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The design of novel quaternary materials can be a chemically challenging endeavor. Here, we show that a new tolerance factor, we herein call the quaternary tolerance factor (QTF), akin to the Goldschmidt ratio, can be applied to a homologous series of quaternary materials to aid in the prediction of structural stability in new phases. Single crystals of nine new members of the A2Ln4Cu2nQ7+nhomologous series were synthesized (A= K, Rb, Cs, Ln= Sm, Gd, Tb, Dy, Er, Yb, Lu, Q= S, Se) for n= 1, 2, and 3 using a reactive KCl flux method as the sole potassium source. This homologous series is notable for being the largest of all known chalcogenide homologies and thus serves as a case study for understanding quaternary structural relationships. We present a thorough structural analysis of these newly synthesized compounds and place them in the context of all previously reported members of the homologous series. We then report a generalizable tolerance factor capable of predicting structurally interrelated quaternary materials from an a priorisphere-packing approach for the design of new materials.

Here, we report the development of a hydrogen-free, topotactic oxygen deintercalation technique using alkali metal aluminum gallium amalgams (AxAlGa, where A = Li, Na, K). These amalgams provide a uniquely tunable system where the choice of alkali metal, its concentration, and the Al:Ga composition alter its reductive properties. We demonstrate the utility of this method in topotactically removing oxygen from bulk and thin film specimens of LnNiO3(Ln = La, Nd) to form the infinite layer of nickelate LnNiO2(Ln = La, Nd). For example, Na0.25AlGa affords bulk LaNiO2from LaNiO3at 300 °C for 120 h, while the same amalgam at 265 °C for 48 h affords the intermediate La2Ni2O5(LaNiO2.5). Other alterations in time and temperature as well as the choice of alkali metal (A) and its concentration (x) in AxAlGa allow further exploration of the topotactic reduction. Compared to standard techniques based on hydrogen gas or hydrides such as LiH, NaH, and CaH2, these amalgams offer an elegant tunability of the reduction potential, enabling control over the rate and degree of oxygen removal without the risk of hydrogen intercalation.

We report superconductivity in the full Heusler compound LiPd2Si (space group Fm3̅m, No. 225) at a critical temperature of Tc= 1.3 K and a normalized heat capacity jump at Tc, ΔC/γTc= 1.1. The low-temperature isothermal magnetization curves imply type-I superconductivity, as previously observed in LiPd2Ge. We show, based on density functional theory calculations and using the molecular orbital theory approach, that while LiPd2Si and LiPd2Ge share the Pd cubic cage motif that is found in most of the reported Heusler superconductors, they show distinctive features in the electronic structure. This is due to the fact that Li occupies the site which, in other compounds, is filled with an early transition metal or a rare-earth metal. Thus, while a simple valence electron count–property relationship is useful in predicting and tuning Heusler materials, inclusion of the symmetry of interacting frontier orbitals is also necessary for the best understanding.

Bi2WO6has been actively investigated as a viable photocatalysis substitute for TiO2. This along with progress in designing qubit hosts using W5+centers encourages the development of single crystal growths of this material using the floating zone technique. Single crystals of Bi2WO6–xwere grown using a laser diode floating zone furnace. Laue diffraction and single crystal X-ray diffraction confirm development of single crystalline domains. Williamson–Hall analysis shows annealed floating zone crystals contain less strain compared to unannealed and flux grown samples. Fitting of the heat capacity data shows two optical phonon modes modeled by Einstein oscillators, with the lower energy oscillator decreasing post annealing. The band gap is estimated as 2.6 eV using hyperspectral imaging, showing an additional absorption band present in the oxygen-deficient samples compared to those grown via flux. This additional absorption is tunable via annealing post growth. Overall, this technique demonstrates the feasibility of growing large single crystals of Bi2WO6with tunable W5+centers for potential application in photocatalysis and quantum information.

Time-reversal invariance (TRS) and inversion symmetry (IS) are responsible for the topological band structure in Dirac semimetals (DSMs). These symmetries can be broken by applying an external magnetic or electric field, resulting in fundamental changes to the ground state Hamiltonian and a topological phase transition. We probe these changes using universal conductance fluctuations (UCF) in the prototypical DSM, Cd3As2. With increasing magnetic field, the magnitude of the UCF decreases by a factor of 2, in agreement with numerical calculations of the effect of broken TRS. In contrast, the magnitude of the UCF increases monotonically when the chemical potential is gated away from the charge neutrality point. We attribute this to Fermi surface anisotropy rather than broken IS. The concurrence between experimental data and theory provides unequivocal evidence that UCF are the dominant source of fluctuations and offers a general methodology for probing broken-symmetry effects in topological quantum materials.

Electrons in solids often adopt complex patterns of chemical bonding driven by the competition between energy gains from covalency and delocalization, and energy costs of double occupation to satisfy Pauli exclusion, with multiple intermediate states in the transition between highly localized, and magnetic, and delocalized, and nonmagnetic limits. Herein, we report a chemical pressure-driven transition from a proper Mn magnetic ordering phase transition to a Mn magnetic phase crossover in EuMn2P2the limiting end member of the EuMn2X2(X = Sb, As, P) family of layered materials. This loss of a magnetic ordering occurs despite EuMn2P2remaining an insulator at all temperatures, and with a phase transition to long-range Eu antiferromagnetic order at TN≈ 17 K. The absence of a Mn magnetic phase transition contrasts with the formation of long-range Mn order at T≈ 130 K in isoelectronic EuMn2Sb2and EuMn2As2. Temperature-dependent specific heat and 31P NMR measurements provide evidence for the development of short-range Mn magnetic correlations from T≈ 250–100 K, interpreted as a precursor to covalent bond formation. Density functional theory calculations demonstrate an unusual sensitivity of the band structure to the details of the imposed Mn and Eu magnetic order, with an antiferromagnetic Mn arrangement required to recapitulate an insulating state. Our results imply a picture in which long-range Mn magnetic order is suppressed by chemical pressure, but that antiferromagnetic correlations persist, narrowing bands and producing an insulating state.

Double Dirac materials are a topological phase of matter in which a non-symmorphic symmetry enforces greater electronic degeneracy than normally expected – up to eightfold. The cubic palladium bronzes NaPd3O4and LaPd3S4are built of Pd3X4(X = O, S) anionic frameworks that are ionically bonded to A cations (A = Na, La). These materials were recently identified computationally as harboring eightfold fermions. Here we report the preparation of single crystals and electronic properties of LaPd3S4. Measurements down to T= 0.45 K and in magnetic fields up to μ0H= 65 T are consistent with normal Fermi liquid physics of a Dirac metal in the presence of dilute magnetic impurities. This interpretation is further confirmed by analysis of specific heat, magnetization measurements and comparison to density functional theory (DFT) calculations. Through a bonding analysis of the DFT electronic structure of NaPd3O4and LaPd3S4, we identify the origin of the stability of the anionic Pd3X4framework at higher electron counts for X = S than X = O, and propose chemical tuning strategies to enable shifting the 8-fold fermion points to the Fermi level.

PbTiO3is an established high temperature ferroelectric and component of multiferroic devices. Single crystal growth of clean PbTiO3has largely been limited to flux growth, in part due to the volatility of PbTiO3near the melting point. We demonstrate the ability to grow single crystals of PbTiO3using the laser diode floating zone technique. Crystal quality is examined using Laue, powder, and single crystal X-ray diffraction. Low temperature specific heat and annealing experiments using thermogravimetric analysis/differential thermal analysis were used to compare the disorder and vacancies generated in the laser diode floating zone with those produced by flux growth. Samples grown using the floating zone method showed minimal oxygen deficiency, while samples grown via flux had a higher density of vacancies and metal impurities (determined using glow discharge mass spectrometry), resulting in room temperature ferromagnetic behavior. The use of laser diodes as a heating source in the optical floating zone technique is essential in the stability of the zone growth and could be applied for production and zone refinement of other volatile materials.

Metal–organic frameworks (MOFs) provide exceptional chemical tunability and have recently been demonstrated to exhibit electrical conductivity and related functional electronic properties. The kagomé lattice is a fruitful source of novel physical states of matter, including the quantum spin liquid (in insulators) and Dirac fermions (in metals). Small-bandgap kagomé materials have the potential to bridge quantum spin liquid states and exhibit phenomena such as superconductivity but remain exceptionally rare. Here we report a structural, thermodynamic, and transport study of the two-dimensional kagomé metal–organic frameworks Ni3(HIB)2and Cu3(HIB)2(HIB = hexaiminobenzene). Magnetization measurements yield Curie constants of 0.989 emu K (mol Ni)−1Oe–1and 0.371 emu K (mol Cu)−1Oe–1, respectively, close to the values expected for ideal S= 1 Ni2+and S= 1/2Cu2+. Weiss temperatures of −10.6 and −14.3 K indicate net weak mean field antiferromagnetic interactions between ions. Electrical transport measurements reveal that both materials are semiconducting, with gaps (Eg) of 22.2 and 103 meV, respectively. Specific heat measurements reveal a large T-linear contribution γ of 148(4) mJ mol-fu–1K–2in Ni3(HIB)2with only a gradual upturn below ∼5 K and no evidence of a phase transition to an ordered state down to 0.1 K. Cu3(HIB)2also lacks evidence of a phase transition above 0.1 K, with a substantial, field-dependent, magnetic contribution below ∼5 K. Despite them being superficially in agreement with the expectations of magnetic frustration and spin liquid physics, we ascribe these observations to the stacking faults found from a detailed analysis of synchrotron X-ray diffraction data. At the same time, our results demonstrate that these MOFs exhibit localized magnetism with simultaneous proximity to a metallic state, thus opening up opportunities to explore the connection between the insulating and metallic ground states of kagomé materials in a highly tunable chemical platform.

The superconducting analogue to the semiconducting diode, the Josephson diode, has long been sought with multiple avenues to realization being proposed by theorists1–3. Showing magnetic-field-free, single-directional superconductivity with Josephson coupling, it would serve as the building block for next-generation superconducting circuit technology. Here we realized the Josephson diode by fabricating an inversion symmetry breaking van der Waals heterostructure of NbSe2/Nb3Br8/NbSe2. We demonstrate that even without a magnetic field, the junction can be superconducting with a positive current while being resistive with a negative current. The ΔIcbehaviour (the difference between positive and negative critical currents) with magnetic field is symmetric and Josephson coupling is proved through the Fraunhofer pattern. Also, stable half-wave rectification of a square-wave excitation was achieved with a very low switching current density, high rectification ratio and high robustness. This non-reciprocal behaviour strongly violates the known Josephson relations and opens the door to discover new mechanisms and physical phenomena through integration of quantum materials with Josephson junctions, and provides new avenues for superconducting quantum devices.

Combining neutron diffraction with pair distribution function analysis, we have uncovered hidden reduced symmetry in the correlated metallic d1perovskite, SrVO3. Specifically, we show that both the local and global structures are better described using a GdFeO3distorted (orthorhombic) model as opposed to the ideal cubic ABO3perovskite type. Recent reports of imaginary phonon frequencies in the density functional theory (DFT)-calculated phonon dispersion for cubic SrVO3suggest a possible origin of this observed non-cubicity. Namely, the imaginary frequencies computed could indicate that the cubic crystal structure is unstable at T = 0 K. However, our DFT calculations provide compelling evidence that point defects in the form of oxygen vacancies, and not an observable symmetry breaking associated with calculated imaginary frequencies, primarily result in the observed non-cubicity of SrVO3. These experimental and computational results are broadly impactful because they reach into the thin-film and theoretical communities who have shown that SrVO3is a technologically viable transparent conducting oxide material and have used SrVO3to develop theoretical methods, respectively.

Oxide perovskites offer improved stability compared to halide perovskite compounds for optoelectronic applications. Here, we report the first gold-containing double perovskite, Ba2AuIO6, and compare it to Ba2AgIO6and Ba2NaIO6. Ba2AuIO6and Ba2AgIO6exhibit a monoclinic distortion from the cubic perovskite structure possessed by Ba2NaIO6and have similar lattice constants despite the nominally larger size of Au+compared to Ag+. Ba2AgIO6shows photoluminescence (PL) at 2.10 eV, and Ba2AuIO6exhibits PL at 1.30 and 1.47 eV. As prepared, both compounds appear stable under visible light at room temperature but decompose when subjected to gentle heating followed by illumination. Our data suggest that this behavior is due to the presence of −OH defects in the crystal structures. This discovery provides a new route to semiconductors with a near-IR band gap and identifies engineering challenges that must be addressed to use oxide perovskites for optoelectronic devices.

Chemical bonding in 2D layered materials and van der Waals solids is central to understanding and harnessing their unique electronic, magnetic, optical, thermal, and superconducting properties. Here, we report the discovery of spontaneous, bidirectional, bilayer twisting (twist angle ∼4.5°) in the metallic kagomé MgCo6Ge6at T= 100(2) K via X-ray diffraction measurements, enabled by the preparation of single crystals by the Laser Bridgman method. Despite the appearance of static twisting on cooling from T∼300 to 100 K, no evidence for a phase transition was found in physical property measurements. Combined with the presence of an Einstein phonon mode contribution in the specific heat, this implies that the twisting exists at all temperatures but is thermally fluctuating at room temperature. Crystal Orbital Hamilton Population analysis demonstrates that the cooperative twisting between layers stabilizes the Co-kagomé network when coupled to strongly bonded and rigid (Ge2) dimers that connect adjacent layers. Further modeling of the displacive disorder in the crystal structure shows the presence of a second, Mg-deficient, stacking sequence. This alternative stacking sequence also exhibits interlayer twisting, but with a different pattern, consistent with the change in electron count due to the removal of Mg. Magnetization, resistivity, and low-temperature specific heat measurements are all consistent with a Pauli paramagnetic, strongly correlated metal. Our results provide crucial insight into how chemical concepts lead to interesting electronic structures and behaviors in layered materials.

A family of high entropy oxides with the formula Mg2Ta3Ln3O14(Ln = La, Pr, Nd, Sm, Eu, Gd) has been discovered and synthesized. Single crystals, 5 mm OD × 2.5 cm, for Ln = Nd have been grown using the laser optical floating zone technique. Crystal orientations are confirmed by Laue diffraction, and structure solutions were obtained via single crystal X-ray diffraction. The structure is found to be a partially disordered pyrochlore, space group Fd-3m, fractional chemical formula (Mg0.25Nd0.75)2(Mg0.25Ta0.75)2O7. Magnetization measurements indicate ordinary paramagnetic behavior in all compounds down to T= 2 K, except in the Eu variant which possesses Van Vleck paramagnetism. Specific heat measurements for Ln = Nd shows no phase transitions between T= 300 and 2 K. We demonstrate the ability to prepare magnetically disordered materials by substitution of Mg with Ni, Mn, and Co, demonstrating the flexibility of this family in accommodating defects. The stabilization of these compounds could be due to the entropy gain associated with defects, showcasing a “materials by design” approach by using disorder to stabilize novel magnetic and optical materials. Our work also demonstrates the feasibility of preparing high entropy oxides in single crystalline form.

Materials with nonsymmorphic symmetries have many applications and have recently come to the forefront as possibly harboring new topological states of matter, such as 8-fold fermions. Here, we report the single crystal growth of Bi2CuO4using the traveling solvent floating zone technique. Using laser heating combined with a 0.875 Bi2CuO4:0.125 Bi2O3solvent, we produce untwinned single crystal pieces. Three-dimensional X-ray microcomputed tomography is used to probe the fundamental origins of twinning, grain formation, and growth. Powder X-ray diffraction and Laue diffraction show that Bi2CuO4crystallizes in the space group P4/ncc(#130), orders antiferromagnetically with TN= 43 K, and, combined with comparisons to the literature, demonstrate the crystallinity and reproducibility of the synthesis. The entropy lost at the magnetic phase transition is ΔSmag= 0.25 ln(2); it arises from a high anisotropy in the magnetic interactions. We carry out a symmetry analysis demonstrating that Bi2CuO4’s magnetic order implies a rich breaking of the parent 8-fold symmetric states. Our results provide a roadmap for the creation of future magnetic derivatives of 8-fold, double Dirac single crystals and related quantum states of matter with nonsymmorphic symmetries. This approach also offers guidance on improving the single growth of nonsymmorphic materials from cuprates to van der Waals solids.

Superconductivity is reported in an endohedral aluminide compound, RuAl6, with Tc= 1.21 K. The normalized heat capacity jump at Tc, ΔC/γTc= 1.58, confirms bulk superconductivity. The Ginzburg–Landau parameter of κ = 9.5 shows that RuAl6is a type-II superconductor. Electronic structure calculations for RuAl6are explored in comparison to its structural analogue ReAl6(Tc= 0.74 K). The stability of the phases is discussed in terms of the crystal orbital Hamilton population (−COHP) analysis. The difference in Tcin the two materials is caused by the significantly stronger electron–phonon coupling found in RuAl6, which is a result of significantly stronger antibonding interactions. The presence of superconductivity in yet another compound made of aluminum clusters possibly expands the correlation of critical temperature and the structure shown for Ga-built clusters.

Kagomé lattice magnets have emerged as a versatile platform on which to discover and explore the underlying physics of quantum-spin liquids and related states of matter, although experimental examples of ideal kagomé lattices remain rare. Here we report that Na2Ti3Cl8is an ideal realization of an insulating S= 1 kagomé magnet. This material undergoes a discrete two-step trimerization upon cooling, transforming from a centrosymmetric, paramagnetic high-temperature (HT) R3mphase to noncentrosymmetric, polar, and trimerized intermediate- (IT) and low-temperature (LT) R3mphases via two successive first-order phase transitions. Symmetry mode decomposition analysis shows that trimerization requires activation of the proper polar order parameter Γ2–and that this mode becomes active at the HT → IT phase transition. The magnitude of this order parameter approximately doubles at the IT → LT transition, with possible activation of a second polar mode, corresponding to Na2and Ti3Cl8displacing layers toward each other, at the IT → LT transition. Specific heat measurements reveal comparable changes in entropy between the LT → IT transition, 18.6(1.0) J (mol of f.u.)−1K–1, and the IT → LT transition, 16.8(1.0) J (mol of f.u.)−1K–1, demonstrating loss of the magnetic degrees of freedom and constraining possible models for the magnetic and electronic structures of the IT and LT phases. Thus, Na2Ti3Cl8demonstrates a novel mechanism to obtain polar structures driven by geometrically frustrated lattices and metal–metal bonding and highlights the rich physics arising from kagomé lattice materials.

Incorporating magnetism into two-dimensional (2D) van der Waals (vdW) heterostructures is crucial for the development of functional electronic and magnetic devices. Here, we show that Nb3X8(X = Cl, Br) is a family of 2D layered trimerized kagomé magnets that are paramagnetic at high temperatures and undergo a first-order phase transition on cooling to a singlet magnetic state. X-ray diffraction shows that a rearrangement of the vdW stacking accompanies the magnetic transition, with high- and low-temperature phases consistent with scanning transmission electron microscopy images of the end members α-Nb3Cl8and β-Nb3Br8. The temperature of this transition is systematically varied across the solid solution Nb3Cl8–xBrx(x= 0–8), with x= 6 having transitions near room temperature. The solid solution also varies the optical properties, which are further modulated by the phase transition. As such, they provide a platform on which to understand and exploit the interplay between dimensionality, magnetism, and optoelectronic behavior in vdW materials.

Three new salt inclusion compounds (CsX)Cu5O2(PO4)2(X= Cl, Br, I), phosphate analogues of the kagomé mineral averievite, are reported. Their crystal structures are composed of trigonal networks of corner-sharing OCu4anion-centered tetrahedra, forming capped-kagomé planes, which can also be regarded as two-dimensional slices along the [111] direction of a pyrochlore lattice. Magnetization and heat capacity measurements reveal strong geometric frustration of this network and complex magnetic behavior. X-ray and neutron diffraction studies show that all three compounds undergo a trigonal-to-monoclinic phase transition upon cooling, with a first-order phase transition seen in CsBr and CsI analogues. Along with the previously reported (CsCl)Cu5O2(VO4)2, these three new compounds belong to a large family of OCu4-based networks, which are a playground for studying frustrated quantum magnetism.

Among oxide compounds with direct metal–metal bonding, the Y5Mo2O12(A5B2O12) structural family of compounds has a particularly intriguing low-dimensional structure due to the presence of bioctahedral B2O10dimers arranged in one-dimensional edge-sharing chains along the direction of the metal–metal bonds. Furthermore, these compounds can have a local magnetic moment due to the noninteger oxidation state (+4.5) of the transition metal, in contrast to the conspicuous lack of a local moment that is commonly observed when oxide compounds with direct metal–metal bonding have integer oxidation states resulting from the lifting of orbital degeneracy typically induced by the metal–metal bonding. Although a monoclinic C2/mstructure has been previously proposed for Ln5Mo2O12(Ln= La–Lu and Y) members of this family based on prior single crystal diffraction data, it is found that this structural model misses many important structural features. On the basis of synchrotron powder diffraction data, it is shown that the C2/mmonoclinic unit cell represents a superstructure relative to a previously unrecognized orthorhombic Immmsubcell and that the superstructure derives from the ordering of interchangeable Mo2O10and LaO6building blocks. The superstructure for this reason is typically highly faulted, as evidenced by the increased breadth of superstructure diffraction peaks associated with a coherence length of 1–2 nm in the c* direction. Finally, it is shown that oxygen vacancies can occur when Ln= La, producing an oxygen deficient stoichiometry of La5Mo2O11.55and an approximately 10-fold reduction in the number of unpaired electrons due to the reduction of the average Mo valence from +4.5 to +4.05, a result confirmed by magnetic susceptibility measurements. This represents the first observation of oxygen vacancies in this family of compounds and provides an important means of continuously tuning the magnetic interactions within the one-dimensional octahedral chains of this system.

Single-crystal growth is a widely explored method of synthesizing materials in the solid state. The last few decades have seen significant improvements in the techniques used to synthesize single crystals, and much of this information has been collected and distributed via different papers and textbooks for the novice. What is often missing from these resources are perspectives on how to use these techniques in unusual ways, frequently combining aspects from different fields of chemistry. These variations on known single crystal growth techniques can help effect success in situations where the conventional technique might otherwise fail, as well as providing control over crucial structural defects. This manuscript informs about key aspects of single crystal growth techniques and variations that enable access to new materials and control over defects. We provide examples of materials that have been successfully grown as single crystals with each individual technique and highlight how the target material influences and informs the choice of technique and/or application of variations. Finally, we offer a case study, focusing on the floating zone technique, in which we delve into the growth of large single crystalline materials, as well as how the process can be influenced by modifications to attempt the growth of materials that might not otherwise be suitable for the technique. The presence of all of these sections in a single paper is meant to assist novice crystal growers in comparing, contrasting, and ultimately selecting a suitable technique or techniques for their experiments.

A new misfit layered compound with the stoichiometry (EuS)1+δ(NbSe2)2(δ ≈ 0.13) has been successfully synthesized. High-resolution transmission electron microscopy and powder X-ray diffraction confirm the misfit structure with (EuS)–(EuS) spacing of 18.30(1) Å. Magnetization, electrical resistivity, heat capacity, and thermal transport measurements show that the material is a heavily doped semiconductor or poor metal with a low thermal conductivity of ∼1 W/m K and an antiferromagnetic ordering transition at TN= 4.7 K. In contrast to the parent materials, the misfit is neither ferromagnetic nor superconducting down to T= 0.4 K. We find evidence of a field-driven transition to a ferromagnetic state due to reorientation of ferromagnetic EuS layers at μoH= 0.5 T at T= 2 K.

We have identified six new 4d4and 4d5compounds with isolated RuCl6octahedra, with formulas (HMA)4RuCl6·Cl (1; MA = methylamine), (HGly)4RuCl6·Cl (2; gly = glycine), (HGly)3RuCl6·2H2O (3), (NH4)2RuCl6(4), (HPy)2RuCl6(5; py = pyridine), and H2(4,4′-bpy)RuCl6(6; 4,4′-bpy = 4,4′-bipyridine). We find that the temperature-dependent magnetization is well described by single-ion physics in the presence of spin–orbit coupling and negligible superexchange interactions. Further, we find that many compounds in the literature are also well described by single-ion physics, and our results demonstrate the importance of considering single-ion physics when evaluating candidate geometric frustrated magnets in the presence of spin–orbit coupling.

Ages of history are defined by the underlying materials that promoted human development: stone, bronze, and iron ages. Since the middle of the last century, humanity has lived in a silicon age, where the development of the transistor ushered in new technologies previously thought inconceivable. But as technology has advanced, so have the requirements for new materials to sustain increasing physical demands. The field of solid state chemistry is dedicated to the discovery of new materials and phenomena, and though most materials discoveries in history have been through serendipity rather than careful reaction design, the last few decades have seen an increase in the number of materials discovered through a consideration of chemical reaction kinetics and thermodynamics. Materials by design have changed the way solid state chemists approach the synthesis of possible materials with interesting and useful properties.