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Paper des Monats
- ja (11)
In this letter, we demonstrate the robust presence of an elastic microstructure in a Zr-based metallic glass (MG) with a characteristic length-scale of the order of 100 nm. This length scale increases systematically towards the MG surface in differently sized casts, whereas thermal relaxation homogenizes both the internal length-scale gradient and the magnitude of the elastic fluctuations. Strongest changes during relaxation arise in the stiffest parts of the elastic microstructure. These findings indicate that the elastic microstructure emerges due to cooling constraints and may therefore be a microstructural manifestation of the internal residual stresses that arise during MG-solidification.
An attempt has been made in this work, to observe the influence on alloy aging by the sodium oxide (Na2O) in solar salt (60 wt% NaNO3 + 40 wt% KNO3). The accelerated aging was established by adding Na2O (0.005, 0.07, 0.135 and 0.2 wt%) to the solar salt and their effect on corrosion of 316L stainless steel (SS) at 600 ◦C in that oxide-rich solar salts for 168 h in synthetic air was investigated. Corrosion is significantly more in oxide-rich solar salt compared to pure solar salt. Strikingly, the oxide scale-base metal interface is wavy in solar salt containing 0.005 % Na2O clearly shows the oxide addition to salt melt influences Cr-rich inner oxide layer formation and its selective dissolution at early stage that leads to non-uniform corrosion. Interestingly, with increase of Na2O to 0.07 %, steel corrosion proceeded uniformly by accelerated disintegration of Cr-rich inner layer and subsequent dissolution. Severe scale spallation and weight loss in nitrate melt containing 0.2 % Na2O fostering more rapid corrosion, alarming that substantial tolerance of oxide content in solar salt is ≥ 0.135 % for an acceptable corrosion of 316L SS. Despite preferential dissolution of Cr and scale degradation/spallation with increased oxide content in solar salt, the corrosion layer in all cases comprised of sodium ferrite, and Cr-rich Cr-Fe mixed oxides with the Ni enrichment at the scale-metal interface. Competing processes between oxide scale growth, degradation and dissolution or even spallation has been discussed with an emphasis of Na2O addition to solar salt.
The control of stress development in cast ceramics during drying is usually one of critical steps in ceramic processes, which is important also for additive manufacturing technologies using a suspension as feedstock. This work introduces a method based on the cantilever deflection method, to simultaneously quantify the kinetics of solvent evaporation, the shrinkage and the intensity of in-plane stresses developed during drying. Particular attention is given here to the experimental limits of the method and to the optimization of the experimental conditions to suitably measure the intensity of in-planar stress in the coating. The optimized method is applied to
four alumina slurries for the water-based additive manufacturing technology LSD-print. Four stages of drying are identified and discussed in relation with the granulometry and morphology of the alumina ceramic particles.
The integration of additive manufacturing with traditional processes, termed hybrid additive manufacturing, has expanded its application domain, particularly in the repair of gas turbine blade tips. However, process-related defects in additively manufactured materials, interface formation, and material property mismatches in dual-material structures can significantly impact the fatigue performance of components. This investigation examines the low cycle fatigue and fatigue crack growth behaviors in dual-material specimens of nickel-based alloys, specifically the additively manufactured STAL15 and the cast alloy 247DS, at elevated temperatures. Low cycle fatigue experiments were conducted at temperatures of 950 °C and 1000 °C under a range of strain levels (0.3%–0.8%) and fatigue crack growth tests were conducted at 950 °C with stress ratios of 0.1 and −1. Fractographic and microscopic analyses were performed to comprehend fatigue crack initiation and crack growth mechanisms in the dual-material structure. The results consistently indicated crack initiation and fatigue fracture in the additively manufactured STAL15 material. Notably, fatigue crack growth retardation was observed near the interface when the crack extended from the additively manufactured STAL15 material to the perpendicularly positioned interface. This study highlights the importance of considering yield strength mismatch, as well as the potential effects of residual stresses and grain structure differences, in the interpretation of fatigue crack growth behavior at the interface.
Advanced ceramics printed with photon-based additive manufacturing deals with anisotropic mechanical properties from the layer-by-layer manufacturing. Motivated by the success in using highly filled transparent slurries containing nanoparticles for powder-based two-photon-polymerization (2PP) for advanced ceramic printing, this works approach is the transfer to Xolography, a volumetric additive manufacturing technology based on linear two-photon excitation and without recoating steps. This paper reports the results of a preliminary investigation optimizing the photocurable slurry to the requirements of Xolography in terms of transparency, over a significantly larger mean free path, compared to 2PP. A feedstock filled with 70 % weight fraction of ceramic particles (∼30 vol%) exhibiting an exceptionally high degree of transparency in the relevant wavelength range of 400–800 nm was prepared from 5 nm zirconia nanoparticles. The high transparency of the photocurable slurry is attributed to the near-monomodal particle size distribution of the zirconia nanoparticles used.
AbstractTwo‐photon polymerization (2PP) additive manufacturing (AM) utilizes feedstocks of ceramic nanoparticles of a few nanometers in diameter, enabling the fabrication of highly accurate technical ceramic design with structural details as small as 500 nm. The performance of these materials is expected to differ from conventional AM ceramics, as nanoparticles and three‐dimensional printing at high resolution introduce new microstructural aspects. This study applies 2PP‐AM of yttria‐stabilized zirconia to investigate the mechanical response behavior under compressive load, probing the influence of smallest structural units induced by the line packing during the printing process, design of sintered microblocks, and sintering temperature and thereby microstructure. We find a dissipative mechanical response enhanced by sintering at lower temperatures than conventional. The pursued 2PP‐AM approach yields a microstructured material with an increased number of grain boundaries that proposedly play a major role in facilitating energy dissipation within the here printed ceramic material. This microplastic response is further triggered by the filigree structures induced by hollow line packing at the order of the critical defect size of ceramics. Together, these unique aspects made accessible by the 2PP‐AM approach contribute to a heterogeneous nano‐ and microstructure, and hint toward opportunities for tailoring the mechanical response in future ceramic applications.
Characteristics of environmental stress cracking of PE-HD induced by biodiesel and diesel fuels
(2024)
In the context of the increasing effect of carbon dioxide emissions on the global climate biodiesel produced from renewable sources has emerged as a promising contender replacing fossil fuels, especially in long-range transport vehicles, using existing engines and infrastructure.
High-density polyethylene is one of the prevailing materials for pipe and container applications for storage and transport of such fuels, both, from fossil and renewable resources. The contact with the respective fuels raises questions concerning material compatibility as biodiesel exhibits significant differences compared to conventional diesel fuel affecting its sorption and plasticization behavior in polyethylene. In this study, its behavior with respect to environmental stress cracking, considered one of the most frequent damage mechanisms leading to failure of polymer parts and packaging, was evaluated using the well-established Full Notch Creep Test. This
approach allows for a detailed fracture surface analysis using imaging techniques, such as optical and laser scanning microscopy, as well as infrared spectroscopy. Comparing the environmental stress cracking behavior in standard surfactant solutions with that in biodiesel and diesel, respective crack propagation rates, showing different levels of acceleration, were determined and details of the underlying mechanisms could be revealed.
Furthermore, the specific infrared absorption of the biodiesel’s ester functionality allows its semi-quantitative determination on the fracture surface of the tested specimens after failure. Thus, a preferred uptake of sorptive fluids in the fracture zone due to local morphological changes of the polyethylene could be directly evidenced by infrared spectroscopy.
Ni-Cu alloys are promising for application at temperatures between 400–900 °C and reducing atmospheres with high C-contents. Typically, under such conditions, metallic materials in contact with the C-rich atmosphere are degraded by a mechanism called metal dusting (MD). Ni-Cu-alloys do not form protective oxide scales, but their resistance is attributed to Cu, which catalytically inhibits the C-deposition on the surface. Adding other alloying elements, such as Mn or Fe, was found to enhance the MD attack of Ni-Cu alloys again. In this study, the effect of the Mn and Fe is divided into two affected areas: the surface and the bulk. The MD attack on binary Ni-Cu alloys, model alloys with Fe and Mn additions, and commercial Monel Alloy 400 is experimentally demonstrated. The surface electronic structure causing the adsorption and dissociation of C-containing molecules is investigated for model alloys. Analytical methods such as scanning electron microscopy combined with energy-dispersive X-ray spectroscopy, electron probe microanalysis combined with wavelength-dispersive X-ray spectroscopy, X-ray diffraction analysis, and near-edge X-ray absorption fine structure measurements were used. The results are correlated to CALPHAD calculations and atomistic simulations combining density functional theory calculations and machine learning. It is found that the Cu content plays a significant role in the surface reaction. The effect of Mn and Fe is mainly attributed to oxide formation. A mechanism explaining the enhanced attack by adding both Fe and Mn is proposed.
Glassy solids evolve towards lower-energy structural states by physical aging. This can be characterized by structural relaxation times, the assessment of which is essential for understanding the glass’ time-dependent property changes. Conducted over short times, a continuous increase of relaxation times with time is seen, suggesting a time-dependent dissipative transport mechanism. By focusing on micro-structural rearrangements at the atomic-scale, we demonstrate the emergence of sub-diffusive anomalous transport and therefore temporal fractional diffusion in a metallic glass, which we track via coherent x-ray scattering conducted over more than 300,000 s. At the longest probed decorrelation times, a transition from classical stretched exponential to a power-law behavior occurs, which in concert with atomistic simulations reveals collective and intermittent atomic motion. Our observations give a physical basis for classical stretched exponential relaxation behavior, uncover a new power-law governed collective transport regime for metallic glasses at long and practically relevant time-scales, and demonstrate a rich and highly non-monotonous aging response in a glassy solid, thereby challenging the common framework of homogeneous aging and atomic scale diffusion.
Additive manufacturing techniques, such as laser powder bed fusion (PBF-LB), are well known for their exceptional freedom in part design. However, these techniques are also characterized by the development of large thermal gradients during production and thus residual stress (RS) formation in produced parts. In this context, neutron diffraction enables the non-destructive characterization of the bulk RS distribution. By control of the thermal gradients in the powder-bed plane by scan strategy variation we study the impact of in-process scan strategy variations on the microstructure and the three-dimensional distribution of RS. Microstructural analysis by means of electron backscatter diffraction reveals sharp microstructure transitions at the interfaces ranging from 100-200 µm. The components of the RS tensor are determined by means of neutron diffraction and the principal stress directions and magnitudes are determined by eigenvalue decomposition. We find that the distribution of RS in the powder-bed plane corresponds to the underlying scan strategy. When the alternating scan vectors align with the x- and y sample coordinate axes, the principal stress directions co-align. In the present geometry, nearly transverse isotropic stress states develop when the scan vectors are either aligned 45° between x and y or continuously rotated by 67° between each layer.
Advanced optical materials inspired by natural minerals and non-toxic light elements, such as the Hackmanites (Na8Al6Si6O24(Cl,S)2), find vast possibilities of applications as they can simultaneously perform photochromism and persistent luminescence (PersL). In this work, we have explored a rapid and energy-efficient microwaveassisted (MASS) methodology for the synthesis of PersL and photochromic hackmanites. In addition, we have prepared hackmanite materials using a zeolite-free precursor to control the Na–Al–Si ratio and study its influence on the materials photoluminescent properties. The PersL hackmanites showed a white-bluish emission color, with up to 2 h of emission time. Zeolite-free photochromic materials were able to change the color from white to purple/blue efficiently with a few seconds of 254 nm excitation, but the usage of zeolite precursors enhanced the overall optical performance. Microwave synthesis times of 10–40 min were demonstrated to be optimal, as longer times boosted the formation of nepheline spurious phase, which decreases luminescence efficiency. In this way, the MASS method led to a reduction of reaction time up to 98 %, yielding hackmanite materials with similar photoluminescent or photochromic properties compared to those obtained by a 24 h conventional solid-state synthesis. This work represents a significant improvement toward coupling eco-friendly synthetic processes to
eco-friendly solid-state materials for PersL illumination and PersL/photochromism optical marking.
Viscous crack healing in soda–lime–magnesium–silicate–ZrO<sub>2</sub> glass matrix composites
(2024)
AbstractThe present study investigates the influence of the crystal volume content on viscous crack healing in glass ceramic glass sealants. To ensure constant microstructure during healing, soda–lime–magnesium silicate glass matrix composites with varied volume fractions of ZrO2 filler particles were used. Crack healing was studied on radial cracks induced by Vickers indentation, which were stepwise annealed to monitor the healing progress by confocal laser scanning microscopy. Confirming previous studies, healing of radial cracks in pure glass was found delayed by global flow phenomena like crack widening and crack edge and tip rounding to minimize the sample surface. With increasing ZrO2 filler content, these global flow phenomena were progressively inhibited whereas local flow phenomena like sharp crack tip healing could still occur. As a result, crack healing was even accelerated by filler particles up to a maximum filler content of 17 vol% whereas crack healing was fully suppressed only at 33 vol% filler content.
AbstractGallium fluoride phosphate glasses feature low refractive index, high energy radiation resistance, wide transmission range, and favorable emission characteristics of rare‐earth dopants. For the development of optimized glass compositions, a fundamental understanding of these properties in terms of glass structure is sought. We report nuclear magnetic resonance (NMR) structural studies of glasses in the system xGa(PO3)3–(40 − x)GaF3–20BaF2–20ZnF2–20SrF2 (x = 5, 10, 15, 20, and 25 mol%). 31P NMR results with 71Ga recoupling show that the network structure is dominated by P–O–Ga linkages, and no P–O–P linkages exist. 71Ga NMR results show that Ga is mainly six‐coordinated featuring a mixed fluoride/phosphate coordination. Quantitative estimates of this ligand distribution around gallium were obtained by 71Ga{31P} spin echo double resonance (REDOR) measurements. Photophysical properties suggest changes in the Eu(III) ligand distribution toward a fluoride‐dominated environment at low P/F ratio while the glass network is largely sustained by bridging oxygen atoms via P–O–Ga linkages.
Development of efficient portable sensors for accurately detecting biomarkers is crucial for early disease diagnosis, yet remains a significant challenge. To address this need, we introduce the enhanced luminescence lateral-flow assay, which leverages highly luminescent upconverting nanoparticles (UCNPs) alongside a portable reader and a smartphone app. The sensor’s efficiency and versatility were shown for kidney health monitoring as a proof of concept. We engineered Er3+- and Tm3+-doped UCNPs coated with multiple layers, including an undoped
inert matrix shell, a mesoporous silica shell, and an outer layer of
gold (UCNP@mSiO2@Au). These coatings synergistically enhance emission by over 40-fold and facilitate biomolecule conjugation, rendering UCNP@mSiO2@Au easy to use and suitable for a broad range of bioapplications. Employing these optimized nanoparticles in lateral-flow assays, we successfully detected two acute kidney injury-related biomarkers-kidney injury molecule-1 (KIM-1) and neutrophil gelatinase-associated lipocalin (NGAL)-in urine samples. Using our sensor platform, KIM-1 and NGAL can be accurately detected and quantified
within the range of 0.1 to 20 ng/mL, boasting impressively low limits of detection at 0.28 and 0.23 ng/mL, respectively. Validating our approach, we analyzed clinical urine samples, achieving biomarker concentrations that closely correlated with results obtained via ELISA. Importantly, our system enables biomarker quantification in less than 15 min, underscoring the performance of our novel UCNP-based approach and its potential as reliable, rapid, and user-friendly diagnostics.
In this work, the thermoelectric material calcium cobaltite Ca3Co4O9 (CCO), a promising p-type conducting thermoelectric oxide with anisotropic properties, was processed by the powder aerosol deposition method (PAD) to form a dense ceramic CCO film with a thickness in the µm range. The prepared films were characterized regarding their microstructure and thermoelectric properties between room temperature and 900 °C. After heat treatment at 900 °C, the CCO PAD film in-plane shows excellent properties in terms of electrical conductivity (280 S/cm at 900 °C) and Seebeck coefficient (220 µV/K at 900 °C). The calculated power factor in-plane (ab) reaches with 1125 µW/(m K2) 40 % of the single crystal value, surpassing the known-properties of CCO bulk ceramics. Examination of the microstructure shows a strong fiber texture of the film as well as a strong coarsening of the grains during the first heat treatment up to 900 °C.
Ceramic additive manufacturing (AM) requires a complex process chain with various post-processing steps that require expensive machines and special expertise. The key to further market penetration is AM that makes it possible to integrate into an already established ceramic process chain. Most successful AM technologies for ceramics are, however, based on processes that initially have been developed for polymeric materials. For ceramics AM, polymers or precursors are loaded with ceramic particles. This strategy facilitates the entry into AM, however the introduction of organic additives into the ceramic process chain represents a considerable technological challenge to ultimately obtain a ceramic component after additive shaping. In the present communication, two technologies based on ceramic suspensions will be introduced, the “layerwise slurry deposition” (LSD) and “laser induced slip casting” (LIS) technology. Both technologies take advantage of the high packing densities reached by conventional slip casting and moreover enable the processing of fines, even nanoparticles.
A key aspect in the development of multilayer inductors is the magnetic permeability of the ferrite layers. Here, the effects of different processing steps on the permeability of a NiCuZn ferrite is investigated. Dry pressed, tape cast, and co‐fired multilayer samples are analyzed. An automated data pipeline is applied to structure the acquired experimental data according to a domain ontology based on PMDco (Platform MaterialDigital core ontology). Example queries to the ontology show how the determined process‐property correlations are accessible to non‐experts and thus how suitable data for component design can be identified. It is demonstrated how the inductance of co‐fired multilayer inductors is reliably predicted by simulations if the appropriate input data corresponding to the manufacturing process is used.This article is protected by copyright. All rights reserved.
This data article presents a set of primary, analyzed, and digitalized mechanical testing datasets for nine copper alloys. The mechanical testing methods including the Brinell and Vickers hardness, tensile, stress relaxation, and low-cycle fatigue (LCF) testing were performed according to the DIN/ISO standards. The obtained primary testing data (84 files) mainly contain the raw measured data along with the testing metadata of the processes, materials, and testing machines. Five secondary datasets were also provided for each testing method by collecting the main meta- and measurement data from the primary data and the outputs of data analyses. These datasets give materials scientists beneficial data for comparative material selection analyses by clarifying the wide range of mechanical properties of copper alloys, including Brinell and Vickers hardness, yield and tensile strengths, elongation, reduction of area, relaxed and residual stresses, and LCF fatigue life. Furthermore, both the primary and secondary datasets were digitalized by the approach introduced in the research article entitled “Toward a digital materials mechanical testing lab” [1]. The resulting open-linked data are the machine-processable semantic descriptions of data and their generation processes and can be easily queried by semantic searches to enable advanced data-driven materials research.
AbstractTwo‐photon polymerization (2PP) additive manufacturing (AM) utilizes feedstocks of ceramic nanoparticles of a few nanometers in diameter, enabling the fabrication of highly accurate technical ceramic design with structural details as small as 500 nm. The performance of these materials is expected to differ from conventional AM ceramics, as nanoparticles and three‐dimensional printing at high resolution introduce new microstructural aspects. This study applies 2PP‐AM of yttria‐stabilized zirconia to investigate the mechanical response behavior under compressive load, probing the influence of smallest structural units induced by the line packing during the printing process, design of sintered microblocks, and sintering temperature and thereby microstructure. We find a dissipative mechanical response enhanced by sintering at lower temperatures than conventional. The pursued 2PP‐AM approach yields a microstructured material with an increased number of grain boundaries that proposedly play a major role in facilitating energy dissipation within the here printed ceramic material. This microplastic response is further triggered by the filigree structures induced by hollow line packing at the order of the critical defect size of ceramics. Together, these unique aspects made accessible by the 2PP‐AM approach contribute to a heterogeneous nano‐ and microstructure, and hint toward opportunities for tailoring the mechanical response in future ceramic applications.
Automated computational workflows are a powerful concept that can improve the usability and reproducibility of simulation and data processing approaches. Although used very successfully in bioinformatics, workflow environments in materials science are currently commonly applied in the field of atomistic simulations. This work showcases the integration of a discrete element method (DEM) simulation of powder pressing in the convenient SimStack workflow environment. For this purpose, a Workflow active Node (WaNo) was developed to generate input scripts for the DEM solver using LIGGGHTS Open Source Discrete Element Method Particle Simulation code. Combining different WaNos in the SimStack framework makes it possible to build workflows and loop over different simulation or evaluation conditions. The functionality of the workflows is explained, and the added user value is discussed. The procedure presented here is an example and template for many other simulation methods and issues in materials science and engineering.
Addressing a strategy for publishing open and digital research data, this article presents the approach for streamlining and automating the process of storage and conversion of research data to those of semantically queryable data on the web. As the use case for demonstrating and evaluating the digitalization process, the primary datasets from low‐cycle‐fatigue testing of several copper alloys are prepared. The fatigue test ontology (FTO) and ckan.kupferdigital data management system are developed as two main prerequisites of the data digitalization process. FTO has been modeled according to the content of the fatigue testing standard and by reusing the basic formal ontology, industrial ontology foundry core ontology, and material science and engineering ontology. The ckan.kupferdigital data management system is also constructed in such a way that enables the users to prepare the protocols for mapping the datasets into the knowledge graph and automatically convert all the primary datasets to those machine‐readable data which are represented by the web ontology language. The retrievability of the converted digital data is also evaluated by querying the example competency questions, confirming that ckan.kupferdigital enables publishing open data that can be highly reused in the semantic web.
Quantum dots (QDs) are remarkable semiconductor nanoparticles, whose optical properties are strongly size-dependent. Therefore, the real-time monitoring of crystal growth pathway during synthesis gives an excellent opportunity to a smart design of the QDs luminescence. In this work, we present a new approach for monitoring the formation of QDs in aqueous solution up to 90 °C, through in situ luminescence analysis, using CdTe as a model system. This technique allows a detailed examination of the evolution of their light emission. In contrast to in situ absorbance analysis, the in situ luminescence measurements in reflection geometry are particularly advantageous once they are not hindered by the concentration increase of the colloidal suspension. The synthesized particles were additionally characterized using X-ray diffraction analysis, transition electron microscopy, UV-Vis absorption and infrared spectroscopy. The infrared spectra showed that 3-mercaptopropionic acid (MPA)-based thiols are covalently bound on the surface of QDs and microscopy revealed the formation of CdS. Setting a total of 3 h of reaction time, for instance, the QDs synthesized at 70, 80 and 90 °C exhibit emission maxima centered at 550, 600 and 655 nm. The in situ monitoring approach opens doors for a more precise achievement of the desired emission wavelength of QDs.
The glass system (50NaPO3–20BaF2–10CaF2–20GdF3)-xTbCl3 with x = 0.3, 1, 3, 5, and 10 wt % was investigated. We successfully produced transparent glass ceramic (GC) scintillators with x = 1 through a melt-quenching process followed by thermal treatment. The luminescence and crystallization characteristics of these materials were thoroughly examined using various analytical methods. The nanocrystallization of Tb3+-doped Na5Gd9F32 within the doped fluoride-phosphate glasses resulted in enhanced photoluminescence (PL) and radioluminescence (RL) of the Tb3+ ions. The GC exhibited an internal PL quantum yield of 33 % and the integrated RL intensity across the UV-visible range was 36 % of that reported for the commercial BGO powder scintillator. This research showcases that Tb-doped fluoridephosphate GCs containing nanocrystalline Na5Gd9F32 have the potential to serve as efficient scintillators while having lower melting temperature compared to traditional silicate and germanate glasses.
Upconverting nanoparticles are essential in modern photonics due to their ability to convert infrared light to visible light. Despite their significance, they exhibit limited brightness, a key drawback that can be addressed by combining them with plasmonic nanoparticles. Plasmon-enhanced upconversion has been widely demonstrated in dry environments, where upconverting nanoparticles are immobilized, but constitutes a challenge in liquid media where Brownian motion competes against immobilization.
This study employs optical tweezers for the three-dimensional manipulation of an individual upconverting nanoparticle, enabling the exploration of plasmon-enhanced upconversion luminescence in water. Contrary to expectation, experiments reveal a long-range (micrometer scale) and moderate (20%) enhancement in upconversion luminescence due to the plasmonic resonances of gold nanostructures. Comparison between experiments and numerical simulations evidences the key role of Brownian motion. It is demonstrated how the three-dimensional Brownian fluctuations of the upconverting nanoparticle lead to an “average effect” that explains the magnitude and spatial extension of luminescence enhancement.
Modern dry pressing of ceramic powders using spray‐dried granulates cannot avoid the occurrence of defects related to persisting inter‐ and intra‐granulate interstitial voids. These constitute the parent defect size population limiting the application of polycrystalline ceramics in high‐stress conditions. The mitigation of such defects could widen the range of application in technical and biomedical engineering, reduce the safety range for design, and extend the lifetime of components. Herein, the Weibull size‐effect on strength in size‐partitioned Yttria‐stabilized zirconias (YSZ) feedstocks is used to explore the viability of changing the density distribution of granulate sizes as an effective strategy to obtain a denser particle packing that could reduce the size distribution of strength‐limiting pressing defects. In a direct assessment of critical defect size using multiscale strength testing with a dataset of ≈1300 values, the success of such an approach in increasing the strength reliability for small volume components is demonstrated, along with its ultimate failure in altering the defect size distribution in sintered YSZ ceramics across several length scales. Finally, it is shown that granule morphology (spherical or dimpled) fails to affect the defect density and size distribution in YSZ ceramics.
Compared to mechanisms like solid solution strengthening, the stacking fault energy (SFE) should be considered as a further factor that influences the material properties. The effect of SFE of alloys or individual elements on strength and resistance can vary considerably. In the high-temperature regime above 700 ◦C, there are still significant gaps in the knowledge about the effect of the SFE on the mechanical properties of single-phase alloys. The effect of SFE on creep resistance of two face-entered cubic equiatomic medium and high entropy alloys, CrCoNi and CrMnFeCoNi, respectively, is evaluated to fill parts of these gaps. Using the Bridgman solidification process, the alloys were produced as single crystals and crept under vacuum at 700 ◦C up to 1100 ◦C. This work shows a significant impact of the lower SFE of CrCoNi on the creep behavior compared to the results of previous investigations of CrMnFeCoNi. The creep resistance of the former is higher over the complete temperature range. At very high temperatures, the strengthening effect of the stacking faults is significantly present. The formation of tetragonal stacking faults and extended dislocation nodes can be identified as the reason for this effect.
Self-healing polymers have been developed to improve durability and reduce costs associated with maintenance during service. The addition of thermoplastics to thermosets to produce mendable polymers appears as a promising selfhealing technique. In this study, poly (ethylene-co-methacrylic acid) (EMAA) was added to epoxy resin and the effects of EMAA addition on epoxy properties were evaluated. Specimens with two different contents of thermoplastic and particles sizes were manufactured. A two-level full factorial experimental design was used to evaluate the effect of particle size and particle content on properties of epoxy modified with addition of EMAA. Tensile tests and dynamic mechanical analysis (DMA) were used and the evaluated responses were tensile strength, modulus of elasticity, and glass transition temperature (Tg). X-ray computed tomography (XCT) was used to investigate particle size and concentration after manufacturing. It was found that the particle concentration has greater effects on stress–strain behavior of epoxy while Tg was not significantly affected by neither of the analyzed entrance variables.
Relation of craze to crack length during slow crack growth phenomena in high‐density polyethylene
(2024)
The craze‐crack mechanism occurring in high‐density polyethylene (HDPE) causing slow crack growth and environmental stress cracking is investigated in detail with respect to the relation of crack length and the related craze zone. This is essential for the understanding of the resulting features of the formed fracture surface and their interpretation in the context of the transition from crack propagation to ductile shear deformation. It turns out that an already formed craze zone does not inevitably result in formation of a propagating crack, but could also undergo ductile failure. For the examination, the full notch creep test (FNCT) was employed with a subsequent advanced fracture surface analysis that was performed using various imaging techniques: light microscopy, laser scanning microscopy, scanning electron microscopy, and X‐ray micro computed tomography scan. FNCT specimens were progressively damaged for increasing durations under standard test conditions applying Arkopal, the standard surfactant solution, and biodiesel as test media were used to analyze the stepwise growth of cracks and crazes. From considerations based on well‐established fracture mechanics approaches, a theoretical correlation between the length of the actual crack and the length of the preceding craze zone was established that could be evidenced and affirmed by FNCT fracture surface analysis. Moreover, the yield strength of a HDPE material exposed to a certain medium as detected by a classic tensile test was found to be the crucial value of true stress to induce the transition from crack propagation due to the craze‐crack mechanism to shear deformation during FNCT measurements.
Highlights
- Progress of crack formation in high‐density polyethylene is analyzed by different imaging techniques
- Determined growth rates depend on distinction between craze zone and crack
- The ratio of the present crack to the anteceding craze zone is validated theoretically
- The transition from crack propagation to ductile shear deformation is identified
- An already formed craze zone may still fail by ductile mechanisms
Advancements in bulk metallic glass thermoplastic forming unleash the potential to fabricate microscale metallic features with unparalleled precision and durability, i.e. microspine gripping structures for mobility platforms on planetary or in-space robots. Four designs of grippers were fabricated and rigorously tested. Coefficient of friction on four test surfaces were measured and compared to SiC paper and Velcro. The hardness and elasticity of the bulk metallic glasses make them a game-changer in the field, offering a superior alternative to conventional nonmetallic grippers.
An interlaboratory study, involving eigth international laboratories and coordinated by COMTES FHT (Czech Republic), was conducted to validate tensile measurements obtained using miniature specimens on additively manufactured (AM) components and artifacts. In addition to AM 316L stainless steel (316L SS), a wrought highstrength steel (34CrNiMo6V, equivalent to AISI 4340) was also used. Based on the results, a precision statement in accordance with ASTM E691 standard practice was developed, intended for inclusion in a proposed annex to the ASTM E8/E8M tension testing method. The primary outcomes of the study highlighted the agreement between yield and tensile strength measured from miniature and standard-sized tensile specimens. Furthermore, most tensile properties exhibited similar standard deviations, offering users insight into the efficacy of miniature specimen applications.
The present work addresses powder bed binder jetting additive manufacturing by selective magnesium phosphate cement activation. Despite the potential of this technology to aid the digitalization of the construction industry, the effect of processing parameters on the mechanical performance of printed materials has not yet been studied to generate a guideline for the further development of the technology. Statistical methodologies were used to screen the effect of four printing process parameters (printing speed, layer thickness, raster angle, and build direction on flexural and compressive strength). As the exploited technology works with constant fluid pressure, the physical interpretation of the effect of each factor can be considered taking into account the interactions between the binder materials in the powder bed. Analysis of variance (ANOVA) indicated that printing speed and layer thickness significantly affect mechanical performances. Furthermore, the layout of samples for the printing process is preferable to be parallel the printhead movement. An anisotropic behavior was observed, and the samples subjected to compressive forces parallel to the layer plane possessed lower strength values. This effect can be interpreted as a result of a weak area of low density in between layers, leading to a pronounced delamination under compression. Even though the strength of the printed material is not suitable for a structural concrete, it can be marginally improved by design of experiment and optimized for non-structural applications, such as for porous artificial stone. Design of experiment coupled with ANOVA methods can be used in the future to support the development of novel material mixtures, thus expanding the fields of application of this novel additive manufacturing technology.
A widespread recovery of waste heat requires a cost‐effective production of thermoelectric generators. Thermoelectric oxides are predestined for use at high temperatures. For manufacturing reasons, a multilayer generator design will be easily scalable and cost‐effective. To evaluate the potential of ceramic multilayer technology for that purpose, a multilayer of the promising thermoelectric oxides calcium cobaltite (Ca3Co4O9), calcium manganate (CMO, CaMnO3), and glass–ceramic insulation layers is fabricated. Cracks and reaction layers at the interfaces are observed in the microstructure. The compositions of these reaction layers are identified by energy‐dispersive X‐ray spectroscopy and X‐ray diffraction. Mechanical and thermal properties of all layers are compiled from literature or determined by purposeful sample preparation and testing. Based on this data set, the internal stresses in the multilayer after co‐firing are calculated numerically. It is shown that tensile stresses in the range of 50 MPa occur in the CMO layers. The reaction layers have only a minor influence on the level of these residual stresses. Herein, it is proven that the material system is basically suitable for multilayer generator production, but that the co‐firing process and the layer structure must be adapted to improve densification and reduce the tensile stresses in the CMO.
The current lack of quantitative knowledge on processing-microstructure–property relationships is one of the major bottlenecks in today’s rapidly expanding field of additive manufacturing. This is centrally rooted in the nature of the processing, leading to complex microstructural features. Experimentally-guided modeling can offer reliable solutions for the safe application of additively manufactured materials. In this work, we combine a set of systematic experiments and modeling to address creep anisotropy and its correlation with microstructural characteristics in laser-based powder bed fusion (PBF-LB/M) additively manufactured Inconel-738LC (IN738LC). Three sample orientations (with the tensile axis parallel, perpendicular, and 45° tilted, relative to the building direction) are crept at 850 °C, accompanied by electron backscatter secondary diffraction (EBSD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM) investigations. A crystal plasticity (CP) model for Ni-base superalloys, capable of modeling different types of slip systems, is developed and combined with various polycrystalline representative volume elements (RVEs) built on the experimental measurements. Besides our experiments, we verify our modeling framework on electron beam powder bed fusion (PBF-EB/M) additively manufactured Inconel-738LC. The results of our simulations show that while the crystallographic texture alone cannot explain the observed creep anisotropy, the superlattice extrinsic stacking faults (SESF) and related microtwinning slip systems play major roles as active deformation mechanisms. We confirm this using TEM investigations, revealing evidence of SESFs in crept specimens. We also show that the elongated grain morphology can result in higher creep rates, especially in the specimens with a tilted tensile axis.
High‐temperature KCl‐induced corrosion of high Cr and Ni alloys investigated by in‐situ diffraction
(2024)
High‐temperature KCl‐induced corrosion in laboratory air was observed in situ utilizing X‐ray diffraction. High Cr‐containing model alloys (Fe‐13Cr, Fe‐18Cr‐12Ni, and Fe‐25Cr‐20Ni) were coated with KCl and exposed to dry air at 560°C. KCl‐free alloys were studied in the equivalent atmosphere as a reference. After exposure to KCl‐free environments, all alloys showed the formation of very thin oxide layers, indicating good corrosion resistance. In contrast, KCl‐bearing alloys showed distinct damage after exposure.
Functional fatigue of shape-memory alloys is a considerable threat to the reliable service of actuation devices. Here, we demonstrate the essentially degradation-free cyclic phase-transformation behavior of Ni-Mn-Ga microcrystals up to one million stress-driven superelastic cycles. Cyclic dissipation amounts to about 1/5 of the bulk counterpart and remains unaffected during cycling, even after the introduction of dislocation structures via plastic straining. Plastic yielding and the transformation stress largely exceed the known bulk values. However, the transformation-stress is found to depend on plastic pre-straining, which suggests that the size-affected transformation stress is sensitive to the initial defect structure and that it can be tuned by a targeted introduction of dislocations. These findings demonstrate the high suitability of Ni-Mn-Ga as a robust shape-memory alloy in small-scale functional device engineering.
Additive manufacturing of metals – and in particular building with laser-based powder bed fusion – is highly flexible and allows high-resolution features and feedstock savings. Meanwhile, though space stations in low Earth orbit are established, a set of visits to the Moon have been performed, and humankind can send out rovers to explore Venus and Mars, none of these milestone missions is equipped with technology to manufacture functional metallic parts or tools in space. In order to advance space exploration to long-term missions beyond low Earth orbit, it will be crucial to develop and employ technology for in-space manufacturing (ISM) and in-situ resource utilisation (ISRU). To use the advantages of laser-based powder bed fusion in these endeavours, the challenge of powder handling in microgravity must be met. Here we present a device capable of building parts using metallic powders in microgravity. This was proven on several sounding rocket flights, on which occasions Zr-based metallic glass parts produced by additive manufacturing in space were built. The findings of this work demonstrate that building parts using powder feedstock, which is more compact to transport into space than wire, is possible in microgravity environments. This thus significantly advances ISRU and ISM and paves the way for future tests in prolonged microgravity settings.
Objectives
The aim of the study was to investigate the impact of organic additives (binder, plasticizer, and the cross-linking ink) in the formulation of water-based feedstocks on the properties of a dental feldspathic glass-ceramic material developed for the slurry-based additive manufacturing technology “LSD-print.”
Material and methods
Three water-based feldspathic feedstocks were produced to study the effects of polyvinyl alcohol (AC1) and poly (sodium 4-styrenesulfonate) (AC2) as binder systems. A feedstock without organic additives was tested as the control group (CG). Disc-shaped (n = 15) and bar (n = 7) specimens were slip-cast and characterized in the green and fired states. In the green state, density and flexural strength were measured. In the fired state, density, shrinkage, flexural strength (FS), Weibull modulus, fracture toughness (KIC), Martens parameters, and microstructure were analyzed. Disc-shaped and bar specimens were also cut from commercially available CAD/CAM blocks and used as a target reference (TR) for the fired state.
Results
In the green state, CG showed the highest bulk density but the lowest FS, while the highest FS in the green state was achieved with the addition of a cross-linking ink. After firing, no significant differences in density and a similar microstructure were observed for all slip-cast groups, indicating that almost complete densification could be achieved. The CAD/CAM specimens showed the highest mean FS, Weibull modulus, and KIC, with significant differences between some of the slip-cast groups.
Significance
These results suggest that the investigated feedstocks are promising candidates for the slurry-based additive manufacturing of restorations meeting the class 1a requirements according to DIN EN ISO 6871:2019–01.
In this work we instigated the fragmentation of Au microparticles supported on a thin amorphous carbon film by irradiating them with a gradually convergent electron beam inside the Transmission Electron Microscope. This phenomenon has been generically labeled as “electron beam-induced fragmentation” or EBIF and its physical origin remains contested. On the one hand, EBIF has been primarily characterized as a consequence of beam-induced heating. On the other, EBIF has been attributed to beam-induced charging eventually leading to Coulomb explosion. To test the feasibility of the charging framework for EBIF, we instigated the fragmentation of Au particles under two different experimental conditions. First, with the magnetic objective lens of the microscope operating at full capacity, i.e. background magnetic field B = 2 T, and with the magnetic objective lens switched off (Lorenz mode), i.e. B = 0 T. We observe that the presence or absence of the magnetic field noticeably affects the critical current density at which EBIF occurs. This strongly suggests that magnetic field effects play a crucial role in instigating EBIF on the microparticles. The dependence of the value of the critical current density on the absence or presence of an ambient magnetic field cannot be accounted for by the beam-induced heating model. Consequently, this work presents robust experimental evidence suggesting that Coulomb explosion driven by electrostatic charging is the root cause of EBIF.
In this work we instigated the fragmentation of Au microparticles supported on a thin amorphous carbon film by irradiating them with a gradually convergent electron beam inside the Transmission Electron Microscope. This phenomenon has been generically labeled as ‘‘electron beam-induced fragmentation’’ or EBIF and its physical origin remains contested. On the one hand, EBIF has been primarily characterized as a consequence of beam-induced heating. On the other, EBIF has been attributed to beam-induced charging eventually leading to Coulomb explosion. To test the feasibility of the charging framework for EBIF, we instigated the fragmentation of Au particles under two different experimental conditions. First, with the magnetic objective lens of the microscope operating at full capacity, i.e. background magnetic field 𝐵 = 2 T, and with the magnetic objective lens switched off (Lorenz mode), i.e. 𝐵 = 0 T. We observe that the presence or absence of the magnetic field noticeably affects the critical current density at which EBIF occurs. This strongly suggests that magnetic field effects play a crucial role in instigating EBIF on the microparticles. The dependence of the value of the critical current density on the absence or presence of an ambient magnetic field cannot be accounted for by the beam-induced heating model. Consequently, this work presents robust experimental evidence suggesting that Coulomb explosion driven by electrostatic charging is the root cause of EBIF.
This research deals with the development of the Vickers hardness knowledge graph, mapping the example dataset in them, and exporting the data-mapped knowledge graph as a machine-readable Resource Description Framework (RDF). Modeling the knowledge graph according to the standardized test procedure and using the appropriate upper-level ontologies were taken into consideration to develop the highly standardized, incorporable, and industrial applicable models. Furthermore, the Ontopanel approach was utilized for mapping the real experimental data in the developed knowledge graphs and the resulting RDF files were successfully evaluated through the SPARQL queries.
AbstractThis study applies Semantic Web technologies to advance Materials Science and Engineering (MSE) through the integration of diverse datasets. Focusing on a 2000 series age-hardenable aluminum alloy, we correlate mechanical and microstructural properties derived from tensile tests and dark-field transmission electron microscopy across varied aging times. An expandable knowledge graph, constructed using the Tensile Test and Precipitate Geometry Ontologies aligned with the PMD Core Ontology, facilitates this integration. This approach adheres to FAIR principles and enables sophisticated analysis via SPARQL queries, revealing correlations consistent with the Orowan mechanism. The study highlights the potential of semantic data integration in MSE, offering a new approach for data-centric research and enhanced analytical capabilities.
This study investigates the room‐ and high‐temperature (650 °C) tensile and low‐cycle‐fatigue behavior of Inconel 718 produced by laser powder bed fusion (PBF‐LB/M) with a four‐step heat treatment and compares the results to the conventional wrought material. The microstructure after heat treatment is characterized on different length scales. Compared to the wrought variant, the elastic and yield properties are comparable at both test temperatures while tensile strength, ductility, and strain hardening capacity are lower. The fatigue life of the PBF‐LB/M variant at room temperature is slightly lower than that of the wrought material, while at 650 °C, it is vice versa. The cyclic stress response for both material variants is characterized by cyclic softening, which is more pronounced at the higher test temperature. High strain amplitudes (≥0.7%) at room temperature and especially a high testing temperature result in the formation of multiple secondary cracks at the transitions of regions comprising predominantly elongated grain morphology and columns of stacked grains with ripple patterns in the PBF‐LB/M material. This observation and pronounced crack branching and deflection indicate that the cracks are controlled by sharp micromechanical gradients and local crystallite clusters.
Processing and cytocompatibility of Cu-doped and undoped fluoride-containing bioactive glasses
(2024)
Sintered or additive-manufactured bioactive glass (BG) scaffolds are highly interesting for bone replacement applications. However, crystallization often limits the high-temperature processability of bioactive glasses (BGs). Thus, the BG composition must combine high bioactivity and processability. In this study, three BGs with nominal molar (%) compositions 54.6SiO2-1.7P2O3-22.1CaO-6.0Na2O-7.9K2O-7.7MgO (13–93), 44.8SiO2-2.5P2O3-36.5CaO-6.6Na2O-6.6K2O-3.0CaF2 (F3) and 44.8SiO2-2.5P2O3-35.5CaO-6.6Na2O-6.6K2O-3.0CaF2-1.0CuO (F3–Cu) were investigated. The dissolution and ion release kinetics were investigated on milled glass powder and crystallized particles (500–600 μm). All glasses showed the precipitation of hydroxyapatite (HAp) crystals after 7 days of immersion in simulated body fluid. No significant differences in ion release from glass and crystalline samples were detected. The influence of surface roughness on cytocompatibility and growth of preosteoblast cells (MC3T3-E1) was investigated on sintered and polished BG pellets. Results showed that sintered BG pellets were cytocompatible, and cells were seen to be well attached and spread on the surface after 5 days of incubation. The results showed an inverse relation of cell viability with the surface roughness of pellets, and cells were seen to attach and spread along the direction of scratches.
Extended X-ray absorption fine structure (EXAFS) conducted on an equiatomic MoNbTaW bcc medium-entropy alloy that was annealed at 2273 K reveals unexpectedly small 1st and 2nd shell element-specific lattice distortions. An experimental size-mismatch parameter, δexp, is determined to be ca. 50% lower than the corresponding calculated value. Around W, short-range order (SRO) preferring 4d elements in the 1st and 2nd shells persists. A Nb-W ordering is found, which is reminiscent of ordering emerging at lower temperatures in the B2(Mo,W;Ta,Nb)- and B32(Nb,W)-phases. With high-temperature ordering preferences in fcc also foreshadowing low-temperature phase, these findings suggest a general feature of high-temperature SRO.
The digitalization of materials science and engineering (MSE) is currently leading to remarkable advancements in materials research, design, and optimization, fueled by computer‐driven simulations, artificial intelligence, and machine learning. While these developments promise to accelerate materials innovation, challenges in quality assurance, data interoperability, and data management have to be addressed. In response, the adoption of semantic web technologies has emerged as a powerful solution in MSE. Ontologies provide structured and machine‐actionable knowledge representations that enable data integration, harmonization, and improved research collaboration. This study focuses on the tensile test ontology (TTO), which semantically represents the mechanical tensile test method and is developed within the project Plattform MaterialDigital (PMD) in connection with the PMD Core Ontology. Based on ISO 6892‐1, the test standard‐compliant TTO offers a structured vocabulary for tensile test data, ensuring data interoperability, transparency, and reproducibility. By categorizing measurement data and metadata, it facilitates comprehensive data analysis, interpretation, and systematic search in databases. The path from developing an ontology in accordance with an associated test standard, converting selected tensile test data into the interoperable resource description framework format, up to connecting the ontology and data is presented. Such a semantic connection using a data mapping procedure leads to an enhanced ability of querying. The TTO provides a valuable resource for materials researchers and engineers, promoting data and metadata standardization and sharing. Its usage ensures the generation of finable, accessible, interoperable, and reusable data while maintaining both human and machine actionability.
Thermoelectric generators are very attractive devices for waste heat energy harvesting as they transform a temperature difference into electrical power. However, commercially available generators show poor power density and limited operation temperatures. Research focuses on high‐temperature materials and innovative generator designs. Finding the optimal design for a given material system is challenging. Here, a theoretical framework is provided that allows appropriate generator design selection based on the particular material properties. For high‐temperature thermoelectric oxides, it can be clearly deduced that unileg multilayer generators have the highest potential for effective energy harvesting. Based on these considerations, prototype unileg multilayer generators from the currently best thermoelectric oxide Ca3Co4O9 are manufactured for the first time by industrially established ceramic multilayer technology. These generators exhibit a power density of 2.2 mW/cm² at a temperature difference of 260 K, matching simulated values and confirming the suitability of the technology. Further design improvements increase the power density by a factor of 22 to facilitate practicable power output at temperature differences as low as 7 K. This work demonstrates that reasonable energy harvesting at elevated temperatures is possible with oxide materials and appropriate multilayer design.
The unusual behavior observed in the coefficient of thermal expansion and specific heat capacity of CrFeNi, CoCrNi, and CoCrFeNi medium/high-entropy alloys is commonly referred to as the K-state effect. It is shown to be independent of the Curie temperature, as demonstrated by temperature-dependent magnetic moment measurements. CoCrFeNi alloy is chosen for detailed characterization; potential reasons for the K-state effect such as texture, recrystallization, and second-phase precipitation are ruled out. An examination of the electronic structure indicates the formation of a pseudo-gap in the Density of States, which suggests a specific chemical interaction between Ni and Cr atoms upon alloying. Hybrid Monte Carlo/Molecular Dynamic (MC/MD) simulations indicate the presence of non-negligible chemical short-range order (CSRO). Local lattice distortions are shown to be negligible, although deviations around Cr and Ni elements from those expected in a fully disordered structure are experimentally observed by X-ray absorption spectroscopy. The determined bonding distances are in good agreement with MC/MD calculations. A mechanism is proposed to explain the anomalies and calorimetric experiments and their results are used to validate the mechanism.
Irradiation assisted stress corrosion cracking (IASCC) is a form of intergranular stress corrosion cracking that occurs in irradiated austenitic alloys. It requires an irradiated microstructure along with high temperature water and stress. The process is ubiquitous in that it occurs in a wide range of austenitic alloys and water chemistries, but only when the alloy is irradiated. Despite evidence of this degradation mode that dates back to the 1960s, the mechanism by which it occurs has remained elusive. Here, using high resolution electron backscattering detection to analyze local stress-strain states, high resolution transmission electron microscopy to identify grain boundary phases at crack tips, and decoupling the roles of stress and grain boundary oxidation, we are able to unfold the complexities of the phenomenon to reveal the mechanism by which IASCC occurs. The significance of the findings impacts the mechanical integrity of core components of both current and advanced nuclear reactor designs worldwide.
In the past two decades, numerous relaxation or physical aging experiments of metallic glasses have revealed signatures of intermittent atomic-scale processes. Revealed via intensity cross-correlations from coherent scattering using X-ray photon correlation spectroscopy (XPCS), the observed abrupt changes in the time-domain of atomic motion does not fit the picture of gradual slowing down of relaxation times and their origin continues to remain unclear. Using a binary Lennard-Jones model glass subjected to microsecond-long isotherms, we show here that temporally and spatially heterogeneous atomic-cluster activity at different length-scales drive the emergence of highly non-monotonous intensity cross-correlations. The simulated XPCS experiments reveal a variety of time-dependent intensity-cross correlations that, depending on both the structural evolution and the 𝑞-space sampling, give detailed insights into the possible structural origins of intermittent aging measured with XPCS.
Using the method of directional solidification, single crystals of experimental nickel-based superalloys with negative, zero, and positive γ/γ' misfits are obtained. The γ' solvus, solidus, and liquidus temperatures of the alloys are determined, and the microstructures of the alloys after directional solidification, heat treatment, and creep tests are investigated. Creep tests are performed at temperatures of 800 and 1000°C. It is found that single crystals of the alloy with a negative γ/γ' misfit have the highest creep resistance and lifetime (the crystal lattice period of the γ' phase is smaller than that of the γ matrix).