Nanocrystals exhibit size-dependent structural behaviour because surface and interface effects become increasingly important as the characteristic domain size decreases. In this work, we investigate the size dependence of three diffraction-derived structural parameters - lattice parameter, isotropic Debye-Waller coefficient and microstrain - by combining molecular dynamics simulations of spherical Pd, Fe and Ti nanocrystals with powder diffraction analysis and comparison with representative literature data. The atomistic results show that small nanocrystals are characterized by a mean compressive state together with pronounced surface-stress inhomogeneity, while enhanced atomic displacements are concentrated in the outer coordination shells. On this basis, three simple nanoscale hypotheses are proposed. The lattice parameter is described as an ideal capillarity-driven reference trend with leading 1/D (where D is the particle diameter) behaviour, although comparison with experimental data confirms that this quantity is not universal and may be strongly modified by surface chemistry, defects, non-stoichiometry and morphology. By contrast, the Debye-Waller coefficient follows a more general 1/D decrease, consistent with a surface-shell picture of enhanced vibrational and static disorder. Microstrain arises from surface-stress gradients and, in the small-particle limit, exhibits a natural 1/D2 dependence associated with surface-stress heterogeneity; over broader size ranges, a mixed 1/D + 1/D2 form provides a more effective description. These results support a heuristic surface-driven interpretation of nanoscale structural disorder and clarify the different degrees of generality of the three scaling laws.

Literature values of the lattice thermal conductivity for Cu 2+ y Zn 1− y SnS x Se 4− x (CZTSSe) systems showing inverse trends with S and Se contents, attributed to phonon grain-boundary scattering.

Abstract High-entropy oxides containing more than five different cations have emerged as platforms for diverse functionalities, including magnetism. We synthesized a high-entropy oxide with an ilmenite-type structure (Mg0.2Mn0.2Co0.2Ni0.2Zn0.2)TiO3 and revealed that it undergoes long-range antiferromagnetic ordering below TN ∼ 9.5 K despite strong cation disorder. Neutron diffraction measurements showed that the magnetic structure comprises ferromagnetic honeycomb planes that stack antiferromagnetically, analogous to those of the parent CoTiO3 and NiTiO3 ilmenites. Derivatives of the high-entropy ilmenite were obtained by substituting one of the divalent cations of (Mg0.2Mn0.2Co0.2Ni0.2Zn0.2)TiO3 with an equimolar amount of Li+ ions and trivalent cations. The antiferromagnetic order remains robust against aliovalent doping that introduces extra disorder owing to cations with different valence states. In contrast, when the cation ratio was tuned to a Mn-rich composition of (Mg0.2Mn0.3Co0.15Ni0.15Zn0.2)TiO3, spin-glass freezing was observed, most likely because of the enhanced competition between the in-plane magnetic interactions. This suggests that long-range magnetic ordering in high-entropy materials is formed by a subtle balance of competing interactions, and fine-tuning of constituent magnetic ions provides control over their magnetic ground states.

In this study, the self-assembly of HgX2 (X=Cl, Br, I) and an electron-deficient tetrazine-based ligand [3,6-bis (pyridin-3-yl)-1,2,4,5-tetrazine (3,3 '-pytz)] was utilized. By anion-controlled approach, and using reactant diffusion method in methanol-ethanol solvent system, three structurally different coordination polymers with general formula [Hg(3,3 '-pytz)X2]n, namely [Hg(3,3 '-pytz)Cl2]n(1), [Hg(3,3 '-pytz)Br2]n(2), and [Hg(3,3 '-pytz) I2]n(3) have been prepared. The synthesized compounds were characterized using several techniques, including FT-IR, TGA, and elemental analysis. The crystal structures have been determined from single-crystal X-ray diffraction (SCXRD) data (compounds 2 and 3), and powder X-ray diffraction (PXRD) data (compound 1). Our structural analysis reveals that the structure of compound 1 is a 2D wavy sheet, whereas compounds 2 and 3 exhibit 1D helical and zig-zag chains, respectively. The presence of non-covalent intermolecular interactions was confirmed using Hirshfeld surface analysis. This study aims to deepen our understanding of anion-controlled structural design by extending its application beyond the established frameworks associated with Cd(II) systems to include Hg(II) coordination polymers. By investigating the non-covalent interactions between various anions and Hg(II), we provide new insights into how these anions can influence the structural properties and functionalities of coordination polymers. This research not only broadens the scope of anion-controlled design principles but also opens new avenues for the synthesis of advanced materials with tailored characteristics for specific applications in fields such as materials science and environmental remediation.

Kesterite compounds of the form Cu2+yZn1-ySnSxSe4-x (CZTSSe) have attracted considerable interest as sustainable thermoelectric materials due to their earth-abundant composition and intrinsically low lattice thermal conductivity. However, several studies on polycrystals report an unexpected trend in which the selenide exhibits higher lattice thermal conductivity than the sulphide, contrary to expectations based on atomic mass and lattice stiffness. In this work, we investigate the origin of this behaviour and shed light on how microstructural, chemical, and structural features affect the thermoelectric performance across the CZTSSe compositional series. First-principles calculations indicate that the intrinsic lattice dynamics favour lower lattice thermal conductivity in Se-rich compositions. In contrast, experimental results show that microstructural effects dominate phonon transport in polycrystalline samples. In particular, larger porosity, smaller grain size, and reduced grain connectivity strongly suppress the lattice thermal conductivity in sulphide-rich compounds, leading to an apparent inversion of the expected CZTS-CZTSe thermal conductivity trend. In addition, electronic transport analysis reveals an increase in weighted mobility above the order-disorder phase transition temperature, observed across all compositions, and resulting in improved performance. This effect is attributed to the band convergence effect related to the increased structural symmetry promoted by Cu-Zn disorder, approaching a pseudo-cubic structure. Despite the lower intrinsic carrier mobility in sulphide-rich compositions, their suppressed lattice thermal conductivity results are comparable to thermoelectric performance across the series, with zT values up to similar to 0.5 at 723 K. These results demonstrate that microstructural effects can outweigh intrinsic chemical trends and play a critical role in determining thermal transport and thermoelectric performance in kesterite materials.

The zinc oxalate (ox) triazolate (trz)-based MOF, Calgary Framework 20 (CALF-20), exhibits remarkable cycling stability for carbon dioxide and water adsorption and desorption and is therefore a promising candidate material for CO2 sequestration on an industrial scale. Upon gas and vapor loading and unloading, the MOF shows pronounced structural dynamics leading to a variety of potential CALF-20 polymorphs. A systematic in situ study on CO2 and H2O ad- and desorption using high-resolution, laboratory X-ray powder diffraction (XRPD) shows that the CO2-breathing behavior changes upon gas loading. A CO2 uptake initially distorts the rectangular pore into a diamond shape. Upon further CO2 incorporation, the breathing behavior changes, and the pore becomes more rectangular, again. At low temperatures (-70 °C), the uptake of CO2 occurs in a core-shell mechanism, and the gas is bound strongly to the framework and cannot be removed by dynamic vacuum. During water uptake of CALF-20, two distinct hydrated phases can be identified. The overall water loading capacity is independent of temperature between 25 and 60 °C. In this paper, we demonstrate that recent advances in X-ray powder diffraction hard- and software enable a detailed investigation of the loading and breathing behavior of a crystalline MOF using laboratory equipment, turning this into easily accessible investigations.

Diffuse scattering is a component of the powder pattern bearing information on the local atomic structure and disorder of crystalline materials. It is visible in the X-ray diffraction patterns of binary structures like Ag2O, which has a large mean squared displacement for its constituent elements. Pair distribution function (PDF) analysis is widely employed to extract this local structural information, embedded in the widths of PDF peaks. However, obtaining the PDF from experimental data requires a Fourier transform, which introduces aberrations in the transformed data due to instrument resolution, complicating the distinction between its static and dynamic components. In this work, the analysis of thermal diffuse scattering is performed directly on the X-ray powder pattern, using the traditional Rietveld method integrated with a correlated displacement model for atomic pairs. The Ag2O case study data were collected using synchrotron radiation at room temperature, supplemented by laboratory experiments up to 200°C. An Einstein model was used to obtain the harmonic and anharmonic force constants of the system. The force constants were also obtained via density functional theory and ab initio molecular dynamics simulations and showed similar values to the experiments. The analysis reveals the complex dynamic structure of Ag2O, characterized by high anisotropy in phonon dispersion relations and the presence of soft phonon modes, which explain the significant displacement parameters observed. The proposed approach can be easily employed for other binary or more complex systems to understand the dynamics of local forces through X-ray diffraction analysis.

Covalent organic frameworks (COFs) have been developed as photosensitizers for photocatalytic energy conversion over the past decade; however, COF photocatalysts have yet to demonstrate the ability to harvest near-infrared light (above 760 nm, approximately 53% of the solar spectrum) for fuel or chemical conversion. In this work we introduce a post-synthetic functionalization strategy for COFs by incorporating a palladacycle directly into the COF backbone, extending the light absorption of an azobenzene-based COF into the near-infrared region. This approach enables homogeneous, atomically distributed palladium functionalization with a high loading of 12 wt% and without noticeable formation of palladium nanoparticles. The cyclopalladated COF, TpAzo-CPd, was used as a catalyst for photocatalytic hydrogen peroxide production under 810 nm illumination. This study demonstrates the use of COFs for near-infrared photocatalysis and opens the door to palladium-single-site COF catalysts for a wide range of chemical transformations.

The Cu2+y Zn1-y SnS x Se4-x (0 <= x <= 4; y = 0, 0.125) system is an earth-abundant, nontoxic chalcogenide with tunable polymorphism and chemical disorder, making it a promising candidate for sustainable thermoelectric and photovoltaic applications. Recent stabilization of cubic sphalerite Cu2ZnSnS4 and Cu2ZnSnSe4 via mechanochemical synthesis has demonstrated enhanced thermoelectric performance attributed to low-energy optical phonon modes and topological conduction pathways for charge carriers. In this study, we explore the role of anion substitution and Cu-induced CuZn antisite disorder in stabilizing the cubic phase and driving its transformation to the partially disordered tetragonal kesterite structure at high temperature. A combination of X-ray diffraction, Raman spectroscopy, and first-principles simulations (DFT, DFPT, AIMD) reveals that Cu-rich compositions deviate from Vegard's law, show increased stacking fault density, and exhibit pronounced distortion in the tetrahedral motifs. AIMD results indicate that the higher symmetry of the cubic phase permits a broad distribution of tetrahedral configurations, stabilizing disorder and stacking faults. Upon thermal activation, entropy favors the emergence of more stable S/Se-Cu3Sn, S/Se-Cu2ZnSn, and S/Se-CuZn2Sn motifs, stabilizing the kesterite phase with a reduced quantity of microstructural defects. Notably, in compositions close to Cu2+y Zn1-y SnS2Se2, classified as high-entropy alloys, Baur bond and angle distortions peak, suggesting structural robustness despite high defect concentrations. This work provides a fundamental understanding of microstructural disorder from the atomic motif level, offering valuable guidelines for tuning phase stability and properties in Cu2+y Zn1-y SnS x Se4-x kesterite and sphalerite materials.

A comprehensive investigation of the phase composition of eight commercial clinkers was conducted through state-of-the-art synchrotron (SXRD) and laboratory (LXRD) X-ray diffraction, and supporting techniques. Challenges involved in polymorph and minor phase quantification, and the effects of foreign ions on the clinker chemistry were addressed. SXRD yielded higher C3S and lower C2S contents than LXRD, besides higher C3S M3. Visual identification of C3S predominant polymorphs did not always match the Rietveld results for LXRD. Using orthorhombic-C3A in the refinement of samples that did not have this polymorph led to an underestimation C4AF and alpha ' H-C2S. Axial divergence made the quantification of beta-C2S inaccurate for non-monochromatic LXRD. C3S formation was governed by the sulfate/magnesium ratio and Na2Oeq content rather than LSF, while C3S polymorphism was governed by the sulfate/magnesium + alkali ratio. Optimal chemistry ranges were proposed for maximizing C3S formation. C3A polymorphism was generally controlled by the sulfate/alkali ratio.

Polycrystalline ceramic and small single-crystal samples of Co-containing calcium vanadate(V) with apatite structure were prepared for the first time. The Co2+ ions enter the apatite trigonal channels formally substituting protons of the OH- groups and form separate O-Co-O atomic groups elongated in the c direction, Co being additionally weakly coordinated to an oxygen atom of a VO4 group. At a high Co content, the hexagonal apatite structure undergoes a triclinic distortion followed by partial ordering of the Co2+ ions. The dc magnetic data fit well to a model of a zero-field split S = 3/2 state with a large negative D of -22 to -25 cm-1, suggesting a strong easy-axis magnetic anisotropy. The ac susceptibility measurements below T = 10 K reveal a multichannel slow relaxation of the magnetization in non-zero dc field. The temperature dependence of the relaxation time can be described by an Orbach process with the remagnetization energy barrier Ueff being equal to experimentally determined 2|D|. Modelling of the electronic structure shows that, with a small increase of the crystal field strength, the high-spin Co2+ ion changes its ground state from one with an unquenched orbital moment L = 3 to a fully orbitally quenched one. Both states are characterized by easy-axis magnetization vectors directed approximately perpendicular to each other with a smooth rotation of the vector at intermediate crystal fields. The model explains the weak magnetic anisotropy observed in the triclinic single crystal as well as the earlier reported ability of the dioxocobaltate(II) ion to behave like a single-ion magnet with either a high Ueff of hundreds of cm-1 or a moderate one of tens of cm-1. To the best of our knowledge that represents the first instance of the conversion of the d-element ground electronic state from orbitally degenerate to non-degenerate by a slight variation of the crystal field.

Halogen bonding enables the mechanochemical ball-milling isomerization of an otherwise persistent cis-coordinated metal complex into the corresponding trans-isomer. The importance of halogen bonding for enabling the cis→trans isomerization of the metal centre is evidenced by real-time in situ synchrotron powder X-ray diffraction monitoring of the ball-milling experiments that showed the transient appearance of a cis-geometry metal-organic halogen-bonded (MOXB) cocrystal, which is rapidly replaced by the corresponding trans-geometry one, with any excess, non-halogen-bonded cis-geometry complex being retained throughout the milling experiment. The importance of cocrystallization for cis→trans isomerization is supported by periodic density-functional theory calculations which show that the process becomes notably more enthalpically favourable in the presence of the halogen bond donor. The presented work indicates that the formation of MOXB cocrystals can open the door to new, metal-based responsive behaviours, different from those of parent solid-state coordination complexes.

Efficient hydrogen isotope separation remains the biggest challenge due to the nearly identical physicochemical properties of H2 and D2. Through in situ neutron powder diffraction and gas adsorption experiments, we investigate the hydrogen isotopologue-induced structural dynamics of the triazole-based metal-organic framework [Mn(ta)2]. Gas loading induces a measurable lattice expansion, more pronounced for H2 than D2, and two distinct adsorption sites are identified with a subtle but significant difference in the occupancy of H2 and D2 at 60 K. Cryogenic thermal desorption spectroscopy after exposure to a 1:1 isotope mixture reveals an exceptionally high D2/H2 selectivity of 32.5 at 60 K. When exposed to a D2/H2 mixture of 5:95, D2 enriches to 75% in a single cycle. Given the commercial availability of the ligand and the scalability of the dia-framework topology across divalent transition metals, upscaling for industrial-scale deuterium separation is a realistic prospect. Our results give crucial molecular-level insights into isotopologue-induced structural dynamics in triazolate-based MOFs and provide guidance for improvement of isotope separation materials.

The deuterium isotope effect on the honeycomb iridate H3LiIr2O6, a quantum spin-orbit-entangled liquid, was examined by synthesizing D3LiIr2O6. The structural refinements indicate the different character of the interlayer OH and OD bonds, which results in a giant isotope effect on the magnetic interactions; the antiferromagnetic Curie-Weiss temperature |θCW| of D3LiIr2O6 increases to ~ 170 K from ~ 100 K of H3LiIr2O6. Nevertheless, the quantum liquid state is robust against the deuterium isotope exchange in contrast to the theoretical prediction that the Kitaev spin liquid is stable only for a limited phase space of magnetic interactions. The bond- and site disorders associated with disordered OD(H) bonds, in combination with Kitaev physics, may play a role in realizing the quantum liquid state.

Polycrystalline single-phase bulk hydrogrossulars (Ca3Al2(SiO4)3-x(OH)4x (0 ≤ x ≤ 3)) of various compositions were synthesized for the first time utilizing hydrothermal treatment at 200 °C of the phyllosilicate strätlingite (Ca2Al2SiO2(OH)10·2.25H2O) in its mother liquor. The reproducibility of previously reported synthetic methods for both Si-free katoite and hydrogrossulars was evaluated. Analysis of the thermal behavior of hydrogrossulars based on TG-DTA and variable-temperature XRPD showed a significant increase in thermal stability upon silicon incorporation due to the reinforcement of the lattice with SiO4 tetrahedra. By tracking changes in the lattice parameters upon heating, we showed that the linear thermal expansion coefficients decrease with higher degrees of Si substitution (17.19 × 10-6 K-1 and 14.20 × 10-6 K-1 for Ca3Al2(OH)12 and Ca3Al2(SiO4)1.28(2)(OH)6.88(8), respectively). Temperature-induced partial dehydration of the SiO4-stabilized lattice results in the formation of tetrahedral Al sites as defects due to the removal of two oxygen atoms from the initial octahedral environment. Near-complete dehydration (450-850 °C) leads to the loss of the long-range structure, which later on crystallizes at 900 °C as a mixture of different minerals, e.g. calcio-olivine (γ-Ca2SiO4), gehlenite (Ca2Al2SiO7), krotite (CaAlO2), or mayenite (Ca12Al14O33).

The interplay of spin-orbit coupling with other relevant parameters gives rise to the rich phase competition in complex ruthenates featuring octahedrally coordinated Ru4+. While locally, spin-orbit coupling stabilizes a nonmagnetic Jeff = 0 state, intersite interactions resolve one of two distinct phases at low temperatures: an excitonic magnet stabilized by the magnetic exchange of upper-lying Jeff = 1 states or Ru2 molecular orbital dimers driven by direct orbital overlap. Pyrochlore ruthenates A2Ru2O7 (A = rare earth, Y) are candidate excitonic magnets with geometrical frustration. We synthesized In2Ru2O7 with covalent In─O bonds. This pyrochlore ruthenate hosts a local Jeff = 0 state at high temperatures; however, at low temperatures, it forms a unique nonmagnetic ground state with nearly linear Ru─O─Ru molecules, in stark contrast to other A2Ru2O7 compounds. The disproportionation of covalent In─O bonds drives Ru2O molecule formation, quenching not only the local spin-orbit singlet but also geometrical frustration.

Multinary earth-abundant chalcogenides, like kesterite, Cu2ZnSnS4 (CZTS), have attracted attention in sustainable energy applications like photovoltaics and thermoelectrics. High-energy ball milling provides a facile way for the synthesis of pure cubic CZTS. This sulfide crystallizes in a sphalerite-type structure with complete occupational disorder in the cationic substructure and a considerable amount of stacking faults. Heating of the material leads to the slow and irreversible transition into disordered, tetragonal kesterite, which is associated with a significant decrease in thermoelectric properties. Hence, a deep understanding of the phase transition process and its kinetics is a prerequisite for further crystal engineering. In situ X-ray powder diffraction and Raman spectroscopy supported by density functional theory calculations and ab initio molecular dynamics simulations (AIMD) were employed to gain microstructural insights into the phase transition process. Heating leads to a growth of the crystalline domains, which is associated with a reduction of strain. The domain growth reduces the stabilization of the metastable cubic phase by nanostructuring. This eventually leads to the segregation of tin cations, which corresponds to the beginning of the transition into the tetragonal phase. AIMD simulations indicate that the presence of faulting planes promotes the tin diffusion. As stacking faults appear to be energetically less favorable in the tetragonal disordered form, the stacking fault disorder is reduced upon heating, leading to an additional strain reduction.

We report on a new polymorph of silver antimonate AgSbO3 discovered with the use of high-pressure high-temperature synthesis at 16 GPa and 1380 °C. The crystal structure is determined from X-ray powder diffraction, and we find this new high-pressure phase crystallizes in monoclinic space group C2/c with the following values: a = 8.4570(3) Å, b = 9.8752(3) Å, c = 8.9291(3) Å, β = 91.1750(12)°, and V = 745.56(4) Å3. We synthesized the high-pressure (16 GPa) AgSbO3 phase from the ilmenite phase as a precursor. This high-pressure monoclinic AgSbO3 consists of a three-dimensional network of corner- and edge-sharing SbO6 octahedra with channels along the c-direction containing Ag atoms. We also synthesize AgSbO3 in the defect pyrochlore phase at 4 GPa from the same ilmenite precursor and compare the Raman spectra and the cation-anion bonding of all three AgSbO3 phases. The absence of a cubic perovskite form of AgSbO3 even at pressures of ≤16 GPa is likely due to the covalency of the Sb-O bonds and the moderate electronegativity of Ag+. Hybridization of Ag d and O p orbitals results in a variation of Ag-O distances that correlates with the band gap, which is in qualitative agreement with the density of states around the Fermi level from our density functional calculations. We compare AgSbO3 with other ABX3 compounds to elucidate the dependence of the structure on the constituent atoms.

Single-phase barium hexaferrite powders with crystallite sizes in a single-domain region and with the general composition BaFe12-xMnxO19, where x = 0, 2, 4, 6, were synthesized applying a citric sol-gel auto-combustion technique with final annealing temperatures of 900 - 1200 degrees C. The crystal structures were refined, and the magnetic properties were studied. The observed variations in atomic positions with the Mn-for-Fe substitution revealed presence of Mn in three oxidation state +2, +3, and +4, with a preference of Mn2+ to the tetrahedral 4f(1) site and Mn4+ to the octahedral 2a and 12k sites. With the Mn-doping, the samples' magnetization decreased, while coercivity increased and reached 8.4 kOe for x = 6. The rise of the annealing temperature resulted in a slight growth of magnetization with a general tendency of the coercivity to decrease. A Curie temperature decreased with the Mn-doping remaining above room temperature for the maximal doping.

The oxygen evolution reaction (OER) provides the protons for many electrocatalytic power-to-X processes, such as the production of green hydrogen from water or methanol from CO2. Iridium oxohydroxides (IOHs) are outstanding catalysts for this reaction because they strike a unique balance between activity and stability in acidic electrolytes. Within IOHs, this balance varies with the atomic structure. While amorphous IOHs perform best, they are least stable. The opposite is true for their crystalline counterparts. These rules-of-thumb are used to reduce the loading of scarce IOH catalysts and retain the performance. However, it is not fully understood how activity and stability are related at the atomic level, hampering rational design. Herein, we provide simple design rules (Figure 12) derived from the literature and various IOHs within this study. We chose crystalline IrOOH nanosheets as our lead material because they provide excellent catalyst utilization and a predictable structure. We found that IrOOH signals the chemical stability of crystalline IOHs while surpassing the activity of amorphous IOHs. Their dense bonding network of pyramidal trivalent oxygens (μ3Δ-O) provides structural integrity, while allowing reversible reduction to an electronically gapped state that diminishes the destructive effect of reductive potentials. The reactivity originates from coordinative unsaturated edge sites with radical character, i.e., μ1-O oxyls. By comparing to other IOHs and literature, we generalized our findings and synthesized a set of simple rules that allow prediction of stability and reactivity of IOHs from atomistic models. We hope that these rules will inspire atomic design strategies for future OER catalysts.