Nearest-neighbor Shell Research Articles

Lattice Distortion Promotes Incipient Plasticity in Multiprincipal Element Alloys.

Multiprincipal element alloys usually exhibit earlier pop-in events than pure metals and dilute solid solutions during nanoindentation experiments. To understand the origin of this phenomenon, large-scale atomic simulations of nanoindentation were performed on a series of metallic materials to investigate the underlying physics of incipient plasticity at the nanoscale. Statistical result shows that lattice distortion δ and normalized critical pressure pc/Es follow a power-law relationship. Via quantitative analysis on the relative positions of the atoms within the nearest neighbor shell, the physical origin of premature incipient plasticity is revealed as severe lattice distortion induces large relative atomic displacement, so only a small indentation strain is required to meet the critical displacement threshold that triggers incipient plasticity. Therefore, for perfect crystals, lattice distortion is an intrinsic and determinative factor that affects the first pop-in event.

First-principles study of behaviors of point defects in Mo-14 Re alloy

Molybdenum alloys with rhenium additions of 14 % (Mo-14 Re) are regarded as structural materials for advanced nuclear reactors. The performance of Mo-14 Re alloy under irradiation is crucial for its application. Irradiation performance is related to the behaviors of point defects produced by irradiation. The behaviors of point defects in Mo-14 Re alloy were investigated using first-principles methods in this work. Compared with the results in pure Mo alloy, the formation energy and the migration energy of vacancy in Mo-14 Re were both reduced, and the migration energy of interstitial dumbbell increased while the formation energy decreased in Mo-14 Re. In Mo-14 Re, vacancy preferred to form and diffuse faster in Re-enriched environment. Knowing the number of Re atoms in the 1NN (first nearest neighbor) shell of the vacancy and saddle point, the vacancy formation energy and migration energy can be estimated. Since the interstitial atom has a certain orientation, the distribution of the atoms around it is anisotropic. To estimate the interstitial formation energy, it was necessary to count the number of Re atoms at the tensile and compressive sites at the 1NN shell around the interstitial. The interstitial motion was three-dimensional (3D) in Mo-14 Re. At 1200 K, the diffusion coefficient of Re atom was a little higher than that of Mo atom, which could lead to the segregation of Re atoms at defect sinks and the formation of Re-enriched phase. It is possible to investigate the longer-term evolution of microstructure using cluster dynamics (CD) or kinetic monte carlo (KMC) techniques based on these results.

A new analytical surface energy model for arbitrary (h k l) planes in BCC and FCC metals

A new analytical surface energy model (Eq. 9) that is free of adjustable parameters has been developed to accurately predict the surface energies of arbitrary (h k l) planes in both BCC and FCC ground-state pure metals at 0 K, using only (100), (110) and (111) surface energies as input. The formulation is established by expanding the original broken-bond model up to the 3rd nearest neighbor shell and considering the surface relaxation effect. In addition, this model consists of only one single formula per crystal structure, overcoming the geometric complexities in previous models in which multiple equations are needed for different surface groups. The analytical model has been validated through the comparison with 4357 independent surface energies. These data include the energies of 517 unique surfaces per metal in Fe, Cr, W, Cu, Ni, and Al (a total of 3102 surface energies) that are calculated through our molecular dynamics simulations, and excellent agreement is obtained. The validation data also include 1255 independent surface energies in literature or online database for up to 46 BCC and FCC metals that were calculated by either empirical potentials or density functional theory. The agreement is still very good for most of the data, demonstrating the robustness of our new model.

Solvation Shell Anatomy of H2S and CO Dissolved in Reline and Ethaline Deep Eutectic Solvents.

Rising atmospheric concentrations of anthropogenic hydrogen sulfide (H2S) and carbon monoxide (CO) as a result of industrialization have encouraged researchers to explore innovative technologies for capturing these gases. Deep eutectic solvents (DESs) are an alternative media for mitigating H2S and CO emissions. Herein, we have employed ab initio molecular dynamics simulations to investigate the structures of the nearest-neighbor solvation shells surrounding H2S and CO when they are dissolved in reline and ethaline DESs. We aim to delineate the structural arrangement responsible for favorable H2S and CO capture by analyzing the key interactions between H2S and CO solutes with various components of the DESs. We observe that in the reline-H2S system, chloride and carbonyl oxygen of urea are found to have the closest distance interaction with hydrogen atoms of the H2S solute. The sulfur atom of H2S is found to be predominantly solvated by hydrogen and oxygen atoms of urea molecules and the hydroxyl hydrogen of choline cations. The chloride ions and ethylene glycol molecules predominantly govern the solvation of H2S in the ethaline-H2S system. In both the DESs, H2S is solvated by the hydroxyl group of the choline cations rather than by their ammonium group. In the reline-CO system, all the atoms of urea along with chloride dominate the immediate solvation shell around CO. In the ethaline-CO system, hydroxyl oxygen and hydrogen atoms of ethylene glycol are found in the nearest solvation structure around CO. Both the DESs exhibit a stronger solvent-solute charge-transfer tendency toward the H2S solute compared to CO.

An Experimental High-Throughput to High-Fidelity Study Towards Discovering Al–Cr Containing Corrosion-Resistant Compositionally Complex Alloys

Compositionally complex alloys hold the promise of simultaneously attaining superior combinations of properties, such as corrosion resistance, light-weighting, and strength. Achieving this goal is a challenge due in part to a large number of possible compositions and structures in the vast alloy design space. High-throughput methods offer a path forward, but a strong connection between the synthesis of an alloy of a given composition and structure with its properties has not been fully realized to date. Here, we present the rapid identification of corrosion-resistant alloys based on combinations of Al and Cr in a base Al–Co–Cr–Fe–Ni alloy. Previously unstudied alloy stoichiometries were identified using a combination of high-throughput experimental screening coupled with key metallurgical and electrochemical corrosion tests, identifying alloys with excellent passivation behavior. The alloy native oxide performance and its self-healing attributes were probed using rapid tests in deaerated 0.1-mol/L H2SO4. Importantly, a correlation was found between the electrochemical impedance modulus of the exposure-modified air-formed film and self-healing rate of the CCAs. Multi-element extended x-ray absorption fine structure analyses connected more ordered type chemical short-range order in the Ni–Al 1st nearest-neighbor shell to poorer corrosion resistance. This report underscores the utility of high-throughput exploration of compositionally complex alloys for the identification and rapid screening of a vast stoichiometric space.Graphical

Spin-lattice-dynamics analysis of magnetic properties of iron under compression

Compression of a magnetic material leads to a change in its magnetic properties. We examine this effect using spin-lattice dynamics for the special case of bcc-Fe, using both single- and poly-crystalline Fe and a bicontinuous nanofoam structure. We find that during the elastic phase of compression, the magnetization increases due to a higher population of the nearest-neighbor shell of atoms and the resulting higher exchange interaction of neighboring spins. In contrast, in the plastic phase of compression, the magnetization sinks, as defects are created, increasing the disorder and typically decreasing the average atom coordination number. The effects are more pronounced in single crystals than in polycrystals, since the presence of defects in the form of grain boundaries counteracts the increase in magnetization during the elastic phase of compression. Also, the effects are more pronounced at temperatures close to the Curie temperature than at room temperature. In nanofoams, the effect of compression is minor since compression proceeds more by void reduction and filament bending—with negligible effect on magnetization—than by strain within the ligaments. These findings will prove useful for tailoring magnetization under strain by introducing plasticity.

Local chemical inhomogeneities in TiZrNb-based refractory high-entropy alloys

(1) The local chemical order features in the TiZrNb-based alloys are as follows: (i) For the TiZrNb alloy, the Ti-Zr pair is the most favored, while there exists relatively weaker Nb-Nb pair; (ii) For the TiZrHfNb alloy, Ti and Nb prefer to pair with Zr and Hf, respectively; (iii) For TiZrHfNbTa, Ta is prone to form sub-nanoscale segregation, in addition to the existing chemical preference among Ti, Zr, Hf and Nb. (2) Accompanying the LCO, there exists compositional undulation in the TiZrHfNb alloy on nanometer scale, arising from the preferred local enrichment of [(Ti, Zr)] or [(Hf, Nb)] CSROs. (3) The local chemical inhomogeneity evolves strongly with temperature, from the RSS structure at high temperatures to the pronounced tendency of forming chemically favored pairs at low temperatures. The LCO develops beyond the range of CSRO, to a characteristic length scale of at least one nanometer. (4) The predicted yield strengths of the RSS samples are generally lower than the experimental values by ∼ 100 MPa, while those calculated for CSRO-containing samples approach the experimental measurements. This strongly suggests the need to take into account the contribution of CSRO (and/or other local chemical inhomogeneities) to achieve a more accurate prediction of the yield strength of TiZrNb-based bcc HEAs. (5) When the strong CSRO-promoting Ti is replaced by Ta, the resultant TaZrHfNb alloy is found to contain only a weak degree of local chemical order, unlike the three representative TiZrNb-based HEAs in the present study. (6) Our work reveals the trend of the chemical inhomogeneities and compositional undulation that would develop as intrinsic features in these TiZrNb-based bcc HEAs. Meanwhile, the CSRO tendency also sheds light on the fertile emergence of (Ti,Zr,O)- complexes that form upon the addition of oxygen/nitrogen into such HEAs to purposely accentuate (sub)nanometer-scale chemical complexes/heterogeneities. Multi-principal element solid solutions are prone to develop local chemical inhomogeneities, i.e. , chemical order/clustering and/or compositional undulation. However, these structural details from short-range (first couple of nearest-neighbor atomic shells) to nanometer length scale are very challenging to resolve in both experimental characterization and computer simulations. For instance, Monte Carlo modeling based on density-functional-theory calculations is severely limited by the sample size and the simulation steps practical in the simulations. Adopting the cluster expansion approach, here we systematically reveal the local chemical inhomogeneity, including chemical order and compositional fluctuation, in three representative equiatomic TiZrNb-based body-centered cubic refractory high-entropy alloys (HEAs): TiZrNb, TiZrHfNb and TiZrHfNbTa. Ti-Zr pairs are found to exhibit the highest degree of chemical preference among all atomic pairs. Such chemical short-range order (CSRO) induces an accompanying compositional undulation, both extending to characteristic dimensions of the order of one nanometer. The chemical inhomogeneity trend uncovered for this series of TiZrNb-based HEAs is expected to impact their mechanical properties; e.g. , incorporating the CSRO effects in a current model significantly improves its agreement with experimental measured yield strength.

Structure of jammed ellipse packings with a wide range of aspect ratios.

Motivated in part by the recent observation of liquid glass in suspensions of ellipsoidal colloids, we examine the structure of jammed two-dimensional ellipse packings over a much wider range of particle aspect ratios (α, the ratio of the major and minor axis lengths) than has been previously attempted. We determine the jamming densities ϕJ(α) to high precision, and find empirical analytic formulae that predict ϕJ(α) to within less than 0.1% for all 1≤α≤10, for three different particle dispersities. Then we explore how these packings' local structural order varies with α. We find that the densest packings possess unusually-well-defined nearest-neighbor shells, including both a higher fraction fZ=6 of particles with exactly six contacts and a previously-unreported short-range order marked by "kinetically suppressed" regions in their positional-orientational pair correlation function g(r,Δθ). We also show that the previously-reported approach to isostaticity (coordination number ZJ → Ziso ≡ 6) with increasing α is interrupted and then reversed as local nematic order increases: ZJ(α) drops towards 4 as ellipses are more often trapped by contacts with a parallel-oriented neighbor on either side and a perpendicularly-oriented neighbor on either end. Finally we show that ϕJ/ϕs (where ϕs is the saturated RSA packing density) is nearly α-independent for systems that do not develop substantial local hexatic or nematic order during compression.

Effect of cationic chemical disorder on defect formation energies in uranium–plutonium mixed oxides

At the atomic scale, uranium–plutonium mixed oxides (U,Pu)O2 are characterized by cationic chemical disorder, which entails that U and Pu cations are randomly distributed on the cation sublattice. In the present work, we study the impact of disorder on point defect formation energies in (U,Pu)O2 using interatomic-potential and density functional theory (DFT + U) calculations. We focus on bound Schottky defects (BSD) that are among the most stable defects in these oxides. As a first step, we estimate the distance RD around the BSD up to which the local chemical environment significantly affects their formation energy. To this end, we propose an original procedure in which the formation energy is computed for several supercells at varying levels of disorder. We conclude that the first three cation shells around the BSD have a non-negligible influence on their formation energy (RD≃7.0Å). We apply then a systematic approach to compute the BSD formation energies for all the possible cation configurations on the first and second nearest neighbor shells around the BSD. We show that the formation energy can range in an interval of 0.97 eV, depending on the relative amount of U and Pu neighboring cations. Based on these results, we propose an interaction model that describes the effect of nominal and local composition on the BSD formation energy. Finally, the DFT + U benchmark calculations show a satisfactory agreement for configurations characterized by a U-rich local environment and a larger mismatch in the case of a Pu-rich one. In summary, this work provides valuable insights on the properties of BSD defects in (U,Pu)O2 and can represent a valid strategy to study point defect properties in disordered compounds.

Heterogeneity and Nanostructure of Superconcentrated LiTFSI-EmimTFSI Hybrid Aqueous Electrolytes: Beyond the 21 m Limit of Water-in-Salt Electrolyte.

Ionic liquids such as EmimTFSI (1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide) have been found to improve the solubility of LiTFSI salt in water-in-salt electrolyte (WiSE) from 21 to 60 m. However, the molecular origin of such enhancement in the solubility is still unknown. In the present work, we elucidate the microscopic structures of LiTFSI-EmimTFSI-based hybrid aqueous electrolytes and compare them with the structure of LiTFSI-based WiSE using molecular dynamics simulations. Our analysis reveals the presence of alternating water-rich clusters and TFSI-rich extended domains in the WiSE. In these clusters and domains, the Li+ ions reside such that the total number of oxygen atoms around them is conserved to four, where water contributes about three oxygen atoms. The addition of EmimTFSI in the WiSE results in removal of water from the nearest-neighbor solvation shell of TFSI- ions but not from the Li+ ions. Significant structural changes are observed when LiTFSI salt is further added to LiTFSI-EmimTFSI aqueous solution. In both the hybrid electrolytes, water and Emim+ cations are found to avoid each other. The simulated X-ray scattering structure factor reveals the presence of larger length-scale heterogeneity in the most concentrated solution of the hybrid aqueous electrolyte. We observe that this nanoscale heterogeneity originates from a water-TFSI-Emim-TFSI-water-TFSI-Emim-TFSI-like arrangement in which Li+ ions are dispersed such that the coordination number of oxygen atoms around them is enhanced to five, wherein the major contribution comes from the TFSI- ions. We envision that the enhanced LiTFSI solubility originates from the replacement of water molecules with TFSI- ions in the first solvation shell of Li+ ions.

Structural and electronic properties of the random alloy ZnSexS1−x

In this article we employ density functional theory in the generalized gradient approximation to investigate the structural and electronic properties of the solid solution alloy $\text{Zn}\text{Se}_x\text{S}_{1-x}$ in the wurtzite structure. We analyzed the character of the bond lengths and angles at the atomic scale, using a supercell approach that does not impose any constraint on the crystal potential. We show that the bond lengths of pristine ZnS and ZnSe compounds are almost preserved between nearest neighbors, which is different from what would be anticipated if Vegard's law were valid at the atomic level. We also show that bond lengths start behaving in accordance to Vegard's law from the third shell of nearest neighbors onward, which in turn determines the average lattice parameters of the alloys determined by diffraction experiments. Fundamental building blocks around the anions are identified and are shown to be non-rigid but still volume preserving. Finally, the geometrical analysis is connected to the trend exhibited by the electronic structure, and in particular by the band gap. The latter is found to exhibit a small deviation from the linearity with respect to the Se concentration, in accordance to available experimental data. By assuming a quadratic dependence, we can extract a bowing parameter and analyze various contributions to it with various calculations under selected constraints. The structural deformation in response to the doping process is shown to be the driving force behind the deviation from linearity. The difference in stiffness between ZnS and ZnSe is showed to play a key role in the asymmetric behavior of the bowing parameter observed in the S-rich and Se-rich regions.

First-order phase transition in a two dimensional BM3 model.

The phase behavior of a Biroli-Mézard model on the two dimensional square lattice in which hard-core particles can have at most three nearest neighboring occupied sites is investigated by means of grand-canonical Monte Carlo simulations. Finite-size scaling analysis of relevant thermodynamic quantities obtained via the histogram reweighting technique reveals that at high-density, the model undergoes a first-order phase transition with preferential sublattice occupation to a crystal phase with enantiomorph ground state configurations, in close analogy to the hard-core lattice gas with the exclusion range extended up to the third shell of nearest neighbors.

Engineering defect energy landscape of CoCrFeNi high-entropy alloys by the introduction of additional dopants

The concept of high-entropy alloys (HEAs) focusing on tuning the overall chemical complexity represents a novel alloy design strategy. In contrast, alloying of a metallic matrix with minor doping elements with limited and localized tunability has been a common practice to improve material performance. Combining the idea of globally engineering defect energy landscape in HEAs and the localized doping strategy in dilute alloys, in this work, we explore doping effects of minor elements in a HEA matrix to further enhance the overall and localized chemical tunability, aiming to improve its irradiation resistance. Specifically, we study the influence of minor Al, Cu, Ti, and Pd substitutional doping elements on defect energetics in a CoCrFeNi model HEA based on density-functional theory (DFT) calculations. The DFT results indicate that the formation and migration energies of vacancies can be strongly influenced when a dopant is introduced at the first nearest neighbor shells around a vacancy. On the other hand, interstitial energetics are only slightly affected. Among the four elements, Ti and Pd generally decrease vacancy formation energies and increase vacancy migration energies more significantly than Al and Cu. The doping effects become more pronounced when the concentration of the substitutional dopants increases. Based on the energy distributions obtained from DFT, we build a kinetic Monte Carlo (kMC) model to assess the impact of dopants on vacancy-mediated diffusivity in the doped HEAs. Our results suggest that Ti and Pd can lower the tracer diffusivity in the considered HEAs and act as trapping sites, whereas Cu may enhance the atomic transport. This work indicates that substitutional doping in HEAs is an effective strategy in metallurgy to further tune the defect and transport properties of complex alloys.

Ultrafast atomic view of laser-induced melting and breathing motion of metallic liquid clusters with MeV ultrafast electron diffraction

Under the irradiation of an ultrafast intense laser, solid materials can be driven into nonequilibrium states undergoing an ultrafast solid-liquid phase transition. Understanding such nonequilibrium states is essential for scientific research and industrial applications because they exist in various processes including laser fusion and laser machining yet challenging in the sense that high resolution and single-shot capability are required for the measurements. Herein, an ultrafast diffraction technique with megaelectron-volt (MeV) electrons is used to resolve the atomic pathway over the entire laser-induced ultrafast melting process, from the initial loss of long-range order and the formation of high-density liquid to the progressive evolution of short-range order and relaxation into the metastable low-density liquid state. High-resolution measurements using electron pulse compression and a time-stamping technique reveal a coherent breathing motion of polyhedral clusters in transient liquid aluminum during the ultrafast melting process, as indicated by the oscillation of the interatomic distance between the center atom and atoms in the nearest-neighbor shell. Furthermore, contraction of interatomic distance was observed in a superheated liquid state with temperatures up to 6,000 K. The results provide an atomic view of melting accompanied with internal pressure relaxation and are critical for understanding the structures and properties of matter under extreme conditions.

Unveiling nonmonotonic chemical trends in the solubility of H in complex Fe-Cr-Mn carbides by means of ab initio based approaches

The microstructure of advanced high-strength steels often shows a sensitive dependence on alloying. For example, adding Cr to improve the corrosion resistance of medium-Mn steels also enhances the precipitation of carbides. The current study focuses on the behavior of H in such complex multicomponent carbides by employing different methodological strategies. We systematically analyze the impact of Cr, Mn, and Fe using density functional theory (DFT) for two prototype precipitate phases, ${\mathrm{M}}_{3}\mathrm{C}$ and ${\mathrm{M}}_{23}{\mathrm{C}}_{6}$, where M represents the metal sublattice. Our results show that the addition of these alloying elements yields strong nonmonotonic chemical trends for the H solubility. We identify magnetovolume effects as the origin for this behavior, which depend on the considered system, the sites occupied by H, and short- vs long-range interactions between H and the alloying elements. We further show that the H solubility is directly correlated with the occupation of its nearest-neighbor shells by Cr and Mn. Based on these insights, DFT data from H containing binary-metal carbides are used to design a ridge regression based model that predicts the solubility of H in the ternary-metal carbides (Fe-Cr-Mn-C).

Xenon mobility in γ-uranium and uranium–molybdenum alloys

Diffusion in bcc uranium and U–Mo alloys is of great interest because fission gas and other fission products impact the performance of nuclear fuels. We investigate the mobility of xenon and molybdenum in bcc uranium (γ-U) and metallic U–Mo alloys by calculating the migration energies of xenon and molybdenum for various local compositions using density functional theory. We also calculate the solute–vacancy binding energies of different solutes to vacancies in bcc uranium. We find that the solute–vacancy binding energy in bcc uranium is significantly higher than it is in other bcc metals (e.g., Fe and W). We also find that the migration energy of molybdenum is substantially higher than the migration energy of xenon, indicating that xenon is much more mobile than molybdenum in bcc uranium. The presence of molybdenum in the nearest-neighbor shell around a xenon atom typically increases the migration energy of xenon, which indicates a reduction of xenon mobility in U–Mo alloys compared to pure bcc uranium.

Effects of transition metal dopants on the electronic structure of potassium niobate

Potassium niobate (KNbO3) is an important ferroelectric and photorefractive material that finds multiple nonlinear optical and photorefractive applications such as two-beam coupling and dynamic holography. We employ standard Density Functional Theory to examine two defect complexes in KNbO3 doped with 3-d transition metals. These defect complexes involve the substitution of a Nb with a 3-d transition metal element and (1) a coordinating oxygen vacancy induced in the nearest-neighbor oxygen shell or (2) a non-coordinating oxygen vacancy induced in the supercell as far away as possible from substitution impurity. With the exception of Ti and V, the 3-d transition metal dopants studied here may represent viable dopants for purposes of extending the photorefractive spectral response of KNbO3. Our results indicate that each of these complexes introduces defect states into the gap of KNbO3. Furthermore, we notice that the distribution of impurity states changes quite systematically across the 3-d transition metal row, and we note the effects of the disruption of the crystal field in the case of the coordinating O vacancy on the position and ordering of defect states within the gap. Substituting KNbO3 with transition metal ions can, therefore, significantly affect its optical and infrared properties, exemplifying how a detailed understanding of the electronic structure can be an important tool in tailoring the properties of this material for ferroelectric and photorefractive applications.

Medium-range atomic correlation in simple liquids. II. Theory of temperature dependence

The spatial atomic correlations in liquids and glasses extend often significantly beyond the nearest neighbors. Such correlations, called the medium-range order (MRO), affect many physical properties, but their nature is not well understood. In this article the variation of the MRO with temperature is calculated based upon the concept of the atomic-level pressure, focusing on simple liquids, such as metallic liquids. It is shown that the structural coherence length that characterizes MRO follows the Curie-Weiss law with a negative Curie temperature as observed by experiment and simulation. It is also shown that the glass transition is induced by freezing of the MRO, rather than the freezing of the nearest-neighbor shell. The implications of these results are discussed.

Density functional theory calculations of the thermodynamic and kinetic properties of point defects in β-U

Density functional theory (DFT) calculations of the thermodynamic and kinetic properties of point defects in the β phase of uranium are reported. Defect energies and entropies were calculated using 2 × 2 × 2 supercells and the Generalized Gradient Approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) for the exchange-correlation potential. Due to computational cost, calculations of the vibrational properties governing entropies were performed by only displacing atoms within (roughly) the 3rd or 4th nearest neighbor shell of the defect, which implicitly assumes that atoms beyond this distance are unaffected by the defect. Migration barriers were estimated by nudged elastic band (NEB) calculations. The low symmetry of the β -U phase (the unit cell is tetragonal and contains 30 atoms) results in many point defect configurations and even more migration pathways. A connectivity map, starting from the most stable point defects, was developed in order to identify the rate-limiting step controlling the net diffusion rate in each crystallographic direction. The uranium self-diffusivity tensor was calculated by combining the defect formation energies , entropies, migration barriers and attempt frequencies. The fastest diffusion rate was determined to be a vacancy mechanism in the z crystallographic direction. The predicted uranium self-diffusivity for this mechanism agrees well with available experimental data. The diffusion mechanisms and rates identified in this study will inform fuel performance models of swelling and gas evolution.

Magnetic structures of Mn-rich and of Fe-rich TmMn6−xFexSn6 stannides with (Mn, Fe) kagome networks and related Sn119 hyperfine magnetic fields

Stannides ${\mathrm{TmMn}}_{6\text{\ensuremath{-}}x}{\mathrm{Fe}}_{x}{\mathrm{Sn}}_{6}$, with hexagonal ${\mathrm{HfFe}}_{6}{\mathrm{Ge}}_{6}$-type structures, were studied by x-ray and neutron diffraction, magnetic measurements, and by $^{119}\mathrm{Sn}$ M\"ossbauer spectroscopy. Transition metal atoms form kagome networks in (001) planes with an intraplanar ferromagnetic coupling of their moments. At temperatures >\ensuremath{\sim}20 to 50 K, Mn-rich stannides ($x=0.4$, 0.6, 1.2) have an AFII easy-plane antiferromagnetic (AFM) structure, with interplanar couplings + + \ensuremath{-} \ensuremath{-} along the $c$ axis. The thulium sublattice orders magnetically at low temperature. The complexity of the resultant neutron diffraction patterns arises from a mixture of several magnetic phases, some being incommensurate. The Tm sublattice does not order >1.6 K in Fe-rich stannides ($x=4.25$, 4.5, 5.0). Fe-rich stannides have an AFI AFM structure, this time with interplanar couplings + \ensuremath{-} + \ensuremath{-}. The $M=\mathrm{Mn}/\mathrm{Fe}$ magnetic moments are directed along the $c$ axis for $x=5$ at any temperature. Further, neutron diffraction shows that moments rotate from the $c$ axis toward the basal plane >4.2 K with maximum rotation angles of \ensuremath{\sim}70\ifmmode^\circ\else\textdegree\fi{} and \ensuremath{\sim}55\ifmmode^\circ\else\textdegree\fi{} reached at \ensuremath{\sim}50 and \ensuremath{\sim}80 K for $x=4.25$ and 4.50, respectively. Transferred hyperfine fields at tin sites of ${\mathrm{TmMn}}_{6\text{\ensuremath{-}}x}{\mathrm{Fe}}_{x}{\mathrm{Sn}}_{6}$ stannides are the moduli of $^{119}\mathrm{Sn}$ vectorial hyperfine magnetic fields that are modeled for the AFI and AFII magnetic structures, assuming a random substitution of Mn with Fe. Models involve sums of dipolar-type and of isotropic vector components with simple assumptions about the model parameters. The transferred hyperfine magnetic fields at $^{119}\mathrm{Sn}$ nuclei are measured by M\"ossbauer spectroscopy. The hyperfine magnetic fields of Sn atoms, whose six transition metal nearest neighbors are ferromagnetically coupled, are predicted and observed to vary linearly with their number of Fe first nearest neighbors. The hyperfine magnetic fields on Sn atoms sandwiched between two AFM coupled kagome planes are expected proportional to $|{p}_{2}\ensuremath{-}{p}_{1}|$, where one of the two kagome planes contains ${p}_{1}$ Fe first nearest neighbors and the other ${p}_{2}$. Tin atoms with a ferromagnetic first nearest neighbor shell experience negative hyperfine fields in Mn-rich stannides, whereas they experience positive hyperfine fields in the Fe-rich stannides. This change is explained by a change of sign of the isotropic hyperfine magnetic fields which occurs when going from Mn- to Fe-rich stannides.