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DOE OSTI2025

Insights into the phase stability window, phase transformation behavior, and anisotropic thermal expansion of rhombohedral bismuth oxide

Rhombohedral bismuth oxide has emerged as a promising SOFC electrolyte material, particularly at low-to-intermediate temperatures. The stability window of this phase was explored using a co-doped system, using yttrium and lanthanum or aluminum, over 7.5–25 % total dopant content and 0.907–1.154 Å weighted average dopant cationic radius. The phase transformation behavior of rhombohedral-rich phase mixtures was also investigated in situ from 360 to 656 °C to assess the effects of minor impurity phases and thermal evolution pathways. Our results reveal that low-dopant, rhombohedral-rich compositions exhibit poor structural stability upon heating. Anisotropic thermal expansion behavior was observed over 450–656 °C, serving as a sensitive indicator of sequential phase changes, including the rhombohedral β2-to-β1 transition (∼450 °C), monoclinic phase formation, and delayed or incomplete formation of the cubic phase (∼ 550 °C). These multiple unfavorable phase transitions compromise the mechanical robustness required for SOFC operation. This study underscores the need for compositional tuning to balance ionic conductivity with thermal phase stability in rhombohedral Bi 2 O 3 -based systems.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Enhanced Phase Stability of Sm 2 (Fe, Al) 17 C x

Aluminum doping can improve the phase stability of metastable compound Sm 2 Fe 17 C x with a high carbon content (x > 1.5). We investigated the preferential site substitution of Al, chemical bonding, and structural stability in Sm 2 (Fe,Al) 17 C 3 using first-principle calculations. Our results reveal a strong correlation between the preferential substitution of Fe by Al and the atomic site chemical environment, which affects the overall phase stability. Specifically, Al preferentially occupies the 9d site in Sm 2 (Fe,Al) 17 C 3 . At the same time, Al prefers the site 6c in its parent phase Sm 2 (Fe,Al) 17 . Partial replacement of Fe with Al leads to a more negative formation energy, indicating enhanced thermodynamic stability. Crystal Orbital Hamilton Population (COHP) and Crystal Orbital Bond Index (COBI) analysis suggest that insertion of carbon weakens the bonding strength of Sm-Fe (18f) and Sm-Fe (18h), resulting in metastability of Sm 2 Fe 17 C x . Doping Al strengthens Al-Fe, Al-Sm, Sm-Fe (18f, 18h) and Fe–C bonding in Sm 2 (Fe,Al) 17 C 3 , as revealed by calculated COHP and COBI. These effects contribute to improved phase stability in the Al-doped 2:17 interstitial compound.

chemical bonding↗

DOE OSTI2026

Chemical bonding, phase stability and magnetic property in Sm 2 Fe 17 X 3 (X=H, C, N): A first-principles perspective

As a promising alternative to Nd–Fe–B magnets, the critical rare earth free Sm 2 Fe 17 X 3 (X = C, N) exhibits potential for high-performance magnets. However, their poor phase stability remains a major obstacle to developing bulk magnets. We investigated the phase stability and intrinsic magnetic properties of Sm 2 Fe 17 X 3 (X = H, C, N) using first-principles calculations and chemical bond analysis. The formation energies are negative, while the decomposition energies are −1.53, 0.348, and −0.74 eV per formula unit for X = H, C, and N, respectively, which is responsible for the weak thermal stability. Our chemical bond analysis reveals that the bonding asymmetry between Sm–X and Fe–X interactions creates local structural distortions and degrades the phase stability of Sm 2 Fe 17 X 3 . The project Crystal Orbital Hamilton Population (-pCOHP) analysis indicates that the Sm–X bonding remains positive up to the Fermi level, indicating stable bonding interactions. Here, in contrast, the Fe–X bonding becomes negative near the Fermi level, signifying anti-bonding contributions that reduce structural stability. Interstitial atoms X expand the lattice and enhance Fe magnetic moments, but Fe–X bonding suppresses neighboring Fe moments. Electron transfer from Sm to X modifies the valence state of Sm and the crystal field at the site, contributing to enhanced magnetocrystalline anisotropy in Sm 2 Fe 17 X 3 . Among the interstitial elements, carbon and nitrogen—with their larger atomic radius and higher electronegativity—induce greater lattice expansion and form stronger bonds with neighboring Sm and Fe atoms compared to hydrogen. Consequently, Sm 2 Fe 17 X 3 (X = C and N) exhibits better phase stability and significant improvement in magnetic properties.

Chemical bonding↗

DOE OSTI2025

Theoretical perspective on phase stability and polarization switching in ferroelectric hafnia

Fluorite-based ferroelectric materials are revolutionizing the application space of polar semiconductors. These materials leverage robust polarization of extremely thin films, compatibility with the silicon chip processing, and decades of manufacturing experience to enable a new generation of ferroelectric memory devices. As a new paradigm for ferroelectrics, understanding of phase transitions and the switching mechanism in fluorites is essential both for advancing applications and for fundamental science. In this article, we outline the recent progress that has been made to understand the relative phase stability, phase transition and order parameter coupling, ferroelectric switching through unique nucleation and growth processes, and how defects affect these phases and processes. The main challenges, opportunities, and next steps for leveraging these materials for next-generation devices are reviewed.

Condensed Matter Physics↗

DOE OSTI2025

Low-Density Parity-Check Stabilizer Codes as Gapped Quantum Phases: Stability under Graph-Local Perturbations

We generalize the proof of stability of topological order, due to Bravyi, Hastings, and Michalakis, to stabilizer Hamiltonians corresponding to low-density parity-check (LDPC) codes without the restriction of geometric locality in Euclidean space. We consider Hamiltonians 𝐻 0 defined by ⟦𝑁,𝐾,𝑑⟧ LDPC codes, which obey certain topological quantum order conditions: (i) code distance 𝑑 ≥ 𝑐⁢log (𝑁), implying local indistinguishability of ground states, and (ii) a mild condition on local and global compatibility of ground states—these include good quantum LDPC codes and the toric code on a hyperbolic lattice, among others. We consider stability under weak perturbations that are quasilocal on the interaction graph defined by 𝐻 0 and that can be represented as sums of bounded-norm terms. As long as the local perturbation strength is smaller than a finite constant, we show that the perturbed Hamiltonian has well-defined spectral bands originating from the 𝑂⁡(1) smallest eigenvalues of 𝐻 0 . The band originating from the smallest eigenvalue has 2 𝐾 states, is separated from the rest of the spectrum by a finite energy gap, and has exponentially narrow bandwidth 𝛿 =𝐶⁢𝑁⁢𝑒 −Θ⁡(𝑑) , which is tighter than the best-known bounds even in the Euclidean case. We also obtain that the new ground-state subspace is related to the initial-code subspace by a quasilocal unitary, allowing one to relate their physical properties. Our proof uses an iterative procedure that performs successive rotations to eliminate non-frustration-free terms in the Hamiltonian. Our results extend to quantum Hamiltonians built from classical LDPC codes, which give rise to stable symmetry-breaking phases. These results show that LDPC codes very generally define stable gapped quantum phases, even in the non-Euclidean setting, initiating a systematic study of such phases of matter.

mathematical physics↗

DOE OSTI2025

Interplay between electron localization, magnetic order, and Jahn-Teller distortion dictates LiMnO2 phase stability

The development of manganese (Mn)-rich cathodes for Li-ion batteries promises to alleviate potential supply chain bottlenecks in battery manufacturing. Fundamental challenges in Mn-rich cathodes arise from phenomena such as structural changes due to cooperative Jahn-Teller (JT) distortions of in octahedral environments, Mn migration, and phase transformations to spinel-like order, all of which affect the electrochemical performance. These physically complex phenomena motivate an re-examination of the Li-Mn-O rock-salt space, with a focus on the thermodynamics of the prototypical, polymorphs. It is found that the generalized gradient approximation (GGA-PBEsol) and meta-GGA ( ) density functionals with empirically fitted on-site Hubbard corrections yield spurious stable phases for , such as predicting a phase with -like order ( ) to be the ground state instead of the orthorhombic (Pmmn) phase, which is the experimentally known ground state. Accounting for antiferromagnetic order in each structure is shown to have a substantial effect on the total energies and resulting phase stability. By using hybrid-GGA (HSE06) and GGA with self-consistent Hubbard parameters (on-site and inter-site ) calculated from linear response theory, the experimentally observed phase stability trends are recovered. The calculated on-site between Mn- states in the experimentally observed orthorhombic, layered, and spinel phases are significantly smaller than in and disordered layered structures, by within GGA. The smaller values of are shown to be correlated with a collinear ordering of JT distortions, in which all orbitals are oriented in the same direction. This cooperative JT effect can lead to greater electron delocalization from Mn along the states due to increased Mn-O covalency, which contributes to the greater electronic stability compared to the phases with noncollinear JT arrangements. The structures with collinear ordering of JT distortions also generate greater vibrational entropy, which helps stabilize these phases at high temperature. These phases are shown to be strongly insulating with large calculated band gaps , which are computed using HSE06 and .

Kam, Ronald L↗

DOE OSTI2026

Chemical bond and phase stability of Ga-doped Sm2Fe17Cx magnet

Sm2Fe17C3 phase (2:17) is metastable and exhibits excellent intrinsic hard magnetic properties. Doping elements such as Ga facilitate the formation of a single-phase 2:17 structure in arc-melted Sm2Fe17Cx alloys, which opens a promising route for fabricating fully dense bulk Sm2Fe17Cx magnets via high-temperature techniques such as melting and sintering. First-principles electronic structure calculation indicates that Ga prefers to partially replace Fe at the 9d and 18h crystallographic sites in Sm2Fe17C3 and Sm2Fe17, respectively. This difference in site preference is attributed to the distinct chemical environments surrounding the Fe atoms in the two compounds. Ga substitution favors the Sm–Ga bonding formation while avoiding Ga–C interactions. Doped Ga atoms result in more negative formation energy in Sm2(Fe, Ga)17C3, indicating improved structural stability. Crystal Orbital Hamilton Population analysis reveals that carbon insertion weakens the bonding of Sm-Fe (18h) and Sm-Fe (18f) in Sm2Fe17C3. Ga doping facilitates electron redistribution across chemical bonds, thereby reinforcing Fe(18h)–Sm and Fe(18f)–Sm interactions and stabilizing the carbon-centered octahedral local structure. This synergistic effect contributes significantly to the observed enhancement in phase stability of Sm2(Fe, Ga)17Cx. These findings suggest that chemical bond engineering through the selective doping of Ga can enhance phase stability and facilitate the synthesis of Sm2Fe17C3, providing a viable strategy for developing advanced magnets.

Liu, Xubo [Critical Materials Innovation Hub, Divi↗

DOE OSTI2026

Phase Stability and Electrochemical Performance of La-Site-Doped Li6La3Zr0.5Nb0.5Ta0.5Hf0.5O12 High-Entropy Garnets

We investigate La-site substitution in the high-entropy garnet Li6La3Zr0.5Nb0.5Ta0.5Hf0.5O12 (LLZNTH) using Ba2+, Sr2+, and Sm3+ to elucidate how dopant governs phase stability, Li-site distribution, and electrochemical behavior. X-ray diffraction shows that Sr2+ is incorporated homogeneously into the garnet lattice, whereas the larger Ba2+ and smaller Sm3+ ions partially exceed the structural tolerance, generating secondary phases. Nevertheless, the Sm-doped composition (x = 0.05) exhibits the highest room-temperature ionic conductivity (2.7 × 10–4 S cm–1). Neutron powder diffraction reveals that Sm substitution drives a redistribution of Li+ from the tetrahedral 24 d sites into the higher-mobility 96 h positions, enhancing the connectivity of the three-dimensional Li-ion migration network. A Sm-doping series (x = 0.01–0.05) further shows that only sufficiently high Sm levels induce this redistribution, whereas lower concentrations retain Li arrangements similar to the undoped garnet. Critical current density measurements demonstrate that La-site dopants also influence interfacial stability against Li metal, underscoring a trade-off between bulk transport enhancement and mechanical robustness. Collectively, these findings reveal that in high-entropy garnets improved ionic conductivity can originate not only from phase-pure structures but also from targeted modification of the Li sublattice, even when accompanied by secondary phases, offering a compositional design principle for garnet electrolytes.

Li, Chang [Mechanical Engineering, School of Scien↗

DOE OSTI2025

Microstructural evolution and phase stability in Nb-containing interstitial Fe-Mn-Co-Cr-C high-entropy alloys: An in-situ synchrotron X-ray diffraction study during laser melting

The influence of Nb on phase stability and microstructural evolution in an interstitial Fe-Mn-Co-Cr-C high-entropy alloy was investigated using in-situ synchrotron X-ray diffraction (SXRD) during laser melting. Scheil-Gulliver simulations predict the formation of σ and γ-f.c.c. phases in all three alloys, along with NbC in Nb-containing compositions. SXRD confirmed the presence of most predicted phases, but the σ phase was absent. Nb promotes crystallite refinement and increases dislocation density, though excessive additions reduce refinement efficiency due to solubility limits and secondary phase formation. Furthermore, Nb addition also enhances ε-h.c.p. phase formation by reducing stacking fault energy through NbC-induced carbon depletion. Analysis of intensity peak evolution reveals that Nb alters preferred grain orientations, reducing {111} γ intensity while enhancing {220} γ , leading to a more isotropic grain distribution. Overall, Nb plays a key role in phase selection, microstructure refinement, and preferred orientation evolution, allowing the tailored microstructure of high-entropy alloys via rapid solidification.

Interstitial high entropy alloys↗

DOE OSTI2024

Chemomechanics in alloy phase stability

We describe a first-principles statistical mechanics method to calculate the free energies of crystalline alloys that depend on temperature, composition, and strain. The approach relies on an extension of the alloy cluster expansion to include an explicit dependence on homogeneous strain in addition to site occupation variables that track the degree of chemical ordering. The method is applied to the Si-Ge binary alloy and is used to calculate free energies that describe phase stability under arbitrary epitaxial constraints. We find that while the incoherent phase diagram (in which coexisting phases are not affected by coherency constraints) hosts a miscibility gap, coherent phase equilibrium predicts ordering and negative enthalpies of mixing. Instead of chemical instability, the chemomechanical free energy exhibits instabilities along directions that couple the composition of the alloy with a volumetric strain order parameter. Furthermore, this has fundamental implications for phase field models of spinodal decomposition as it indicates the importance of gradient energy coefficients that couple gradients in composition with gradients in strain.

Materials Science↗

DOE OSTI2024

Phase stability in the Hf-N and Zr-N systems

Hf and Zr nitrides are promising compounds for many technologically important areas, including high-temperature structural applications, quantum computing, and solar and optical applications. Here, this article reports on a comprehensive first-principles statistical mechanics study of phase stability in the Hf-N and Zr-N binary systems. A high solubility of nitrogen in the hcp forms of Hf and Zr is predicted. The rocksalt forms of HfN and ZrN can also tolerate a high degree of off-stoichiometry through the introduction of nitrogen and metal vacancies. The Hf-N binary favors a family of stacking faulted parent crystal structures at intermediate nitrogen concentrations that host a unique form of short-range order among nitrogen interstitials and vacancies. These phases can accommodate some degree of configurational entropy and remain ordered to temperatures as high as 1200 K.

Monte Carlo methods↗

DOE OSTI2025

Phase-stabilized 2D/3D hetero-bilayers via lattice matching for efficient and stable inverted solar cells

2D-on-3D (2D/3D) perovskite heterostructures with engineered energy landscapes offer the potential to realize efficient and stable inverted solar cells. However, managing the energy landscape using 2D perovskites with thicker inorganic layers n > 1 necessitates the usage of the chemically unstable methylammonium MA + . Here, we synthesized formamidinium (FA)-rich and pure-FA n = 3 Ruddlesden-Popper (RPP) and Dion-Jacobson perovskite (DJP) single crystals by identifying ligands with suitably lattice-matched organic and inorganic components of the 2D lattice. These crystals were translated onto 3D perovskites as capping layers, forming 2D/3D hetero-bilayers (HBs). Degradation studies revealed that HBs with butylammonium-based RPPs as capping layers rapidly phase segregate into non-perovskites under combined extrinsic stressors, compromising the underlying 3D layer, whereas FA-rich DJPs based on 3-aminomethylpiperidine retain their phase stability. The DJP HBs also possess a favorable energy landscape and electron transport at the 2D/3D interface, enabling inverted solar cells with a champion PCE of 25.33% and remarkable stability.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2025

Single crystal purification reduces trace impurities in halide perovskite precursors, alters perovskite thin film performance, and improves phase stability

Impurities present in commercially available halide perovskite precursors are known to affect photovoltaic performance. Here, we employ bulk single crystal growth of FAPbI 3 using solvent orthogonality induced crystallization (SONIC) to remove a broad set of extrinsic impurities from commercially available halide perovskite precursors, as verified by detailed chemical analysis. Following SONIC purification, FAPbI 3 films made from PbI 2 of originally low purity (99%) and high purity (99.99%) show improved phase purity and stability under light and heat relative to films made from raw precursors or precursors purified via retrograde powder crystallization (RPC) in 2-methoxyethanol, a method commonly utilized in recent reports of the highest-efficiency perovskite solar cells. In conclusion, single-crystal purification of precursors improves film stability under operational stressors, and the large enhancements in material purity provide a cleaner slate for improved isolation of compositional and additive effects on perovskite phase stability.

14 SOLAR ENERGY↗

DOE OSTI2025

Relative phase stability of L1 2 and DO 22 /DO 23 structures in Al 3 Nb, Al 3 Zr and Al 3 V compounds

The relative stability of the different tri-aluminide (Al 3 M) phases in three binary systems (M = Zr, Nb and V) was assessed for their potential to form fine cubic L1 2 precipitates in additively manufactured alloys. Supersaturated thin films of Al-(8–30) at% M were sputtered and heat treated during in-situ x-ray diffraction (XRD) measurements to observe the temperature ranges of stability for each phase. As-sputtered films were then processed with laser tracks simulating additive manufacturing solidification conditions, and the formation of phases in the laser tracks was correlated with density functional theory (DFT) and nucleation rate calculations. We found that the metastable L1 2 structure is highly competitive with the stable DO 23 structure in the Al-Zr system, but much less stable than the DO 22 structure in the Al-Nb system, and both the DO 22 and Al 8 V 5 structure in the Al-V system. Furthermore, these experimental results were found to be in good agreement with the DFT and kinetic calculations, as we determined that the metastable L1 2 in Al-Zr only requires a small amount of undercooling to favor its nucleation over the stable DO 23 , suggesting additive manufacturing can be a viable pathway to develop Al-Zr alloys strengthened by a high volume fraction of L1 2 Al 3 Zr phase.

Perrin, Alice E. [Oak Ridge National Laboratory (O↗

DOE OSTI2025

MX precipitate behavior in an irradiated advanced Fe-9Cr steel: Self-ion irradiation effects on phase stability

In an effort to optimize Fe-9Cr reduced activation ferritic/martensitic (RAFM) steels and to inform the design and operation of fusion reactors, this work represents the first in a series of cohesive studies dedicated to the evolution of MX-TiC precipitates under accelerated single and dual ion irradiations. This study investigates CNA9, a simplified Fe-9Cr RAFM steel featuring initial MX-TiC precipitate densities of (2.3±0.3)×10²¹ m⁻³. This material was subjected to single self-ion irradiation at damage levels ranging from 1 to 100 displacements per atom (dpa) over a temperature range of 300 to 600°C, with a nominal dose rate of 7×10⁻⁴ dpa/s. Irradiation-induced coarsening was observed, as evidenced by statistically significant increases in mean diameter sizes, at 15 dpa at both 500°C and 600°C, whereas no coarsening was noted at 300°C or 400°C. Further, complete dissolution of precipitates occurred at damage levels of 50 and 100 dpa across the two temperatures tested (300°C and 500°C) while no significant changes were observed at any doses below 15 dpa at 500°C. Experimentally parameterized recoil resolution modeling suggests that the observed radiation stability of MX-TiC precipitates is intricately linked to diffusional changes of solutes resulting from the co-evolution of microstructural features within the experiments. The findings align with current theoretical perspectives on radiation-induced precipitate stability in complex alloys.

36 MATERIALS SCIENCE↗

DOE OSTI2025

MX precipitate behavior in an irradiated advanced Fe-9Cr steel: Helium effects on phase stability

As part of an ongoing series aimed at optimizing Fe-9Cr reduced activation ferritic/martensitic (RAFM) alloys for fusion energy systems, this study explores MX precipitate behavior under dual-ion irradiations, specifically examining correlations between helium transmutation and irradiation-induced damage. Utilizing single and dual-beam ion irradiation, the research explores the combined effects of helium (10–25 appm He/dpa), temperature (400–600 °C), and damage levels (15–100 dpa) on the microstructural evolution of CNA9 steel, a variant of Castable Nanostructured Alloys (CNAs). The study demonstrates that helium co-implantation hinders radiation-enhanced coarsening of MX-TiC precipitates at 500 and 600 °C, maintaining MX-TiC precipitate stability at moderate damage levels (15 dpa) but failing to prevent complete precipitate dissolution at higher damage levels (≥50 dpa) when irradiated at 500 °C. Here, a generalized precipitate stability model suggests that helium-induced suppression of diffusion alters the balance between recoil resolution and back diffusion for MX-TiC precipitates, enhancing the current understanding of precipitate behavior under damage and transmutation simulated dual-ion irradiation conditions.

Characterization↗

DOE OSTI2024

Coherent-Precipitation-Stabilized Phase Formation in Over-Stoichiometric Rocksalt-Type Li Superionic Conductors

Rationalizing synthetic pathways is crucial for material design and property optimization, especially for polymorphic and metastable phases. Over-stoichiometric rocksalt (ORX) compounds, characterized by their face-sharing configurations, are a promising group of materials with unique properties; however, their development is significantly hindered by challenges in synthesizability. Here, taking the recently identified Li superionic conductor, over-stoichiometric rocksalt Li–In–Sn–O (o-LISO) material as a prototypical ORX compound, the mechanisms of phase formation are systematically investigated. It is revealed that the spinel-like phase with unconventional stoichiometry forms as coherent precipitate from the high-temperature-stabilized cation-disordered rocksalt phase upon fast cooling. This process prevents direct phase decomposition and kinetically locks the system in a metastable state with the desired face-sharing Li configurations. This insight enables us to enhance the ionic conductivity of o-LISO to be >1 mS cm -1 at room temperature through low-temperature post-annealing. This work offers insights into the synthesis of ORX materials and highlights important opportunities in this new class of materials.

36 MATERIALS SCIENCE↗

DOE OSTI2024

New Constraints on the Melting Temperature and Phase Stability of Shocked Iron up to 270 GPa Probed by Ultrafast X-Ray Absorption Spectroscopy

Studying the properties and phase diagram of iron at high-pressure and high-temperature conditions has relevant implications for Earth’s inner structure and dynamics and the temperature of the inner core boundary (ICB) at 330 GPa. Also, a hexagonal-closed packed to body-centered cubic (bcc) phase transition has been predicted by many theoretical works but observed only in a few experiments. The recent coupling of high-power laser with advanced x-ray sources from synchrotrons allows for novel approaches to address these issues. Here, we present a study on shock compressed iron up to 270 GPa and 5800 K probed by single-pulse (100 ps FWHM) x-ray absorption spectroscopy (XAS). Based on the analysis of the XAS spectra, we provide structural identification and bulk temperature measurements along the Hugoniot up to the melting. These results rule out the predicted transition to a high-temperature bcc phase and allow one to discriminate among existing equations of state models and melting curves. In particular, we report the first bulk temperature measurement in shock compressed iron on the melting plateau at 240(20) GPa and 5345(600) K. The melting curve resulting from our work extrapolates to a temperature of 6202(514) K at 330 GPa and represents a refined upper bound for the ICB temperature. Published by the American Physical Society 2024

Balugani, S.↗