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DOE OSTI2021

Machine learning elastic constants of multi-component alloys

The present manuscript explores application of machine learning methods for determining elastic constants and other derived mechanical properties of multi-component alloys. Here, a number of machine learning models, including linear regression, neural network and random forest based models, are trained and tested on a dataset of binary alloys generated using density functional theory (DFT) calculations and spanning over a large number of elemental species in the periodic table. Starting with a wide range of simple and easily accessible compositionally-averaged elemental features, a correlation-based feature selection strategy was used to systematically down-select a set of most relevant features towards the prediction of the elasticity tensor components. The true predictive performance and the associated uncertainties of the models were established by testing on unseen data and bootstrapping, respectively. A single and pair-wise feature partial dependence analysis was performed to visualize the average property trends in the multi-dimensional feature space in order to further understand the achieved predictive performance. The utility of the trained model is further demonstrated by obtaining sufficiently accurate yet highly efficient approximations for bulk modulus, Young’s modulus, shear modulus and Poisson’s ratio for alloys beyond the binary space (i.e., two-component alloys) on which the model was originally trained. More importantly, we test and validate the predictive performance of the developed model directly against the experimentally measured elastic constants of technologically relevant multi-component alloys (such as, Ni- and Ti-based alloys). Finally, utility of such a data-enabled route is demonstrated by predicting the possible range of various elastic properties for vast composition space available within the five component Ni-Cr-Fe-Mo-W alloy system in a high-throughput manner.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Phonon-informed Neural Thermal Scattering (NeTS) Optimization for Crystalline Graphite and Beryllium Metal

Fast neutrons born from fission lose energy through scattering interactions in the process of slowing-down. As neutrons thermalize to the order of $k$ $b$ $T$ (where $k$ $b$ is the Boltzmann constant, and $T$ is the temperature of the medium), their de Broglie wavelength and energy approaches the order of inter-atomic spacing and quantized lattice vibrations, i.e., phonons. At thermal energies, the thermal scattering law (TSL), i.e., $S$($α, β$), captures crystal binding contributions to the total reaction rate, or cross section. This dimensionless material property describes the energy ($β$) and momentum ($α$) exchanges available in a medium. Currently, $S$($α, β$) is evaluated in the Full Law Analysis Scattering System Hub (FLASSH) code for discrete inputs and stored as ENDF/B File 7 for 0-phonon elastic (MT 2) and n-phonon inelastic (MT 4) processes. Further processing recasts $S$($α, β$) into cumulative distribution functions for sampling post-collision scattering kinematics. In practice, interpolation schemes are employed to access data between tabulated values. An improvement to this juncture of the nuclear data pipeline is supplying cross sections on-the-fly (OTF), as has been developed for the un-resolved resonance region to minimize non-physical interpolation errors. This capability may improve simulation accuracy for accident and transient analyses, where rapidly varying changes in temperature and pressure are difficult to predict beforehand. To do so, deep artificial neural networks (ANNs) can be employed which collapse non-linear, complex data into a lightweight dictionary of neural weights and biases. This has been successfully demonstrated for the hydrogen in light water $S$($α, β$) dataset in the form of a Neural Thermal Scattering (NeTS) module. In this work, the NeTS framework is extended to consider the impact of material-dependent dynamical features on optimal neural pre-processing and architecture design decisions, such as number of neurons per hidden layer, residual skip connections and neural depth. New NeTS modules for crystalline graphite and beryllium metal illuminate a novel correlation between dynamical nonlinearity and optimal neural parametrization when deploying $S$($α, β$) on-the-fly.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Thick graded interfaces increase wear resistance in Ti/TiN nanolayered thin films

Multilayered composites with nanoscale layer thickness incorporating titanium and titanium nitride (Ti/TiN) are used as a model system to study the effects of heterophase interface structure on elastic and plastic deformation, as well as wear behavior. Here, in this work, hardness, modulus, and wear rate under dry reciprocating sliding contact are quantified as a function of Ti-TiN heterophase interfacial nitrogen gradient thickness for Ti/TiN multilayers with 10–80 nm layer thickness. Hardness and modulus are found to be inversely proportional to layer thickness and independent of interface gradient for most specimens. Wear rate is found to be inversely proportional to interface gradient thickness at constant layer thickness, demonstrating that control of nanoscale interface structure is a valid approach to enhancing wear behavior. The materials studied in this work wear comparably or slower than other Ti- and TiN-based composites in the literature, providing a promising avenue for engineering wear-resistant materials for use in industrially relevant applications.

Graded interfaces↗

DOE OSTI2022

Decoupling indentation size and strain rate effects during nanoindentation: A case study in tungsten

Materials indented at small scales may simultaneously exhibit indentation size and strain rate effects which complicate the identification of the mechanisms that control deformation and strength. Here, in this work, we explore the possibility that indentation size and rate effects in some materials can be decoupled in a simple way. Nanoindentation tests with various load-time histories were carried out to measure the hardness of a tungsten single crystal over a wide range of indentation depths (~500–3600 nm) and indentation strain rates (~5 ×10 –5 –2 ×10 –1 s –1 ). Under these conditions, this material exhibits significant indentation size and rate effects, but the size effect is, to a good approximation, independent of strain rate. It is shown that this behavior can be understood by the Nix-Gao model for the indentation size effect modified to include the effects of a strain rate dependent friction stress. As a consequence, the size and rate dependencies of the hardness can be expressed as the sum of two independent terms: H($\dot{ε}$ i , h c )=H f ($\dot{ε}$ i ) + (H 0 – H f ) $\sqrt{1+ \frac{h^*}{h_c}}$, where H($\dot{ε}$ i , h c ) is the hardness at given indentation strain rate ($\dot{ε}$ i ) and contact depth (h c ), H f ($\dot{ε}$ i ) is the hardness contributed by the rate dependent friction stress, and (H 0 – H f ) and h* are size and rate independent constants that follow from the Nix-Gao analysis. This formula, together with an expression for the rate dependence of H f , was successfully applied to decouple the indentation size and rate effects observed in tungsten. In addition, the physics underlying the rate independence of indentation size effect is discussed, which provides guidance for application of the proposed approach to other materials.

42 ENGINEERING↗

DOE OSTI2021

Stress-induced phase transitions in nanoscale CuInP 2 S 6

Using the Landau-Devonshire approach and available experimental results, we constructed multiwell thermodynamic potential of the layered ferroelectric CuInP 2 S 6 (CIPS). The analysis of temperature dependences of the dielectric permittivity and lattice constants for different applied pressures unexpectedly reveals the critically important role of a nonlinear electrostriction in this material. With the nonlinear electrostriction included we calculated the temperature and pressure phase diagrams and spontaneous polarization of a bulk CIPS, within the assumed range of applicable temperatures and applied pressures. Using the developed thermodynamic potential, we revealed the strain-induced phase transitions in thin epitaxial СIPS films, as well as the stress-induced phase transitions in СIPS nanoparticles, the shape of which varies from prolate needles to oblate disks. Furthermore, w also revealed the strong influence of a mismatch strain, elastic stress, and shape anisotropy on the phase diagrams and polar properties of a nanoscale CIPS, and derived analytical expressions allowing for elastic control of the nanoscale CIPS polar properties. Hence obtained results can be of particular interest for the strain engineering of nanoscale layered ferroelectrics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Acoustic properties, elasticity, and equation of state of glycerol under pressure

Herein we employed high-pressure Brillouin scattering to study the pressure dependencies of acoustic modes of glycerol up to 14 GPa at 300 K. We observed longitudinal acoustic velocities and transverse acoustic velocities for the first time from 5 to 14 GPa. The results allow the determination of a complete set of elastic properties and an accurate determination of the pressure–volume (P–V) equation of state (EOS). EOS parameters, K 0 = 14.9 ± 1.8 GPa and K' 0 = 5.6 ± 0.5, were determined from fits to the data from ambient pressure to 14 GPa. Direct volume measurements of the P–V EOS are consistent with those determined by Brillouin scattering. A deviation from a Cauchy-like relationship for elastic properties was observed, and the pressure dependencies of the photoelastic constants and relaxation times were documented from 5 to 14 GPa. These results have broad implications for glass-forming liquids, viscoelastic theory, and mode coupling theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Density changes in amorphous silicon induced by swift heavy ions

For this study, pure and gold-doped amorphous silicon membranes were irradiated with swift heavy ions (75 MeV Ag or 1.1 GeV Au ions) and studied using small-angle x-ray scattering. The samples that were irradiated with 1.1 GeV Au ions produced a scattering pattern consistent with core-shell-type ion tracks of 2.0 ± 0.1 nm (core) and 7.0 ± 0.3 nm (total) radius irrespective of gold doping, consistent with radii previously observed. The density in the core is nearly 4% different from that of the surrounding material. The entire track (core + shell) is slightly less dense than the surrounding material, yielding an expansion or hammering constant A of 0.036 ± 0.003 nm 2 per ion track, consistent with the macroscopic “hammering” deformation. No tracks were found in samples irradiated with 75 MeV Ag ions, and no signature specific to the gold impurity doping could be observed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Poly(ether‐block‐amide) membrane with deformability and adjustable surface hydrophilicity for water purification

Abstract Freshwater resources are currently insufficient, and another form of freshwater resources, namely, ice, is very interesting except for the issue of how to use new materials for effective purification during the processing procedure. In this article, a new membrane material with multisize pore structure in the cross‐section and intact thin skin layer on the upper and lower surfaces was successfully prepared by adding porogen, filler and setting heating environment during the phase separation process. The membrane exhibits excellent axial deformability, and its elongation at break can reach to 160% strain. Meanwhile, they all show elastic deformation behavior in the range from −60 to 100°C. Even if high content of hydrophobic filler is compounded into these membranes, that is, 5.7 wt% carbon tube content, water contact angle of membrane's surface is only 72.5°, demonstrating obvious hydrophilicity. In addition, in the water purification process, the adsorption rate constant reached ideal value of 0.26 s −1 , and the equilibrium adsorption capacity was about 2.8 g/g, showing fast and efficient water purification ability. In the mode of external heating source or the membrane's heat dissipation, these prepared membranes can melt the ice to obtain purified water and exhibit a controllable purification ability in this process.

Ge, Chengbiao↗

DOE OSTI2022

Deep potential development of transition-metal-rich carbides

In this study, we developed DeepPot-SE type potentials according to the High-Entropy Strategy for Cr 23 C 6 , Fe 23 C 6 , W 23 C 6 , and Mo 23 C 6 systems. Predictive molecular dynamics are then conducted according to various elastic and mechanical properties. Training dataset accuracy is confirmed both numerically and visually. Elastic constants, Poisson Ratio, and bulk modulus are determined and compared to the literature with percent errors ranging between 0.45 and 13.33%. Ground-state lattice constants yield 0.111–1.375% percent error. Linear lattice constant thermal expansion trends are found from 300 to 1500 K as expected. Melting behaviors with clear melting points are observed for each binary. Here, the Birch–Murnaghan Equation of State is suitably fit, providing additional verification of the bulk modulus calculations. Polycrystalline thermal stability is also verified for each binary potential.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Dependence of the Elastic Stiffness Tensors of PETN, α‐RDX, γ‐RDX, ϵ‐RDX, ϵ‐CL‐20, DAAF, FOX‐7, and β‐HMX on Hydrostatic Compression

Abstract The dependence of the components of the elastic stiffness tensors (or elastic constants) of the organic explosives PETN, RDX, CL‐20, DAAF, FOX‐7, and HMX on hydrostatic pressure up to 10 GPa have been computed using dispersion‐corrected density functional theory. We report the evolution of lattice parameters and the non‐zero stiffnesses for the tetragonal, orthorhombic, and monoclinic crystal symmetries. Linear and quadratic dependencies of the components of the elastic stiffness tensors on volumetric compression and hydrostatic pressure are tabulated for use in single crystal plasticity models.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Effect of elastic anisotropy on thermally induced distortions of a laser beam in single cubic syngony crystals with radial cooling. Part I

We have studied thermally induced distortions of a beam in single cubic syngony crystals of all symmetry groups with an anisotropic elastic stiffness tensor. The arithmetic mean and the difference between the thermally induced phase incursions of eigenpolarisations, as well as the angle of incidence of these polarisations, are calculated for a long rod and a thin disk with radial cooling under uniform volume pumping of the active element. The position of the specific crystal orientations unrelated to its symmetry elements is investigated. The effective values of the thermo-optical constant Q in two specific orientations, as well as the thermo-optical constant P in an arbitrary orientation, are found. (invited paper)

36 MATERIALS SCIENCE↗

DOE OSTI2026

Surface Segregation of Liquid Metal Plasma-Facing Component Alloys: A ReaxFF Investigation

Engineering liquid metal alloys offers a transformative pathway for plasma-facing components by enabling chemically tailored surfaces that can simultaneously optimize plasma-material interactions, reduce divertor heat flux, and enhance core plasma confinement, thereby advancing the commercial viability of nuclear fusion power plants. This study, employing an atomistic simulation approach, provides direct evidence that incorporating nonmetal surface-active agents (such as O and H, or their combination) enables strong surface segregation. This capability makes tin−aluminum (Sn−Al) and tin−lithium (Sn−Li) alloys, with suitable compositions, good candidates for PFC applications. Specifically, the presence of low-Z solutes (Li, Al) leads to preferential surface enrichment, which imparts low-Z sputtering characteristics, while the Sn solvent maintains thermophysical stability. To systematically examine this behavior, we developed a ReaxFF force field spanning the full Sn/Al/Li/O/H chemistry, validated it against formation energies and elastic constants, and applied it in reactive molecular dynamics simulations at fusion-relevant temperatures. We also introduced an overlapbased segregation index that captures interfacial compositional separation directly from atomistic density distributions. Here, this metric reveals a clear hierarchy of segregation regimes and provides a unified view across all systems studied. Together, these findings establish a mechanistic link between nonmetal chemistry and interfacial structure, providing a predictive framework for designing self-adaptive, low-sputtering liquid metal alloys for fusion applications.

Alloys↗

DOE OSTI2024

Rapid Design of Cost-Effective Refractory High Entropy Alloys Strengthened by Precipitation

Funded by the ARPA-E ULTIMATE program, this project aims to develop cost-effective refractory high entropy alloys (RHEAs) for gas turbine blades applications at 1300 degree Celsius and above. The alloy design focuses on carbides precipitation strengthening in a strong and ductile solid solution BCC matrix. The goal is to achieve balanced mechanical properties including room temperature ductility & fracture toughness and high temperature strength and creep resistance, while maintaining comparable oxidation resistance and densities to Ni-base superalloys. To accelerate alloy design, multiscale modeling including CALPHAD and first-principles density functional theory (DFT) calculations and machine learning are performed. Specifically, high throughput phase diagram calculations and screening are carried out using CALPHAD; DFT calculations are performed to predict intrinsic ductility, grain boundary strengthening potential, coefficient of thermal expansion (CTE) and temperature-dependent elastic constants. Temperature dependent yield stress, creep strain and CTE are also predicted using machine learning. Down-selected alloys are synthesized in small buttons of about 250g using arc melting for rapid evaluation on microstructure and mechanical properties before employing plasma arc melting and additive manufacturing for producing large ingots. Preliminary computational and experimental results of this project will be presented and future direction in RHEA development will be discussed.

high temperature materials↗

DOE OSTI2022

Fathoming the anisotropic magnetoelasticity and magnetocaloric effect in GdNi

Intermetallic GdNi adopts a CrB type of crystal structure (space group Cmcm), and it orders ferromagnetically via a second-order phase transition at 70 K, exhibiting unusually strong spontaneous striction along the three independent crystallographic axes in the ferromagnetically ordered state. Here we introduce a microscopic model to describe anisotropic changes of lattice parameters and elastic contribution to magnetocaloric effect of GdNi. In the model, results of density functional theory (DFT) calculations are used as inputs into a Hamiltonian that includes elastic energy of an anisotropic crystal lattice, exchange interactions, and Zeeman effect. The magnetic and elastic Hamiltonians are coupled through an anisotropic Bean-Rodbell model of magnetoelastic interactions. This coupling gives rise to anisotropic changes in the lattice parameters observed experimentally, and the model reveals good to reasonable agreements between the current theoretical results and earlier experimental data, thus validating the model within the limits of assumptions made. We also show that DFT calculations with 4f electrons of Gd treated as core electrons lead to a more adequate estimate of elastic constants of GdNi in comparison with the LDA + U method where 4f electrons are treated as valence electrons.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Meso-scale modeling and damage analysis of carbon/epoxy woven fabric composite under in-plane tension and compression loadings

The mechanical properties and damage behaviors of carbon/epoxy woven fabric composite under in-plane tension and compression are studied at the meso-scale level through experiment and simulation. An efficient representative volume element (RVE) modeling method with consistent mesh, high yarn volume fraction and realistic geometry is proposed. The material constitutive laws with plasticity, tension-compression asymmetry and damage evolution are established for the three components - yarn, matrix and interface, respectively. Significantly different mechanical properties and damage evolutions are observed depending on loading conditions and initial geometry characteristics. It shows a non-linear stress-strain curve with clear transition region and intensive damage in tension, while a quasi-linear behavior up to facture is observed in compression with little damage prior to final fracture. Furthermore, compared to the constant Poisson's ratio with straining in compression, a dramatic increase in Poisson's ratio appears in tension. Simulation shows damage mechanisms including transverse damage, matrix damage and delamination, which all play critical roles in the property evolution. In particular, the rapid damage accumulation after elastic deformation destroys the strong bonds and causes the easy deformation of transverse yarns which results in the transition region and large Poisson's ratio in tension. All the mechanical behaviors and damage evolutions are well captured and explained with the current RVE model.

42 ENGINEERING↗

DOE OSTI2021

The ultrahigh pressure stability of silver: An experimental and theoretical study

We measured the atomic volume of Ag in a toroidal diamond anvil cell to a maximum pressure of 416 GPa and calculated the atomic volume and elastic constants of Ag up to 750 and 460 GPa, respectively. Our density functional theory calculations at 0 K utilize an all-electron fully relativistic method and agree well with our volume measurements, particularly at pressures above ~75 GPa. In this work, we corrected our experimental results for non-hydrostaticity using a line shift analysis, and the resulting Vinet equation of state (EOS) parameters are reported. We find that the uniaxial stress sustained by Ag increases linearly up to 4.5 GPa at a pressure of 416 GPa. Our experimental results indicate that the fcc structure of Ag remains stable to at least 416 GPa at room temperature. Our theoretical results show that C44 increases as pressure increases and reaches a maximum at ~100 GPa above which it begins to decrease, a sign that the fcc structure of Ag is becoming unstable, and at V/V 0 = 0.30, the bcc structure is lower in energy than fcc.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Evaluation of Thermal Neutron Scattering Cross Section of Uranium Silicide with Ab Initio Lattice Dynamics

Uranium silicide (U 3 Si 2 ) is a candidate material for the high-density nuclear fuel in commercial light water reactors [1], [2]. Its higher uranium density, 11.3 g-U/cm3, compared to that of uranium dioxide (UO 2 ), 9.7 g-U/cm3, can improve the performance of a nuclear reactor while using low enriched uranium (LEU) and diversify the choice of cladding materials [1]–[3]. It also has a higher thermal conductivity than UO 2 , which can reduce the thermal stress on the material caused by a temperature gradient across the fuel pellet and provide a larger margin for some postulated accidents [1], [2], [4]. Furthermore, compared to U3Si, another high-density fuel candidate, it has better resistance to in-pile swelling due to less irradiation-induced rapid amorphization [1], [3]. Corresponding to its importance in nuclear engineering, many previous studies have reported the properties of U3Si2. Experiments showed that U 3 Si 2 is a paramagnetic (PM) metal, where a slight linear increase in magnetic susceptibility was measured with increasing temperature [5], [6]. In addition, thermodynamic quantities such as thermal expansion coefficient, heat capacity, and thermal conductivity were experimentally determined over a wide temperature range [1], [7], [8]. In several computational studies, ab initio atomistic simulations based on density functional theory (DFT) were performed to calculate various properties including elastic constants, electronic density of states (DOS), and phonon dispersion curves [9]–[12]. Nevertheless, thermal neutron scattering cross sections, which are critical to the prediction of the parameters in reactor physics that are ultimately related to reactor criticality, have not yet been evaluated for U3Si2. The scattering cross section can be calculated from the phonon DOS, or the energy spectrum of lattice vibrations, of the crystalline system [13], [14]. However, there is also no experimental data available for the phonon DOS of U 3 Si 2 . While some computational studies reported the phonon DOS and/or dispersion curves from ab initio simulations [9]–[12], the accuracy cannot be guaranteed because it is unclear whether the spin-polarization behavior of PM U 3 Si 2 was properly described. In the present study, the thermal neutron scattering cross section for U 3 Si 2 is evaluated for the first time by calculating the phonon DOS for U3Si2 from ab initio lattice dynamics (AILD) simulations based on DFT. First, U 3 Si 2 is modeled based on the experimental structure, and AILD simulations are performed on the modeled U3Si2 to optimize the structure. Next, AILD simulations are performed for supercells with atomic displacement to calculate Hellmann-Feynman forces. Based on the calculated forces, partial phonon DOSs for U and Si are obtained, and the thermal neutron scattering law (TSL) for U 3 Si 2 is finally evaluated. To verify the accuracy of the calculations in the present study, the calculation results are compared with experimental data on the structure and heat capacity of U3Si2 [1], [7], [8], [15].

Geometry Optimization↗

DOE OSTI2023

Analysis of phase stability and chemical segregation in the Mo-V alloys using a generalized embedded atom method potential

A new interatomic potential for the Mo-V system is introduced to facilitate the study of phase stability and mechanical properties at lower temperatures. This potential is based on a generalization of the embedded atom method and includes contributions from embedding energy, explicit two- and three-body interactions and nonlocal many-body interaction terms. The parameters of the potential are optimized by using data from ab initio density functional theory (DFT) calculations. The potential is rigorously validated across a range of physical properties, such as elastic constants, equation of states, phonon dispersion curves, point defect properties and melting temperatures for different compositions. Even though our potential is trained on a small dataset, its accuracy is comparable to available machine learning potentials for Mo and V. Furthermore, our results show that an ordered B2 phase is stable at low temperatures in alloys containing 50% V, but the solid solution phase is stable above 800 K. However, such long-range ordering is not observed in V-rich or Mo-rich alloys. In addition, our results show that V segregates to dislocation cores and grain boundaries.

36 MATERIALS SCIENCE↗