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DOE OSTI2023

A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction

This paper introduces a sharp-interface approach to simulating fluid-structure interaction (FSI) involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body immersed Lagrangian-Eulerian (ILE) scheme extends our prior work on integrating partitioned and immersed approaches to rigid-body FSI. Our numerical approach incorporates the geometrical and domain solution flexibility of the immersed boundary (IB) method with an accuracy comparable to body-fitted approaches that sharply resolve flows and stresses up to the fluid-structure interface. Unlike many IB methods, our ILE formulation uses distinct momentum equations for the fluid and solid subregions with a Dirichlet-Neumann coupling strategy that connects fluid and solid subproblems through simple interface conditions. As in earlier work, we use approximate Lagrange multiplier forces to treat the kinematic interface conditions along the fluid-structure interface. This penalty approach simplifies the linear solvers needed by our formulation by introducing two representations of the fluid-structure interface, one that moves with the fluid and another that moves with the structure, that are connected by stiff springs. This approach also enables the use of multi-rate time stepping, which allows us to use different time step sizes for the fluid and structure subproblems. Our fluid solver relies on an immersed interface method (IIM) for discrete surfaces to impose stress jump conditions along complex interfaces while enabling the use of fast structured-grid solvers for the incompressible Navier-Stokes equations. The dynamics of the volumetric structural mesh are determined using a standard finite element approach to large-deformation nonlinear elasticity via a nearly incompressible solid mechanics formulation. This formulation also readily accommodates compressible structures with a constant total volume, and it can handle fully compressible solid structures for cases in which at least part of the solid boundary does not contact the incompressible fluid. Selected grid convergence studies demonstrate second-order convergence in volume conservation and in the pointwise discrepancies between corresponding positions of the two interface representations as well as between first and second-order convergence in the structural displacements. The time stepping scheme is also demonstrated to yield second-order convergence. To assess and validate the robustness and accuracy of the new algorithm, comparisons are made with computational and experimental FSI benchmarks. Test cases include both smooth and sharp geometries in various flow conditions. Furthermore, we also demonstrate the capabilities of this methodology by applying it to model the transport and capture of a geometrically realistic, deformable blood clot in an inferior vena cava filter.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Trivalent Rare Earth Adsorption at Phosphonic Acid Monolayers

The increasing need for rare earth separations requires a detailed understanding of trivalent ion behavior at charged aqueous interfaces. Here, neodymium (Nd) adsorption on Langmuir monolayers of octadecylphosphonic acid (ODPA), a single‐chain phosphonic acid capable of double deprotonation, at the air/water interface, is investigated. Combining sum frequency generation (SFG) spectroscopy with X‐ray fluorescence near total reflection (XFNTR), both the interfacial water ordering and ion density are examined. Under ambient conditions, Nd ions induce enhanced deprotonation of ODPA headgroups, leading to interfacial ion densities as high as 1 Nd per 30 Å 2 . This adsorption behavior arises from a complex interplay between direct electrostatic interactions, ion pairing, and hydration effects, which cannot be fully captured by classical Gouy–Chapman–Stern models. These insights into trivalent ion adsorption mechanisms provide a pathway toward more effective separation processes for rare earth metals.

adsorptions↗

DOE OSTI2019

A coupled microscopy approach to assess the nano-landscape of weathering

Mineral weathering is a balanced interplay among physical, chemical, and biological processes. Fundamental knowledge gaps exist in characterizing the biogeochemical mechanisms that transform microbe-mineral interfaces at submicron scales, particularly in complex field systems. Our objective was to develop methods targeting the nanoscale by using high-resolution microscopy to assess biological and geochemical drivers of weathering in natural settings. Basalt, granite, and quartz (53–250 µm) were deployed in surface soils (10 cm) of three ecosystems (semiarid, subhumid, humid) for one year. We successfully developed a reference grid method to analyze individual grains using: (1) helium ion microscopy to capture micron to sub-nanometer imagery of mineral-organic interactions; and (2) scanning electron microscopy to quantify elemental distribution on the same surfaces via element mapping and point analyses. Here, we detected locations of biomechanical weathering, secondary mineral precipitation, biofilm formation, and grain coatings across the three contrasting climates. To our knowledge, this is the first time these coupled microscopy techniques were applied in the earth and ecosystem sciences to assess microbe-mineral interfaces and in situ biological contributors to incipient weathering.

58 GEOSCIENCES↗

DOE OSTI2018

Vibrational Spectroscopy of Water with High Spatial Resolution

Abstract The ability to examine the vibrational spectra of liquids with nanometer spatial resolution will greatly expand the potential to study liquids and liquid interfaces. In fact, the fundamental properties of water, including complexities in its phase diagram, electrochemistry, and bonding due to nanoscale confinement are current research topics. For any liquid, direct investigation of ordered liquid structures, interfacial double layers, and adsorbed species at liquid–solid interfaces are of interest. Here, a novel way of characterizing the vibrational properties of liquid water with high spatial resolution using transmission electron microscopy is reported. By encapsulating water between two sheets of boron nitride, the ability to capture vibrational spectra to quantify the structure of the liquid, its interaction with the liquid‐cell surfaces, and the ability to identify isotopes including H 2 O and D 2 O using electron energy‐loss spectroscopy is demonstrated. The electron microscope used here, equipped with a high‐energy‐resolution monochromator, is able to record vibrational spectra of liquids and molecules and is sensitive to surface and bulk morphological properties both at the nano‐ and micrometer scales. These results represent an important milestone for liquid and isotope‐labeled materials characterization with high spatial resolution, combining nanoscale imaging with vibrational spectroscopy.

Jokisaari, Jacob R.↗

DOE OSTI2023

A combined kinetic Monte Carlo and phase field approach to model thermally activated dislocation motion

In this work, a kinetic Monte Carlo (KMC) scheme is integrated into a phase field dislocation dynamics (PFDD) model to account for thermal activation. While the implementation is general and could be applied to many different thermally activated processes, we apply the model to simulate a dislocation transmitting through an interface. Two cases are analyzed: a dislocation transmitting through a strong interface, and a dislocation transmitting through a more realistic grain boundary in tungsten. In conclusion, results and trends for both cases are discussed in detail, and ultimately show that the combined KMC-PFDD algorithm is effective in capturing thermally activated dislocation processes.

36 MATERIALS SCIENCE↗

DOE OSTI2017

On the Preconditioning of a Newton-Krylov Solver for a High-Order reconstructed Discontinuous Galerkin Discretization of All-Speed Compressible Flow with Phase Change for Application in Laser-Based Additive Manufacturing

This dissertation focuses on the development of a fully-implicit, high-order compressible ow solver with phase change. The work is motivated by laser-induced phase change applications, particularly by the need to develop large-scale multi-physics simulations of the selective laser melting (SLM) process in metal additive manufacturing (3D printing). Simulations of the SLM process require precise tracking of multi-material solid-liquid-gas interfaces, due to laser-induced melting/ solidi cation and evaporation/condensation of metal powder in an ambient gas. These rapid density variations and phase change processes tightly couple the governing equations, requiring a fully compressible framework to robustly capture the rapid density variations of the ambient gas and the melting/evaporation of the metal powder. For non-isothermal phase change, the velocity is gradually suppressed through the mushy region by a variable viscosity and Darcy source term model. The governing equations are discretized up to 4th-order accuracy with our reconstructed Discontinuous Galerkin spatial discretization scheme and up to 5th-order accuracy with L-stable fully implicit time discretization schemes (BDF2 and ESDIRK3-5). The resulting set of non-linear equations is solved using a robust Newton-Krylov method, with the Jacobian-free version of the GMRES solver for linear iterations. Due to the sti nes associated with the acoustic waves and thermal and viscous/material strength e ects, preconditioning the GMRES solver is essential. A robust and scalable approximate block factorization preconditioner was developed, which utilizes the velocity-pressure (vP) and velocity-temperature (vT) Schur complement systems. This multigrid block reduction preconditioning technique converges for high CFL/Fourier numbers and exhibits excellent parallel and algorithmic scalability on classic benchmark problems in uid dynamics (lid-driven cavity ow and natural convection heat transfer) as well as for laser-induced phase change problems in 2D and 3D.

42 ENGINEERING↗

DOE OSTI2019

Geomechanical Simulation of Big Hill Strategic Petroleum Reserve - Calibration of Model Containing Shear Zone

A finite element numerical analysis model, that consists of a realistic mesh capturing the geometries of Big Hill (BH) Strategic Petroleum Reserve (SPR) site using the multi-mechanism deformation (MD) salt constitutive model and including data taken daily of the wellhead pressure and level of the oil-brine interface, has been upgraded. The upgraded model contains the shear zone to examine the interbed behavior in a realistic manner. The salt creep rate is not uniform in the salt dome, and creep test data for BH salt is limited. Therefore, a model calibration is necessary to simulate the geomechanical behavior of the salt dome. Cavern volumetric closures of SPR caverns calculated from sonar survey reports are used for the field baseline measurement. The structure factor, A 2 , and transient strain limit factor, K 0 , in the M-D constitutive model are used for model calibration. An A 2 value obtained experimentally from the BH salt and K 0 value of WIPP salt are used as the baseline values. To adjust the magnitude of A 2 and K 0 , multiplication factors A 2 F and K 0 F are defined, respectively. The A 2 F and K 0 F values of the salt dome and salt drawdown layer of elements surrounding each SPR cavern have been determined through a number of back fitting analyses. The trendlines of the predictions and sonar data match up well for BH 101, 103, 104, 106, 110, 111, 112, and 113. The prediction curves are close to the sonar data for BH 102 and 114. However, the prediction curves for BH 105, 107, 108, and 109 are not close to the sonar data. An inconsistency was found in the sonar data, i.e. the volume measured later is larger than that before in some time intervals, even if the leached volume is taken into account, for BH 101, 104, 106, 107, and 112. Project discussions are needed to determine possibilities on how to resolve the issues and determine the best path forward for future computer modeling attempts.

02 PETROLEUM↗

DOE OSTI2025

HPC for Optimizing Process Parameters to Control Material Evolution in Seamless Induction Hardening of Wind Turbine Main Shaft Bearings

Work proposed in this project focused on understanding the effect of martensitic transformation in the steel on the potential for cracking during seamless induction hardening (SIH) as a function of process conditions to allow the process to optimally scale up. Large-scale, three-dimensional phase-field simulations of martensitic transformation were performed using MEUMAPPS-SS (Microstructure Evolution Using Massively Parallel Phase-field Simulations – Solid State) code developed at Oak Ridge National Laboratory. The simulations were guided by location-specific thermal history generated by experimental measurements of time-temperature history generated at The Timken Company. The simulations were able to capture the morphological evolution of the martensite variants in an Fe-1.0C-1.5Cr steel based on the Nishiyama-Wasserman (NW) orientation relationship. The simulations were also able to quantify the stress-state at the interface between impinging martensite variants. The simulations indicated that the magnitude of the various stress and strain components were dependent on the sizes of the impinging plates with a reduction in these quantities with reduced plate size in agreement with experimental findings. The results obtained from the simulations will be used to guide the optimization of the alloy thermal conditions to eliminate quench cracking during SIH of bearing steels.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2025

HPC for optimizing process parameters to control material evolution in seamless induction hardening of wind turbine main shaft bearings

17 WIND ENERGY↗

DOE OSTI2019

Twin formation from a twin boundary in Mg during in-situ nanomechanical testing

An important fundamental question regarding deformation twinning is whether it is possible for twins to nucleate at boundaries or interfaces when specific stress fields are present. A corollary that follows from this question is: if this is indeed possible, what determines the proper stress field and how does it occur at the nanoscale? Here, we demonstrate the application of an in-situ nanoindentation approach to confine and dynamically capture the stages in the formation of a deformation twin at an internal twin boundary in single crystal Mg. We observe the formation of contraction twin embryos at the pre-existing extension twin boundary, and the subsequent propagation of the twin embryos into the crystal. We reveal an intermediate step, involving the coalescence of tiny embryos into a larger embryo before the nucleus emanates into the crystal. De-twinnning of the twin embryos is captured during unloading and shown to leave a remnant nanosized twin (<10 nm) after complete unloading. A 3D full-field, crystal plasticity model identifies that the twin type and variant selection of the stable embryo are governed by the internal local stress state prevailing at the pre-existing twin boundary. The possible role played by dislocations and boundary structure (incoherent vs. coherent) in embryo formation, as suggested by the TEM and modeling analyses, are discussed.

grains and interfaces, magnesium alloys, plasticit↗

DOE OSTI2026

D$e^+e^-$ffusion: Capturing the Beam-Beam Physics of $e^+e^-$ Collisions with Diffusion Models

Beam-induced backgrounds at high-luminosity $e^+e^-$ colliders, such as the FCC-ee, are dominated by incoherent pair creation (IPC), and require computationally expensive simulations with dedicated Monte Carlo (MC) event generators. Reliable detector and machine-detector interface studies necessitate event samples that are several orders of magnitude larger than what is practically attainable with existing MC. To alleviate this bottleneck, we present D$e^+e^-$ffusion, a denoising diffusion probabilistic model that operates as a permutation-equivariant, set-valued surrogate for fast IPC simulation. Trained on a small GuineaPig++ sample, D$e^+e^-$ffusion faithfully reproduces the marginal and joint kinematic, angular, and positional distributions of all three IPC production processes. In addition, we assess the fidelity at the detector level by propagating both Geant4 and D$e^+e^-$ffusion events through a Geant4 simulation of the CLD vertex detector and by training a transformer-based two-sample classifier; the classifier achieves an area under the ROC curve of $0.553 \pm 0.016$. The trained model generates events nearly four orders of magnitude faster than Geant4, paving the way for a fast-simulation surrogate for FCC-ee design studies.

Chahine, Antonio [Imperial Coll., London]↗

DOE OSTI2022

Interlayer fusion bonding of semi-crystalline polymer composites in extrusion deposition additive manufacturing

This work focuses on the evolution of interlayer fracture toughness properties of fiber-reinforced, semi-crystalline polymers in the extrusion deposition additive manufacturing (EDAM) process. Further, this work bridges the gap between the additive process conditions (time-temperature history) and the effective layer-to-layer fracture properties developed within a printed component. This is the first step to predict delamination that can occur during printing, during cooling to room temperature after printing, and during service performance of an additively manufactured geometry. A phenomenological model is developed for fusion bonding of semi-crystalline polymer matrix composites by coupling the interdiffusion of polymer chains with the evolution of polymer crystallinity. While the interdiffusion is captured by reptation theory of polymer dynamics, the evolution of crystallinity is modeled by phenomenological crystallization kinetics and crystal melting dynamics. Further, a methodology is developed to determine the critical strain energy release rate, G IC of the interlayer interface and experiments are conducted utilizing the double cantilever beam fracture test geometry. In conclusion, predictions of GIC as a function of thermal history are compared with experiments.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Investigating the Diurnal Radiative, Turbulent, and Biophysical Processes in the Amazonian Canopy‐Atmosphere Interface by Combining LES Simulations and Observations

Abstract We investigate the atmospheric diurnal variability inside and above the Amazonian rainforest for a representative day during the dry season. To this end, we combine high‐resolution large‐eddy simulations that are constrained and evaluated against a comprehensive observation set, including CO 2 concentrations, gathered during GoAmazon2014/15. We design systematic numerical experiments to quantify whether a multilayer approach in solving the explicit canopy improves our canopy‐atmosphere representation. We particularly focus on the relationship between photosynthesis and plant transpiration, and their distribution at leaf and canopy scales. We found the variability of photosynthesis drivers like vapor pressure deficit and leaf temperature to be about 3 times larger for sunlit leaves compared to shaded leaves. This leads to a large spread on leaf stomatal conductance values with minimum and maximum values varying more than 100%. Regarding the turbulent structure, we find wind‐driven stripe‐like shapes at the canopy top and structures resembling convective cells at the canopy. Wind‐related variables provide the best spatiotemporal agreement between model and observations. The potential temperature and heat flux profiles agree with an observed decoupling near the canopy top interface, although with less variability and cold biases of up to 3 K. The increasing complexity on the biophysical processes leads to the largest disagreements for evaporation, CO 2 plant assimilation and soil efflux. The model is able to capture the correct dependences and trends with the magnitudes still differing. We finally discuss the need to revise leaf and soil models and to complete the observations at leaf and canopy levels.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2019

A simple json format for storing and exchanging code calculation and experimental results

Calculation codes and code systems give their results in a plethora of different formats and/or files. For instance, MCNP gives a user the MCNP specific output file, the mctal file, the ptrac file, etc. while PARTISN has a PARTISN specific output file and a number of binary files with various kinds of information about the calculation. However, the results we are interested in are always the same. These can be single values such as the effective multiplication factor k eff or the effective delayed neutron fraction β eff . It can be histogram data (such as particle spectra, reaction rates, sensitivity profiles, etc.) or even pointwise data (for example the nuclide composition as a function of time, etc.). It is also worthwhile to note that this would also apply to experimental data that we may wish to compare with as well. Calculation and experimental results can basically be split into two components: attributes (or metadata) and the actual result itself. Attributes represent information about the result that are not necessarily required for its’ interpretation but that are still good to have. Often, these attributes are what we will want to filter results on. This means that these attributes are often the answer to specific questions we may have about the result. The following is a non exhaustive list of such basic questions: what type of result is it: e.g. the effective multiplication factor k eff , the effective delayed neutron fraction β eff , etc.; which case does it relate to: e.g. a specific ICSBEP case such as PU-MET-FAST-001-001; which code and version produced this result: e.g. MCNP 6.2, etc.; which nuclear data library was used to obtain the result: e.g. ENDF/B-VIII.0 or JEFF 3.3; which nuclide and reaction does it apply to (for reaction rates and sensitivity profiles); which volume in the geometry was it calculated in? The second component of the calculation or experimental result is the actual numerical data of the result. It is this data that we want to compare, exchange, plot, interpret, etc. It consists of values with optional uncertainties and units. It also includes the underlying structure (if any structure is required to interpret the result). Depending on the type of result, it may be a single value (e.g. the effective multiplication factor), an array of values (e.g. a reaction rate or particle spectrum) or even a multidimensional array. In order to exchange results between different organisations, for instance for benchmarking, people often resort to spreadsheets or custom text files that need to be filled out. While this approach works well if little information is to be exchanged, it can become cumbersome when dealing with large amounts of data (like for instance particle spectra for thousands of cases). In addition, such an approach does not always capture the metadata we may be interested in to allow for automated processing of these files. The purpose of this report is to propose a standardised json structure to store any type of result and present an associated python interface to interact with these results directly. For such a structure to be useful, it must fulfill a specific set of functional requirements that we try to meet with this proposal. The format must allow for the calculation result to stand by itself. This means that we should not have to look in multiple places to be able to understand it. For example, if the result relates to a particle spectrum, the group structure in which the result is given should be stored with it. The format should be code agnostic. This means that we do not need to know where it came from to understand it. The format should be result type agnostic. This means that the format must be generic enough so that we can even use it for results we have not thought of yet. The format should be relatively easy to interact with through different scripting or programming languages (i.e. the machine interface) while still providing a clean structure that can be used directly by any human.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

SPARC-X: Quantum simulations at extreme scale - reactive dynamics from first principles

We have developed the massively parallel electronic structure code SPARC-X: a computational framework for performing Kohn-Sham Density Functional Theory (DFT) calculations that can scale linearly with the number of atoms in the system, while being able to leverage petascale and emerging exascale parallel computers to study chemical phenomena at unprecedented length and time scales. SPARC-X exploits a recent breakthrough in electronic structure methodologies: systematically improvable, strictly local, orthonormal, discontinuous real-space bases that efficiently and systematically capture the local chemistry of the system. With further adaptation using new machine-learning techniques and the use of the massively parallel Spectral Quadrature (SQ) electronic structure method, the algorithmic complexity and prefactor associated with DFT calculations involving semilocal as well as hybrid functionals are dramatically reduced. Using petascale computational resources, SPARC-X enables quantum mechanical simulations at length and time scales previously accessible only by empirical approaches, e.g., 1,000,000 atoms for a few picoseconds using semilocal functionals or 1,000 atoms for a few picoseconds using hybrid functionals. Using exascale resources, the sizes and times targeted are two orders of magnitude larger. Such a capability has applications in a wide variety of chemical sciences, including reactive interfaces where large length- and/or long time-scales are needed and traditional force fields fail. This is particularly important in dynamic catalysis, where bond breaking and formation must be understood in detail. We developed, tested, and employed the SPARC-X framework to understand the photocatalytic properties of TiO 2 nanoparticles, revealing finite size effects that cannot be captured with standard model systems or functionals. This integrated development and application strategy ensures that SPARC-X remains a robust, efficient, and scalable software package for quantum simulations on current petascale and emerging exascale computing resources.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Factors controlling injection-induced rupture of intersecting faults during geological sequestration of CO 2

This study addresses coupled multiphase fluid flow and geomechanics effects on potential fault activation associated with subsurface CO 2 injection around intersecting faults. An enhanced fault-representation model is used to capture geomechanical responses of two intersecting faults with finite length during CO 2 injection. The faults are embedded in a strike-slip stress regime of a caprock-reservoir-basement system with the faults represented by zero-thickness interfaces with adjacent finite-thickness damage zones. A sensitivity analysis is conducted to study the effect of fault permeability, slip-weakening behavior, well location relative to the orientation of faults, and well placement (the number and location of injection wells). Five metrics (pressure, CO 2 plume, shear state on the fault, as well as shear displacement and stress path at selected fault monitoring points) are selected to assess CO 2 migration and reactivation of intersecting faults. The results show that induced ruptures are favored by low permeability faults due to high pressure buildup and by slip-weakening behavior resulting from fault strength reduction. The location of one injection well relative to fault orientation determines the magnitude of changes in effective normal stress and shear stress, affecting the location of induced ruptures. Well placement (two injection wells used in the paper) dominates pressure diffusion around the intersection and tips of faults. This redistributes changes in effective normal stress caused by each injection well, influencing the spatial distribution of ruptures along faults. A larger injection volume induces far-field ruptures that are controlled by stress transfer within the injection layer. The findings presented here can provide valuable insights into engineering operations for a long-term, safe, and reliable geologic CO 2 storage.

Fault permeability↗

DOE OSTI2019

Entropic and Enthalpic Effects in Thin Film Blends of Homopolymers and Bottlebrush Polymers

We present a combined experimental and computational study of surface segregation in thin films of nearly athermal blends of linear and bottlebrush polymers. The lengths of bottlebrush backbone (N b ), bottlebrush side chain (N sc ), and linear polystyrene host (N m ) are systematically varied to examine the effects of polymer architecture on phase behavior. From the experiments, combinations of architectural parameters are identified that produce enrichment and depletion of bottlebrush at the polymer–air interface. These surface segregation behaviors are consistent with entropy-dominated thermodynamics. In addition, the experiments reveal conditions where bottlebrush and linear polymers are equally preferred at the surface. Simulations based on the self-consistent field theory (SCFT) qualitatively capture the three types of surface segregation behaviors and highlight the delicate interplay of entropic and enthalpic effects. Finally, our investigations demonstrate that controlling both entropic and enthalpic driving forces is critical for the design of surface-active bottlebrush polymer additives.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Development of a deep machine learning interatomic potential for metalloid-containing Pd-Si compounds

Interatomic potentials based on neural-network machine learning (ML) approach to address the long-standing challenge of accuracy versus efficiency in molecular-dynamics simulations have recently attracted a great deal of interest. In this work, utilizing Pd-Si system as a prototype, we extend the development of neural-network ML potentials to compounds exhibiting various types of bonding characteristics. The ML potential is trained by fitting to the energies and forces of both liquid and crystal structures first-principles calculations based on density-functional theory (DFT). We show that the generated ML potential captures the structural features and motifs in Pd 82 Si 18 and Pd 75 Si 25 liquids more accurately than the existing interatomic potential based on embedded-atom method (EAM). The ML potential also describes the solid-liquid interface of these systems very well. Moreover, while the existing EAM potential fails to describe the relative energies of various crystalline structures and predict wrong ground-state structures at Pd 3 Si and Pd 9 Si 2 composition, the developed ML potential predicts correctly the ground-state structures from genetic algorithm search. The efficient ML potential with DFT accuracy from our study will provide a promising scheme for accurate atomistic simulations of structures and dynamics of complex Pd-Si system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗