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DOE OSTI2026

Microstructure prediction for Ti-22Al-25Nb in laser powder bed fusion

This work presents a physics-informed framework for predicting solidification morphology and defect susceptibility in additively manufactured Ti–22Al–25Nb across a broad processing space. The framework integrates solidification microstructure selection (SMS) analysis with a single-track defect-based printability map to establish a unified methodology linking processing parameters to both interfacial morphology and manufacturability. Thermal gradients G and solidification rates R are first computed using the Thermo-Calc Additive Manufacturing (TC-AM) module, a finite-interface-dissipation (FID) phase-field (PF) model coupled with CALPHAD method is then employed to systematically distinguish planar and dendritic regimes as functions of $G$ and $R$. By superimposing the printability map onto the morphology projections, a comprehensive process–structure framework is obtained. Across most processing conditions, the predicted microstructure is predominantly dendritic, while planar growth emerges only under selected laser power $P$ and scan speed $v$ combinations. In addition to morphology classification, the framework quantifies the dendritic area fraction and introduces a width-based morphology descriptor to characterize the spatial extent of planar/dendritic regions within the melt pool. It provides mechanistic insight into the interplay between solidification physics and defect formation, offering practical guidance for parameter selection and microstructural control in Ti–22Al–25Nb additive manufacturing (AM).

36 MATERIALS SCIENCE↗

DOE OSTI2020

Low-dissipation centred schemes for hyperbolic equations in conservative and non-conservative form

We propose a one-parameter family of low-dissipation centred numerical schemes for solving hyperbolic equations in conservative or non-conservative form, using finite volume or discontinuous Galerkin finite element methods. The new schemes spring out from the multi-dimensional FORCE method and are determined by a single parameter α ≥ 1. Given an increasing sequence of real numbers 1 ≤ α 1 < α 2 < . . . < α K , there corresponds a sequence of numerical schemes with stability restriction associated to a decreasing sequence of Courant numbers 1 > c 1 > c 2 > . . . > c K > 0 and a decreasing sequence of corresponding numerical viscosity functions d 1 > d 2 > . . . > d K . For a given Courant number c k ≤ 1 there is a real number α k > 0 and a corresponding stable scheme with minimal numerical viscosity d k . The proposed schemes suit very well the family of high-order discontinuous Galerkin finite element methods and the recently proposed class of ADER-TR schemes, whose orders of accuracy define decreasing sequences of Courant numbers, as the order of accuracy increases. The centred methods of this paper are stable in 2D and 3D in the frame of simultaneous updating formulae, unlike other centred methods, such as 1D FORCE, which are not. Furthermore, the schemes are highly accurate for slowly-moving waves, which is precisely the kind of waves that traditional centred methods smear disastrously. Additional features of the proposed schemes include ease of implementation and applicability to any hyperbolic system either in conservative or non-conservative form. Here, the proposed schemes are analysed and computationally assessed through a suite of test problems for a linear model system, for the Euler equations in one and two space dimensions, and for the Baer-Nunziato equations for compressible two-phase flow.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Inclusive curvaturelike framework for describing dissipation: Metriplectic 4-bracket dynamics

An inclusive framework for joined Hamiltonian and dissipative dynamical systems that are thermodynamically consistent, i.e., preserve energy and produce entropy, is given. The dissipative dynamics of the framework is based on the metriplectic 4-bracket , a quantity like the Poisson bracket defined on phase space functions, but unlike the Poisson bracket has four slots with symmetries and properties motivated by Riemannian curvature. Metriplectic 4-bracket dynamics is generated using two generators, the Hamiltonian and the entropy, with the entropy being a Casimir of the Hamiltonian part of the system. The formalism includes known previous binary bracket theories for dissipation or relaxation as special cases. Rich geometrical significance of the formalism and methods for constructing metriplectic 4-brackets are explored. Many examples of both finite and infinite dimensions are given.

Physics↗

DOE OSTI2020

Hydrodynamic instabilities and heat transfer characteristics in the duct flow of a fluid in the supercritical thermodynamic regime

The behavior of fluids at supercritical thermodynamic conditions is inherently complex due to large variations in thermodynamic and transport properties. Recent numerical and experimental investigations illustrate ongoing interest for these fluids, especially supercritical CO 2 and supercritical water, for a variety of applications. For example, supercritical water reactors (SCWR) operate in this extreme condition of high-pressure and temperature, resulting in highly dynamic flow fields and unexpected heat transfer regimes. The potential heat transfer benefits in this regime are directly associated with the extreme variations in thermodynamic and transport properties, which occur at, and above, the critical point. This work characterizes the hydrodynamic instabilities that arise for fluids at supercritical thermodynamic conditions when buoyancy forces are significant. Two specific configurations are considered, a natural convection cavity flow, and a mixed convection, heated, horizontal channel flow. Natural convection flow in a cavity is a classical configuration with expected behavior below the critical point. This configuration aids in characterizing the effect of the variable properties in the supercritical thermodynamic regime. Further, limited studies in the existing literature have been conducted for low-Reynolds and intermediate-Rayleigh numbers, mixed-convection channel flows for supercritical water, which is the focus of the channel flow configuration. To investigate the thermally driven hydrodynamic instabilities in this regime, a high-order fully-implicit numerical method is used. Such strong variations in thermophysical properties (in particular, density) are difficult to simulate and an altogether compressible framework is needed. Therefore, the compressible Navier-Stokes equations are solved without any additional assumptions. The fully implicit, high-order in space and time, reconstructed discontinuous Galerkin method as implemented within the multi-physics code called ALE3D (Arbitrary Lagrangian and Eulerian in 2D and 3D), developed at Lawrence Livermore National Laboratory (LLNL), is used. This fully implicit, L-stable method accurately captures the compressible nature of the ow in the limit of very low Mach number. It has been widely accepted that above the critical point, only one phase is observed. However, recent research has indicated the existence of the distinct gas-like and liquid-like regions separated by the Widom line, the locus of the maxima of the specific heat. Along the Widom line, density decreases 6-fold, viscosity drops by a factor of 2, while specific heat spikes by an order of magnitude. These variations, specifically in density and viscosity, produce a thick pseudo-interface and flow dynamics behavior akin to film boiling. A pseudo-film at the heated wall of the cavity and the horizontal channel is observed where buoyancy forces induce mixing through the specific configurations. Further the local Rayleigh and Richardson numbers provide maps of the flow field and the buoyancy forces driving the microscopic mixing. In the first chapter, I describe a background of supercritical fluid and the various applications. The second chapter focuses on the mathematical model and numerical method used for simulations, where a description of the equation of state for supercritical water is described. The third chapter focuses on the natural convection cavity with a heated bottom wall. In this cavity a gas-like and a liquid-like flow within the supercritical thermodynamic regime are observed. The fourth chapter focuses on a forced convection, horizontal channel, distinguishing between the gas-like, liquid-like, and mixed flow regimes. Mixed convection flow, with the addition of gravitational forces in the horizontal channel show the influence of variable properties on the hydrodynamic development, heat transfer, and rising instabilities. The last chapter of this research focuses on characterizing the unstable hydrodynamics through time-averaging processes and analysis of the movement of energy through the developing plumes.

42 ENGINEERING↗

DOE OSTI2023

Imaging Nanoscale Energy Transport and Conversion with Ultrafast Electron Microscopy (Final Technical Report)

Light-matter interactions are ubiquitous in nature and reside at the heart of innumerable technologies. The cascade of processes that occur when a material absorbs a photon of light are exceedingly complex and are interwoven in both space and time, rendering precise determination of the atomic-scale and ultrafast mechanisms immensely challenging. The advent of methods for generating short pulses of light several decades ago led to major advances in understanding the initial moments of light absorption and the resultant effects, though directly interrogating the response of the atoms within the material continued to prove challenging. More recently, methods for generating ultrashort pulses of X-rays and fast electrons have opened the way to probing photoinduced structural dynamics of a wide range of matter in multiple phases. An especially promising laboratory-scale method is ultrafast electron microscopy (UEM), wherein the modalities of conventional transmission electron microscopes (imaging, diffraction, spectroscopy) are extended into the femtosecond temporal regime. Here, the ultrafast imaging and diffraction modalities of UEM were used to study the transient structural aspects of photoexcitation of semiconducting materials (e.g., spatially-resolved electron-phonon coupling, excitation and emission of acoustic phonons, and discrete nanoscale scattering processes). The project had three main objectives: (1) determination of the excitation mechanisms of dense, hypersonic charge-carrier waves and the spatially mediated means by which they couple to the lattice via coherent phonon emission, especially with UEM imaging, wherein effects of nanoscale structural and morphological features on the coupling and relaxation dynamics are expected to dictate nucleation sites and preferred wave vectors, (2) elucidation of photoinduced acoustic-phonon seeding, emergence, propagation, and decay over nanoscale crystal regions and especially with respect to local strain fields and atomic-scale disruptions in lattice order, and (3) interwoven with the first two were efforts aimed at realizing combined angstrom-femtosecond spatiotemporal imaging with UEM. The outcomes and impacts of this project were the generation of new knowledge with respect to fundamental light-matter interactions and, especially, the spatially-mediated excitation and evolution of the structural response of materials following coherent photoexcitation. Importantly, the spatial and temporal resolutions of the UEM imaging modalities used are well-suited for such studies and enable spatially-resolved mechanisms to be determined as a function of atomic order, structural features, and morphology. In addition, ultrafast crystallographic measurements were used to correlate real- and reciprocal-space dynamics in order to determine atomic-scale preferential wave vectors and ultrafast scattering mechanisms, especially as dictated by specimen boundary conditions. The obtained results, as detailed in peer-reviewed publications and presentations, illustrate the importance of ultrafast, angstrom-scale real-space imaging for developing a comprehensive understanding of energy transport and conversion in materials.

47 OTHER INSTRUMENTATION↗

DOE OSTI2020

Physical, numerical, and computational challenges of modeling neutrino transport in core-collapse supernovae

The proposal that core collapse supernovae are neutrino driven is still the subject of active investigation more than 50 years after the seminal paper by Colgate and White. The modern version of this paradigm, which we owe to Wilson, proposes that the supernova shock wave is powered by neutrino heating, mediated by the absorption of electron-flavor neutrinos and antineutrinos emanating from the proto-neutron star surface, or neutrinosphere. Neutrino weak interactions with the stellar core fluid, the theory of which is still evolving, are flavor and energy dependent. The associated neutrino mean free paths extend over many orders of magnitude and are never always small relative to the stellar core radius. Thus, neutrinos are never always fluid like. Instead, a kinetic description of them in terms of distribution functions that determine the number density of neutrinos in the six-dimensional phase space of position, direction, and energy, for both neutrinos and antineutrinos of each flavor, or in terms of angular moments of these neutrino distributions that instead provide neutrino number densities in the four-dimensional phase-space subspace of position and energy, is needed. In turn, the computational challenge is twofold: (i) to map the kinetic equations governing the evolution of these distributions or moments onto discrete representations that are stable, accurate, and, perhaps most important, respect physical laws such as conservation of lepton number and energy and the Fermi–Dirac nature of neutrinos and (ii) to develop efficient, supercomputer-architecture-aware solution methods for the resultant nonlinear algebraic equations. In this review, we present the current state of the art in attempts to meet this challenge.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Deep learning on the 2-dimensional Ising model to extract the crossover region with a variational autoencoder

The 2-dimensional Ising model on a square lattice is investigated with a variational autoencoder in the non-vanishing field case for the purpose of extracting the crossover region between the ferromagnetic and paramagnetic phases. The encoded latent variable space is found to provide suitable metrics for tracking the order and disorder in the Ising configurations that extends to the extraction of a crossover region in a way that is consistent with expectations. The extracted results achieve an exceptional prediction for the critical point as well as agreement with previously published results on the configurational magnetizations of the model. The performance of this method provides encouragement for the use of machine learning to extract meaningful structural information from complex physical systems where little a priori data is available.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

The AGORA High-resolution Galaxy Simulations Comparison Project. VI. Similarities and Differences in the Circumgalactic Medium

Abstract We analyze the circumgalactic medium (CGM) for eight commonly-used cosmological codes in the AGORA collaboration. The codes are calibrated to use identical initial conditions, cosmology, heating and cooling, and star formation thresholds, but each evolves with its own unique code architecture and stellar feedback implementation. Here, we analyze the results of these simulations in terms of the structure, composition, and phase dynamics of the CGM. We show properties such as metal distribution, ionization levels, and kinematics are effective tracers of the effects of the different code feedback and implementation methods, and as such they can be highly divergent between simulations. This is merely a fiducial set of models, against which we will in the future compare multiple feedback recipes for each code. Nevertheless, we find that the large parameter space these simulations establish can help disentangle the different variables that affect observable quantities in the CGM, e.g., showing that abundances for ions with higher ionization energy are more strongly determined by the simulation’s metallicity, while abundances for ions with lower ionization energy are more strongly determined by the gas density and temperature.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Structure-Property Relationships of Additively Manufactured Ni-Nb Alloys [Slides]

In this work, scratch and nanoindentation testing was used to determine hardness, fracture toughness, strain rate sensitivity, and activation volumes on additively manufactured graded and uniform Ni-Nb bulk specimens. Characterization showed the presence of a two phase system consisting of Ni 3 Nb and Ni 6 Nb 7 intermetallics. Intermetallics were multimodal in nature, having grain and cell sizes spanning from a few nanometers to 10s of micrometers. The unique microstructure resulted in impressively high hardness, up to 20 GPa in the case of the compositionally graded sample. AM methods with surface deformation techniques are a useful way to rapidly probe material properties and alloy composition space.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Structure-Property Relationships of Additively Manufactured Ni-Nb Alloys [Slides]

36 MATERIALS SCIENCE↗

DOE OSTI2022

Formulation of the density eigenvalue problem in neutron transport for relevant engineering applications

A new formulation of the density eigenvalue problem for the neutron transport equation is presented. This new eigenvalue, named ζ eigenvalue can be introduced freely in the transport model, acting on a selected portion of the phase space. Despite its broader applications and its connection with the nature of the transport operator, the ζ eigenvalue has been presented here mainly as a design-oriented technique for the efficient evaluation of the critical concentration for a specific nuclide (or mixture of nuclides). This new eigenvalue is particularly adequate to study the definition of the material composition in the criticality design process of a multiplying system. The method is then applied for the study of classical problems such as the critical moderation ratio and the poison concentration to control the reactor. Some results are presented in one dimensional configuration using the multi- group spherical harmonics approach. This eigenvalue formulation proves to be a convenient and useful way to attain criticality, also for complex, realistic systems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part II

X-ray Bragg coherent diffraction imaging (BCDI) has been demonstrated as a powerful 3D microscopy approach for the investigation of sub-micrometre-scale crystalline particles. The approach is based on the measurement of a series of coherent Bragg diffraction intensity patterns that are numerically inverted to retrieve an image of the spatial distribution of the relative phase and amplitude of the Bragg structure factor of the diffracting sample. This 3D information, which is collected through an angular rotation of the sample, is necessarily obtained in a non-orthogonal frame in Fourier space that must be eventually reconciled. To deal with this, the approach currently favored by practitioners (detailed in Part I) is to perform the entire inversion in conjugate non-orthogonal real- and Fourier-space frames, and to transform the 3D sample image into an orthogonal frame as a post-processing step for result analysis. In this article, which is a direct follow-up of Part I, two different transformation strategies are demonstrated, which enable the entire inversion procedure of the measured data set to be performed in an orthogonal frame. The new approaches described here build mathematical and numerical frameworks that apply to the cases of evenly and non-evenly sampled data along the direction of sample rotation ( i.e. the rocking curve). The value of these methods is that they rely on the experimental geometry, and they incorporate significantly more information about that geometry into the design of the phase-retrieval Fourier transformation than the strategy presented in Part I. Finally, two important outcomes are (1) that the resulting sample image is correctly interpreted in a shear-free frame and (2) physically realistic constraints of BCDI phase retrieval that are difficult to implement with current methods are easily incorporated. Computing scripts are also given to aid readers in the implementation of the proposed formalisms.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Controlling topology through targeted composite symmetry manipulation in magnetic systems

The possibility of selecting magnetic space groups by orienting the magnetization direction or tuning magnetic orders offers a vast playground for engineering symmetry-protected topological phases in magnetic materials. In this work, we study how selective tuning of symmetry and magnetism can influence and control the resulting topology in a two-dimensional magnetic system, and we illustrate such a procedure in the ferromagnetic monolayer MnPSe 3 . Density functional theory calculations reveal a symmetry-protected accidental semimetallic (SM) phase for out-of-plane magnetization, which becomes an insulator when the magnetization is tilted in-plane, reaching band-gap values close to 100 meV. We identify an order-2 composite antiunitary symmetry and threefold rotational symmetry that induce the band crossing, and we classify the possible topological phases using symmetry analysis, which we support with tight-binding and k · p models. Breaking of inversion symmetry opens a gap in the SM phase, giving rise to a Chern insulator. We demonstrate this explicitly in the isostructural Janus compound Mn 2 ⁢P 2 ⁢S 3 ⁢Se 3 , which naturally exhibits Rashba spin-orbit coupling that breaks inversion symmetry. Our results map out the phase space of topological properties of ferromagnetic transition-metal phosphorus trichalcogenides, and they demonstrate the potential of the magnetization-dependent metal-to-insulator transition as a spin switch in integrated two-dimensional electronics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

A gauge-compatible Hamiltonian splitting algorithm for particle-in-cell simulations using finite element exterior calculus

A particle-in-cell algorithm is derived with a canonical Poisson structure in the formalism of finite element exterior calculus. The resulting method belongs to the class of gauge-compatible splitting algorithms, which exactly preserve gauge symmetries and their associated conservation laws via the momentum map. We numerically demonstrate this time invariance of the momentum map and its usefulness in establishing precise initial conditions with a desired initial electric field and fixed background charge. The restriction of this canonical, finite element Poisson structure to the 1X2P $1\frac {1}{2}$ -dimensional phase space is also considered and simulated numerically.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Rare Earth Nitrate Hybrid Double Perovskites [Me 4 N] 2 [MLn(NO 3 ) 6 ] (M = Na–Cs; Ln = La–Gd, ex. Pm)

An exploration of the synthetic and structural phase space of rare earth hybrid double perovskites A 2 B'BX 6 (A = organocation, B' = M + , B = M 3+ , X = molecular bridging anion) that include X = NO 3 – and B' = alkali metal is reported, complementing earlier studies of the [Me 4 N] 2 [KB(NO 3 ) 6 ] (B = Am, Cm, La–Nd, Sm–Lu, Y) (Me 4 N = (CH 3 ) 4 N + ) compounds. In the present efforts, the synthetic phase space of these systems is explored by varying the identity of the alkali metal ion at the B'-site. Herein, we report three new series of the form [Me 4 N] 2 [B'B(NO 3 ) 6 ] (B = La–Nd, Sm–Gd; B' = Na, Rb, Cs). The early members of the Na-series crystallize in the trigonal space group R3̅ from La to Nd where a phase transition occurs in the phase between 273 and 300 K, going from R3̅ to the high-symmetry, cubic space group Fm3̅m. The preceding trigonal members of the Na-series also undergo phase transitions to cubic symmetry at temperatures above 300 K, establishing a decreasing trend in the phase-transition temperature. The remainder of the Na-series, as well as the Rb- and Cs-series, all crystallize in Fm3̅m at 300 K. The temperature-dependent phase behavior of the synthesized phases is studied via variable-temperature spectroscopic methods and high-resolution powder X-ray diffractometry. All phases were characterized via single-crystal and powder X-ray diffraction and Fourier transform infrared (FT-IR) and Raman spectroscopic methods. These results demonstrate the versatility of the perovskite structure type to include rare earth ions, nitrate ions, and a suite of alkali metal ions and serve as a foundation for the design of functional rare earth hybrid double perovskite materials such as those possessing useful multiferroic, optical, and magnetic properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

A series of Rb 4 Ln 2 (P 2 S 6 )(PS 4 ) 2 (Ln = La, Ce, Pr, Nd, Sm, Gd) rare earth thiophosphates with two distinct thiophosphate units [P V S 4 ] 3- and [P IV 2 S 6 ] 4-

A series of rubidium rare earth thiophosphates with the formula Rb 4 Ln 2 (P 2 S 6 )(PS 4 ) 2 (Ln = La, Ce, Pr, Nd, Sm, and Gd) were synthesized using the high temperature molten flux crystal growth method utilizing a RbBr flux. Single crystals of all title compounds, as well as phase pure powders of the La-, Ce-, and Sm-containing compositions, were obtained. Single crystals of the title compounds were characterized by single crystal and powder X-ray diffraction for structure and phase identification. Rb 4 Ln 2 (P 2 S 6 )(PS 4 ) 2 crystallizes in the monoclinic crystal system adopting the P2 1 /n space group for the large rare earths (Ln = La, Ce, Pr) and the C2/c space group for the smaller rare earths (Ln = Nd, Sm, Gd). This Rb 4 Ln 2 (P 2 S 6 )(PS 4 ) 2 series is a rare example of thiophosphates containing both tetrahedral [P V S 4 ] 3– and dimeric [P IV 2 S 6 ] 4– thiophosphate units that, in this structural family, link corrugated rare earth sulfide chains into sheets. Here, the band gaps of the materials were determined from UV–Vis data and the fluorescence spectrum of Rb 4 Ce 2 (P 2 S 6 )(PS 4 ) 2 was collected. Optical band gaps were estimated to be 2.9 and 2.4 for the Nd and Sm analogues, respectively.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Feasibility of a Novel Density Functional Method Outside the Kohn-Sham Framework for Modeling Global Potential Energy Surfaces of Molecular Chemical Reactions (Final Technical Report)

The project aimed towards the construction of computational methods capable of modeling the global potential energy surface (PES) of small molecules, molecular ions, and radicals — including the parts of the PES which correspond to chemical reactions, and the reaction paths connecting reactants, intermediates, and reaction products. This goal may seem humble at first glance, but for chemical systems with more than about six atoms in total, at the time the project was proposed, there were no established theoretical methods capable of simulating such systems reliably, not even for small molecules in the gas phase which are electronically benign. This restriction severely hampers our ability to model and control chemical processes under harsh conditions. With the goal of constructing a method capable of modeling such chemical systems, we proposed to pursue a novel approach towards a Multi-Configuration (MC) DFT outside the traditional frameworks of Kohn-Sham theory and other methods of coupling wave function theory with DFT. Rather than being a complete active space (CAS) method, the proposed DOCI-DFT would employ a special restricted form of the active space wave function, called Doubly-Occupied CI (DOCI)—this wave function form is sufficient to describe not only heterolytic, but also homolytic bond dissociation processes at the zeroth order (i.e., as active space wave function). There are no other standard mean field methods which can do so. In the original proposal, we also outlined strong formal and practical arguments speaking for this method. The project proposal was accepted by the Department of Energy and provided two years of seed funding for one graduate student, as well as two years of two weeks PI summer-salary for the PI. However, ultimately the project could not be effectively pursued due to severe interferences outside the context scientific problems and was cancelled. Apart from two weeks of PI salary (and associated fringe & overhead costs issues by the performing institution), no costs were charged against the award, with the entire rest of funding returned to the Department of Energy. This report reiterates the primary background information regarding the project, its original goals, and outlines the preliminary work performed during the two weeks of DOE funding charged.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

High-pressure phase transitions and melt structure of Pb O 2 : An analog for silica

In situ x-ray diffraction measurements and inverse Monte Carlo simulations of pair distribution functions were used to study the structural response of PbO 2 under pressure and to characterize the local structure of liquid PbO 2 . Two phase transitions are observed upon room-temperature compression of crystalline PbO 2 up to ~65 GPa. Here, the starting mixture of rutile structured β– PbO 2 and orthorhombic α– PbO 2 undergoes a transition to a ZrO 2 -type orthorhombic phase with space group Pbca at ~21 GPa. Above 42 GPa, the Pbca phase transforms to a cotunnite-type phase with space group Pnam. In this paper, we also report short-range order in liquid PbO 2 , showing ~8–9-fold and 4–5-fold coordination around Pb and O atoms, respectively.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗