Multiphase Materials Research Articles

Design of multi-material structures using material jetting technology: Topology optimisation, numerical analysis and experiments

This paper presents a thorough experimental/numerical validation of optimised multi-material structures fabricated by material jetting technology. The proposed methodology uses, on the one hand, non-uniform rational basis spline (NURBS) entities to represent the geometric descriptor associated with each material phase constituting the continuum and, on the other hand, a general multi-phase material interpolation scheme to penalise the stiffness tensor of the structure. Two design requirements are included in the problem formulation: the lightness and the minimum length scale of each material phase. The influence of the integer parameters intervening in the definition of the NURBS entity and the influence of different combinations of material phases on the optimised solutions are investigated. The proposed approach is applied to 2D and 3D benchmark structures subjected to prescribed displacements representative of a three-point bending test. Based on the result of the topology optimisation process one of the optimised solutions, balancing the requirements of structural stiffness, lightness, and manufacturing constraints, is selected, manufactured and tested. A comparison between experimental and numerical results (obtained by non-linear analyses) is carried out to show the effectiveness of the approach.

Heat transfer mechanism of TiO2-doped silica aerogel

The remarkable thermal insulation properties of silica aerogel stem from its distinctive three-dimensional nano-network structure, rendering it a promising candidate for diverse applications such as energy-efficient construction and aerospace engineering, among others. Nonetheless, the application of pure silica aerogels at high temperatures is limited due to their nearly transparent nature in the wavelength range of 2–8 µm. To overcome this limitation, the incorporation of opacifiers into pure silica aerogels can effectively augment the overall extinction coefficient of the material, consequently minimizing radiative heat transfer. In this paper, titanium dioxide is used to improve the high-temperature thermal insulation performance of silica aerogels. In order to fully understand the internal heat transfer properties of silica aerogel-based composites theoretically and to provide guidance for the structural design of high-temperature insulation materials, a theoretical model is established. This model accounts for the actual microstructure of the materials as well as the porous structural properties of the secondary particles in silica aerogel. Furthermore, it considers the intricate nature of heat transfer in multiphase hybrid materials. This paper compares the predictions of the model with experimental data. The results show that the theoretical model can quickly and accurately predict the thermal conductivity of TiO2-doped silica aerogels, and the error is controlled within 8 %, with a minimum error of 1.1 %.

An accelerated scheme for solving inhomogeneous elasticity in phase-field method and application to Ni-based multi-component alloys

On the way towards realistic predictions of various material properties for engineering structural materials, efficient computational simulations of microstructural evolution play an indispensable role. In the present work, an in-house phase-field code with inhomogeneous elasticity has been developed aiming to deal with precipitation processes for multi-component alloys with high efficiency. Two different numerical iterative algorithms, named as Model A and B, are implemented to solve inhomogeneous elastic equations. The resulting simulated morphology and energy evolutions under different conditions show consistency for these two algorithms. In order to perform simulation efficiently, a parallel technique based on CUDA (Computer Unified Device Architecture) architecture is used, which greatly improves the computational efficiency. After estimating the computational efficiency of different acceleration techniques for different grid sizes, Model A is extended to simulate concentration and morphology evolutions in the precipitation and rafting processes of γ′ phase in a Ni-based five-component alloy of Ni−Co−Al−Mo−W. Meanwhile, the CALPHAD method and related databases are linked to provide thermodynamic and diffusivity data. Finally, the computation costs of the parallel technique for different simulation scales are explored, testifying that this technique is capable of performing larger scale simulations for multi-component multi-phase structural materials.

Design, synthesis, and influencing factors of medium-/high-entropy Y2(ZrTiGeHfSnSi)2O7 with a pyrochlore structure

A set of medium-/high-entropy pyrochlore oxides (M-HEPOs) with different compositions were designed and synthesized. The phase compositions of the prepared materials were determined through X-ray diffraction and Raman spectroscopy. Among the 24 designed samples, two high-entropy and six medium-entropy samples formed single-phase pyrochlore materials, two medium-entropy samples formed dual-phase pyrochlore materials, and the others formed multiphase materials dominated by the pyrochlore phase. The factors affecting the formation of single-phase pyrochlore structure were studied. The results revealed that size disorder is a major element determining the formation of single-phase pyrochlore, whereas mixing entropy has minimal effect. It is anticipated that this study will provide significant insights into the effects of size disorder and mixing entropy on the formation of M-HEPOs.

The effect of nucleating agent on the multiphase change materials for energy storage in buildings

Phase change materials (PCMs) have the potential to be used for widespread energy storage applications in buildings. However, available PCMs can only function at fixed phase transitional temperatures, restricting their seasonal applicability. To this end, some studies have been carried out to develop multiphase change materials (MCMs). Prior to having competitive advantage, their encapsulation efficiency needs to be improved. In this study, MCM has been developed by combining two microencapsulated PCMs (MEPCMs), through Van der Wall’s interaction forces phenomenon. In-situ polymerisation was adopted to fabricate the MEPCMs by employing RT22 and RT64 as PCMs. The optimalamount of nucleating agent played a crucial role in obtaining high encapsulation efficiencies of microencapsulated RT22 (MERT22) and RT64 (MERT64) by 90.43% and 84.07%, respectively. The developed MCM achieved melting temperatures at 23.01 °C and 56.64 °C, with combined energy storage capacity of 163.17 J/g, and encapsulation efficiency of 83.81%. The MCM also had thermal stability temperature of 142.71 °C, exceeding common building operating temperature. The nucleating agent also affected the sample morphology and particle size distribution, which therefore requires optimisation. There is also the need for thermal enhancement since it remains as one of the limiting factors of PCMs.

Mastering the rheology of fresh concrete: New knowledge from a DFG priority program SPP 2005

AbstractThe processing of cement‐based building materials represents the technological core in the construction and maintenance of structures. However, a scientific framework for mastering rheology‐based processes is still in an early stage of its development. The reason for this is the extremely high complexity of cementitious systems. This complexity includes the high chemical reactivity of mineral binders, the complex multi‐phase nature of fresh concrete or mortar, and a wide range of deformation rates during various technological processes, which result in extremely high demands for characterization and simulation methods. The goal of the DFG Priority Program SPP 2005 “Opus Fluidum Futurum – Rheology of reactive, multiscale, multiphase construction materials” is to ascertain and describe the scientific fundamentals for understanding and, subsequently, designing rheology‐based construction processes as well as for developing innovative, sustainable building materials and associated pioneering processing technologies. The article at hand presents the purpose and the structure of the collaborative research as well as the achievements of the priority program. Furthermore, it offers some insights into ongoing and planned research.

Segmentability evaluation of back-scattered SEM images of multiphase materials

Segmentation methods are very useful tools in the Electron Microscopy inspection of materials, enabling the extraction of quantitative results from microscopy images. Back-Scattered Electron (BSE) images carry information of the mean atomic number in the interaction volume and hence can be used to quantify the phase composition in multiphase materials. Since phase composition and proportion affects the material properties and hence its applications, the segmentation accuracy of such images rendered of critical importance for material science. In this work, the notion of segmentability for BSE images is proposed to define the ability of an image to be segmented accurately. This notion can be used to guide the image acquisition process so that segmentability is maximized and segmentation accuracy is ensured. An index is devised to quantify segmentability based on a combination of the modified Fisher Discrimination Ratio and of the second Minkowski functional capturing intensity and spatial aspects of BSE images respectively. The suggested Segmentability Index (SI) is validated in synthetic BSE images which are generated with a novel algorithm allowing the independent control of spatial distribution of phases and their grayscale intensity histograms. Additionally, SI is applied in real-synthetic BSE images, where the real greyscale distributions of Ordinary Portland Cement (OPC) clinker crystallographic phases are used, to demonstrate the ability of SI to indicate the optimum choice of critical image acquisition settings leading to the more accurate segmentation output.

Modelling and Prediction of Fe/MWCNT Nanocomposites for Hexavalent Chromium Reduction

Chromium (Cr) is a heavy metal pollutant prevalent in freshwater resources. Current investigations into Cr(VI) removal materials primarily involve multi-component materials. Among them, iron nanoparticles and multi-walled carbon nanotubes (MWCNTs) have exhibited great promise of removal capabilities. However, determining the optimal component ratio(s) experimentally still requires a substantial amount of effort. This paper presents a novel, model-based approach which can lessen the burden by predicting the performance of new materials. The model is based on reaction kinetics equations and derives its input parameters from the size and surface area characterisations of the components, individual components removal performance, and their mixture performance at one specific component ratio. The model is validated against experimental results for Fe/MWCNT mixtures at six ratios. The root mean square error of our model is 3.95 mg/g, which is less than 3% of the total adsorption capacity, indicating that the model is reliable. The model can be used to identify the optimal component ratios of the Fe-MWCNT composite and to reveal the relationship between performance and time. To the best of our knowledge, this is the first semi-empirical model that can predict the adsorption capacity of a composite material for heavy metals. The model is founded on the generic reduction theory of adsorption, and model parameters are not tied specifically to Fe/MWCNT. Thus, it can be used for predicting the adsorption reduction properties of other multiphase materials to speed up the new material design process.

Dynamic stability examination of perovskite solar cells: Application of numerical analysis, GAN and African vulture optimization algorithms

The most plentiful energy source, solar energy, can be used even while it's cloudy outside. Around 10,000 times more solar energy is being absorbed by the Earth than is being used by people. For several functions, solar systems may provide fuel, power, heat, cooling, and natural lighting. Solar technology may use photovoltaic panels or solar radiation-concentrating mirrors to turn sunlight into electrical energy. Multiple contexts may benefit from the utilization of solar energy. Hence, enhancing the natural frequency of such a system and comprehending its dynamics are crucial in the engineering sector. The objective of the present study is to reinforce the metal layer of solar cells with multi-phase hybrid nanocomposite materials in order to improve its natural frequency. Carbon fiber (CF) and carbon nanotube (CNT), which are reinforcements with macro- and nanoscale dimensions, respectively, are used to strengthen an aluminum matrix that makes up the final layer of the structure. The introduction of infinite and finite displacement fields simulates the compression applied to a solar panel that is either fully clamped or merely supported. The Kronecker tensor product utilizes the generalized differential quadrature method (GDQM) to resolve the dynamic response of the system. As well as numerical analysis, we highlight advanced methods such as Generative Adversarial Networks (GAN) and African Vulture Optimization (AVO) algorithms, used to address dynamic stability challenges in perovskite solar cells. After that, by coupling the mentioned algorithms, an innovative algorithm for solving the engineering problems is presented. By generating synthetic data and optimizing system performance, scientists aim to analyze dynamic stability, promoting broader adoption of perovskite solar cells in the renewable energy industry. Finally, the dynamics of the perovskite solar cells are then suggested to be enhanced by a variety of physical and geometrical factors utilizing the numerical analysis and methods previously discussed.

Improvement of τf in HfTiO4 microwave dielectric ceramics with Zr‐ and Sn‐substitution

Abstract(Hf1‐xZrx)TiO4 and (Hf1‐xSnx)TiO4 ceramics were prepared through a standard solid‐state reaction route, and the microwave dielectric characteristics were determined together with the microstructures. The single‐phase solid solution in space group Pbcn was obtained in (Hf1‐xZrx)TiO4, while the two‐phase structure with (HfTiO4(s.s.) major phase in space group Pbcn and Sn0.3Ti0.7O2 secondary phase in space group P42/mnm) was determined in (Hf1‐xSnx)TiO4. The temperature coefficient of resonant frequency τf could be significantly improved to near‐zero in both systems, and the best combination of microwave dielectric characteristic was achieved at x = 0.5 in (Hf1‐xZrx)TiO4: εr = 39.0, Qf = 43,150 GHz at 5.3 GHz and τf = 3 ppm/°C, and at x = 0.225 in (Hf1‐xSnx)TiO4: εr = 37.2, Qf = 52,600 GHz at 5.5 GHz and τf = ‐6 ppm/°C. In the solid solutions, the obvious improvement of τf could be deeply linked with the degree of covalency and the restoring forces of structure. While, the intermediate near‐zero τf is achieved by mixing the phases with opposite τf in multiphase materials. The present work provided an effective way to modify the temperature coefficient of resonant frequency in microwave dielectric ceramics.

Multiscale topology optimization framework for natural frequency maximization of multi-morphology lattice structures

This paper proposes a multiscale topology optimization framework for maximizing the natural frequency of multi-morphology lattice structures (MMLSs). The proposed framework addresses the challenges of computational efficiency, design space, numerical convergence, and compatibility between adjacent microstructures in multiscale topology optimization for natural frequency problems. The macrostructural topology, the morphologies categories, distribution regions, volume fractions of different lattice materials (LMs), and the relative densities of lattice unit cells (LUCs) are simultaneously optimized to enhance the structural natural frequency. Specifically, level set functions are utilized to generate prototype LUCs, enabling obtaining graded LUCs by configuration interpolation. Multi-morphology LUCs with smooth characteristics are achieved using the Kriging-assisted morphological post-process and sigmoid function (SF) based hybrid transition strategy. Kriging metamodel-assisted Uniform Multiphase Materials Interpolation (KUMMI) schemes are constructed for the mechanical properties estimation of macro elements to promote the multiscale topology optimization procedure. Distinct processing methods for LUCs' elasticity tensor and density are incorporated within the KUMMI schemes, by which the local mode problem is avoided. The objective order natural frequency is accurately optimized with the modal assurance criterion (MAC) based mode-tracking technique. Numerical examples demonstrate that the developed design framework can efficiently maximize the natural frequency of MMLSs, while also ensuring microstructural connectivity.

Mechanisms of Shock Dissipation in Semicrystalline Polyethylene.

Semicrystalline polymers are lightweight, multiphase materials that exhibit attractive shock dissipation characteristics and have potential applications as protective armor for people and equipment. For shocks of 10 GPa or less, we analyzed various mechanisms for the storage and dissipation of shock wave energy in a realistic, united atom (UA) model of semicrystalline polyethylene. Systems characterized by different levels of crystallinity were simulated using equilibrium molecular dynamics with a Hugoniostat to ensure that the resulting states conform to the Rankine-Hugoniot conditions. To determine the role of structural rearrangements, order parameters and configuration time series were collected during the course of the shock simulations. We conclude that the major mechanisms responsible for the storage and dissipation of shock energy in semicrystalline polyethylene are those associated with plastic deformation and melting of the crystalline domain. For this UA model, plastic deformation occurs primarily through fine crystallographic slip and the formation of kink bands, whose long period decreases with increasing shock pressure.

Multiphasic model of early stage hydration in concrete using the theory of porous media

AbstractThe aim of this paper is to model the behavior of concrete during the initial stage of maturing. Most models consider only thermo‐mechanical phenomena assuming the hygral phenomena of less importance due to high liquid saturation. In order to grasp those effects, the proposed model is an extension of Gawin's model (D. Gawin, F. Pesavento, and B. A. Schrefler, Int J Numer Methods Eng 67(3), 299–331, 2006). The fresh concrete, modeled as porous material, is described within the well‐founded framework of the Theory of Porous Media. The multiphase material consists of a solid phase representing, for example, cement, gravel, etc., and a fluid and gas phase representing the pores filled with water and dry air. Compared to Gawin's model, here, beside the effect of hydration‐dehydration, the effect of evaporation‐condensation will be taken into account. A new formulation for the evaporation process in the fresh concrete is proposed and validated by an experimental study. The presented model is implemented in the research code PANDAS. The proposed model investigates and proves the assumption of Gawin's model to have a linear connection between porosity and hydration degree.

A homogeneous composite approach for improved thermoelectric performance: Repressing lattice thermal conductivity in substoichiometric WO2.90 and WO2.72

Nanostructured phonon-glass thermoelectric materials are highly sought after for heat waste recovery applications. This work introduces a novel phonon-glass multi-phase ceramic material synthesized from sintered mixtures of two sub-stoichiometric tungsten oxides, WO2.90 and WO2.72. Notable measurements were recorded for our sample, denoted as 0.1WO2.72/0.9WO2.90, at 800 °C, with S2σ = 0.51 ± 0.03 mWm−1K−2, representing a tenfold increase compared to the base materials. The lattice thermal conductivity, already displaying phonon-glass characteristics, is further suppressed by the addition of the secondary WO2.72 pentacolumn phase, reaching its lowest value at 0.54 ± 0.25 Wm−1K−1. As a result, the ZT value is enhanced to twice the intrinsic value of the pristine phase. This study demonstrates a novel strategy for improving the thermoelectric performance of oxide-based materials by leveraging a synergistic relationship among several key factors, including phonon-glass nanostructures, tunable electrical properties, and the reduction of lattice thermal conductivity within a homogeneous composite system.

Microstructure Image-Based Finite Element Methodology to Design Abradable Coatings for Aero Engines

Upgrading abradable or wearable coatings in the high-temperature zone of aero engines is advised to increase the efficiency and high-density power in gas turbine engines for military or commercial fixed-wing and rotary-wing aircraft. The development of these coated materials is also motivated by minimization of the number of failures in the blade, as well as increasing their resistance to wear and erosion. It is suggested that abradable coatings or seals be used to accomplish this goal. The space between the rotor and the shroud is minimized thanks to an abradable seal at the blade’s tip. Coatings that can withstand abrasion are often multiphase materials sprayed through thermal spray methods, and which consist of a metal matAzmeerix, oxide particles, and void space. The maintenance of an ideal blend of qualities, such as erosion resistance and hardness, during production determines a seal’s effectiveness. The objective of this research is to develop microstructure-based modelling methodology which will mimic the coating wear process and subsequently help in designing the abradable coating composition. Microstructure modelling, meshing, and wear analysis using many tools such as Fusion360, Hyper Mesh, and LS-Dyna, have been employed to develop an abradable coating model and perform wear analysis using a simulated rub rig test. The relation between percentage composition and morphology variations of metal, oxide, and voids to the output parameters such as hardness, abradability, and other mechanical properties is explored using simulated finite analysis models of real micrographic images of abradable coatings.

Scanning precession electron diffraction data analysis approaches for phase mapping of precipitates in aluminium alloys

Mapping the spatial distribution of crystal phases with nm-scale spatial resolution is an important characterisation task in studies of multi-phase materials. One popular approach is to use scanning precession electron diffraction which enables semi-automatic phase mapping at the nanoscale by collecting a single precession electron diffraction pattern at every probe position over regions spanning up to a few micrometers. For a successful phase mapping each diffraction pattern must be correctly identified. In this work four different approaches for phase mapping of embedded precipitates in an Al-Cu-Li alloy are compared on a sample containing three distinct crystal phases. These approaches are based on: non-negative matrix factorisation, vector matching, template matching and artificial neural networks. To evaluate the success of each approach a ground truth phase map was manually created from virtual images based on characteristic phase morphologies and compared with the deduced phase maps. The percentage accuracy of all methods when compared to the ground truth was satisfactory, with all approaches obtaining scores above 98%. The optimal method depends on the specific task at hand. Non-negative matrix factorisation is suitable with limited prior data knowledge but performs best with few unique diffraction patterns and requires substantial post-processing. It has the advantage of reducing the dimensionality of the dataset and handles weak diffracted intensities well given that they occur repeatedly. The current vector matching implementation is fast, simple, based only on the Bragg spot geometry and requires few parameters. It does however demand that each Bragg spot is accurately detected in each pattern and the current implementation is limited to zone axis patterns. Template matching handles a large range of orientations, including off-axis patterns. However, achieving successful and reliable results often require thorough data pre-processing and do require adequate diffraction simulations. For artificial neural networks a substantial setup effort is demanded but once trained it excels for routine tasks, offering fast predictions. The implemented codes and the data used are available open-source. These resources and the detailed assessment of the methods will allow others to make informed decisions when selecting a data analysis approach for 4D-STEM phase mapping tasks on other material systems.

Influence of the Mn5Ge3/Ge ohmic-contact interface on the Seebeck coefficient of the Mn5Ge3/Ge bilayer

Thermoelectricity is a well-known effect that can be used to convert heat energy into electrical energy. However, the yield of this conversion is still low compared to current photovoltaic technology. It is limited by the intrinsic properties of materials, leading to intensive materials science investigations for the design of efficient thermoelectric (TE) materials. Interface engineering was shown to be a valuable solution for improving materials’ TE properties, supporting the development of multiphase TE materials. In particular, interfaces have been suggested to promote the increase of the Seebeck coefficient of materials without significantly impacting their electrical conductivity through the so-called energy filtering effect. This work aims at determining experimentally the effect of a metal/semiconductor interface exhibiting an ohmic character on the effective Seebeck coefficient of multiphase materials, focusing on the n-type Mn5Ge3/p-type Ge interface. This interface is shown not to contribute to carrier transport, but to contribute to carrier concentration filtering due to carrier injection or recombination. The Seebeck coefficient of the bi-phase material is shown to be dependent on the direction carriers are crossing the interface. The interface effect mainly results from a modification of charge carrier concentrations in the semiconductor.

A distortion-map-based method for morphology generation in multi-phase materials - application to wood

Increased use of multi-phase, wood-based biocomposites may contribute to sustainable development. The porous microstructure offers unique possibilities for modification, but global properties are often predicted based on simplified unit cells and homogenization. For materials design, simulations based on complex 3D microstructures with statistical variability are alternatives to better understanding physical properties. Parametric models are developed in a distortion-map-based method to represent 3D wood microstructures. Basic structures of uniform tubular cells and other features are generated followed by distortion mapping. These maps are highly adaptable and can generate realistic features and variability. Fibers, vessels, and ray cells are realistically distributed. The models are realistic, versatile, and scalable, as well as can be used to simulate the mechanical, optical, and hydrodynamic properties of complex composites. The model is promising for generating large sets of data to train deep learning networks for multi-physics research.

Towards energy filtering in Mg2X-based composites: Investigating local carrier concentration and band alignment via SEM/EDX and transient Seebeck microprobe analysis

A comprehensive understanding of multi-phase materials requires the characterization of transport properties at the micro/nano-scale. Optimized alignments of the conduction bands and valence bands at the interfaces of multi-phase materials can enhance the properties of thermoelectric materials by filtering out undesired charge carriers and is a promising path towards high performance thermoelectric devices. Here, a micro-scale characterization technique using transient Seebeck microprobe analysis, scanning electron microscopy with energy-dispersive X-ray spectroscopy, and electronic transport modelling based on the Boltzmann transport equation modeling is introduced to assess the band diagram and estimate the band offset in multi-phase materials. This characterization technique is applied to a composite of magnesium silicide-based materials. This material class is prone to form self-assembling nano-structured composites driven by a miscibility gap in the solid solutions series. Our analysis reveals changes in carrier concentration upon composite formation and considerable band offsets for both conduction and valence band when synthesizing nominally undoped composites. Employing Bi as dopant we show that Bi exhibits a preference for the Sn-rich phase, changing the carrier concentration differently in the Sn-rich matrix phase compared to the Si-rich secondary phase, effectively altering the band alignment of the composite. This demonstrates that our approach can be utilized to measure and manipulate the band offset within the composite to achieve optimal thermoelectric performance.

Effect of a micro-scale dislocation pileup on the atomic-scale multi-variant phase transformation and twinning

In this paper, we perform concurrent atomistic–continuum (CAC) simulations to assess the contribution of the internal stress induced by the microscale dislocation pileup at an atomically structured interface to the atomic-scale phase transformations (PTs), reverse PTs, and twinning. The main novelty of this work is to unify the atomistic description of the interface and the coarse-grained (CG) description of the lagging dislocations away from the interface within one single framework. Our major findings are: (a) the interface dynamically responds to a pileup by forming steps/ledges, the height of which is proportional to the number of dislocations arriving at the interface; (b) the pileup-induced internal stress concentration profile follows neither the classical Eshelby model nor the super-dislocation model alone, but a combination of them; (c) when the pre-sheared sample is compressed, a direct square-to-hexagonal PT occurs ahead of the pileup tip and eventually grows into a wedge shape. The two variants of the hexagonal phases form a twin with respect to each other; (d) upon a further increase of the loading, part of the newly formed hexagonal phase transforms back to the square phase. The square product phase resulting from this reverse PT forms a twin with respect to the initial square phase. All phase boundaries (PBs) and twin boundaries (TBs) are stationary and correspond to zero thermodynamic Eshelby driving forces; and (e) the microscale dislocation pileup-induced internal shear stress and the structural change at the atomic-scale interface reduces the stress required for initiating a PT by a factor of 5.5, comparing with that in the sample containing no dislocations. This work is the first characterization of the behavior of PTs/twinning resulting from the reaction between a microscale dislocation slip and an atomically structured interface. The gained knowledge will advance our understanding of how the multi-phase material behaves in many complex physical processes, such as the synthesis of multi-phase high-entropy alloys or superhard ceramics under high-pressure torsion, deep mantle earthquakes in geophysics, and so on, which all involve dislocation slip, PTs, twinning, and their interactions across from the atomistic to the microscale and beyond.