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Powder metallurgy is a group of advanced processes for the synthesis, processing, and shaping of various kinds of materials. Initially inspired by ceramics processing, the methodology comprising of the production of a powder and its transformation to a compact solid product has attracted great attention since the end of World War II. At present, there are many technologies for powder production (e.g., gas atomization of the melt, chemical reduction, milling, and mechanical alloying) and its consolidation (e.g., pressing and sintering, hot isostatic pressing, and spark plasma sintering). The most promising ones can achieve an ultra-fine or nano-grained structure of the powder, and preserve it during consolidation. Among these methods, mechanical alloying and spark plasma sintering play a key role. This Special Issue gives special focus to the advancement of mechanical alloying, spark plasma sintering and self-propagating high-temperature synthesis methods, as well as to the role of these processes in the development of new materials.

Modelling forms a vital part of all engineering design, yet many hydraulic engineers are not fully aware of the assumptions they make. These assumptions can have important consequences when choosing the best model to inform design decisions. Considering the advantages and limitations of both physical and mathematical methods, this book will help you identify the most appropriate form of analysis for the hydraulic engineering application in question. All models require the knowledge of their background, good data and careful interpretation and so this book also provides guidance on the range of accuracy to be expected of the model simulations and how they should be related to the prototype. Applications for models include: Open channel systems; Closed conduit flows; Storm drainage systems; Estuaries; Coastal and nearshore structures; Hydraulic structures. An invaluable guide for students and professionals.

The primary objective of the 1-cm geoid experiment in Colorado (USA) is to compare the numerous geoid computation methods used by different groups around the world. This is intended to lay the foundations for tuning computation methods to achieve the sought after 1-cm accuracy, and also evaluate how this accuracy may be robustly assessed. In this experiment, (quasi)geoid models were computed using the same input data provided by the US National Geodetic Survey (NGS), but using different methodologies. The rugged mountainous study area (730 km × 560 km) in Colorado was chosen so as to accentuate any differences between the methodologies, and to take advantage of newly collected GPS/leveling data of the Geoid Slope Validation Survey 2017 (GSVS17) which are now available to be used as an accurate and independent test dataset. Fourteen groups from fourteen countries submitted a gravimetric geoid and a quasigeoid model in a 1′ × 1′ grid for the study area, as well as geoid heights, height anomalies, and geopotential values at the 223 GSVS17 marks. This paper concentrates on the quasigeoid model comparison and evaluation, while the geopotential value investigations are presented as a separate paper (Sánchez et al. in J Geodesy 95(3):1. https://doi.org/10.1007/s00190-021-01481-0 , 2021). Three comparisons are performed: the area comparison to show the model precision, the comparison with the GSVS17 data to estimate the relative accuracy of the models, and the differential quasigeoid (slope) comparison with GSVS17 to assess the relative accuracy of the height anomalies at different baseline lengths. The results show that the precision of the 1′ × 1′ models over the complete area is about 2 cm, while the accuracy estimates along the GSVS17 profile range from 1.2 cm to 3.4 cm. Considering that the GSVS17 does not pass the roughest terrain, we estimate that the quasigeoid can be computed with an accuracy of ~ 2 cm in Colorado. The slope comparisons show that RMS values of the differences vary from 2 to 8 cm in all baseline lengths. Although the 2-cm precision and 2-cm relative accuracy have been estimated in such a rugged region, the experiment has not reached the 1-cm accuracy goal. At this point, the different accuracy estimates are not a proof of the superiority of one methodology over another because the model precision and accuracy of the GSVS17-derived height anomalies are at a similar level. It appears that the differences are not primarily caused by differences in theory, but that they originate mostly from numerical computations and/or data processing techniques. Consequently, recommendations to improve the model precision toward the 1-cm accuracy are also given in this paper.

Physical geodesy applies potential theory to study the Earth’s gravitational field in space outside and up to a few km inside the Earth’s mass. Among various tools offered by this theory, boundary-value problems are particularly popular for the transformation or continuation of gravitational field parameters across space. Traditional problems, formulated and solved as early as in the nineteenth century, have been gradually supplemented with new problems, as new observational methods and data are available. In most cases, the emphasis is on formulating a functional relationship involving two functions in 3-D space; the values of one function are searched but unobservable; the values of the other function are observable but with errors. Such mathematical models (observation equations) are referred to as deterministic. Since observed data burdened with observational errors are used for their solutions, the relevant stochastic models must be formulated to provide uncertainties of the estimated parameters against which their quality can be evaluated. This article discusses the boundary-value problems of potential theory formulated for gravitational data currently or in the foreseeable future used by physical geodesy. Their solutions in the form of integral formulas and integral equations are reviewed, practical estimators applicable to numerical solutions of the deterministic models are formulated, and their related stochastic models are introduced. Deterministic and stochastic models represent a complete solution to problems in physical geodesy providing estimates of unknown parameters and their error variances (mean squared errors). On the other hand, analyses of error covariances can reveal problems related to the observed data and/or the design of the mathematical models. Numerical experiments demonstrate the applicability of stochastic models in practice.

Iron aluminides are still deeply investigated materials for their use in power plants, automotive and chemical industry, and other sectors. This paper shows that it is possible to strongly improve their oxidation behavior by the addition of silicon. The description of the synergic effect of aluminum and silicon on the oxidation behavior of Fe–Al–Si alloys at 800 °C in air is presented. The oxidation rate, microstructure, phase, and chemical composition of these ternary alloys are compared with the binary Fe–Al and Fe–Si alloys. Results showed that the oxidation of Fe–Al–Si ternary alloys provides an oxide layer based on aluminum oxide with a low concentration of iron and silicon. Below this oxide layer, there is a layer of silicides formed as a result of depletion by aluminum, which forms a secondary oxidation protection.

This paper studies the contribution of airborne gravity data to improvement of gravimetric geoid modelling across the mountainous area in Colorado, USA. First, airborne gravity data was processed, filtered, and downward-continued. Then, three gravity anomaly grids were prepared; the first grid only from the terrestrial gravity data, the second grid only from the downward-continued airborne gravity data, and the third grid from combined downward-continued airborne and terrestrial gravity data. Gravimetric geoid models with the three gravity anomaly grids were determined using the least-squares modification of Stokes’ formula with additive corrections (LSMSA) method. The absolute and relative accuracy of the computed gravimetric geoid models was estimated on GNSS/levelling points. Results exhibit the accuracy improved by 1.1 cm or 20% in terms of standard deviation when airborne and terrestrial gravity data was used for geoid computation, compared to the geoid model computed only from terrestrial gravity data. Finally, the spectral analysis of surface gravity anomaly grids and geoid models was performed, which provided insights into specific wavelength bands in which airborne gravity data contributed and improved the power spectrum.

This work highlights new results on the synthesis of the TiAl3 intermetallic phase using self-propagating high-temperature synthesis. This method is considered a promising sintering route for intermetallic compounds. It was found that the reactions proceed in two stages. Below the melting point of aluminum, the Ti2Al5 phase forms at 450 °C after long annealing times by a direct solid-state reaction between the aluminum and titanium, and is converted consequently to TiAl3. This is a completely new finding; until now, many authors have believed in the preferential formation of the TiAl3 phase. The second stage, the self-propagating strongly exothermic reaction, proceeds above the melting point of aluminum. It leads to the formation of the TiAl3 phase accompanied by Ti2Al5 and Ti3Al phases. The reaction mechanism was shown in the form of chemical equations, which were supported by calculating Gibbs energy. Reaction temperatures (Tonset, Tmaximum, and Toffset) were determined after induction heating thanks to recording by an optical pyrometer. This finding provides completely new opportunities for the determination of activation energy at heating rates, in which common calorimeters are not able to detect a response or even measure. Now, the whole procedure will become accessible.

In traditional airborne gravimetry, the vertical component of the gravity vector is used as an approximation of the measured magnitude of the gravity vector, which enters the determination of the local geoid. In this study, a comprehensive computational scheme for determining the local geoid using three components of the airborne gravity vector is presented. Our approach extends the existing one-step method for local geoid modeling by incorporating the full gravity vector measured by airborne sensors as boundary values in the gravimetric boundary-value problem. We derive integral kernel functions along with far-zone contributions for the three components of the airborne gravity vector and apply deterministic modifications to them. To validate our derivations, we use a global geopotential model (GGM)-based airborne gravity vectors burdened with realistic colored noise at one of the most challenging test sites for geoid determination, the 1-cm geoid test area in Colorado (USA). Results of closed-loop tests confirm that applying all three components of the GGM-based airborne gravity vector improves the internal accuracy of the geoid by 50% compared to using only the vertical component. We further use real airborne gravity vectors observed at a test site in the same region and show that the STD of the estimated geoid heights evaluated against the reference geoidal heights along the Geoid Slope Validation Survey of 2017 (GSVS17) Line is 2.3 cm using the “traditional approach” and 1.3 cm including the horizontal components. This indicates a significant improvement in the external accuracy (~ 46%) of the geoid when the full gravity vector is used, without using other heterogeneous observations. Graphical Abstract

Physical heights is one of the most important topics in physical geodesy. Their original concept, introduced in the 19-th century, defined physical heights as lengths of plumblines of the Earth’s gravity field between the geoid and points of interest. There are orthometric heights of surface points, that have been traditionally estimated by spirit levelling and measured gravity; however, the knowledge of the density distribution of topographic masses (masses between the geoid and Earth’s surface) is required that significantly affects their determinability. This was also the main reason why a new type of physical heights was proposed in the mid of the 20-th century. Normal heights approximate orthometric heights in a sense that the Earth’s gravity field is replaced by the normal gravity field, an analytic model based on the theory of an equipotential ellipsoid. This height system has been introduced since that time in different countries in Europe and beyond. Contrary to the classical height system based on orthometric heights, its counterpart based on normal heights may have slightly different definitions. Moreover, normal heights are often defined as heights of points above the quasigeoid. This contribution reviews alternative definitions of normal heights and respective height systems. It is argued that both orthometric and normal heights refer to the geoid. In the case physical heights are estimated by satellite positioning, normal heights must be computed through the height anomaly estimated at each point of interest, whether it is below, at or above the Earth’s surface. On the contrary, orthometric heights of all points along the same plumbline, be it below, at or above the Earth’s surface, are estimated by introducing one value of the geoid height. Normal heights of surface points can be estimated by spirit levelling easier than orthometric heights as no topographic mass density hypothesis is required; however, one has to keep in mind the gravity field approximation used both for their definition and realization.

This paper describes the effect of silicon on the manufacturing process, structure, phase composition, and selected properties of titanium aluminide alloys. The experimental generation of TiAl–Si alloys is composed of titanium aluminide (TiAl, Ti3Al or TiAl3) matrix reinforced by hard and heat-resistant titanium silicides (especially Ti5Si3). The alloys are characterized by wear resistance comparable with tool steels, high hardness, and very good resistance to oxidation at high temperatures (up to 1000 °C), but also low room-temperature ductility, as is typical also for other intermetallic materials. These alloys had been successfully prepared by the means of powder metallurgical routes and melting metallurgy methods.