functional model spectrally consistent with the data. The full error covariance matrices of the monthly GRACE solutions are properly propagated using the law of covariance propagation. Using numerical experiments, we demonstrate the importance of a proper data weighting and of the spectral consistency between functional model and data. The developed methodology is applied to process real GRACE level-2 data (CSR RL05). The obtained mass anomaly estimates are integrated over five drainage systems, as well as over entire Greenland. We find that the statistically optimal data weighting reduces random noise by 35–69%, depending on the drainage system. The obtained mass anomaly time-series are de-trended to eliminate the contribution of ice discharge and are compared with de-trended surface mass balance (SMB) time-series computed with the Regional Atmospheric Climate Model (RACMO 2.3). We show that when using a statistically optimal data weighting in GRACE data processing, the discrepancies between GRACE-based estimates of SMB and modelled SMB are reduced by 24–47%.