The structure and morphology of ${\mathrm{Bi}}_m{\mathrm{Se}}_n$ epitaxial layers with compositions ranging from ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ to the ${\mathrm{Bi}}_1{\mathrm{Se}}_1$ grown by molecular beam epitaxy with different flux compositions are investigated by transmission electron microscopy, high-resolution x-ray diffraction, and atomic force microscopy. It is shown that the lattice structure changes significantly as a function of the beam flux composition, i.e., Se/BiSe flux ratio that determines the stoichiometry of the layers. A perfect ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ phase is formed only with a sufficiently high additional Se flux, whereas ${\mathrm{Bi}}_1{\mathrm{Se}}_1$ is obtained when only a BiSe compound source without additional Se is used. For intermediate values of the excess Se flux during growth, ${\mathrm{Bi}}_2{\mathrm{Se}}_{3-\delta }$ layers are obtained with the Se deficit $\delta$ varying between 0 and 1. This Se deficit is accommodated by incorporation of additional Bi-Bi double layers into the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ structure that otherwise exclusively consists of Se-Bi-Se-Bi-Se quintuple layers. While a periodic insertion of such Bi double layers would result in the formation of natural ${\mathrm{Bi}}_m{\mathrm{Se}}_n$ superlattices, we find that this Bi double-layer insertion is rather stochastic with a high degree of disorder depending on the film composition. Therefore, the structure of such epilayers is better described by a one-dimensional paracrystal model, consisting of disordered sequences of quintuple and double layers rather than by strictly periodic natural superlattices. From detailed analysis of the x-ray diffraction data, we determine the dependence of the lattice parameters $a$ and $c$ and distances of the individual (0001) planes $d_j$ as a function of composition, evidencing that only the in-plane lattice parameter $a$ shows a linear dependence on composition. The simulation of the diffraction curves with the random stacking paracrystal model yields an excellent agreement with the experimental data and it brings quantitative information on the randomness of the stacking sequence, which is compared to growth modeling using Monte Carlo simulations. The analysis of transmission electron microscopy data furthermore confirms that the Bi-Bi bilayers contain a large amount of vacancies of up to 25%. Conductivity and Hall data confirm that ${\mathrm{Bi}}_m{\mathrm{Se}}_n$ phases containing Bi-Bi double layers exhibit a rather semimetallic behavior.

The physical properties of the mixed-valent iron oxide $\beta \text{−}{\mathrm{NaFe}}_2{\mathrm{O}}_3$ were investigated by means of synchrotron radiation x-ray diffraction, magnetization, electrical resistivity, differential scanning calorimetry, ${}^{23}\mathrm{Na}$ NMR, and ${}^{57}\mathrm{Fe}\mathrm{M}\ddot{\mathrm{o}}\mathrm{ssbauer}$ measurements. This compound has double triangular layers consisting of almost perfect regular ${\mathrm{Fe}}_4$ tetrahedra, which suggests geometrical frustration. We found that this compound exhibits an electrostatically unstable double-stripe-type charge ordering, which is stabilized by the cooperative compression of ${\mathrm{Fe}}^{3+}{\mathrm{O}}_6$ octahedra, owing to a valence change and ${\mathrm{Fe}}^{2+}{\mathrm{O}}_6$ octahedra due to Jahn-Teller distortion. Our results indicate the importance of electron-phonon coupling for charge ordering in the region of strong charge frustration.

Material strength and moduli can be determined from dynamic high-pressure ramp-release experiments using an indirect method of Lagrangian wave profile analysis of surface velocities. This method, termed self-consistent Lagrangian analysis (SCLA), has been difficult to calibrate and corroborate with other experimental methods. Using nonequilibrium molecular dynamics, we validate the SCLA technique by demonstrating that it accurately predicts the same bulk modulus, shear modulus, and strength as those calculated from the full stress tensor data, especially where strain rate induced relaxation effects and wave attenuation are small. We show here that introducing a hold in the loading profile at peak pressure gives improved accuracy in the shear moduli and relaxation-adjusted strength by reducing the effect of wave attenuation. When rate-dependent effects coupled with wave attenuation are large, we find that Lagrangian analysis overpredicts the maximum unload wavespeed, leading to increased error in the measured dynamic shear modulus. These simulations provide insight into the definition of dynamic strength, as well as a plausible explanation for experimental disagreement in reported dynamic strength values.

A single crystal of RuAs obtained with the Bi-flux method shows obvious successive metal-insulator transitions at $T_{\mathrm{MI}1}\sim 255$ K and $T_{\mathrm{MI}2}\sim 195$ K. The x-ray diffraction measurement reveals the formation of a superlattice of $3\times 3\times 3$ of the original unit cell below $T_{\mathrm{MI}2}$, accompanied by a change of the crystal system from the orthorhombic structure to the monoclinic one. Simple dimerization of the Ru ions is not seen in the ground state. The multiple As sites observed in the nuclear quadrupole resonance spectrum also demonstrate the formation of the superlattice in the ground state, which is clarified to be nonmagnetic. The divergence in $1/T_1$ at $T_{\mathrm{MI}1}$ shows that a symmetry lowering by the metal-insulator transition is accompanied by strong critical fluctuations of some degrees of freedom. Using the structural parameters in the insulating state, the first-principles calculation reproduces successfully the reasonable size of nuclear quadrupole frequencies ${\nu }_Q$ for the multiple As sites, ensuring the high validity of the structural parameters. The calculation also gives a remarkable suppression in the density of states near the Fermi level, although the gap opening is insufficient. A coupled modulation of the calculated Ru $d$-electron numbers and the crystal structure proposes the formation of a charge density wave in RuAs. Some lacking factors remain, but it is shown that a lifting of degeneracy protected by the nonsymmorphic symmetry through the superlattice formation is a key ingredient for the metal-insulator transition in RuAs.

Heat capacity, thermal expansion, and magnetization of ytterbium boride $\mathrm{Yb}{\mathrm{B}}_{50}$ were studied at temperatures 0.6–300 K, 5–300 K, and 2–300 K, respectively. We revealed two smooth peaks at about 4.0 and 60 K in the temperature dependence of the heat capacity. A comparison with the heat capacity of the diamagnetic isostructural boride $\mathrm{Lu}{\mathrm{B}}_{50}$ shows that these anomalies can be attributed to excitations in the ytterbium sublattice (Schottky anomalies). A scheme for splitting of the ground ${}^{2}F_{7/2}$ multiplet of $\mathrm{Y}{\mathrm{b}}^{3+}$ ions in the crystal field is proposed. Reliability of the proposed crystal-field energies of the $\mathrm{Y}{\mathrm{b}}^{3+}$ ions is confirmed by the analysis of temperature dependencies of magnetic susceptibility and magnetization in applied magnetic fields up to 55 kOe. A clear anisotropy of the thermal expansion and a negative expansion within a wide temperature range (40–185 K) were observed. Assuming that this anomaly of the thermal expansion in higher borides is caused by the specific thermal evolution of a crystal lattice observed earlier, in particular, in $\mathrm{Lu}{\mathrm{B}}_{50}$, and the interaction of rare-earth ions with lattice strains, we have determined phenomenological Grüneisen parameters which characterize effects due to thermal transitions of $\mathrm{Y}{\mathrm{b}}^{3+}$ ions between the ground and excited states. A phase transition of $\mathrm{Yb}{\mathrm{B}}_{50}$ to any magnetically ordered state was not observed down to the lowest temperatures of experiments.

Noncollinear hexagonal antiferromagnets with almost zero net magnetization were recently shown to demonstrate giant anomalous Hall effect. Here, we present the structural and magnetic properties of noncollinear antiferromagnetic ${\mathrm{Mn}}_3\mathrm{Sn}$ thin films heteroepitaxially grown on Y:${\mathrm{ZrO}}_2$ (111) substrates with a Ru underlayer. The ${\mathrm{Mn}}_3\mathrm{Sn}$ films were crystallized in the hexagonal $D{0}_{19}$ structure with $c$-axis preferred (0001) crystal orientation. The ${\mathrm{Mn}}_3\mathrm{Sn}$ films are discontinuous, forming large islands of approximately 400 nm in width, but are chemical homogeneous and characterized by near perfect heteroepitaxy. Furthermore, the thin films show weak ferromagnetism with an in-plane uncompensated magnetization of $M=34$ kA/m and coercivity of ${\mu }_0{H}_{\mathrm{c}}=4.0$ mT at room temperature. Additionally, the exchange bias effect was studied in ${\mathrm{Mn}}_3\mathrm{Sn}$/Py bilayers. Exchange bias fields up to ${\mu }_0{H}_{\mathrm{EB}}=12.6$ mT can be achieved at 5 K. These results show ${\mathrm{Mn}}_3\mathrm{Sn}$ films to be an attractive material for applications in antiferromagnetic spintronics.

We present molecular beam epitaxial grown single- and double-side $\delta$-doped InAlSb/InSb quantum wells with varying distances down to 50 nm to the surface on GaSb metamorphic buffers. We analyze the surface morphology as well as the impact of the crystalline quality on the electron transport. Comparing growth on GaSb and GaAs substrates indicates that the structural integrity of our InSb quantum wells is solely determined by the growth conditions at the GaSb/InAlSb transition and the InAlSb barrier growth. The two-dimensional electron gas samples show high mobilities of up to $349000$ ${\mathrm{cm}}^2$/Vs at cryogenic temperatures and $58000$ ${\mathrm{cm}}^2$/Vs at room temperature. With the calculated Dingle ratio and a transport lifetime model, ionized impurities predominantly remote from the quantum well are identified as the dominant source of scattering events. The analysis of the well-pronounced Shubnikov–de Haas oscillations reveals a high spin-orbit coupling with an effective $g$-factor of $-38.4$ in our samples. Along with the smooth surfaces and long mean free paths demonstrated, our InSb quantum wells are increasingly competitive for nanoscale implementations of Majorana mode devices.

Antiferromagnetic MnPt exhibits a spin reorientation transition (SRT) as a function of temperature, and off-stoichiometric Mn-Pt alloys also display SRTs as a function of concentration. The magnetocrystalline anisotropy in these alloys is studied using first-principles calculations based on the coherent potential approximation and the disordered local moment method. The anisotropy is fairly small and sensitive to the variations in composition and temperature due to the cancellation of large contributions from different parts of the Brillouin zone. Concentration and temperature-driven SRTs are found in reasonable agreement with experimental data. Contributions from specific band-structure features are identified and used to explain the origin of the SRTs.

Magnetism of the binary intermetallic compound ${\mathrm{MnGa}}_4$ is reinvestigated. Band-structure calculations predict antiferromagnetic behavior in contrast to Pauli paramagnetism reported previously. Magnetic susceptibility measurements on single crystals indeed reveal an antiferromagnetic transition at $T_N=393\mathrm{K}$. Neutron powder diffraction and ${}^{69,71}\mathrm{Ga}$ nuclear quadrupole resonance spectroscopy show collinear antiferromagnetic order with magnetic moments aligned along the [111] direction of the cubic unit cell. The magnetic moment of 0.80(3) ${\mu }_B$ at 1.5 K extracted from the neutron data is in good agreement with the band-structure results.

The potential of conjugated polymers to compete with inorganic materials in the field of semiconductor is conditional on fine-tuning of the charge carriers mobility. The latter is closely related to the material morphology, and various studies have shown that the bottleneck for charge transport is the connectivity between well-ordered crystallites, with a high degree of $\pi \text{−}\pi$ stacking, dispersed into a disordered matrix. However, at this time there is a lack of theoretical descriptions accounting for this link between morphology and mobility, hindering the development of systematic material designs. Here we propose a computational model to predict charge carriers mobility in conducting polymer PEDOT depending on the physicochemical properties of the system. We start by calculating the morphology using molecular dynamics simulations. Based on the calculated morphology we perform quantum mechanical calculation of the transfer integrals between states in polymer chains and calculate corresponding hopping rates using the Miller-Abrahams formalism. We then construct a transport resistive network, calculate the mobility using a mean-field approach, and analyze the calculated mobility in terms of transfer integrals distributions and percolation thresholds. Our results provide theoretical support for the recent study [Noriega et al., Nat. Mater. 12, 1038 (2013)] explaining why the mobility in polymers rapidly increases as the chain length is increased and then saturates for sufficiently long chains. Our study also provides the answer to the long-standing question whether the enhancement of the crystallinity is the key to designing high-mobility polymers. We demonstrate, that it is the effective $\pi \text{−}\pi$ stacking, not the long-range order that is essential for the material design for the enhanced electrical performance. This generic model can compare the mobility of a polymer thin film with different solvent contents, solvent additives, dopant species or polymer characteristics, providing a general framework to design new high mobility conjugated polymer materials.

Sublimation is a fundamental phase transition that has a profound impact on both natural phenomena and advanced manufacturing technologies. Although great strides have been made in the study of ice growth from melt and vapor, little consideration has been given to the effect of sublimation on the morphological features that develop in the ice microstructure. In this experimental study, we demonstrate the effect of vapor pressure on the mesoscopic faceting observed and show that a vapor-pressure-specific wavelength characterizes the periodic features that arise during sublimation. The ability to control the length scale of these features not only provides us with new insights into the mesoscopic roughness of ice crystals, but also presents the potential to exploit this effect in a plethora of applications from comet dating to ice-templated tissue engineering scaffolds.

Ferroelectrics possess spontaneous electric polarization at macroscopic scales which nonetheless imposes strict limitations on the material classes. Recent discoveries of untraditional symmetry-breaking phenomena in reduced material dimensions have indicated feasibilities to extend polar properties to broader types of materials, potentially opening up the freedom for designing materials with hybrid functionalities. Here, we report the unusual electromechanical properties of $\mathrm{L}{\mathrm{a}}_2\mathrm{M}{\mathrm{o}}_2{\mathrm{O}}_9$ (LAMOX) oxygen ion conductors, systematically investigated at both bulk and surface length levels. We first observed giant electrostriction effects in $\mathrm{L}{\mathrm{a}}_2\mathrm{M}{\mathrm{o}}_2{\mathrm{O}}_9$ bulk ceramics that are thermally enhanced in concert with their low-energy oxygen-vacancy hopping dynamics. Moreover, while no clear bulk polarization was detected, the surface phases of LAMOX were found to be manifestly polar, likely originating from the coupling between the intrinsic structural flexibilities with strain gradients (i.e., flexoelectricity) and/or chemical heterogeneities present in the materials. These findings identify $\mathrm{L}{\mathrm{a}}_2\mathrm{M}{\mathrm{o}}_2{\mathrm{O}}_9$ as a promising electromechanical material system and suggest that the flexible structural and chemical configurations in ionically active materials could enable fundamentally different venues to accommodate electric polarization.

Nexus metals represent a new type of topological material in which nodal lines merge at nexus points. Here we propose novel networks in nexus systems through intertwining between nexus fermions and additional nodal lines. These nexus networks can be realized in recently synthesized carbon honeycomb materials. In these carbon honeycombs, we demonstrate a phase transition between a nexus network and a system with triply degenerate points and additional nodal lines. The Landau level spectra show unusual magnetic transport properties in the nexus networks. Our results pave the way toward realizations of new topological materials with novel transport properties beyond standard Weyl/Dirac semimetals.

Unambiguous magnetic characterization of room-temperature multiferroic materials remains challenging due in part to the difficulty of distinguishing their very weak ferromagnetism from magnetic impurity phases and other contaminants. In this study, we used polarized neutron reflectivity to probe the magnetization of $\mathrm{B}{\mathrm{i}}_6\mathrm{FeCoT}{\mathrm{i}}_3{\mathrm{O}}_{18}$ and $\mathrm{LaB}{\mathrm{i}}_5\mathrm{FeCoT}{\mathrm{i}}_3{\mathrm{O}}_{18}$ in their epitaxial thin films while eliminating a variety of impurity contributions. Our results show that $\mathrm{LaB}{\mathrm{i}}_5\mathrm{FeCoT}{\mathrm{i}}_3{\mathrm{O}}_{18}$ exhibits a magnetization of about $0.016\pm 0.027{\mu }_{\mathrm{B}}/\mathrm{Fe}\text{−}\mathrm{Co}$ pair at room temperature, while the $\mathrm{B}{\mathrm{i}}_6\mathrm{FeCoT}{\mathrm{i}}_3{\mathrm{O}}_{18}$ thin film only exhibits a weak magnetic moment below room temperature, with a saturation magnetization of $0.049\pm 0.015{\mu }_{\mathrm{B}}/\mathrm{Fe}\text{−}\mathrm{Co}$ pair at 50 K. This polarized-neutron-reflectivity study places an upper magnetization limit on the matrix material of the magnetically doped Aurivillius oxides and helps to clarify the true mechanism behind the room-temperature magnetic performance.

Synthetic barlowite, $\mathrm{C}{\mathrm{u}}_4{\left(\mathrm{OH}\right)}_6\mathrm{BrF}$, has emerged as a new quantum spin liquid (QSL) host, containing kagomé layers of $S=1/2\mathrm{C}{\mathrm{u}}^{2+}$ ions separated by interlayer $\mathrm{C}{\mathrm{u}}^{2+}$ ions. Similar to synthetic herbertsmithite, $\mathrm{ZnC}{\mathrm{u}}_3{\left(\mathrm{OH}\right)}_6\mathrm{C}{\mathrm{l}}_2$, it has been reported that $\mathrm{Z}{\mathrm{n}}^{2+}$ substitution for the interlayer $\mathrm{C}{\mathrm{u}}^{2+}$ induces a QSL ground state. Here we report a scalable synthesis of single crystals of $\mathrm{C}{\mathrm{u}}_4{\left(\mathrm{OH}\right)}_6\mathrm{BrF}$. Through x-ray, neutron, and electron diffraction measurements coupled with magic angle spinning ${}^{19}\mathrm{F}$ and ${}^1\mathrm{H}$ NMR spectroscopy, we resolve the previously reported positional disorder of the interlayer $\mathrm{C}{\mathrm{u}}^{2+}$ ions and find that the structure is best described in the orthorhombic space group, Cmcm, with lattice parameters $a=6.665\left(13\right)\AA ,b=11.521\left(2\right)\AA ,c=9.256\left(18\right)\AA$, and an ordered arrangement of interlayer $\mathrm{C}{\mathrm{u}}^{2+}$ ions. Infrared spectroscopy measurements of the O—H and F—H stretching frequencies demonstrate that the orthorhombic symmetry persists upon substitution of $\mathrm{Z}{\mathrm{n}}^{2+}$ for $\mathrm{C}{\mathrm{u}}^{2+}$. Specific heat and magnetic susceptibility measurements of Zn-substituted barlowite, $\mathrm{Z}{\mathrm{n}}_{\mathrm{x}}\mathrm{C}{\mathrm{u}}_{4-\mathrm{x}}{\left(\mathrm{OH}\right)}_6\mathrm{BrF}$, reveal striking similarities with the behavior of $\mathrm{Z}{\mathrm{n}}_{\mathrm{x}}\mathrm{C}{\mathrm{u}}_{4-\mathrm{x}}{\left(\mathrm{OH}\right)}_6\mathrm{C}{\mathrm{l}}_2$. These parallels imply universal behavior of copper kagomé lattices even in the presence of small symmetry-breaking distortions. Thus, synthetic barlowite demonstrates universality of the physics of synthetic $\mathrm{C}{\mathrm{u}}^{2+}$ kagomé minerals and furthers the development of real QSL states.

We present a numerical investigation of the size scaling of static friction in incommensurate two-dimensional contacts performed for different lateral loading configurations. Results of model simulations show that both the absolute value of the force $F_s$ and the scaling exponent $\gamma$ strongly depend on the loading configuration adopted to drive the slider along the substrate. Under edge loading, a sharp increase of static friction is observed above a critical size corresponding to the appearance of a localized commensurate dislocation. Noticeably, the existence of sublinear scaling, which is a fingerprint of superlubricity, does not conflict with the possibility to observe shear-induced localized commensurate regions at the contact interface. Atomistic simulations of gold islands sliding over graphite corroborate these findings, suggesting that similar elasticity effects should be at play in real frictional contacts.

Opaque substrates precluded, so far, transmission studies of II-VI semiconductor microcavities. This work presents the design and molecular beam epitaxy growth of semimagnetic (Cd,Zn,Mn)Te quantum wells embedded into a (Cd,Zn,Mg)Te-based microcavity, which can be easily separated from the GaAs substrate. Our lift-off process relies on the use of a MgTe sacrificial layer which stratifies in contact with water. This allowed us to achieve a II-VI microcavity prepared for transmission measurements. We evidence the strong light-matter coupling regime using photoluminescence, reflectivity, and transmission measurements at the same spot on the sample. By comparing a series of reflectance spectra before and after lift-off, we prove that the microcavity quality remains high. Thanks to Mn content in quantum wells we show the giant Zeeman splitting of semimagnetic exciton-polaritons in our transmitting structure.

Although $S=1/2$ kagomé systems have been intensely studied theoretically, and within the past decade been realized experimentally, much less is known about the $S=1$ analogs. While the theoretical ground state is still under debate, it has been found experimentally that $S=1$ kagomé systems either order at low temperatures or enter a spin glass state. In this work, ${\mathrm{YCa}}_3{\left(\mathrm{VO}\right)}_3{\left({\mathrm{BO}}_3\right)}_4$ (YCVBO) is presented, with trivalent vanadium. Owing to its unusual crystal structure, the metal-metal bonding is highly connected along all three crystallographic directions, atypical of other kagomé materials. Using neutron scattering it is shown that YCVBO fails to order down to at least 50 mK and exhibits broad and dispersionless excitations. ${}^{11}\mathrm{B}$ NMR provides evidence of fluctuating spins at low temperatures while dc magnetization shows critical scaling that is also observed in systems near a quantum critical point such as Herbertsmithite, despite its insulating nature and $S=1$ magnetism. The evidence shown indicates that YCVBO is naturally tuned to be a quantum disordered magnet in the limit of $T=0$ K.

A Gd $K$-edge anomalous x-ray scattering (AXS) study is performed on the rare-earth $\left(R\right)$ phosphate glass, ${\left(\mathrm{G}{\mathrm{d}}_2{\mathrm{O}}_3\right)}_{0.230}{\left({\mathrm{P}}_2{\mathrm{O}}_5\right)}_{0.770}$, in order to determine $\mathrm{Gd}\cdots \mathrm{Gd}$ separations in its local structure. The minimum rare-earth separation is of particular interest given that the optical properties of these glasses can quench when rare-earth ions become too close to each other. To this end, a weak $\mathrm{Gd}\cdots \mathrm{Gd}$ pairwise correlation is located at $4.2\left(1\right)\AA$, which is representative of a metaphosphate $R\cdots R$ separation. More intense first-neighbor $\mathrm{Gd}\cdots \mathrm{Gd}$ pairwise correlations are found at the larger radial distributions, 4.8(1), 5.1(1), and $5.4\left(1\right)\AA$. These reflect a mixed ultraphosphate and metaphosphate structural character, respectively. A second-neighbor $\mathrm{Gd}\cdots \mathrm{Gd}$ pairwise correlation lies at $6.6\left(1\right)\AA$ which is indicative of metaphosphate structures. Meta- and ultraphosphate classifications are made by comparing the $R\cdots R$ separations against those of rare-earth phosphate crystal structures, $R{\left(\mathrm{P}{\mathrm{O}}_3\right)}_3$ and $R{\mathrm{P}}_5{\mathrm{O}}_{14}$, respectively, or difference pair-distribution function $\left(\mathrm{\Delta }\mathrm{PDF}\right)$ features determined on similar glasses using difference neutron-scattering methods. The local structure of this glass is therefore found to display multiple rare-earth ion environments, presumably because its composition lies between these two stoichiometric formulae. These $\mathrm{Gd}\cdots \mathrm{Gd}$ separations are well-resolved in $\mathrm{\Delta }\mathrm{PDFs}$ that represent the AXS signal. Indeed, the spatial resolution is so good that it also enables the identification of $R\cdots X(X=R$, P, O) pairwise correlations up to $r\sim 9\AA$; their average separations lie at $r\sim 7.1\left(1\right)$, 7.6(1), 7.9(1), 8.4(1), and $8.7\left(1\right)\AA$. This is a report of a Gd $K$-edge AXS study on an amorphous material. Its demonstrated ability to characterize the local structure of a glass up to such a long range of $r$ heralds exciting prospects for AXS studies on other ternary noncrystalline materials. However, the technical challenge of such an experiment should not be underestimated, as is highlighted in this work where probing AXS signal near the Gd $K$ edge is found to produce inelastic x-ray scattering that precludes the normal AXS methods of data processing. Nonetheless, it is shown that AXS results are not only tractable but they also reveal local structure of rare-earth phosphate glasses that is important from a materials-centered perspective and which could not be obtained by other materials characterization methods.