The researchers compared reference sesquioxides Gd₂O₃, Dy₂O₃, Y₂O₃, Yb₂O₃ and Lu₂O₃ with HEO-Lu and HEO-Tb, both having the nominal composition (Dy₀.₂Y₀.₂Gd₀.₂Yb₀.₂X₀.₂)₂O₃, where X was lutetium or terbium. The multicomponent materials were prepared by coprecipitating aqueous rare-earth nitrate solutions with ammonium carbonate at a carbonate-to-cation molar ratio of 10, followed by calcination at 800 °C. Laboratory X-ray diffraction, synchrotron total scattering, thermogravimetric analysis, differential scanning calorimetry, heat-capacity measurements, X-ray photoelectron spectroscopy and optical absorption spectroscopy were used to assess phase structure, composition, thermal behavior, oxidation state and band gaps.

The reference sesquioxides adopted the cubic bixbyite structure with space group Ia-3 and showed essentially constant mass from 25 to 1,000 °C during thermogravimetric analysis under dry nitrogen. Their differential scanning calorimetry traces contained no detectable endothermic or exothermic events, consistent with stable stoichiometry and no detected phase or oxygen-sublattice transitions. Terbium oxide behaved differently: the material analyzed was effectively Tb₁₁O₂₀, and it underwent sequential mass losses of about 1.0% near 700 K and 1.9% at 950 K under nitrogen. The measured cumulative loss of 2.9% agreed with the theoretical 2.78% for the pathway Tb₁₁O₂₀ to Tb₇O₁₂ and then Tb₂O₃.

Laboratory diffraction showed that HEO-Lu and HEO-Tb both crystallized as single-phase cubic bixbyite oxides, with no detected secondary phases or peak splitting. In contrast, the single-component terbium material produced reflections assigned to triclinic Tb₁₁O₂₀ with space group P-1. Synchrotron total-scattering measurements of HEO-Tb gave sharp, symmetric cubic reflections and pair distribution functions with well-defined Ln–O and Ln–Ln correlations. No coherent sequence of residual peaks matched the characteristic correlations expected for Tb₁₁O₂₀-type environments, and no additional local distortions or terbium-rich short-range order were detected at the measurement resolution.

The cubic HEO-Tb phase persisted after direct calcination at 800 °C for one or two hours and at 1,500 °C for one hour, as well as after an additional 16 hours at either 800 or 1,500 °C. Scanning electron microscopy coupled with energy-dispersive X-ray spectroscopy found substantially uniform, co-localized distributions of Dy, Y, Gd, Yb and Tb after treatment at 1,500 °C for one and 16 hours, with no detected micrometer-scale terbium enrichment or depletion. These results support substantial thermal and compositional robustness across the investigated processing window, although ex situ measurements do not establish that the phase is the global equilibrium free-energy minimum.

Surface-sensitive X-ray photoelectron spectroscopy found that the main Tb 3d component of HEO-Tb was centered at 147.7 eV, consistent with trivalent terbium, and no intensity was detected in the characteristic Tb⁴⁺ region at 152–156 eV. The measurement excluded detectable Tb⁴⁺ at the surface but could not distinguish intermediate oxidation states or assess the bulk composition. Thermogravimetric analysis of HEO-Tb instead measured a 0.94% mass loss near 700 K, close to the 0.92% expected for a nominal M₂O₃.₂ composition, which the authors interpreted as consistent with some terbium being oxidized during synthesis in air and subsequently reduced under nitrogen.

HEO-Lu closely followed the molar average heat capacity of its constituent oxides. HEO-Tb instead had a systematically higher heat capacity and could not be described as a simple weighted combination of the pure oxides. Its curve included a shallow feature of approximately 10 kJ mol⁻¹ K⁻¹ spanning 450–510 K and a broader, stronger feature of about 40 kJ mol⁻¹ K⁻¹ from 700 to 760 K. The authors associated these positive deviations with phonon broadening and enhanced low-frequency vibrational activity associated with chemical disorder, while noting that compositional dilution, disrupted terbium–terbium connectivity and local chemical environments could also contribute.

Optical absorption measurements gave band gaps of 4.9 eV for HEO-Lu and 4.8 eV for HEO-Tb. These were wider than the measured gaps of Lu₂O₃ at 4.4 eV and Tb₂O₃ at 4.5 eV, respectively, and were not equimolar averages of the constituent values. Y₂O₃, Gd₂O₃ and Dy₂O₃ had gaps of approximately 4.8–4.9 eV, while Yb₂O₃ measured 4.6 eV. The high-entropy results were consistent with reduced defect-related absorption and, in HEO-Tb, the absence of detectable mixed-valence intragap states under the measurement conditions, although the spectra alone do not establish configurational entropy as the unique cause.

The study covered only two equimolar five-cation compositions produced by one wet-chemical route and examined over a defined range of thermal and atmospheric conditions. The authors described the materials as very likely robust high-entropy oxides rather than universally established entropy-stabilized oxides. Local chemical short-range order, nanoscale segregation, extremely slow decomposition and transformations at other oxygen chemical potentials could not be excluded. The reported evidence therefore supports retention of a homogeneous cubic bixbyite framework and altered thermal, optical and oxygen-handling behavior, while leaving the independent contribution of configurational entropy unresolved.

Subject of Research: Experimental study of structural, thermal, optical and oxygen-handling behavior in two five-cation rare-earth high-entropy oxides

Article Title: Entropy-assisted stabilization of cubic bixbyite phases in multicomponent rare-earth oxides

Article References: de Nigris, A., Spiridigliozzi, L., Dell’Agli, G., & Ambrosone, L. (2026). Entropy-assisted stabilization of cubic bixbyite phases in multicomponent rare-earth oxides. Journal of Materials Science, 61(42), 32656-32672. https://doi.org/10.1007/s10853-026-13752-2

Image Credits: AI Generated

DOI: 10.1007/s10853-026-13752-2

Keywords: rare-earth oxides, high-entropy oxides, bixbyite structure, terbium, configurational entropy, crystal structure, phonon behavior, band gap, oxygen handling, Entropy-assisted, stabilization, cubic

The core problem the researchers set out to solve is one of data scarcity. Machine learning thrives on large, consistent datasets, but additively manufactured austenitic stainless steels, the family that includes workhorses such as 304L and 316L, have only been studied intensively for roughly a decade. Every published experiment reports different process parameters, different powder chemistries, different build orientations and different testing conditions, which makes the mapping from composition to mechanical properties noisy and fragmented. Casting, by contrast, has more than a century of carefully documented composition-property relationships. The insight behind the new work is that although casting and additive manufacturing produce very different microstructures, the fundamental thermodynamics that govern whether an alloy solidifies as stable austenite, forms ferrite, or sits near a phase boundary are shared across processes. If the model could learn those underlying phase-stability relationships from casting data, the relative ordering of compositions might transfer to printing even when the absolute strength numbers do not.

To make that transfer possible, the team needed descriptors that capture metallurgical meaning rather than raw elemental percentages. They turned to two of the oldest and most trusted quantities in stainless steel metallurgy: the chromium equivalent and the nickel equivalent. These equivalents, familiar to generations of engineers through the Schaeffler diagram used to predict weld microstructures, condense the effects of ferrite-stabilizing elements such as chromium, molybdenum and silicon, and austenite-stabilizing elements such as nickel, manganese, carbon and nitrogen, into two intuitive axes. By expressing each alloy’s composition in terms of these empirical descriptors, the researchers gave the machine learning algorithm a physically informed coordinate system in which alloys with similar phase behavior cluster together, regardless of whether their properties were measured in a foundry or beside a laser powder bed.

On top of this descriptor choice, the authors introduced a divide-and-conquer strategy for model construction. Rather than forcing a single algorithm to describe the entire composition space, including the treacherous regions near phase boundaries where small chemical changes cause dramatic microstructural shifts, the divide-and-conquer model partitions the data into sub-regions defined by phase stability and trains separate predictors within each partition. The study evaluated this framework against three targets: ultimate tensile strength, elongation, and a combined tensile property defined as the product of strength and elongation, a single figure of merit that rewards alloys that are both strong and ductile rather than merely one or the other. The results were impressive. The divide-and-conquer model achieved coefficients of determination of 0.944 for ultimate tensile strength, 0.812 for elongation, and 0.899 for the combined property, and its mean absolute percentage errors were lower than those of ten commonly used machine learning models tested for comparison.

But a model that only predicts well on the data it was trained on is of limited use for designing new alloys. The real test came when the researchers coupled their model to a genetic algorithm, an optimization technique inspired by biological evolution that iteratively breeds candidate compositions toward better predicted performance. This inverse design loop allows the researchers to start from a desired property profile and work backwards to a chemical recipe, rather than laboriously testing one composition after another. The genetic algorithm searches the composition space through the lens of the divide-and-conquer model, proposing candidate austenitic stainless steels whose predicted strength-ductility combinations exceed those of conventional grades. The team then took the most promising candidates out of the computer and into the laboratory, fabricating them by additive manufacturing and measuring their actual tensile behavior.

Here the study delivers its most important and nuanced finding. When the printed alloys were tested, their absolute strength and ductility values did not match the model’s numerical predictions exactly, a systematic deviation the authors attribute to the profound process differences between slow, equilibrium-like casting solidification and the rapid, cyclic thermal history of layer-by-layer printing. Casting produces coarse, slowly formed grains, while additive manufacturing generates fine, rapidly solidified structures with unique sub-grain features, dislocation densities and segregation patterns that can dramatically alter mechanical response. Yet when the researchers compared the relative rankings of different compositions, the agreement was essentially perfect. The order in which the model predicted the compositions would perform, from best to worst, matched the order observed in the printed specimens. For the predicted improvement in ultimate tensile strength between two specific compositions, the relative error was as low as 0.81 percent, a level of agreement that would have been unthinkable without the phase-stability-based partitioning scheme.

This distinction between absolute and relative prediction is more than a statistical curiosity; it is the conceptual heart of the paper. In alloy development, engineers often care less about predicting an exact tensile strength to the nearest megapascal than about knowing which of a hundred candidate chemistries deserves the expense of a printing trial. The new work demonstrates that the relative composition-property relationships encoded in chromium and nickel equivalents possess genuine cross-process transferability. The physics of phase stability, it turns out, is a kind of universal language spoken by both the foundry crucible and the laser powder bed, and a model that learns that language from abundant casting data can say meaningful things about alloys it has never seen printed. This effectively converts a century of casting knowledge into a screening tool for a technology that is barely out of its adolescence.

The practical implications are considerable. Austenitic stainless steels are among the most widely printed structural metals, appearing in aerospace brackets, marine components, chemical processing equipment, nuclear applications and biomedical implants. Each new application pushes toward compositions tuned for specific balances of strength, ductility, corrosion resistance, printability and cost, and researchers have explored everything from in-situ alloying and nanoparticle additions to grain-boundary engineering to squeeze more performance from these alloys. Traditionally, exploring that composition space meant printing and testing dozens or hundreds of variants, an expensive and slow process given the cost of spherical metal powders and machine time. The new approach enables efficient preliminary screening using nothing more than compositional information and prior casting data, allowing researchers to discard poor candidates computationally and reserve laboratory resources for the handful of compositions most likely to succeed. Trend prediction, in which the model indicates how strength or ductility will shift as an element is added or removed, further guides the direction of experimental campaigns.

The study also speaks to a broader movement in materials science toward hybrid approaches that blend data-driven methods with physical understanding. Purely black-box machine learning models can interpolate well within their training data but often fail catastrophically when extrapolating to new processing routes or composition regimes, and their predictions can be difficult for metallurgists to trust or interpret. By anchoring the model in empirical descriptors with clear physical meaning and by structuring the learning problem around phase stability, the researchers preserved interpretability while retaining the efficiency of modern algorithms. The strategy echoes and extends recent successes in which machine learning has accelerated the discovery of high-entropy alloys, titanium alloys and aluminum alloys, but the cross-process element is distinctive: it explicitly addresses the situation every emerging manufacturing technology faces, where the data needed for good models do not exist yet and must be borrowed, intelligently, from adjacent fields.

There remain, of course, limits to what the approach can do. The systematic deviations in absolute property predictions mean that final qualification of any new alloy will still require real additive manufacturing experiments, and the model’s transferability rests on the assumption that phase stability remains the dominant organizing principle across processes, an assumption that may weaken for compositions near critical boundaries or for properties dominated by process-specific defects such as porosity and residual stress. The authors are candid that their method provides a pathway for preliminary screening and trend prediction rather than a replacement for experimental validation. Even so, the demonstration that a relative error of 0.81 percent is achievable for cross-process strength predictions marks a genuine advance. For a field racing to design alloys tailored to the extreme thermal conditions of 3D printing, the message is liberating: the data you need may already exist, sitting in decades of casting handbooks, waiting for the right physics-informed algorithm to translate them into the language of the laser.

Subject of Research: Machine learning-driven composition design of austenitic stainless steels for additive manufacturing using cross-process casting data and empirical phase-stability descriptors

Article Title: Composition design of austenitic stainless steels for additive manufacturing: a cross-process data and empirical knowledge-driven approach

Article References: Chen, C., Li, B., Tang, M., & Chen, H. (2026). Composition design of austenitic stainless steels for additive manufacturing: a cross-process data and empirical knowledge-driven approach. Journal of Materials Science. https://doi.org/10.1007/s10853-026-13666-z

Image Credits: AI Generated

DOI: 10.1007/s10853-026-13666-z

Keywords: additive manufacturing, austenitic stainless steel, machine learning, alloy design, chromium equivalent, nickel equivalent, divide-and-conquer model, genetic algorithm, tensile properties, phase stability, casting data, materials science

The research team, led by scientists at the Federal University of Minas Gerais, the Federal University of São Carlos, and the University of São Paulo in Brazil, adopted an integrated strategy that combined theoretical modeling, thermodynamic optimization, and full experimental validation. At the heart of the approach was the Varvenne-Luque-Curtin model of solid-solution strengthening in concentrated FCC alloys, which quantifies how atomic size misfit and local elastic modulus fluctuations impede dislocation motion. The model predicts a critical resolved shear stress that is converted into yield strength using a Taylor factor of 3.06, incorporating temperature and strain-rate dependence through thermally activated dislocation glide.

A crucial refinement came from the effective atomic radii for strength, or EARS, methodology. Because atomic sizes in a multicomponent solid solution differ from their pure-element values, using tabulated radii introduces systematic errors. The team compared two EARS parameter sets, the original proposal by Coury and colleagues and an updated version by Santana, Kiminami, and Coury that corrects an overestimation of strengthening at high chromium contents. Although the two sets differ by only a few picometers, those tiny differences propagate through the misfit terms of the strengthening equations and significantly change the predicted strength, underscoring how sensitive the model is to atomic-scale inputs. The researchers also incorporated a lattice-parameter expression accounting for Cr-Co short-range ordering previously reported in the Cr-Co-Ni subsystem.

Using these tools, the team mapped predicted solid-solution strengthening across compositional subsystems of the CrMnFeCoNi space. All curves peaked when chromium content ranged between roughly 40 and 60 atomic percent, a consequence of mixing large chromium atoms with smaller nickel and cobalt atoms to maximize lattice distortion. This guided the selection of three quinary alloys: Cr35Mn5Fe5Co5Ni50 (alloy A), Cr42Mn6Fe6Co6Ni40 (alloy B), and Cr42Mn5Fe5Co9Ni39 (alloy C), all designed to match the strength of the ternary reference Cr45Co27.5Ni27.5 (alloy R), the strongest single-phase FCC solid solution reported to date within the system. Notably, the new compositions deliberately reduce cobalt, addressing both economic and sustainability concerns tied to cobalt supply chains.

CALPHAD thermodynamic calculations using the TCHEA 5 database were then employed to check phase stability, predicting single-phase FCC fields above 1150 degrees Celsius for all four compositions. The alloys were synthesized by non-consumable arc melting with repeated remelting for chemical homogeneity, followed by cold rolling, homogenization at 1150 degrees Celsius, water quenching, a second 70 percent cold reduction, and a final anneal. X-ray diffraction and scanning electron microscopy confirmed a single FCC structure in alloys R and A, exactly as predicted. Alloys B and C, however, told a more complicated story: both exhibited a small fraction of a Cr-rich body-centered cubic (BCC) phase decorating grain boundaries, despite the thermodynamic calculations indicating that BCC should not form at the processing temperatures employed.

This discrepancy between prediction and experiment is one of the study’s most instructive findings. The calculated onset of BCC stability in alloys B and C lies close to the processing temperature, so thermodynamic uncertainties, kinetic effects, and local compositional heterogeneities were sufficient to push the alloys across the phase boundary. The Cr-rich BCC phase contained roughly 62 atomic percent chromium and about 23 percent nickel, and appeared as particles averaging about 1.5 micrometers in diameter, occupying approximately 8 percent of alloy B and 4 percent of alloy C. Interestingly, the calculations correctly ranked alloy B as more prone to BCC formation than alloy C, suggesting the database captures trends even when it misplaces the boundary.

That unexpected second phase turned out to be a hidden gift. Because the BCC particles pinned grain boundaries during recrystallization and grain growth, they produced a dramatic Zener-pinning refinement of the microstructure. The grain sizes of the annealed alloys tell the story vividly: 210 plus or minus 96 micrometers for alloy A and 90 plus or minus 35 micrometers for alloy R, but only 7 plus or minus 3 micrometers for alloy B and 11 plus or minus 4 micrometers for alloy C, despite identical processing. Alloy B’s grains were roughly thirteen times finer than those of the reference alloy and thirty times finer than alloy A. The measured grain sizes agreed well with classical pinning models relating stabilized grain diameter to particle size and second-phase fraction, which also explains why alloy C, with less second phase, ended up coarser than alloy B.

The mechanical consequences were substantial. Alloy B reached a yield strength of about 430 megapascals and alloy C about 410 megapascals, compared with 240 megapascals for alloy A and 315 megapascals for the reference alloy R, a direct payoff of grain-boundary strengthening layered on top of the intrinsic solid-solution contribution. Alloy A, though softer, delivered impressive ductility of 61 percent elongation with an ultimate tensile strength of 682 megapascals, outperforming the coarse-grained Cantor alloy while using far less cobalt, a combination attractive for damage-tolerant structural applications. Vickers microhardness measurements plotted against inverse square root of grain size followed the Hall-Petch relationship, revealing that the reference alloy possessed the highest intrinsic hardness, consistent with its superior solid-solution strengthening from atomic size and elastic misfit, while alloys B and C drew more of their strength from refined grains.

Ultimately, the study delivers a nuanced verdict on computational alloy design. Solid-solution strengthening predictions proved a genuinely useful first filter for navigating an enormous compositional space and identifying promising Cr- and Ni-enriched candidates, and the strategy succeeded in offsetting the property losses expected from reducing cobalt. Yet the final mechanical response was determined not by the initial predictions alone but by how composition reshaped phase stability and microstructure during processing. The authors emphasize that refinements to thermodynamic databases will be needed for reliable phase-stability forecasting in chromium-rich multicomponent systems. In an era when aerospace, nuclear, and biomedical applications demand ever-tougher structural materials, this work offers a practical blueprint: use physics-based models to explore the compositional frontier, then let controlled processing and a keen eye for the unexpected turn computational candidates into real, strong, ductile metals.

Subject of Research: Compositional design of CrMnFeCoNi multicomponent alloys guided by solid-solution strengthening predictions and CALPHAD modeling

Article Title: Compositional design of CrMnFeCoNi multicomponent alloys based on solid-solution strengthening predictions

Article References: Lopes, M. H. T., Rodrigues, A. V., de Souza, P. M., Stumpf, G. C., Figueiredo, R. B., Coury, F. G., Mazzer, E. M., Pereira, P. H. R., & Wolf, W. (2026). Compositional design of CrMnFeCoNi multicomponent alloys based on solid-solution strengthening predictions. Journal of Materials Science: Metallurgy, 1(1), Article 17. https://doi.org/10.1007/s44492-026-00020-2

Image Credits: AI Generated

DOI: 10.1007/s44492-026-00020-2

Keywords: high-entropy alloys, CrMnFeCoNi, solid-solution strengthening, CALPHAD, grain refinement, Hall-Petch relationship, FCC alloys, Zener pinning, yield strength, cobalt reduction, phase stability, alloy design