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The synthesis of ternary nitrides is uniquely difficult, in large part because elemental N$_2$ is relatively inert. However, lithium reacts readily with other metals and N$_2$, making Li-M-N the most numerous sub-set of ternary nitrides. Here, we use Li$_2$ZrN$_2$, a ternary with a simple synthesis recipe, as a precursor for ion exchange reactions towards AZrN$_2$ (A = Mg, Fe, Cu, Zn). In situ synchrotron powder X-ray diffraction studies show that Li$^+$ and Mg$^{2+}$ undergo ion exchange topochemically, preserving the layers of octahedral [ZrN$_6$] to yield a metastable layered polymorph of MgZrN$_2$ (spacegroup $R\overline{3}m$) rather than the calculated ground state structure ($I41/amd$). UV-vis measurements show an optical absorption onset near 2.0 eV, consistent with the calculated bandgap for this polymorph. Our experimental attempts to extend this ion exchange method towards FeZrN$_2$, CuZrN$_2$, and ZnZrN$_2$ resulted in decomposition products (A + ZrN + 1/6 N$_2$), an outcome that our computational results explain via the higher metastability of these phases. We successfully extended this ion exchange method to other Li-M-N precursors by synthesizing MgHfN$_2$ from Li$_2$HfN$_2$. In addition to the discovery of metastable $R\overline{3}m$ MgZrN$_2$ and MgHfN$_2$, this work highlights the potential of the 63 unique Li-M-N phases as precursors to synthesize new ternary nitrides.

Recent high-throughput computational searches have predicted many novel ternary nitride compounds providing new opportunities for materials discovery in under explored phase spaces. Nevertheless, there are hardly any predictions and/or syntheses that incorporate only transition metals into new ternary nitrides. Here, we report on the synthesis, structure, and properties of MnCoN$_2$, a new ternary nitride material comprising only transition metals and N. We find that crystalline MnCoN$_2$ can be stabilized over its competing binaries, and over a tendency of this system to become amorphous, by controlling growth temperature within a narrow window slightly above ambient condition. We find that single-phase MnCoN$_2$ thin films form in a cation-disordered rocksalt crystal structure, which is supported by ab-initio calculations. X-ray photoelectron spectroscopy analysis suggests that MnCoN$_2$ is sensitive to oxygen through various oxides and hydroxides binding to cobalt on the surface. X-ray absorption spectroscopy is used to verify that Mn$^{3+}$ and Co$^{3+}$ cations exist in an octahedrally-coordinated environment, which is distinct from a combination of CoN and MnN binaries and in agreement with the rocksalt-based crystal structure prediction. Magnetic measurements suggest that MnCoN$_2$ has a canted antiferromagnetic ground state below 10 K. We extract a Weiss temperature of $\theta$ = -49.7 K, highlighting the antiferromagnetic correlations in MnCoN$_2$.

Empirical A-site cation substitution has advanced the stability and efficiency of hybrid organic-inorganic lead halide perovskites solar cells and the functionality of X-ray detectors. Yet, the fundamental mechanisms underpinning their unique performance remain elusive. This multi-modal study unveils the link between nanoscale structural dynamics and macroscopic optoelectronic properties in these materials by utilising X-ray diffuse scattering, inelastic neutron spectroscopy and optical microscopy complemented by state-of-the-art machine learning-assisted molecular dynamics simulations. Our approach uncovers the presence of dynamic, lower-symmetry local nanodomains embedded within the higher-symmetry average phase in various perovskite compositions. The properties of these nanodomains are tunable via the A-site cation selection: methylammonium induces a high density of anisotropic, planar nanodomains of out-of-phase octahedral tilts, while formamidinium favours sparsely distributed isotropic, spherical nanodomains with in-phase tilting, even when crystallography reveals cubic symmetry on average. The observed variations in the properties of dynamic nanodomains are in agreement with our simulations and are directly linked to the differing macroscopic optoelectronic and ferroelastic behaviours of these compositions. By demonstrating the influence of A-site cation on local nanodomains and consequently, on macroscopic properties, we propose leveraging this relationship to engineer the optoelectronic response of these materials, propelling further advancements in perovskite-based photovoltaics, optoelectronics, and X-ray imaging., Comment: Main text and supplementary information. Main text 16 pages, 4 figures. Supplementary information 42 pages, 36 figures

Recent computational studies have predicted many new ternary nitrides, revealing synthetic opportunities in this underexplored phase space. However, synthesizing new ternary nitrides is difficult, in part because intermediate and product phases often have high cohesive energies that inhibit diffusion. Here, we report the synthesis of two new phases, calcium zirconium nitride (CaZrN$_2$) and calcium hafnium nitride (CaHfN$_2$), by solid state metathesis reactions between Ca$_3$N$_2$ and $M$Cl$_4$ ($M$ = Zr, Hf). Although the reaction nominally proceeds to the target phases in a 1:1 ratio of the precursors via Ca$_3$N$_2$ + $M$Cl$_4$ $\rightarrow$ Ca$M$N$_2$ + 2 CaCl$_2$, reactions prepared this way result in Ca-poor materials (Ca$_xM_{2-x}$N$_2$, $x<1$). A small excess of Ca$_3$N$_2$ (ca. 20 mol\%) is needed to yield stoichiometric Ca$M$N$_2$, as confirmed by high-resolution synchrotron powder X-ray diffraction. In situ synchrotron X-ray diffraction studies reveal that nominally stoichiometric reactions produce Zr$^{3+}$ intermediates early in the reaction pathway, and the excess Ca$_3$N$_2$ is needed to reoxidize Zr$^{3+}$ intermediates back to the Zr$^{4+}$ oxidation state of CaZrN$_2$. Analysis of computationally-derived chemical potential diagrams rationalizes this synthetic approach and its contrast from the synthesis of MgZrN$_2$. These findings additionally highlight the utility of in situ diffraction studies and computational thermochemistry to provide mechanistic guidance for synthesis.

Synthesis is a major challenge in the discovery of new inorganic materials. Currently, there is limited theoretical guidance for identifying optimal solid-state synthesis procedures. We introduce two selectivity metrics, primary and secondary competition, to assess the favorability of target/impurity phase formation in solid-state reactions. We used these metrics to analyze 3,520 solid-state reactions in the literature, ranking existing approaches to popular target materials. Additionally, we implemented these metrics in a data-driven synthesis planning workflow and demonstrated its application in the synthesis of barium titanate (BaTiO$_3$). Using an 18-element chemical reaction network with first-principles thermodynamic data from the Materials Project, we identified 82,985 possible BaTiO$_3$ synthesis reactions and selected nine for experimental testing. Characterization of reaction pathways via synchrotron powder X-ray diffraction reveals that our selectivity metrics correlate with observed target/impurity formation. We discovered two efficient reactions using unconventional precursors (BaS/BaCl$_2$ and Na$_2$TiO$_3$) that produce BaTiO$_3$ faster and with fewer impurities than conventional methods, highlighting the importance of considering complex chemistries with additional elements during precursor selection. Our framework provides a foundation for predictive inorganic synthesis, facilitating the optimization of existing recipes and the discovery of new materials, including those not easily attainable with conventional precursors., Comment: Minor revisions (updated abstract, added discussion, added precursor purities, formatting). The first two authors contributed equally to this work. 53 pages, 7 figures

Bulk solid state synthesis of nitride materials usually leads to thermodynamically stable, cation-ordered crystal structures, whereas thin film synthesis tends to favor disordered, metastable phases. This dichotomy is inconvenient both for basic materials discovery, where non-equilibrium thin film synthesis methods can be useful to overcome reaction kinetic barriers, and for practical technology applications where stable ground state structures are sometimes required. Here, we explore the uncharted Mg-W-N chemical phase space, using rapid thermal annealing to reconcile the differences between thin film and bulk powder syntheses. Combinatorial co-sputtering synthesis from Mg and W targets in a N$_2$ environment yielded cation-disordered Mg-W-N phases in the rocksalt (0.1< Mg/(Mg+W) <0.9), and hexagonal boron nitride (0.7< Mg/(Mg+W) <0.9) structure types. In contrast, bulk synthesis produced a cation-ordered polymorph of MgWN$_2$ that consists of alternating layers of rocksalt-like [MgN$_6$] octahedra and nickeline-like [WN$_6$] trigonal prisms (denoted "rocksaline"). Thermodynamic calculations corroborate these observations, showing rocksaline MgWN$_2$ is stable while other polymorphs are metastable. We also show that rapid thermal annealing can convert disordered rocksalt films to this cation-ordered polymorph near the MgWN$_2$ stoichiometry. Electronic structure calculations suggest that this rocksalt-to-rocksaline structural transformation should also drive a metallic-to-semiconductor transformation. In addition to revealing three new phases (rocksalt MgWN$_2$ and Mg$_3$WN$_4$, hexagonal boron nitride Mg$_3$WN$_4$, and rocksaline MgWN$_2$), these findings highlight how rapid thermal annealing can control polymorphic transformations, adding a new strategy for exploration of thermodynamic stability in uncharted phase spaces.

Synthesis remains a challenge for advancing materials science. A key focus of this challenge is how to enable selective synthesis, particularly as it pertains to metastable materials. This perspective addresses the question: how can ``spectator'' elements, such as those found in double ion exchange (metathesis) reactions, enable selective materials synthesis? By observing reaction pathways as they happen (\emph{in situ}) and calculating their energetics using modern computational thermodynamics, we observe transient, crystalline intermediates that suggest that many reactions attain a local thermodynamic equilibrium dictated by local chemical potentials far before achieving a global equilibrium set by the average composition. Using this knowledge, one can thermodynamically ``shortcut'' unfavorable intermediates by including additional elements beyond those of the desired target, providing access to a greater number of intermediates with advantageous energetics and selective phase nucleation. Ultimately, data-driven modeling that unites first-principles approaches with experimental insights will refine the accuracy of emerging predictive retrosynthetic models for complex materials synthesis.

Magnetic semiconductors may soon improve the energy efficiency of computers, but materials exhibiting these dual properties remain underexplored. Here, we report the computational prediction and realization of a new magnetic and semiconducting material, MnSnN$_2$, via combinatorial sputtering of thin films. Grazing incidence wide angle X-ray scattering and laboratory X-ray diffraction studies show a wide composition tolerance for this wurtzite-like MnSnN$_2$, ranging from $20\% <$ Mn/(Mn+Sn) $< 65$\% with cation disorder across this composition space. Magnetic susceptibility measurements reveal a low-temperature transition ($T^{\mathrm{*}} \approx 10$ K) for MnSnN$_2$ and strong antiferromagnetic correlations, although the ordering below this transition may be complex. This finding contrasts with bulk MnSiN$_2$ and MnGeN$_2$, which exhibited antiferromagnetic ordering above 400 K in previous studies. Spectroscopic ellipsometry identifies an optical absorption onset of 1 eV for the experimentally-synthesized phase exhibiting cation disorder, consistent with the computationally-predicted 1.2 eV bandgap for the cation-ordered structure. Electronic conductivity measurements confirm the semiconducting nature of this new phase by showing increasing conductivity with increasing temperature. This work adds to the set of known semiconductors that are paramagnetic at room temperature and will help guide future work targeted at controlling the structure and properties of semiconducting materials that exhibit magnetic behavior.

A cloud-hosted web-based software application, nmfMapping, for carrying out a nonnegative matrix factorization of a set of powder diffraction or atomic pair distribution function datasets is described. This app allows structure scientists to rapidly find trends in sets of related data such as from in situ and operando diffraction experiments. The application is easy to use and does not require any programming expertise. It is available at the pdfitc.org website., Comment: 19 Pages, 7 Figures, submitted to Acta Crystallographica Section A

Ternary nitride materials hold promise for many optical, electronic, and refractory applications yet their preparation via solid-state synthesis remains challenging. Often, high pressures or reactive gasses are used to manipulate the effective chemical potential of nitrogen, yet these strategies require specialized equipment. Here we report on a simple two-step synthesis using ion-exchange reactions that yield rocksalt-derived MgZrN$_2$ and Mg$_2$NbN$_3$, as well as layered MgMoN$_2$. All three compounds show nearly temperature-independent and weak paramagnetic responses to an applied magnetic field at cryogenic temperatures indicating phase pure products. The key to synthesizing these ternary materials is an initial low-temperature step (300-450 $^{\circ}$C) to promote Mg-M-N bond formation. Then the products are annealed (800-900 $^{\circ}$C) to increase crystalline domains of the ternary product. Calorimetry experiments reveal that initial reaction temperatures are determined by phase transitions of reaction precursors, whereas heating directly to high temperatures results in decomposition. These two-step reactions provide a rational guide to material discovery of other bulk ternary nitrides.

In sharp contrast to molecular synthesis, materials synthesis is generally presumed to lack selectivity. The few known methods of designing selectivity in solid-state reactions have limited scope, such as topotactic reactions or strain stabilization. This contribution describes a general approach for searching large chemical spaces to identify selective reactions. This novel approach explains the ability of a nominally "innocent" Na$_2$CO$_3$ precursor to enable the metathesis synthesis of single-phase Y$_2$Mn$_2$O$_7$ -- an outcome that was previously only accomplished at extreme pressures and which cannot be achieved with closely related precursors of Li$_2$CO$_3$ and K$_2$CO$_3$. By calculating the required change in chemical potential across all possible reactant-product interfaces in an expanded chemical space including Y, Mn, O, alkali metals, and halogens, using thermodynamic parameters obtained from density functional theory calculations, we identify reactions that minimize the thermodynamic competition from intermediates. In this manner, only the Na-based intermediates minimize the distance in the hyperdimensional chemical potential space to Y$_2$Mn$_2$O$_7$, thus providing selective access to a phase which was previously thought to be metastable. Experimental evidence validating this mechanism for pathway-dependent selectivity is provided by intermediates identified from in situ synchrotron-based crystallographic analysis. This approach of calculating chemical potential distances in hyperdimensional compositional spaces provides a general method for designing selective solid-state syntheses that will be useful for gaining access to metastable phases and for identifying reaction pathways that can reduce the synthesis temperature, and cost, of technological materials., Comment: 30 pages with 5 figures. The first two authors contributed equally to this work

Hybrid halide perovskite semiconductors exhibit complex, dynamical disorder while also harboring properties ideal for optoelectronic applications that include photovoltaics. However, these materials are structurally and compositionally distinct from "traditional" compound semiconductors composed of tetrahedrally-coordinated elements with an average valence electron count of silicon. As discussed here, the additional dynamic degrees of freedom of hybrid halide perovskites underlie many of their potentially transformative physical properties. Neutron scattering and spectroscopy studies of the atomic dynamics of these materials have yielded significant insights to the functional properties. Specifically, inelastic neutron scattering has been used to elucidate the phonon band structure, and quasi-elastic neutron scattering (QENS) has revealed the nature of the uncorrelated dynamics pertaining to molecular reorientations. Understanding the dynamics of these complex semiconductors has elucidated the temperature-dependent phase stability and origins of the defect-tolerant electronic transport from the highly polarizable dielectric response. Furthermore, the dynamic degrees of freedom of the hybrid perovskites provides additional opportunities for application engineering and innovation., Comment: 25 pages. 8 Figures

We validate the use of matrix factorization for the automatic identification of relevant components from atomic pair distribution function (PDF) data. We also present a newly developed software infrastructure for analyzing the PDF data arriving in streaming manner. We then apply two matrix factorization techniques, Principal Component Analysis (PCA) and Non-negative Matrix Factorization (NMF), to study simulated and experiment datasets in the context of in situ experiment.

Interest in inorganic ternary nitride materials has grown rapidly over the past few decades, as their diversity of chemistries and structures make them appealing for a variety of applications. Due to synthetic challenges posed by the stability of N2, the number of predicted nitride compounds dwarfs those that have been synthesized, offering a breadth of opportunity for exploration. This review summarizes the fundamental properties and structural chemistry of ternary nitrides, leveraging metastability and the impact of nitrogen chemical potential. A discussion of prevalent defects, both detrimental and beneficial, is followed by a survey of synthesis techniques and their interplay with metastability. Throughout the review, we highlight applications (such as solid-state lighting, electrochemical energy storage, and electronic devices) in which ternary nitrides show particular promise.

Fe3PO4O3 forms a non-centrosymmetric lattice structure (space group R3m) comprising triangular motifs of Fe^{3+} coupled by strong antiferromagnetic interactions (|\Theta_{CW}| > 900 K). Neutron diffraction from polycrystalline samples shows that strong frustration eventually gives way to an ordered helical incommensurate structure below T_N = 163 K, with the helical axis in the hexagonal ab plane and a modulation length of ~ 86 \AA. The magnetic structure consists of an unusual needle-like correlation volume that extends past 900 \AA along the hexagonal c-axis but is limited to ~ 70 \AA in the ab plane, despite the three-dimensional nature of the magnetic sublattice topology. The small in-plane correlation length, which persists to at least T = T_N/40, indicates a robust blocking of long-range order of the helical magnetic structure, and therefore stable domain walls, or other defect spin textures, must be abundant in Fe3PO7. Temperature dependent neutron powder diffraction reveals small negative thermal expansion below T_N. No change in lattice symmetry is observed on cooling through T_N, as revealed by high resolution synchrotron X-ray diffraction. The previously reported reduced moment of the Fe^{3+} ions (S=5/2), \mu ~ 4.2 \mu_B, is confirmed here through magnetization studies of a magnetically diluted solid solution series of compounds, Fe3-xGaxPO4O3, and is consistent with the refined magnetic moment from neutron diffraction 4.14(2) \mu_B. We attribute the reduced moment to a modified spin density distribution arising from ligand charge transfer in this insulating oxide., Comment: 16 pages, 16 figures. Minor changes to text

We report x-ray total scattering and pair distribution function (PDF) studies of the structural relaxation around interstitial manganese (Mn$_i$) in ferromagnetic Mn$_{1+\delta}$Sb ($0.03 \le \delta \le 0.23$) alloys, guided by density functional theory (DFT). Refinements to the experimental PDF using a crystallographically constrained structural model indicate an expansion in the equatorial plane of the Mn$_i$Sb$_5$ trigonal bipyramidal site, which introduces significant positional disorder in addition to the nominally-random occupation of interstitial voids. Observation of a weak diffuse signal near the symmetry-forbidden (001) reflection position is indicative of correlated disorder from the clustering of Mn$_i$. Density functional relaxation of supercells approximating the $\delta = 0.08$, $0.15,$ and $0.23$ compositions provides improved models that accurately describe the short-range structural distortions captured in the PDFs. Such structural relaxation increases the DFT calculated moment on Mn$_i$, which aligns antiparallel to the primary Mn moments, but leads to insubstantial changes in the average Mn and Sb moments and moments of Mn and Sb proximal to interstitials, thus providing a more accurate description of the observed bulk magnetic properties., Comment: 10 pages, 9 figures. Supplemental material available upon request

With the increased availability of high intensity time-of-flight neutron and synchrotron X-ray scattering sources that can access wide ranges of momentum transfer, the pair distribution function method has become a standard analysis technique for studying disorder of local coordination spheres and at intermediate atomic separations. In some cases, rational modeling of the total scattering data (Bragg and diffuse) becomes intractable with least-squares approaches and necessitates reverse Monte Carlo (RMC) simulations using large supercells. However, the extraction of meaningful information from the resulting atomistic ensembles is challenging, especially at intermediate length scales. We use representational analysis to describe displacements of atoms in RMC ensembles from an ideal crystallographic structure. Rewriting the displacements in terms of a local basis that is descriptive of the ideal crystallographic symmetry provides a robust approach to characterizing medium-range order (and disorder) and symmetry breaking in complex and disordered crystalline materials. This method enables the extraction of statistically relevant displacement modes (orientation, amplitude, and distribution) of the crystalline disorder and provides directly meaningful information in a symmetry-adapted basis set that is most descriptive of the crystal chemistry and physics., Comment: 14 pages; 13 figures

KNi$_2$Se$_2$ exhibits an increase of symmetry on cooling below $T\le50$ K, as observed by Raman spectroscopy and synchrotron x-ray diffraction. X-ray absorption spectroscopy confirms that the symmetry increase is due to changes in nickel-nickel interactions and suppression of charge density wave fluctuations. Density functional theory calculations reveal a zone- boundary lattice instability that provides a model of the room-temperature x-ray pair distribution function data, but fails to describe the higher local symmetry observed for $T\le50$K. Together, these results support many- body correlation effects as drivers for the unusual heavy fermion electronic ground state in KNi$_2$Se$_2$., Comment: 4 figures

The emergence of complex electronic behaviour from simple ingredients has resulted in the discovery of numerous states of matter. Many examples are found in systems exhibiting geometric magnetic frustration, which prevents simultaneous satisfaction of all magnetic interactions. This frustration gives rise to complex magnetic properties such as chiral spin structures orbitally-driven magnetism, spin-ice behavior exhibiting Dirac strings with magnetic monopoles, valence bond solids, and spin liquids. Here we report the synthesis and characterization of LiZn2Mo3O8, a geometrically frustrated antiferromagnet in which the magnetic moments are localized on small transition metal clusters rather than individual ions. By doing so, first order Jahn-Teller instabilities and orbital ordering are prevented, allowing the strongly interacting magnetic clusters in LiZn2Mo3O8 to probably give rise to an exotic condensed valence-bond ground state reminiscent of the proposed resonating valence bond state. Our results also link magnetism on clusters to geometric magnetic frustration in extended solids, demonstrating a new approach for unparalleled chemical control and tunability in the search for collective, emergent electronic states of matter., Comment: 30 pages, 10 figures

Understanding the complexities of electronic and magnetic ground states in solids is one of the main goals of solid-state physics. Materials with the canonical ThCr$_2$Si$_2$-type structure have proved particularly fruitful in this regards, as they exhibit a wide range of technologically advantageous physical properties described by "many-body physics," including high-temperature superconductivity and heavy fermion behavior. Here, using high-resolution synchrotron X-ray diffraction and time-of-flight neutron scattering, we show that the isostructural mixed valence compound, KNi$_2$S$_2$, displays a number of highly unusual structural transitions, most notably the presence of charge density wave fluctuations that disappear on cooling. This behavior occurs without magnetic or charge order, in contrast to expectations based on all other known materials. Furthermore, the low-temperature electronic state of KNi$_2$S$_2$ is found to exhibit many characteristics of heavy-fermion behavior, including a heavy electron state ($m^*/m_e \sim$ 24), with a negative coefficient of thermal expansion, and superconductivity below $T_c$ = 0.46(2) K. In the potassium nickel sulfide, these behaviors arise in the absence of localized magnetism, and instead appear to originate in proximity to charge order., Comment: 10 pages, 14 Figures

Based on specific heat and magnetoresistance measurements, we report that a "heavy" electronic state exists below $T \approx$ 20 K in KNi$_2$Se$_2$, with an increased carrier mobility and enhanced effective electronic band mass, $m$* = 6$m_b$ to 18$m_b$. This "heavy" state evolves into superconductivity at $T_c$ = 0.80(1) K. These properties resemble that of a many-body heavy-fermion state, which derives from the hybridization between localized magnetic states and conduction electrons. Yet, no evidence for localized magnetism or magnetic order is found in KNi$_2$Se$_2$ from magnetization measurements or neutron diffraction. Instead, neutron pair-distribution-function analysis reveals the presence of local charge-density-wave distortions that disappear on cooling, an effect opposite to what is typically observed, suggesting that the low-temperature electronic state of KNi$_2$Se$_2$ arises from cooperative Coulomb interactions and proximity to, but avoidance of, charge order.

In many ostensibly crystalline materials, unit-cell-based descriptions do not always capture the complete physics of the system due to disruption in long-range order. In the series of cobalt hydroxides studied here, Co(OH)$_{2-x}$(Cl)$_x$(H$_2$O)$_{n}$, magnetic Bragg diffraction reveals a fully compensated N\'eel state, yet the materials show significant and open magnetization loops. A detailed analysis of the local structure defines the aperiodic arrangement of cobalt coordination polyhedra. Representation of the structure as a combination of distinct polyhedral motifs explains the existence of locally uncompensated moments and provides a quantitative agreement with bulk magnetic measurements and magnetic Bragg diffraction.