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At least 847 records · Page 47

Multiple magnetic orders in LaFeAs 1-x P x O uncover universality of iron-pnictide superconductors

The iron-pnictide superconductors have generated tremendous excitement as the competition between magnetism and superconductivity has allowed unique in-roads towards elucidating a microscopic theory of unconventional high-temperature superconductivity. In addition to the stripe spin density wave ($C^a_{2M}$) phase observed in the parent compounds of all iron-pnictide superconductors, two novel magnetic orders have recently been discovered in different parent structures: an out-of-plane collinear double-Q ($C^c_{4M}$) structure in the hole-doped (Ca, Sr, Ba) 1-x (Na) x Fe 2 As 2 and Ba 1-x K x Fe 2 As 2 families, and a spin vortex crystal “hedgehog” ($C^{ab}_{4M}$) structure in the CaKFe 4 As 4 family. Using neutron diffraction, we demonstrate that LaFeAs 1-x P x O contains all three magnetic orders within a single-phase diagram as a function of substitution, all of which compete strongly with superconductivity. Our experimental observations combined with theoretical modeling demonstrate how the reduction in electronic correlations by chemical substitution results in larger Fermi surfaces and the sequential stabilization of multiple magnetic anisotropies. Our work presents a unified narrative for the competing magnetic and superconducting phases observed in various iron-pnictide systems with different crystal structures and chemistry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Precipitation of dopants on acceptor-doped LaMnO3±δ revealed by defect chemistry from first principles

Perovskite oxides degrade at elevated temperatures while precipitating dopant-rich particles on the surface. A knowledge-based improvement of surface stability requires a fundamental and quantitative understanding of the dopant precipitation mechanism on these materials. We propose that dopant precipitation is a consequence of the variation of dopant solubility between calcination and operating conditions in solid oxide fuel cells (SOFCs) and electrolyzer cells (SOECs). To study dopant precipitation, we use 20% (D = Ca, Sr, Ba)-doped LaMnO3+δ (LDM20) as a model system. We employ a defect model taking input from density functional theory calculations. The defect model considers the equilibration of LDM20 with a reservoir consisting of dopant oxide (DO), peroxide (DO2), and O2 in the gas phase. The equilibrated non-stoichiometry of the A-site and B-site as a function of temperature, T, and oxygen partial pressure, p(O2), reveals three regimes for LDM20: A-site deficient (oxidizing conditions), A-site rich (atmospheric conditions), and near-stoichiometric (reducing conditions). Assuming an initial A/B non-stoichiometry, we compute the dopant precipitation boundaries in a p–T phase diagram. Our model predicts precipitation both under reducing (DO) and under highly oxidizing conditions (DO2). We found precipitation under anodic, SOEC conditions to be promoted by large dopant size, while under cathodic, SOFC conditions precipitation is promoted by initial A-site excess. The main driving forces for precipitation are oxygen uptake by the condensed phase under oxidizing conditions and oxygen release assisted by B-site vacancies under reducing conditions. Possible strategies for mitigating dopant precipitation under in electrolytic and fuel cell conditions are discussed.

Hess, Franziska (ORCID:000000024460643X)↗

Flexocaloric effect near a ferroelastic transition

A Ginzburg-Landau model embedded into a vibrational model is used to study the flexocaloric effect in a beam near a ferroelastic transition. The caloric response upon bending is characterized by the isothermal entropy change and the adiabatic temperature change of the beam. Here, we obtain a larger response relative to the strength of the applied forces at temperatures slightly above the transition temperature. It is also obtained that the maximum caloric response is almost linear with the bending angle of the beam, whereas the relation between the bending angle and the applied forces is highly nonlinear. Small hysteresis associated with the phase transition is obtained for sufficiently large bending forces due to the existence of a critical point in the temperature-stress phase diagram of the ferroelastic material. Finally, the microstructure changes with bending in the beam are consistent with previous experimental observations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Pressure of origin of primary mid-ocean ridge basalts

Evidence bearing on the pressure of origin of primary mid-ocean ridge basalts (MORBs) is reviewed. Consideration is given to the constraints derived from pseudoliquidus phase diagrams, the importance of silica contents in primitive MORB glasses, and the mineral compositions in the residual mantle. It is noted that the least depleted abyssal periodotite orthopyroxenes show the dominance of melting and primary MORB genesis at pressures of about 20-25 kbar, a value substantially greater than that (10 kbar) predicted by high-pressure phase equilibrium studies of MORBs.

Elthon, Don↗

The stability of hibonite, melilite and other aluminous phases in silicate melts: Implications for the origin of hibonite-bearing inclusions from carbonaceous chondrites

Phase fields in which hibonite and silicate melt coexist with spinel CaAl4O7, gehlenitic melilite, anorthite or corundum at 1 bar in the system CaO-MgO-Al2O3-SiO2-TiO2 were determined. The hibonites contain up to 1.7 wt% SiO2. For TiO2, the experimentally determined partition coefficients between hibonite and coexisting melt D(sub i)(sup Hib/L), vary from 0.8 to 2.1 and generally decrease with increasing TiO2 in the liquid. Based on Ti partitioning between hibonite and melt, bulk inclusion compositions and hibonite-saturated liquidus phase diagrams, the hibonite in hibonite-poor fluffy Type A inclusions from Allende and at least some hibonite from hibonite-rich inclusions is relict, although much of the hibonite from hibonite-glass spherules probably crystallized metasably from a melt. Bulk compositions for all of these CAIs are consistent with an origin as melite + hibonite + spinel + perovskite phase assembalges that were partially altered and in some cases partially or completely melted. The duration of the melting event was sufficient to remove any Na introduced by the alteration process but frequently insufficient to dissolve all of the original hibonite. Simple thermochemical models developed for meteoritic melilite and hibonite solid solutions were used to obtain equilibration temperatures of hibonite-bearing phase assemblages with vapor. Referenced to 10(exp -3) atm, hibonite + corundum + vapor equilibrated at approximately 1260 C and hibonite + spinel +/- melilite + vapor at 1215 +/- 10 C. If these temperatures reflect condensation in a cooling gas of solar composition, then hibonite +/- corundum condensed first, followed by spinel and then melilite. The position of perovskite within this sequence is uncertain, but it probably began to condense before spinel. This sequence of phase appearances and relative temperatures is generally consistent with observed textures but differs from expectations based on classical condensation calculations in that equilibration temperatures are generally lower than predicted and melilite initially condenses with or even after spinel. Simple thermochemical modes for the substitution of trace elements into the Ca site of meteoritic hibonites suggest that virtually all Eu is divalent in early condensate hibonites but that Eu(2+)/Eu(#+) decreases by a factor of 20 or more during the course of condensation primarily because the ratio is proportional to the partial pressure of Al, which decreases dramatically as aluminous phase condense. The relative sizes of Eu and Yb anomalies in meteoritic hibonites and inclusions may be partly due to this effect.

Beckett, J. R.↗

Vapor–liquid equilibrium of water with the MB-pol many-body potential

Among the many existing molecular models of water, the MB-pol many-body potential has emerged as a remarkably accurate model, capable of reproducing thermodynamic, structural, and dynamic properties across water's solid, liquid, and vapor phases. In this work, we assessed the performance of MB-pol with respect to an important set of properties related to vapor-liquid coexistence and interfacial behavior. Through direct coexistence classical molecular dynamics simulations at temperatures of 400 K < T < 600 K, we calculated properties such as equilibrium coexistence densities, vapor-liquid interfacial tension, vapor pressure, and enthalpy of vaporization and compared the MB-pol results to experimental data. We also compared rigid vs fully flexible variants of the MB-pol model and evaluated system size effects for the properties studied. We found that the MB-pol model predictions are in good agreement with experimental data, even for temperatures approaching the vapor-liquid critical point; this agreement was largely insensitive to system sizes or the rigid vs flexible treatment of the intramolecular degrees of freedom. Furthermore, these results attest to the chemical accuracy of MB-pol and its high degree of transferability, thus enabling MB-pol's application across a large swath of water's phase diagram.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Fuzzy spheres in stringy matrix models: quantifying chaos in a mixed phase space

We consider a truncation of the BMN matrix model to a configuration of two fuzzy spheres, described by two coupled non-linear oscillators dependent on the mass parameter μ. The classical phase diagram of the system generically (μ ≠ 0) contains three equilibrium points: two centers and a center-saddle; as μ → 0 the system exhibits a pitchfork bifurcation. We demonstrate that the system is exactly integrable in quadratures for μ = 0, while for very large values of μ, it approaches another integrable point characterized by two harmonic oscillators. The classical phase space is mixed, containing both integrable islands and chaotic regions, as evidenced by the classical Lyapunov spectrum. At the quantum level, we explore indicators of early and late time chaos. The eigenvalue spacing is best described by a Brody distribution, which interpolates between Poisson and Wigner distributions; it dovetails, at the quantum level, the classical results and reemphasizes the notion that the quantum system is mixed. We also study the spectral form factor and the quantum Lyapunov exponent, as defined by out-of-time-ordered correlators. These two indicators of quantum chaos exhibit weak correlations with the Brody distribution. We speculate that the behavior of the system as μ → 0 dominates the spectral form factor and the quantum Lyapunov exponent, making these indicators of quantum chaos less effective in the context of a mixed phase space.

AdS-CFT correspondence↗

Phase behavior of continuous-space systems: A supervised machine learning approach

The phase behavior of complex fluids is a challenging problem for molecular simulations. Supervised machine learning (ML) methods have shown potential for identifying the phase boundaries of lattice models. In this work, we extend these ML methods to continuous-space systems. We propose a convolutional neural network model that utilizes grid-interpolated coordinates of molecules as input data of ML and optimizes the search for phase transitions with different filter sizes. We test the method for the phase diagram of two off-lattice models, namely, the Widom–Rowlinson model and a symmetric freely jointed polymer blend, for which results are available from standard molecular simulations techniques. The ML results show good agreement with results of previous simulation studies with the added advantage that there is no critical slowing down. We find that understanding intermediate structures near a phase transition and including them in the training set is important to obtain the phase boundary near the critical point. The method is quite general and easy to implement and could find wide application to study the phase behavior of complex fluids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Phase separation during the direct powder bed fusion of SiC

Powder bed fusion (PBF) is an attractive additive manufacturing option for fabrication of SiC object with complex geometries. However, the density and microstructure controls remain a challenge. This study is aimed at understanding laser–SiC interactions, with emphasis on microstructure-processing relationships, to identify potential solutions for the process improvement. SiC tubes were fabricated by PBF of pure SiC powders without sintering additives. Further, comprehensive analysis by X-ray diffraction, Raman spectroscopy, and electron microscopy indicated that binding of SiC particles was achieved by incongruent melting of SiC to a Si/C mixture containing SiC micro- and nanocrystallites. The phase evolution under laser irradiation of SiC was explained by phase diagrams. This study uncovered the PBF SiC microstructure at different length scales and the relationship between the microstructure and the processing parameters.

36 MATERIALS SCIENCE↗

Constraints on Mantle Plume Melting Conditions in the Martian Mantle Based on Improved Melting Phase Relationships of Olivine-Phyric Shergottite Yamato 980459

Martian meteorite Yamato 980459 (hereafter Y98) is an olivine-phyric shergottite that has been interpreted as closely approximating a martian mantle melt [1-4], making it an important constraint on adiabatic decompression melting models. It has long been recognized that low pressure melting of the Y98 composition occurs at extremely high temperatures relative to martian basalts (1430 degC at 1 bar), which caused great difficulties in a previous attempt to explain Y98 magma generation via a mantle plume model [2]. However, previous studies of the phase diagram were limited to pressures of 2 GPa and less [2, 5], whereas decompression melting in the present-day martian mantle occurs at pressures of 3-7 GPa, with the shallow boundary of the melt production zone occurring just below the base of the thermal lithosphere [6]. Recent experimental work has now extended our knowledge of the Y98 melting phase relationships to 8 GPa. In light of this improved petrological knowledge, we are therefore reassessing the constraints that Y98 imposes on melting conditions in martian mantle plumes. Two recently discovered olivine- phyric shergottites, Northwest Africa (NWA) 5789 and NWA 6234, may also be primary melts from the martian mantle [7, 8]. However, these latter meteorites have not been the subject of detailed experimental petrology studies, so we focus here on Y98.

Kiefer, Walter S.↗

Development of Innovative Non-Concentrated Alloy (NCA) Fuel Cladding for Advanced Nuclear Reactors

As the nuclear energy sector advances toward next-generation reactors, the need for high-performance fuel cladding materials has become increasingly urgent. Traditional alloys like zirconium and stainless steel are reaching their performance limits under higher temperatures, more corrosive coolants, and extended irradiation. This report presents the development of a new class of fuel cladding materials based on Non-Concentrated Alloys (NCAs) ? multi-element systems designed to deliver enhanced mechanical strength, corrosion resistance, and radiation tolerance. Through a combination of computational modeling (Computer Coupling of Phase Diagrams and Thermochemistry: CALPHAD), simulation-guided alloy selection, and experimental fabrication via arc melting and spark plasma sintering (SPS), three strategic alloy design paths were explored: (1) FeCrAl-based NCAs, (2) refractory-lean neutron-efficient alloys, and (3) equimolar high-entropy compositions. Microstructural analysis confirmed the formation of stable body-centered cubic BCC_A2 phases, while mechanical testing demonstrated hardness values significantly exceeding those of conventional cladding materials. The results highlight the tunability of NCA systems and their potential for balancing strength and ductility ? a critical consideration for in-reactor performance. Looking forward, future work will focus on thermomechanical optimization, CALPHAD refinement, and benchmarking against industry standards to enable scalable deployment. This work not only advances the science of nuclear materials but also supports broader goals in nuclear safety, performance, and nuclear energy innovation.

36 - MATERIALS SCIENCE↗

Soluble limit and criticality of fermions in $\mathbb Z_2$ gauge theories

Quantum information theory and strongly correlated electron systems share a common theme of macroscopic quantum entanglement. In both topological error correction codes and theories of quantum materials (spin liquid, heavy fermion and high-$T_c$ systems), entanglement is implemented by means of an emergent gauge symmetry. Inspired by these connections, in this paper we introduce a simple model for fermions moving in the deconfined phase of a $\mathbb Z_2$ gauge theory by coupling Kitaev's toric code to mobile fermions. This permits us to exactly solve the ground state of this system and map out its phase diagram. Reversing the sign of the plaquette term in the toric code permits us to tune the ground state between an orthogonal metal and an orthogonal semimetal in which gapless quasiparticles survive despite a gap in the spectrum of original fermions. The small-to-large Fermi surface transition between these two states occurs in a stepwise fashion with multiple intermediate phases. By using a diagrammatic technique, we are able to explore physics beyond the integrable point to examine various instabilities of the deconfined phase and to derive the critical theory at the transition between deconfined and confined phases. We outline how the fermionic toric code can be implemented as a quantum circuit, thus providing an important link between quantum materials and quantum information theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

High Throughput Computational Framework of Materials Properties for Extreme Environments

This project aims to establish a framework capable of efficiently predicting the properties of structural materials for service in harsh environments over a wide range of temperatures and over long periods of time. The approach is to develop and integrate high throughput first-principles calculations in combination with machine learning (ML) methods, perform high throughput CALPHAD (calculations of phase diagrams) modeling, and carry out finite element method (FEM) simulations. Relevant to high temperature service in fossil power system, nickel-based superalloys such as Inconel 740 and Haynes 282 as well as the associated (Ni-Cr-Co)-Al-C-Fe-Mn-Mo-Nb-Si-Ti system, were investigated. The present framework was built on the concept of phase-based property data, in which properties of individual phases are modeled as a function of internal and external independent variables. This project established an open-source infrastructure with the following capabilities: (1) High throughput implementation of first-principles calculations at finite temperatures and variable compositions using both accurate phonon calculations and the efficient Debye model for thermodynamic properties, elastic constants, diffusion coefficients, vacancy formation, stacking and twin faults, and dislocation mobility; i.e., using the developed code DFTTK; (2) Machine learning capabilities to predict the above properties so that the number of first-principles calculations can be significantly reduced; e.g., using the developed code SIPFENN; (3) High throughput CALPHAD modeling of the above properties as a function of temperature and composition using our unique capability based on ESPEI and PyCalphad; (4) New capabilities to predict the stress-strain behavior of individual phases; and (5) New models for tensile strength prediction in common FEM software with the crystal plasticity finite element simulations (CPFEM).

, Ni-based superalloys↗

Transferability of data-driven, many-body models for CO 2 simulations in the vapor and liquid phases

Here, extending on the previous work by Riera et al. [J. Chem. Theory Comput. 16, 2246–2257 (2020)], we introduce a second generation family of data-driven many-body MB-nrg models for CO 2 and systematically assess how the strength and anisotropy of the CO 2 –CO 2 interactions affect the models’ ability to predict vapor, liquid, and vapor–liquid equilibrium properties. Building upon the many-body expansion formalism, we construct a series of MB-nrg models by fitting one-body and two-body reference energies calculated at the coupled cluster level of theory for large monomer and dimer training sets. Advancing from the first generation models, we employ the charge model 5 scheme to determine the atomic charges and systematically scale the two-body energies to obtain more accurate descriptions of vapor, liquid, and vapor–liquid equilibrium properties. Challenges in model construction arise due to the anisotropic nature and small magnitude of the interaction energies in CO 2 , calling for the necessity of highly accurate descriptions of the multidimensional energy landscape of liquid CO 2 . These findings emphasize the key role played by the training set quality in the development of transferable, data-driven models, which, accurately representing high-dimensional many-body effects, can enable predictive computer simulations of molecular fluids across the entire phase diagram.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Dynamical phase transition in a strongly hybridized phonon-triplon chain

In this article, we study a dimerized spin-1/2 chain, such as CuGeO 3 , hosting triplon excitations coupled to optical phonons under weak terahertz laser driving. Both phonons and triplons weakly lose energy into the surrounding baths, forming a non-equilibrium steady state. In the strong phonon-triplon coupling regime, phonons near the two-triplon continuum hybridize strongly with triplons. Using mean-field Lindblad dynamics, we show that strong hybridization induces sharp first-order phase transitions—either single or simultaneous double—in the emission spectrum, mainly due to nonlinearities in the chain and the instantaneous breaking of spatial inversion symmetry, as captured by the phonon displacement. Using mean-field Floquet analysis of harmonic modes in both sectors, we analytically confirm the existence of these phase transitions. Furthermore, we map the complete steady-state phase diagram by varying key control parameters and provide experimentally relevant parameters for observing these transitions in laser-driven CuGeO 3 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A Multi-Scale Computational Platform for Predictive Modeling of Corrosion in Al-Steel Joints (Final Report)

The research team proposed to develop innovative multi-scale models to predict corrosion and the resulting mechanical performances in aluminum-steel joints. The methods of joining considered are resistance spot welding, self-piercing riveting, and rivet-welding, all suitable for mass production applications. The multi-scale models integrate high throughput first-principle calculations based on density functional theory (DFT), high throughput calculation of phase diagrams (CALPHAD) modeling, and finite element method (FEM) simulations. These models are to be validated through laboratory experiments. Furthermore, the models are available as open source so as to enable scientists and engineers in the community to adapt and contribute to the development and application. The approaches rely on the research team’s extensive experience on the prediction of properties of individual phases at finite temperatures and variable compositions through DFT calculations, and our broad expertise on dissimilar material joining and their corrosion. The proposed computational framework enables high throughput computations for improved predictions of corrosion and the associated mechanical performance in dissimilar material joints, resulting in significant reduction in computational time needed by the current state-of-the-art methods. With the participation of researchers from three universities, an auto manufacturer, two manufacturing technology/equipment suppliers, and a software developer/vendor, the interdisciplinary research team applies the technical development on both phase-based modeling and laboratory experiments into the automobile body joining processes for validation and technology demonstration. The global cost of corrosion was estimated at about 3.4% of the global GDP in 2013. By using available corrosion control practices, it is estimated a saving between 15-35% of the cost of corrosion. In the U.S., more than $276 billion is spent repairing corrosion damage. Prediction of the corrosion and its impact on performance of the dissimilar material joints is critical for reducing the massive number of the current corrosion-based recalls for automobiles. Thus, the project goal is to develop models to enable predictive maintenance and end-of-life planning of multi-metal joints with risk of corrosion under different conditions such as exposure to high temperatures in summer and salt solutions in winter, quantified through its pH. An academia-industry consortium led by the University of Michigan and including Pennsylvania State University, University of Illinois Urbana-Champaign, University of Georgia, General Motors Company, Livermore Software Technology Corporation, and Optimal Process Technologies, LLC. created multi-scale models for prediction of corrosion in aluminum-steel joint structures such of them used in vehicle subassemblies – chassis and transmission systems. Starting from the first principle calculations, the team developed mathematical and data-driven models to predict the metallic components, which are formed during joining of two metals, for example aluminum and steel - a lightweight multilateral system which is currently used in more than 60% car bodies. These models were used for simulating chemical reactions that are happening when the joining metallic components are exposed to high temperatures and different pH values. The team was able to predict how the corrosion installs on the metallic components and how they lead to a sudden failure of components in cars. Newly developed machine learning algorithms combining Science, Technology, Engineering and Math disciplines, advanced finite element simulation and experimental validations have been integrated in a platform for prediction of the corrosion evolution and prediction the failure of joints under mechanical loadings and fatigue. Moreover, based on machine learning and inverse analysis, the team proposed solutions for designing new metallic alloys less susceptible to corrosion when joining multi-material assembles. An average of 4% error compared with experiments was achieved for the most common joints that are used in vehicle subassemblies.

36 MATERIALS SCIENCE↗

Evolution of Indarch (EH4 Chondrite) at 1 GPa and High Temperature

The chondritic meteorites are materials that are as old as the solar system itself characterized by variations in bulk chemical and oxidation state, and have long been considered possible building blocks that accreted to form the terrestrial inner planets. Enstatite chondrites contain nearly FeO free enstatite, silicon-rich kamacite and various sulfides indicating formation under highly reducing conditions. These materials could have participated in the formation of the Earth. However, "fingerprinting" of meteoritic materials has shown that no known meteoritic class corresponds to a hypothetical bulk Earth composition in every aspect. To derive constraints on early accretion and differentiation processes and possibly resolve the debate on the formation of the Earth, it is required to study experimentally a variety of chondritic materials and investigate their melting relations and elemental partitioning behavior at variable pressure (P), temperature (T) and oxygen fugacities (fO2). Variations in fO2 can indeed change chemical features and phase equilibria dramatically. The P-T phase diagrams of peridotites and carbonaceous chondrites have been extensively studied experimentally up to pressures and temperatures corresponding to the transition zone and lower mantle. Even though partial melting experiments have been conducted at ambient pressure on the enstatite chondrite Indarch, enstatite meteorites have never been experimentally investigated at high PT. The following investigation focuses on the effect of the fO2 on the phase relations of Indarch, an EH4 chondrite.

Berthet, S.↗

Interfacial Electromechanics Predicts Phase Behavior of 2D Hybrid Halide Perovskites

Quasi-two-dimensional (2D) mixed-cation hybrid halide perovskites (A' 2 A N–1 M N X 3N+1 ; A' = large organic molecule with cationic group, A = [Cs + , CH 3 NH 3 + , HC(NH 2 ) 2 + ], M = [Pb, Sn, Ge], X = [I – , Br – , Cl – ]) have rapidly emerged as candidates to improve the structural stability and device lifetime of 3D perovskite semiconductor devices under operating conditions. The addition of the large A' cation to the traditional AMX 3 structure introduces several synthetic degrees of freedom and breaks M–X bonds, giving rise to peculiar critical phase behavior in the phase space of these complex materials. In this work, we propose a thermodynamic model parametrized by first-principles calculations to generate the phase diagram of 2D and quasi-2D perovskites (q-2DPKs) based on the mechanics and electrostatics of the interface between the A' cations and the metal halide octahedral network. Focusing on the most commonly studied methylammonium lead iodide system where A' is n-butylammonium (BA; CH 3 (CH 2 ) 3 NH 3 + ), we find that the apparent difficulty in synthesizing phase-pure samples with a stoichiometric index N > 5 can be attributed to the energetic competition between repulsion of opposing interfacial dipole layers and mechanical relaxation induced by interfacial stress. Our model shows quantitative agreement with experimental observations of the maximum phase-pure stoichiometric index (N crit ) and explains the nonmonotonic evolution of the lattice parameters with increasing stoichiometric index (N). This model is generalizable to the entire family of q-2DPKs and can guide the design of photovoltaic and optical materials that combine the structural stability of the q-2DPKs while retaining the charge carrier properties of their 3D counterparts.

14 SOLAR ENERGY↗