Contrast In Material Properties Research Articles

Heterogeneous phase deformation in a dual-phase tungsten alloy mediated by the tungsten/matrix interface: Insights from compression experiments and crystal plasticity modeling

Tungsten heavy alloy (WHA) is a typical multiphase alloy material consisting of hard tungsten (W) and soft matrix (γ) phases. When loaded, the two phases deform quite differently due to the large difference in their mechanical properties. At present, our understanding of phase deformation and behavior in the multiphase context is relatively poor compared to the single phase case. Such insight is necessary, however, for the design of multiphase alloys having optimal phase microstructure and corresponding material behavior. By combining mechanical testing and crystal plasticity modeling, the relationship between phase microstructure and multiphase alloy deformation behavior is systematically investigated in this work. The results demonstrate that deformation in the W and γ phases is quite different and related to the contrast in material properties between the two phases. Deformation heterogeneity in the multiphase alloy is characterized by the strain gradient near/across the W/γ interface and differences in phase deformation states in relation to the contrast in phase material properties and phase volume fraction. It is found that dislocation pile-up and twinning are the main mechanisms mediating heterogeneous deformation in the region around W/γ interfaces. Based on this insight, a novel design strategy for multiphase alloys is proposed based on optimization of the contrast in phase mechanical properties and the phase volume fractions. This strategy can be employed to design new tungsten alloys and other multi-phase alloys.

Expanded Stability of Layered SnSe-PbSe Alloys and Evidence of Displacive Phase Transformation from Rocksalt in Heteroepitaxial Thin Films.

Bulk PbSnSe has a two-phase region, or miscibility gap, as the crystal changes from a van der Waals-bonded orthorhombic 2D layered structure in SnSe-rich compositions to the related 3D-bonded rocksalt structure in PbSe-rich compositions. This structural transition drives a large contrast in the electrical, optical, and thermal properties. We realize low temperature direct growth of epitaxial PbSnSe thin films on GaAs via molecular beam epitaxy using an in situ PbSe surface treatment and show a significantly reduced two-phase region by stabilizing the Pnma layered structure out to Pb0.45Sn0.55Se, beyond the bulk limit around Pb0.25Sn0.75Se at low temperatures. Pushing further, we directly access metastable two-phase films of layered and rocksalt grains that are nearly identical in composition around Pb0.50Sn0.50Se and entirely circumvent the miscibility gap. We present microstructural and compositional evidence for an incomplete displacive transformation from a rocksalt to layered structure in these films, which we speculate occurs during the sample cooling to room temperature after synthesis. In situ temperature-cycling experiments on a Pb0.58Sn0.42Se rocksalt film reproduce characteristic attributes of a displacive transition and show a modulation in electronic properties. We find well-defined orientation relationships between the phases formed and reveal unconventional strain relief mechanisms involved in the crystal structure transformation using transmission electron microscopy. Overall, our work adds a scalable thin film integration route to harness the dramatic contrast in material properties in PbSnSe across a potentially ultrafast crystalline-crystalline structural transition.

Frictional slip wave solutions for dynamic sliding between a layer and a half-space

Interfacial waves propagate along the interface between two elastic solids, and are the subject of basic interest to diverse scientific fields, like, seismology, geophysics, material science and composite structures. The focus of the present work is to analyse the interfacial waves arising due to frictional slipping between an elastic layer and an elastic half-space having dissimilar elastic properties, wherein the deformations are confined to the plane of the solids. The interfacial friction is modelled by employing a slip-dependent friction law. The elastodynamic relations between the displacement discontinuities across the fractured interface and the associated traction components of stress for pure slip events (no crack opening along the interface) are obtained. This allows us to derive a secular dispersion relation governing the interfacial wave solutions. The dispersion relation relating the phase velocity and wavenumber is analysed numerically. A family of solutions are shown to exist depending on the critical slip distance, δc, a parameter governing the interfacial friction law, and on the contrast in material properties. We demonstrate the existence of a number of wave modes, all being dispersive in nature. The fundamental wave mode with the lowest phase velocity exists over the largest range of wavenumbers, while other wave modes exist only at sufficiently high non-dimensional wavenumber. The dispersion curves for the frictional slip waves are found to lie between the dispersion curves for the cases of the smooth and the bonded interface. As a case study, the present model is used to study the dispersion of slip waves propagating in Earth's crust-mantle geophysical model. The field observations of surface wave dispersion appear to be in good agreement with that of the frictional slip waves studied here. Based on our results, we suggest an alternative explanation for the observed surface wave dispersion at the regional and global scales. It is suggested that frictional slip waves at the crust-mantle interface could propagate with phase velocities similar to the Rayleigh and Love surface waves.

Impact of sedimentary basins on Green’s functions for static slip inversion

SUMMARY Earthquakes often occur in regions with complex material structure, such as sedimentary basins or mantle wedges. However, the majority of co-seismic modelling studies assume a simplified, often homogeneous elastic structure in order to expedite the process of model construction and speed up calculations. These co-seismic forward models are used to produce Green’s functions for finite-fault inversions, so any assumptions made in the forward model may introduce bias into estimated slip models. In this study, we use a synthetic model of a sedimentary basin to investigate the impact of 3-D elastic structure on forward models of co-seismic surface deformation. We find that 3-D elastic structure can cause changes in the shape of surface deformation patterns. The magnitude of this effect appears to be primarily controlled by the magnitude of contrast in material properties, rather than the sharpness of contrast, the fault orientation, the location of the fault, or the slip orientation. As examples of real-world cases, we explore the impact of 3-D elastic structure with a model of the Taipei basin in Taiwan and a simulated earthquake on the Sanchaio fault, and with a 3-D geologic model of the San Francisco Bay Area and a slip model of the 1984 Morgan Hill earthquake on the Calaveras fault. Once again, we find that the presence of the basin leads to differences in the shape and amplitude of the surface deformation pattern, but we observe that the primary differences are in the magnitude of surface deformation and can be accounted for with a layered elastic structure. Our results imply that the use of homogeneous Green’s functions may lead to bias in inferred slip models in regions with sedimentary basins, so, at a minimum, a layered velocity structure should be used.

Simulation of a bubble rising at high Reynolds number with mass-conserving finite element lattice Boltzmann method

A mass-conserving finite element lattice Boltzmann equation (FE-LBE) method for the simulation of a bubble rising in viscous fluid at high Reynolds number with large material property contrast is presented in this work. The presented model consists of the conservative phase-field equation for interface capturing and the pressure-velocity formulation of lattice Boltzmann equation (LBE) for recovering the hydrodynamic properties. In this computational framework, LBE is regarded as a special space time discretization of the discrete Boltzmann equation in the characteristic direction and the streaming step is carried out by solving a linear advection equation in an Eulerian framework. We conduct extensive investigations for numerical accuracy and stability through performing multiple benchmark simulations for single bubble rising in a viscous fluid in different flow regimes. The complex dynamics of a high Reynolds number bubble rising with path and shape oscillations are studied and compared to available experimental results. The simulated evolution of the bubble mean shape with Archimedes number, path and shape oscillations in different oscillation regimes, and wake dynamics of the bubble show a good agreement with available experimental data. The current model offers a remarkable improvement in mass conservation compared to the Cahn-Hilliard based FE-LBE model.

Crystal plasticity based predictions of mechanical properties from heterogeneous steel microstructures

An accurate understanding of the influence of the microstructure on mechanical properties as well as how the material behaves in forming tests is vital for product development and process improvement. The heterogeneity of the microstructure is very different for the various families of steel grades. As a consequence spatial stress and strain distributions on the micro scale will also differ a lot in these materials during forming operations. In the important family of Dual Phase (DP) steel grades. the combination of ductile ferrite phase and hard martensite particles enables an excellent hardening behaviour. However these micro constituents also result in a strong locally heterogeneous behaviour caused by the high material property contrast. To enable an accurate prediction of the materials response in forming processes advanced microstructure models as well as fast crystal plasticity code is essential. Within Tata Steel both are available. A Multi-Level Voronoi microstructure generator, capable of generating very complex Representative Volume Elements, is directly connected to the DAMASK code of the Max Planck Institüt für Eisenforschung. This crystal plasticity software is based on an ultrafast Fourier Spectral Solver. Crystal plasticity simulations with different loading cases (e.g. uni-axial, plane strain, simple shear) study various effects of microstructure heterogeneity on stress and strain distributions as well as on global hardening behaviour. Outcome is that not only the volume fraction but also the spatial distribution of the martensite particles has a large impact on local stresses and strains as well as on average hardening behaviour. Another important heterogeneity parameter is the carbon content, which influences strongly the hardness and hardenability of the martensite particles. An attempt is made to incorporate also this effect in crystal plasticity simulations.

On the competition between dislocation transmission and crack nucleation at phase boundaries

The interaction of dislocations with phase boundaries is a complex phenomenon, that is far from being fully understood. A two-dimensional Peierls-Nabarro finite element (PN-FE) model for studying edge dislocation transmission across fully coherent and non-damaging phase boundaries was recently proposed. This paper brings a new dimension to the complexity by extending the PN-FE model with a dedicated cohesive zone model for the phase boundary. With the proposed model, a natural interplay between dislocations, external boundaries and the phase boundary, including decohesion of that boundary, is provided. It allows one to study the competition between dislocation transmission and phase boundary decohesion. Commonly, the interface potentials required for glide plane behaviour and phase boundary decohesion are established through atomistic simulations. They are corresponding to the misfit energy intrinsic to a system of two bulks of atoms that are translated rigidly with respect to each other. It is shown that the blind utilisation of these potentials in zero-thickness interfaces (as used in the proposed model) may lead to a large quantitative error. Accordingly, for physical consistency, the potentials need to be reduced towards zero-thickness potentials. In this paper a linear elastic reduction is adopted. With the reduced potentials for the glide plane and the phase boundary, the competition between dislocation transmission and phase boundary decohesion is studied for an 8-dislocation pile-up system. Results reveal a strong influence of the phase contrast in material properties as well as the phase boundary toughness on the outcome of this competition. In the case of crack nucleation, the crack length shows an equally strong dependency on these properties.

A computational approach towards modelling dislocation transmission across phase boundaries

ABSTRACTTo study the nanoscopic interaction between edge dislocations and a phase boundary within a two-phase microstructure the effect of the phase contrast on the internal stress field due to the dislocations needs to be taken into account. For this purpose a 2D semi-discrete model is proposed in this paper. It consists of two distinct phases, each with its specific material properties, separated by a fully coherent and non-damaging phase boundary. Each phase is modelled as a continuum enriched with a Peierls–Nabarro (PN) dislocation region, confining dislocation motion to a discrete plane, the glide plane. In this paper, a single glide plane perpendicular to and continuous across the phase boundary is considered. Along the glide plane bulk induced shear tractions are balanced by glide plane shear tractions based on the classical PN model. The model's ability to capture dislocation obstruction at phase boundaries, dislocation pile-ups and dislocation transmission is studied. Results show that the phase contrast in material properties (e.g. elastic stiffness, glide plane properties) alone creates a barrier to the motion of dislocations from a soft to a hard phase. The proposed model accounts for the interplay between dislocations, external boundaries and phase boundary and thus represents a suitable tool for studying edge dislocation–phase boundary interaction in two-phase microstructures.

Subwavelength light confinement and enhancement enabled by dissipative dielectric nanostructures.

Dissipative loss in optical materials is considered one of the major challenges in nano-optics. Here we show that, counter-intuitively, a large imaginary part of material permittivity contributes positively to subwavelength light enhancement and confinement. The Purcell factor and the fluorescence enhancement of dissipative dielectric bowtie nanoantennas, such as Si in ultraviolet (UV), are demonstrated to be orders of magnitude higher than their lossless dielectric counterparts, which is particularly favorable in deep UV applications where metals are plasmonically inactive. The loss-facilitated field enhancement is the result of a large material property contrast and an electric field discontinuity. These dissipative dielectric nanostructures can be easily achieved with a great variety of dielectrics at their Lorentz oscillation frequencies, thus having the potential to build a completely new material platform boosting light-matter interaction over broader frequency ranges, with advantages such as bio-compatibility, CMOS compatibility, and harsh environment endurance.

Matrix equilibration in method of moment solutions of surface integral equations

Basic theory of matrix equilibration is presented, relating it to other techniques for decreasing the condition number of matrix equations obtained by the method of moments (MOM) applied to surface integral equations (SIEs). It is shown that matrix equilibration is a general technique that can be used for both (1) balancing field and source quantities in SIEs, which is used to decrease the condition number in the case of SIEs of mixed type and high contrast in material properties, and (2) scaling basis and test functions in MOM, which is used to decrease the condition number in the case of higher-order bases and patches of different sizes. In particular, it is demonstrated that a combination of such balancing and scaling can be performed using simple matrix equilibration based on magnitudes of diagonal elements and 2-norms of rows/columns of the MOM matrix.

Trade-offs in sensitivity and sampling depth in bimodal atomic force microscopy and comparison to the trimodal case.

This paper presents experiments on Nafion® proton exchange membranes and numerical simulations illustrating the trade-offs between the optimization of compositional contrast and the modulation of tip indentation depth in bimodal atomic force microscopy (AFM). We focus on the original bimodal AFM method, which uses amplitude modulation to acquire the topography through the first cantilever eigenmode, and drives a higher eigenmode in open-loop to perform compositional mapping. This method is attractive due to its relative simplicity, robustness and commercial availability. We show that this technique offers the capability to modulate tip indentation depth, in addition to providing sample topography and material property contrast, although there are important competing effects between the optimization of sensitivity and the control of indentation depth, both of which strongly influence the contrast quality. Furthermore, we demonstrate that the two eigenmodes can be highly coupled in practice, especially when highly repulsive imaging conditions are used. Finally, we also offer a comparison with a previously reported trimodal AFM method, where the above competing effects are minimized.

Correlating structure topological metrics with bulk composite properties via neural network analysis

Given a database of any quantifiable set of cause and effect, machine learning methods can be trained to predict future effects based upon an assumed set of causes. In this paper, neural networks are trained to predict the bulk Young’s modulus and electrical conductivity of a two-phase composite with high material property contrast, based upon a sample’s microstructure. Various structure metrics are used to quantify the topological connectivity and disorder of analytically generated heterogeneous samples. The neural network is trained to predict the Young’s modulus and coefficient of electrical conductivity based upon values calculated for a training set of samples using a finite element model. By repeating the process with various subset of structure metrics we can determine which metrics—or combination of metrics—have the strongest influence in accurately predicting bulk material properties. Not only are neural net predictions of bulk properties in good agreement with calculated values for the 2D two-phase composites, but the insights into which metrics most strongly correlate with these properties (in this case, the connectivity metrics) may help focus the development of improved structure–property relations.

Spatially-resolved hydraulic conductivity estimation via poroelastic magnetic resonance elastography.

Poroelastic magnetic resonance elastography is an imaging technique that could recover mechanical and hydrodynamical material properties of in vivo tissue. To date, mechanical properties have been estimated while hydrodynamical parameters have been assumed homogeneous with literature-based values. Estimating spatially-varying hydraulic conductivity would likely improve model accuracy and provide new image information related to a tissue's interstitial fluid compartment. A poroelastic model was reformulated to recover hydraulic conductivity with more appropriate fluid-flow boundary conditions. Simulated and physical experiments were conducted to evaluate the accuracy and stability of the inversion algorithm. Simulations were accurate (property errors were < 2%) even in the presence of Gaussian measurement noise up to 3%. The reformulated model significantly decreased variation in the shear modulus estimate (p << 0.001) and eliminated the homogeneity assumption and the need to assign hydraulic conductivity values from literature. Material property contrast was recovered experimentally in three different tofu phantoms and the accuracy was improved through soft-prior regularization. A frequency-dependence in hydraulic conductivity contrast was observed suggesting that fluid-solid interactions may be more prominent at low frequency. In vivo recovery of both structural and hydrodynamical characteristics of tissue could improve detection and diagnosis of neurological disorders such as hydrocephalus and brain tumors.

Multiple regimes of operation in bimodal AFM: understanding the energy of cantilever eigenmodes

One of the key goals in atomic force microscopy (AFM) imaging is to enhance material property contrast with high resolution. Bimodal AFM, where two eigenmodes are simultaneously excited, confers significant advantages over conventional single-frequency tapping mode AFM due to its ability to provide contrast between regions with different material properties under gentle imaging conditions. Bimodal AFM traditionally uses the first two eigenmodes of the AFM cantilever. In this work, the authors explore the use of higher eigenmodes in bimodal AFM (e.g., exciting the first and fourth eigenmodes). It is found that such operation leads to interesting contrast reversals compared to traditional bimodal AFM. A series of experiments and numerical simulations shows that the primary cause of the contrast reversals is not the choice of eigenmode itself (e.g., second versus fourth), but rather the relative kinetic energy between the higher eigenmode and the first eigenmode. This leads to the identification of three distinct imaging regimes in bimodal AFM. This result, which is applicable even to traditional bimodal AFM, should allow researchers to choose cantilever and operating parameters in a more rational manner in order to optimize resolution and contrast during nanoscale imaging of materials.

Surface geophysical exploration: developing noninvasive tools to monitor past leaks around Hanford’s tank farms

A characterization program has been developed at Hanford to image past leaks in and around the underground storage tank facilities. The program is based on electrical resistivity, a geophysical technique that maps the distribution of electrical properties of the subsurface. The method was shown to be immediately successful in open areas devoid of underground metallic infrastructure, due to the large contrast in material properties between the highly saline waste and the dry sandy host environment. The results in these areas, confirmed by a limited number of boreholes, demonstrate a tendency for the lateral extent of the underground waste plume to remain within the approximate footprint of the disposal facility. In infrastructure-rich areas, such as tank farms, the conventional application of electrical resistivity using small point-source surface electrodes initially presented a challenge for the resistivity method. The method was then adapted to directly use the buried infrastructure, specifically the steel-cased wells that surround the tanks, as "long" electrodes for both transmission of electrical current and measurements of voltage. Overcoming the drawbacks of the long electrode method has been the focus of our work over the past 7years. The drawbacks include low vertical resolution and limited lateral coverage. The lateral coverage issue has been improved by supplementing the long electrodes with surface electrodes in areas devoid of infrastructure. The vertical resolution has been increased by developing borehole electrode arrays that can fit within the small-diameter drive casing of a direct push rig. The evolution of the program has led to some exceptional advances in the application of geophysical methods, including logistical deployment of the technology in hazardous areas, development of parallel processing resistivity inversion algorithms, and adapting the processing tools to accommodate electrodes of all shapes and locations. The program is accompanied by a full set of quality assurance procedures that cover the layout of sensors, measurement strategies, and software enhancements while insuring the integrity of stored data. The data have been shown to be useful in identifying previously unknown contaminant sources and defining the footprint of precipitation recharge barriers to retard the movement of existing contamination.

A robust Nitsche’s formulation for interface problems

In this work, we propose a novel weighting for the interfacial consistency terms arising in a Nitsche variational form. We demonstrate through numerical analysis and extensive numerical evidence that the choice of the weighting parameter has a great bearing on the stability of the method. Consequently, we propose a weighting that results in an estimate for the stabilization parameter such that the method remains well behaved in varied settings; ranging from the configuration of embedded interfaces resulting in arbitrarily small elements to such cases where a large contrast in material properties exists. An important consequence of this weighting is that the bulk as well as the interfacial fields remain well behaved in the presence of (a) elements with arbitrarily small volume fractions, (b) large material heterogeneities and (c) both large heterogeneities as well as arbitrarily small elements. We then highlight the accuracy and efficiency of the proposed formulation through numerical examples, focusing particular attention on interfacial quantities of interest.

Dynamics of surface-coupled microcantilevers in force modulation atomic force microscopy – magnetic vs. dither piezo excitation

Force modulation atomic force microscopy is widely used for mapping the nanoscale mechanical properties of heterogeneous or composite materials using low frequency excitation of a microcantilever scanning the surface. Here we show that the excitation mode – magnetic or dither piezo, has a major influence on the surface-coupled microcantilever dynamics. Not only is the observed material property contrast inverted between these excitation modes but also the frequency response of the surface-coupled cantilever in the magnetic mode is near-ideal with a clear resonance peak and little phase distortion thus enabling quantitative mapping of the local mechanical properties.

SH-wave propagation and resonance phenomena in a periodically layered composite structure with a crack

This paper presents a dynamic analysis of time-harmonic plane SH-waves propagating in periodically multilayered elastic composites with a strip-like crack. The total wave field in the multilayered elastic structure is described as a sum of incident wave field modeled by the transfer matrix method and the scattered wave field governed by an integral representation containing the crack-opening-displacement. The integral equation derived from the boundary conditions on the crack-faces is solved numerically by a Galerkin method. The paper focuses on resonant and non-resonant regimes of anti-plane wave motion in a stack of elastic layers weakened by a single strip-like crack and wave localization in the vicinity of the crack. The scattered extra displacement induced by the presence of the crack is investigated in detail for both situations of high and low contrast in material properties. Numerical results for the average crack-opening-displacement, the transmission coefficient, the stress intensity factor and the average energy flow are presented and discussed to reveal wave resonance and localization phenomena within the band-gaps and the pass-bands.

Octave omnidirectional band gap in a three-dimensional phononic crystal

We report on the experimental observation of a one-octave-large omnidirectional elastic band gap for longitudinal waves in a three-dimensional phononic crystal consisting of face-centered-cubic arrays of close-packed steel beads in a solid epoxy matrix. The 60% relative width of the band gap is larger than expected based on the contrast in material properties, and is confirmed by band structure diagram and transmission spectra computations. The coupling between shear and longitudinal polarizations is pointed out as a mechanism for enlarging the band gap by comparing with the steel beads in water matrix case.

Higher harmonics and phase contrast in liquid environment dynamic atomic force microscopy – tools for observing material property contrast in biological samples at high resolution and speed

Extended abstract of a paper presented at Microscopy and Microanalysis 2010 in Portland, Oregon, USA, August 1 – August 5, 2010.