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Magnetocaloric Behavior in Ternary Europium Indides EuT5In: Probing the Design Capability of First-PrinciplesBased Methods on the Multifaceted Magnetic Materials Inna Bigun, Simon Steinberg, Volodymyr Smetana, Yaroslav Mudryk, Yaroslav Kalychak, Ladislav Havela, Vitalij Pecharsky, and Anja-Verena Mudring Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.6b04782 • Publication Date (Web): 27 Jan 2017 Downloaded from http://pubs.acs.org on January 31, 2017

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Chemistry of Materials

Magnetocaloric Behavior in Ternary Europium Indides EuT5In: Probing the Design Capability of First-Principles-Based Methods on the Multifaceted Magnetic Materials Inna Bigun,1,2 Simon Steinberg,3 Volodymyr Smetana,3 Yaroslav Mudryk,3 Yaroslav Kalychak,1 Ladislav Havela,2 Vitalij Pecharsky,3,4 and Anja-Verena Mudring3,4,* 1

Department of Analytical Chemistry, Ivan Franko National University of L’viv, Kyryla and Mefodia Str. 6, 79005 L’viv, Ukraine 2 Department of Condensed Matter Physics, Charles University, Ke Karlovu 5, 121 16 Prague 2, Czech Republic 3 Ames Laboratory, U.S. Department of Energy, Iowa State University, Ames, Iowa 50011-3020, USA 4 Department of Materials Sciences and Engineering, Iowa State University, Ames, Iowa, 50011-2300, USA

Abstract The most favorable structures and the types of magnetic ordering predicted from firstprinciples-based methods in a family of closely related transition-metal-rich indides EuT5In (T = Cu, Ag, Au) are gauged against relevant experiments. The EuT5In compounds adopt a different structure for each different coinage metal – EuCu5In (hR42; R3m, a = 5.0933(7), c = 30.557(6) Å), EuAg5In, (oP28; Pnma, a = 9.121(2), b = 5.645(1), c = 11.437(3) Å), and EuAu5In (tI14; I4/mmm, a = 7.1740(3), c = 5.4425(3) Å) crystallize with the Sr5Al9, CeCu6 and

YbMo2Al4

structure

types,

respectively.

EuCu5In

and

EuAg5In

order

antiferromagnetically at TN = 12 and 6 K, respectively, whereas EuAu5In is ferromagnetic below TC = 13 K. EuCu5In exhibits complex magnetism: after the initial drop at TN, the magnetization rises again below 8 K, and a weak metamagnetic-like transition occurs at 2 K in µ0H = 1.8 T. The electronic heat capacity of EuCu5In, γ = ~400 mJ/mol K2, points to strong electronic correlations. Spin-polarized densities of states suggest that the magnetic interactions in the three materials studied are supported via mixing 4f and 5d states of Eu. A chemical bonding analysis based on the Crystal Orbital Hamilton populations reveals the tendency to maximize overall bonding as a driving force to adopt a particular type of crystal structure.

Introduction One of the central objectives of materials research is the identification of structural preferences in solids to facilitate focused syntheses of materials with desired properties.1 In

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particular, compounds with intrinsic disorder may serve as model systems for advanced combinatorial syntheses combined with quantum chemical methods to address the “coloring problem,” and for the targeted manipulation of material properties via chemical substitutions.1,2 The structural arrangements in such materials are dominated by the site and bond energies, which affect the adoption of a given structure type and chemical compositions, and, ultimately, physical properties.1 For instance, based on their respective compositions, complex metallic alloys (CMAs) show a number of useful properties that range from giant magnetocaloric effects3,4 and thermoelectricity5-7 to unusual plasticity.8 Even though the (electronic) stabilities for certain CMAs can be correctly addressed by the Hume-Rothery concept,9 the rationalization of the structural and site preferences in a number of structurally complex solids goes beyond this principle.10 Development and applications of several other valence electron treatments for intermetallic compounds, including Wade´s rules11-13 and the Zintl concept,14-17 emphasize the need for universal prescriptions to understand and, hence, predict the structure-bonding relationships and stability tendencies for solids. Yet, the majority of simple approaches apply to only limited numbers of intermetallic compounds18 and are quite restricted in their abilities to predict the structural preferences when valence electron counts are identical. One structurally diverse19-23 class of intermetallic compounds that also reveals a range of interesting properties, e.g., hydrogen storage capabilities, heavy fermion anomalies, and Kondo effects,22,24,25 is a family with the general formula RT5M (R = rare-earth element, T = transition metal; M = (post-)transition metal, for some cases, mixed with T). Our impetus to isolate a representative of the rhombohedral EuNi5In-type26 for the unknown EuCu5In was motivated by a recent examination on the Eu–Ni–In system indicating that the intercalation of hydrogen has a substantial impact on the structure as well as the physical properties of EuNi5In.27 On the other hand, investigation28 of the Eu−Au−In system points to the presence of a tetragonal, YbMo2Al4-type29-derived disordered crystal structure for EuAu5In, which has the same valence electron count as tentative EuCu5In; yet, one has to keep in mind that the influence of relativistic effects increases considerably from copper to its heavier homologue gold.30 Due to the relativistic effects31,32 gold exhibits substantial 6s−5d orbital mixings in its bonding, which were also encountered in the bonding analyses of different gold-rich complex intermetallic compounds.33-37 The exploration28 of the Au-rich areas for the ternary system Eu−Au−In was further encouraged by the previous discoveries of the diamond-like Au networks in Ae(Au,M)7 and Ae2(Au,M)9 (Ae = Sr, Ba, Eu; M = Al, Zn, Ga, Cd, In, Sn; not all combinations),38-43 the indide EuAu17.7In4.344 and the stannides R3Au7Sn3 (R = Y, Gd)45 2 ACS Paragon Plus Environment

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pointing to a large potential for the presence of unknown ternary Au-rich materials with rareearth and post transition elements. Inspired by more recent research using first-principles based methods to predict the theoretical stabilities of unknown 18-electron ABX compounds,46 the thermoelectric performances of binary A1B1 materials,47,48 the origins of the giant magnetocaloric effect in Fe2P-based materials49 or the occurrence of topological insulators,50 we probed the structural preferences for EuT5In (T = Cu, Au) on the basis of the total energies of diverse “EuT5In” (T = Cu, Au) models derived from DFT-based optimizations. The crystal structures predicted from total energies for the different models are actually in excellent agreement with the experimental determinations of the crystal structures for EuT5In (T = Cu, Au). In addition to the predictions of the structural preferences for EuT5In (T = Cu, Au), the electronic band structures of the models corresponding to the lowest total energies were inspected to project the physical characteristics for these materials. The magnetic ground states suggested by the aforementioned computations agree with the results of the magnetic properties measurements suggesting antiferromagnetic and ferromagnetic ground state for EuCu5In and EuAu5In, respectively; however, detailed investigation of the temperature-dependent magnetization and heat capacity data for the former compound reveal a complex metamagnetic-like behavior for EuCu5In. To detect possible structural transitions induced by replacements of Cu by its heavier homologues (Ag, Au), we also investigated the crystal structure and physical properties of a potential EuAg5In. In this contribution, we provide the results of our survey of the series EuT5In (T = Cu, Ag, Au).

Experimental Details Computational Details. Electronic structure calculations have been accomplished utilizing density functional theory (DFT)-based methods. Because the crystal structure of EuAu5In features disordered 4d sites with mixed Au/In occupancies, diverse ordered models representing the composition “EuAu5In” have been developed. Consequently, indium atoms have been assigned solely to the 4d sites in all models, which have been evaluated to identify the maximal number of the heteroatomic Au−In contacts (all structural parameters of the “EuAu5In” models are provided in the SI, Tables S7−S12). Furthermore, total energies have been estimated to verify the structural model evolved from the solutions and refinements of the X-ray intensity data sets. In each “EuAg5In” model the indium atoms have been assigned to a particular anion site (8d, 4c, 4c, 4c, or 4c), while the total energy of each “EuAg5In” model was calculated to identify the electronically most favourable structure. 3 ACS Paragon Plus Environment


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Full structural optimizations and spin-polarized band structure calculations were performed with the projector augmented wave (PAW) method of Blöchl51 as adopted in the Vienna ab initio simulation package (VASP).52-56 Correlation and exchange were described by the generalized gradient approximation of Perdew, Burke and Ernzerhof (GGA−PBE).57 Although this functional type has shown its strength in total-energy calculations of magnetic materials, yet, the strong correlations of localized electrons are usually underestimated by exchange-correlation-functionals in DFT-based computations.58 Thus, an effective on-site Coulomb interaction term (Ueff = 3.00 eV) was added to the Kohn-Sham Hamiltonian of all spin-polarized computations to account for the strong correlations within the Eu-4f states.28,5961

A preliminary scan of different Ueff has been performed in our previous work28 in order to

find optimal value corresponding to the experimentally observed and predicted position of Eu-4f bands.62 The energy cutoff of the plane wave basis set was 500 eV, while the first Brillouin zones were sampled by starting meshes of 4 × 4 × 4 up to 8 × 8 × 8 k-points. Full structural optimizations were completed until the energy difference between two iterative steps fell below 10-7 eV/cell. Chemical bonding analyses of the band structures for the “EuAg5In” and “EuAu5In” models with the lowest total energies, the “EuCu5In”-I model, and EuCu5In were completed based on the crystal orbital Hamilton populations (−COHP) and their respective integrated values, which were computed using the tight-binding linear-muffin-tin-orbital (TB-LMTO) method with the atomic sphere approximation (ASA) in the Stuttgart code.63-65 Additionally the –ICOHP data for the selected systems were subtracted from the VASP calculations using the LOBSTER code66,67 to check for consistency. In the –COHP method the off-site projected DOS are weighted with the corresponding Hamilton matrix elements to reveal bonding, nonbonding and antibonding interactions between atom pairs.58,68 The structural and positional parameters of all models, for which the structures were fully optimized using VASP, were transferred to the TB−LMTO−ASA software package with the aid of the WXDragon program.69 The Wigner-Seitz (WS) spheres were generated automatically, while the computations also included empty spheres and optimizations of the overlapping potentials to guarantee optimal approximations of full potentials. The basis sets used the following orbitals (orbitals treated in the downfolded technique70 are in parentheses): Cu-4s/-4p/-3d, Ag-5s/-5p/-4d/(-4f), Au-6s/-6p/-5d/(-5f), Eu-6s/(-6p)/-5d, In-5s/-5p/(-5d)/(-4f) with the corresponding WS radii [Å]: Cu, 2.73−2.57; Ag, 3.06−2.90; Au, 3.10−2.93; Eu, 4.00−3.60; In, 3.09−3.00. As the analyses of the magnetic properties and the spin-polarized DOS of EuT5In (T = Cu−Au) pointed to localized Eu-4f atomic orbitals (AO), the latter were treated as 4 ACS Paragon Plus Environment

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core-like states within all TB−LMTO-based band structure calculations − an approach that has been previously applied to other rare-earth metal-containing materials.28,45,61,71-73 Reciprocal space integrations were completed with the tetrahedron method74 using sets of 12 × 12 × 12, 15 × 15 × 15, 6 × 12 × 6, 24 × 24 × 24, 24 × 24 × 24 and 8 × 4 × 8 k-points for EuCu5In, “EuCu5In”-I, “EuAg5In”, “EuAu5In”-I, “EuAu5In”-III and “EuAu5In”-IV respectively. Syntheses. The starting materials - copper (99.99%, Alfa Aesar), silver (99.99%, Alfa Aesar) and gold (99.999%, BASF) pieces, europium (99.9%, MPC, Ames Laboratory) and indium ingots (99.999% Alfa Aesar) - were stored and handled under dry argon atmosphere (H2O < 0.1 ppmv) in a glove box. The europium powder was obtained from filing larger ingots, which were mechanically polished prior each sample preparation. Stoichiometric mixtures of ~ 100 mg to 1g total were loaded in pre-cleaned, one-side welded tantalum tubes that were closed inside the glove box, subsequently sealed by arc-welding under Ar and, then, enclosed by evacuated silica Schlenk flasks or silica jackets. The following temperature programs were applied to obtain high purity samples of EuT5In (T = Cu, Ag, Au): heat to 800–900 °C in four hours, keep that temperature for three-four hours, cool to room temperature with a rate of 50 °C/h. The products appeared as silver (Ag and Au) or yellow-brown (Cu) powders containing crystals with metallic luster, and remained stable against exposure to air and moisture similar to the behavior of other gold-rich phases.45 X-ray Diffraction Studies. The purities of the products were checked based on phase analysis of sets of powder X-ray diffraction data (PXRD), which were collected on STOE STADI P (Stoe & Cie, Darmstadt, Germany; area detector; Cu-Kα1 radiation, λ = 1.54059 Å) and Philips X’Pert (Phillips, Amsterdam, The Netherlands; strip detector, Cu-Kα1 radiation, λ = 1.54059 Å) diffractometers at room temperature. Powders of the products were dispersed on Mylar sheets, which were placed between two split Al rings. An external silicon standard was used for an accurate determination of the lattice parameters. The WinXPow software package75 was employed for the handling of the raw powder X-ray intensity data sets and the phase analyses of the samples. The latter confirmed high yields of the reaction products: phase pure EuAg5In and EuAu5In and negligible amount of an unknown non-magnetic impurity in EuCu5In (Figure S1). The crystal structures of all compounds were determined from solutions and refinements of sets of single crystal X-ray intensity data, which were collected on an APEX CCD diffractometer (Bruker Inc., Madison, USA; Mo-Kα radiation; λ = 0.71073 Å) with at least 800 frames in φ- and ω-scan modes and exposures of 15 s per frame at room temperature 5 ACS Paragon Plus Environment


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(~ 296 K). The crystals (~50 µm) were selected from the bulk samples and mounted on glass fibres, while the qualities of the selected single crystals were controlled by preliminary testing based on 36 frames. The raw reflection intensities were integrated with the aid of the SAINT program as implanted in the SMART76 software package, while multi-scan absorption corrections were carried out with the program SADABS.77 Applications of the extinction conditions with the aid of XPREP algorithms within the SHELXTL suite78 to the X-ray intensity data sets lead to the identifications of the space groups R-3m (no. 166), Pnma (no. 62) and I4/mmm (no. 139) for EuCu5In (I), EuAg5In (II) and EuAu5In (III), respectively. The crystal structures were solved by means of direct methods (SHELXS-97), the same program79 was used for full-matrix least-square refinements on F2 including anisotropic atomic displacement parameters. The position of In in II was assigned due to the distinctly different thermal ellipsoids and in full agreement with the other compounds of the structure type. This assignment is further substantiated by DFT-based calculations (see Structural and Site Preferences in the EuT5In Series). In initial refinements of the structure solution of III the assignments of indium atoms on the 4d sites resulted in low anisotropic atomic displacement parameters and high residual electron density peaks for that position; however, refinements of the 4d sites with gold lead to non-reasonable anisotropic atomic displacement parameters for gold. Accordingly, this position was refined with mixed Au/In occupancies with common atomic parameters for both gold and indium. The composition of III derived from the structure solutions and refinements of the X-ray intensity data sets was further corroborated by elemental analyses based on an energydispersive X-ray spectrum (below). Examinations of the refined structure models using the ADDSYM algorithm implanted in the PLATON software package80 did not reveal any possible higher symmetry for any of the reported compounds. Table 1 contains details of the single crystal X-ray measurements and results of the refinements of I, II and III, while atomic positions and equivalent anisotropic displacement parameters of all compounds are listed in Table 2. Energy Dispersive X-ray Analyses. Quantitative analysis based on integrations of the peaks of the energy-dispersive X-ray (EDX) spectrum for EuAu5In was undertaken to corroborate the composition determined from the structure solutions and refinements of the single-crystal X-ray intensity data sets for that compound. A fine powder of III was dispersed on a conductive carbon layer, which was mounted on a sample holder, and subsequently transferred to a JEOL JSM-6010PLUS/LA scanning electron microscope (SEM) equipped 6 ACS Paragon Plus Environment

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with an EDX spectroscope. The sample was also imaged using the secondary electrons. Details of the measurement, an image of the sample surface (Figure S2), an EDX spectrum (Figure S3) and quantitative analyses of the compositions close to and at the sample surface of III (Table S2) are provided in the Supporting Information. Physical Properties Measurements. Magnetic measurements were performed by means of a Magnetic Property Measurement System (MPMS, Quantum Design, San Diego, USA) on powder samples with approx. mass of 10-20 mg, which were fixed inside of glass capillaries with 2 mm diameter. The contribution of the latter can be neglected due to its weakly diamagnetic signal. The magnetic measurements were performed in the temperature range 2300 K and in applied magnetic fields as high as 7 T. The heat capacity measurements were carried out for T = Cu, Au on the Quantum Design Physical Property Measurement System (PPMS, Quantum Design, San Diego, USA).

Results and Discussion Structural and Site Preferences in the EuT5In Series. The applications of DFT-based methods to forecast the properties of hypothetical compounds has found its way into synthesis planning as it allows predicting compound formations, accelerating the discoveries of new materials.46,81 Because recent explorations of the Eu−Ni−In26,27 and the Eu−Au−In28 systems revealed two different structure types, while maintaining the same overall EuT5In compositions, the total energies have been evaluated for two possible EuCu5In models with both the EuNi5In26 and the EuAu5In28 structures (Figure 1). This approach will reveal if the adoption of a structure type for the unknown EuCu5In is preferred due to steric (Ni (1.24 Å) and Cu (1.32 Å) have similar atomic covalent radii82) or electronic (Cu and Au have the same valence electron counts) reasons. Prior to the evaluation of the structural preferences between the EuNi5In- and EuAu5In-based models of EuCu5In, the “EuAu5In” scheme that corresponds to the lowest total energy has been first identified for the reason that the determination of the crystal structure of III revealed the presence of one disordered atomic site (Wyckoff position 4d; Table 2). Because more recent research28 on a series of representatives adopting the YbMo2Al429 type of structure revealed a clear site preference for the mixed Au/In occupancy on the 4d rather than the 8h positions, Au/In disorders have been simulated solely for the 4d sites (Figure S4 and Tables S7−S12). Among intermetallic compounds with mixed atomic sites the models of the hypothetical structures with the minimal number of homoatomic interactions are of great interest, as the scheme with the maximal number of heteroatomic 7 ACS Paragon Plus Environment


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contacts tends to have the lowest total energy and, therefore, is expected to provide the most favorable structure model to compare to the experimentally determined one.28,83-86 A topological analysis of the coordination spheres for the 4d sites brings to light that a maximum of 10 and minimum of 8 heteroatomic Au−In contacts per In atom can be achieved in the structure of III. To verify that the lowest total energy is obtained for the “EuAu5In” scheme with the maximal number of the heteroatomic Au−In interactions, the total energies have been determined for different “EuAu5In” models, for which the numbers of the Au−In interactions vary from 8 to 10 per indium atom (Figure S4). A comparison of the total energies for all schemes bares that the structures of “EuAu5In”-I, “EuAu5In”-III and “EuAu5In”-IV have the largest relative contributions of the Au−In contacts to all Au/In−Au/In interactions and the lowest total energies. “EuAu5In”-I corresponds to the lowest total energy of all inspected “EuAu5In” schemes and it was chosen as a starting point for the considerations on the structural preferences between the EuNi5In-type and the EuAu5In-type for EuCu5In and the electronic band structure of III. In addition to the models of “EuAu5In”-I to “EuAu5In”-VI, the total energy was also evaluated for a hypothetical rhombohedral EuNi5In26-type “EuAu5In” representative (“EuAu5In”-rh) to identify the structural preferences between the rhombohedral and the tetragonal structure types for EuAu5In. A comparison of the total energies for “EuAu5In”-rh and “EuAu5In”-I indicates that the tetragonal one is preferred over the EuNi5In-type species. Because “EuAu5In”-rh and “EuAu5In”-I have the same valence electron (VE) counts and VE concentrations, which hinder the applications of electron counting rules to forecast and to justify the structural preferences for this particular system, both models were examined for the presence of steric effects (“ideal packing of atoms”) in their respective crystal structures. The space filled by the atoms within the unit cell was calculated as87 SF =

4π 3V

∑ with as the

atomic covalent radius82 of the atom i, as the amount of the atoms of sort i and V as the volume of the unit cell from the DFT-based structure optimizations (see “Computational Details”). Additional and more accurate evidence of the compactness of an atom packing within a given crystal structure comes from the density of the respective material,87 which was evaluated using the unit cell volumes determined by the DFT-based structure optimizations (Table 3). The density of the structure model of the tetragonal “EuAu5In”-I is higher than that of the rhombohedral “EuAu5In”-rh (Table 3). Accordingly, a denser packing of atoms (“highest space filling”) is expected for tetragonal species of EuAu5In; yet, in the case of the Cu8 ACS Paragon Plus Environment

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containing models, there is no clear difference between the calculated densities of EuCu5In and “EuCu5In”-I, since the densities of both models differ by less than 1%. This suggests that the screening for steric reasons is rather inapt for this particular system. Prominent examples, for which the influence of geometrical factors on the respective adopted crystal structure has also been considered to be significant, are Laves phases; however, analyses of structural relationships evaluated from purely geometrical factors underestimate (or, better, neglect) the impact of aspects arising from (strong) chemical bonding for a given system.88-90 Consequently, the structural preferences between the “EuAu5In”-I-type and the EuNi5In-type structures for EuT5In (T = Cu, Au) were not only examined based on geometrical factors, but also on the information about the total energies of the respective models calculated by DFTbased methods including aspects of (chemical) bonding.91 A comparison of the total energies for the rhombohedral EuCu5In and “EuAu5In”-rh and the tetragonal “EuT5In”-I (T = Cu, Au) models reveals that the lowest total energies are achieved for the schemes corresponding to the structures of EuCu5In and “EuAu5In”-I and, hence, predicts the rhombohedral structure for EuCu5In and a tetragonal structure for EuAu5In. Indeed, the experimental determinations of the crystal structure for I indicate a rhombohedral EuNi5In26-type structure for EuCu5In and agree with the predictions based on the total energy computations of the different models. Note that the calculated densities (Table 3) of the EuCu5In and the “EuAu5In”-I models show only minor deviations from those observed for the crystal structures of I and III, respectively (Table 1). The energy difference of 392 meV between the total energies of EuCu5In and “EuCu5In”-I suggests a significant influence of (chemical) bonding on the electronic structures of the different models and its origin will be examined in more detail below (see Electronic Structures section). In addition to the evaluation of the preferences to adopt a certain structure for EuT5In (T = Cu, Au), we also probed the magnetic ground states for the structure models of EuCu5In and “EuAu4In2”. The crystal structure of the latter model is derived from that of III (YbMo2Al4-type29) through assignments of full indium occupations on the disordered Au/In positions (Wyckoff position 4d; Table 2; computational details of the structure optimizations and electronic band structure calculations for that model have been reported elsewhere28). Assuming that the magnetic moments arise solely from the spins of the Eu 4f electrons, the total energies of EuCu5In and “EuAu4In2” models correlating to both ferromagnetic and antiferromagnetic ground states (Figure S5) were computed. The AFM EuCu5In model is 27.2 meV/cell lower in total energy than the FM structure. An analog examination of the total energies for the FM- and AFM-“EuAu4In2”-models revealed that the total energy of the 9 ACS Paragon Plus Environment


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ferromagnetic structure is 8.2 meV/cell lower than that of the AFM model. Hence, the ground states of copper- and gold-containing compounds, respectively, are AFM and FM. In fact, an analysis of the temperature-dependent magnetization data for EuT5In (T = Cu, Au) confirms the predictions based on the total energy computations, because EuCu5In and EuAu5In undergo paramagnetic-antiferromagnetic and paramagnetic-ferromagnetic transformations, respectively (see Physical Properties). To probe for the presence of possible structural transitions from the EuCu5In- to the YbMo2Al4-type within the series EuT5In (T = Cu, Ag, Au), we also investigated the structural preferences for the compound with the corresponding composition in the Eu−Ag−In system; yet, the structure solutions and refinements of the X-ray intensity data sets for single crystals selected from samples loaded as “EuAg5In” revealed a CeCu6-type92 structure for II. An accurate location of the indium sites in the crystal structure of II from the solutions and refinements of the single-crystal X-ray intensity data sets is difficult, because Ag and In have nearly identical atomic X-ray scattering factors.93 Also, geometrical analysis of the coordination spheres for the anion sites in the structure of II does not provide further hints for the identification of the indium positions due to the nearly identical covalent radii of the elements (Ag: 1.45 Å; In: 1.42 Å82) and was applied only for comparison with similar compounds containing Ag and/or In. The only and rather indirect hint was the In (Zn,Sn) position in the RCu5M series.94 To provide further justification for the assignments of indium atoms on the 4c sites (Table 2), the total energies of different “EuAg5In” models, in which one of the positions was fully or partially occupied by In resulting in four In atoms per unit cell for each model, have been evaluated. In this approach the scheme corresponding to the lowest total energy will provide the most favorable structure to compare to the experimentally determined model.28,83 Prior to all total energy calculations full structural optimizations including the atomic coordinates along with the unit cell volumes and shapes have been accomplished for all “EuAg5In” models (Table 4). A comparison of the total energies for all models reveals that the In1 Theor. model, in which the indium atoms reside on the same positions as suggested by close inspections of the thermal displacement parameters in the refined crystal structure of II, corresponds to the lowest total energy. Furthermore, the structural optimizations with In in that position lead to the lattice parameters that are the closest to the experimentally determined lattice constants. The total energy differences are rather large to guarantee the preferred site occupation of In in the “selected” position; however, partial, especially, minor mixed occupations of some 10 ACS Paragon Plus Environment

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positions by Ag and In as well as existence of some solid solution cannot be completely ruled out. In that light it is worth noting that two such representatives with other group 11 metals, namely, SrAu4.3In1.735 and UCu5.3Ga0.7,95 have been reported. The last example is notable due to the truly random distribution of Ga and Cu in the structure. On the other hand, Au and In atoms, which have similar atomic covalent radii (In: 1.42 Å; Au: 1.36 Å),82 show almost total separation and mix just in one position in the crystal structure of SrAu4.3In1.7.35 In summary, an evaluation of the total energies computed by means of DFT-based methods for diverse “EuT5In” (T = Cu, Au) models predicts a rhombohedral EuNi5In26-type structure for EuCu5In and a tetragonal structure for EuAu5In. This outcome is in fair agreement with the experimental determinations of the crystal structures for I and III, which will be briefly inspected in the following. In addition, to the descriptions of the crystal structures for I and III, a concise portrayal of the “EuAg5In” structure model corresponding to the lowest total energy is also provided. Structural Details. EuCu5In (I) formally belongs to the Sr5Al9 structure type96 and its crystal structure is best described as intergrown slabs of the CaCu5-, MgCu2- and NiAs-types (an analysis of the stacking of the intergrowth segments in the isostructural EuNi5In has been reported elsewhere26).97-99 The structure of I features Cu tetrahedral formations: a unit of two face-sharing Cu4 tetrahedra is connected via a corner to a third Cu4 tetrahedron. These Cu4 triple tetrahedral units of composition [Cu6/2Cu2] are connected via common vertices to form double 2D Kagomé nets parallel to the ab-plane (Figure 1a). The two crystallographically distinct europium sites in the structure of I differ in the numbers of surrounding atoms and the geometry of their respective coordination spheres. In particular, each Eu2 atom is surrounded by 12 Cu4 tetrahedra or 12 Cu1 atoms forming a hexagonal prism, which is capped axially (hexagonal faces) and equatorially (rectangular sides) by two In and six Cu3 atoms, respectively. Eu1 is surrounded by eight Cu4 tetrahedra and the coordination polyhedron is a Cu6In6 icosahedron with six Cu-capped In3 faces or, alternatively, six equatorially, two basecapped pentagonal antiprism (Figure S10). To date, the Sr5Al9 structure type has been only adopted by nine compounds (ICSD database)94 that belong to two different groups if classified by their formal cation/anion ratio: the first one comprises alkali- and alkaline-earth-containing members and the compositions A5M9, while the second class includes compounds with the formula RT5M. The variation of the compositions does not reveal any “magic number” in terms of valence electron counts even within any subgroup; yet, the c/a ratio for representatives of both groups is almost 11 ACS Paragon Plus Environment


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identical, ~6.05, indicating the major influence of geometric factors on the structure formation. The relative changes of the Eu environment within the series EuNi5In26, EuCu5In and, finally, EuCu5Cd23 are striking: there is an evident increase of certain interatomic contacts and the unit cell parameters from EuNi5In to EuCu5In. The indicative changes appear in the Eu−In interatomic contacts (+3–4 %). On the other hand, the differences in the Eu–Cu distances and the unit cell parameters between EuCu5In and EuCu5Cd are negligible (0–0.5 %). EuAg5In (II) crystallizes with the CeCu6 structure type92 and is the second silver-containing – beside the solid solution CeCu5-xAgx100 (x < 1) – and the first Ag-rich representative of this type of structure. Similar to I, the class of compounds that adopt this structure type can be formally divided into two subgroups with and without post-transition elements, respectively. The vast majority of the compounds45 contain copper mixed with other transition elements (Au, Ni, Fe) and frequently form solid solutions. The Eu atoms reside on the Wyckoff site 4c, while clear assignments of the Ag and In atoms on the remaining Wyckoff positions through structure solutions and refinements of the single-crystal X-ray intensity data sets for II is difficult due to the similar atomic scattering factors and covalent radii of silver and indium.82,93 Because the statistical occupation of these elements on the given atomic site in the structure of II cannot be excluded, the total energies of different “EuAg5In” models were evaluated using density functional theory (DFT)-based methods (Electronic Structures section) to address the site preferences in II. In the following the structure, which corresponds to the lowest total energy determined by the (DFT)-based computations, will be considered as a working model and used for comparison with the related disordered compounds.28,83 The structure of II consists of face- and vertex-sharing Ag4 and Ag3In tetrahedra that surround the europium atoms. Groups of three Ag4 agglomerates are connected via two common faces to trimers (Ag6, Figure 1b, violet), which share two common vertices with neighboring trimers forming Ag6 chains along the a-direction. Every such chain is connected to six neighboring chains via Ag3In tetrahedra. This position rationalizes the location of In playing the role of a connecting link. Note that two Cu4 tetrahedra of each Cu trimer in the structure of I are also condensed via one common face in analogy to the Ag6 units in II, whereas the third Cu4 component has solely one Cu atom in common with the remaining Cu5 unit (Cu8, Figure 1a). The number of nearest neighboring atoms for both Ag and In positions is 12; however, only the latter accommodates four Eu atoms in the first coordination sphere. Europium is surrounded by 19 neighboring atoms including 15 silver and four indium atoms.

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The Ag–Ag distances range from 2.756(2) to 3.006(2) Å, whereas the Ag–In separation is from 2.765(2) to 3.056(1) Å. At the first glance one may expect partial anion exchanges between these positions; however, evaluations of the total energy for diverse models do not provide any indication of partial anion exchange. Further reasonable explanation evolves from an inspection of the local atomic environment and bond saturation. The shortest Ag–In contact (2.765(2) Å) is surrounded by three Eu atoms, while all other Ag– In contacts have five common neighbors, two Eu and three Ag. A very similar situation was observed for the decagonal approximant Na8Au9.8Ga7.2,101 which contains extremely short M– M (M = Au or Ga) bonds surrounded by a small number of electropositive elements. The In positions are also well separated from Eu, 3.521(1)–3.774(1) Å, while Eu–Ag distances are widely distributed between 3.217(1) and 3.692(1) Å. EuAu5In (III) crystallizes with the YbMo2Al4 type of structure,29 which, similarly to CeCu6, exists with and without post-transition elements and can be separated into two groups:21,59,102105

full occupations of the three crystallographic positions (2a, 4d and 8h) by different

elements lead to compounds with the stoichiometry XY2Z4; however, good miscibility of Au with p or group 12 elements allows formations of solid solutions with wide ranges of compositions reaching XYZ5. The 4d positions in the crystal structure of EuAu5In are partially disordered and commonly occupied by Au and In atoms in nearly 50/50 proportion. The analysis of the EDX spectrum for the layers at and close to the surface of a EuAu5In single-crystal confirmed the presence of all component elements and, furthermore, significant deviations from the stoichiometry of XY2Z4 (Figure S3 and Table S2). The crystal structure of III is built of Eu@M20 polyhedra (D4h, Figure 1c) sharing common faces along the c direction (Au4 squares) and body diagonals (rhombic Au2M2 ≈ Au3In). The Eu@M20 polyhedron represents truncated tetragonal Au12 bipyramids surrounded by M8 tetragonal prism (orange and blue atoms respectively). The Eu and the (Au/In)2 sites are maximally separated (3.8364(1) Å in comparison to 3.1066(4) Å for dEu–Au1), while every atom of the Eu coordination sphere is common for one more identical polyhedron. From this point of view the structure is closer to the triel-rich alkali-metal-gold ternaries AAu2Ga4 forming the similar rows of stacking polyhedra106,107 than to the CeCu6-type EuAg5In. Physical Properties. Because the crystal structures of the three EuT5In (T = Cu, Ag, Au) compounds are different for each T, different physical behavior of each compound is expected. Since EuCu5In and EuAu5In were obtained in a nearly single phase condition, they 13 ACS Paragon Plus Environment


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were studied in detail using magnetization and heat capacity measurements. The EuAg5In sample contained a magnetic impurity phase (possibly EuO) and, therefore, was not studied in detail. EuCu5In (I). The magnetic measurements performed as a function of temperature, M(T), in an applied magnetic field of µ0H = 0.1 T, indicate antiferromagnetic (AFM) type of magnetic ordering in EuCu5In. The Néel temperature, TN, is 12 K. It is clearly seen, however, that the magnetic ground state is not simple AFM, because after the initial drop at TN the magnetization starts to rise again at T1 = 8 K. The increase of magnetic field to 1 T does not change the M(T) dependence – both the peak at TN = 12 K and the rise of magnetization below 8 K are still observed (Figure ). The linear temperature dependence of the inverse susceptibility indicates that the Curie-Weiss law is followed between 50 and 300 K. The linear fit of χ-1(T) in this range yields the effective moment peff = 8.1 µB/f.u. and the Weiss temperature θp = -13 K (inset to Figure ). The peff value corresponding to 4f7 (theoretical value 7.94 µB) indicates that europium is divalent in EuCu5In and the θp value confirms antiferromagnetic interactions in this compound. However, the field dependence of magnetization, M(H), at T = 2 K (Figure ) shows that the magnetic properties of EuCu5In are more complex than the low-field data indicate. While the M(H) is essentially linear up to µ0H = 1.6 T, in agreement with the AFM state, a weak but clear metamagnetic-like transition occurs at critical field µ0Hcr = 1.8 T. Above 2 T, the magnetization continues to increase with field, although the dM/dH rate above Hcr is lower than below 1.6 T, and has a weak tendency to saturation. Considering the divalent nature of Eu (gJ = 7 µB/atom), the magnetic moment at 7 T reaches ~55 % of its full value, so the Eu moments are not fully aligned above the metamagnetic transition. As the f7 configuration has only the spin moment and the orbital moments are missing, there can be only a weak magnetocrystalline anisotropy, which does not restrict non-collinearity of the moments. Hence, only exchange interactions (RKKY interactions of variable sign) are determining the moments directions and resisting the aligning effect of external magnetic field, which leads to a gradual rotation of moments, not to spin-flip transitions. More insight is provided by the heat capacity, Cp, measurements. The two magnetic phase transitions can be clearly identified on the Cp(T) dependence: a major anomaly appears at TN and there is a second anomaly around T = 5 K (Figure ). However, a closer look using the Cp/T vs. T2 plot shows that the low-temperature anomaly essentially consists of two closely located peaks, a weaker one at 4 K and a stronger one at 6 K (Figure ). Cp measurements performed in magnetic fields show that the anomalies respond to the magnetic 14 ACS Paragon Plus Environment

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field in a different way. The anomaly at TN is rapidly suppressed by applied field and the entropy is transferred towards higher temperatures as in ferromagnets. The anomalies at low temperatures also shift to higher temperatures, but the development is only incremental and the anomaly is actually more pronounced in higher fields (Figure ). Moreover, it appears that the double-peak structure of the anomaly changes into a single peak (inset to Figure ), due to either suppression of the 4 K peak or merging it with the 6 K peak. Because the magnetic contribution to the low-temperature heat capacity of EuCu5In is strong and extending to very low temperatures, it is not possible to determine the electronic contribution to the specific heat accurately using the common Cp/T vs. T2 plot method close to the low-T limit. However, since no crystal electric field effects occur for the f7 configuration, no magnetic entropy should appear in the paramagnetic state. Having still a reasonable linear part of Cp/T vs. T2 up to 400 K2, we try to extrapolate from the paramagnetic state to T = 0. The determined γ-coefficient in EuCu5In is close to 270 mJ/mol K2, which is one order of magnitude higher compared to what is expected for a typical transition metal. The slope of Cp/T vs. T2 gives also an estimate for the Debye temperature of ΘD = 256 K. The localization of the 4f states which form the full f7 moment means that they cannot contribute to the Fermi level electron density and their bare density of states cannot therefore affect the Sommerfeld coefficient γ. Electron-electron correlations, which may be responsible for the many-body enhancement (via valence fluctuations or Kondo effect), are also not expected to be important in such a situation, and this phenomenon is worth to be explored by microscopic methods. The magnetocaloric effect (MCE) was calculated using heat capacity difference for three different magnetic field changes, 0-0.5 T, 0-2 T, and 0-5 T. However, the MCE for 0.5 T was found too weak for the analysis. The calculated magnetic entropy change and the adiabatic temperature change are presented in Figure 6. The observed MCE behavior correlates well with the complex magnetic structure suggested above. Namely, there are two sign inversions in the temperature dependence of the MCE for µ0H = 0-2 T: a weak direct effect changes into an even weaker inverse effect at 5 K before a strong direct effect is observed around 15 K. For the 5 T data there is technically no sign inversion but the shape of the MCE curve is similar to the one for 2 T. This reflects the complicated magnetic phase diagram and in particular the fact that the sign of exchange interactions is temperature and magnetic field dependent in EuCu5In. When the magnetic field increases to 5 T, the ferromagnetic alignment dominates and only the direct effects are observed. However, the AFM component remains present, as judged by the value of net magnetic moment at 2 K (Figure ). 15 ACS Paragon Plus Environment


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EuAg5In (II). The magnetization of EuAg5In measured as a function of temperature in the field of 0.1 T reveals a cusp at TN = 6 K which we interpret as an antiferromagnetic transition (Figure ). The anomaly at higher temperatures can be attributed to small amount (< 1 %) of EuO (ferromagnet with TC = 77 K) present in the sample. Its extrinsic character is evidenced by the type of anomaly in the 1/χ(T) representation. The field dependence of magnetization at T = 2 K shows that no ferromagnetic alignment is reached up to 7 T. An anomaly appearing at µ0H = 3 T indicates that the magnetization processes change at this field (Figure ). This can be again taken as an indication of a more complex magnetic phase diagram. The Curie-Weiss fit of the inverse susceptibility between 100 and 300 K gives the peff. = 7.7 µB/f.u. and θp = 3 K (Figure ). EuAu5In (III). Unlike the previous two compounds, EuAu5In is a simple ferromagnet with a Curie temperature of TC = 13 K (inset to Figure 9.). The M(H) dependencies measured at T = 2, 5, 8, and 11 K (Figure 1) show the fast approach to saturation to a value of ~7.5 µB/Eu, which somewhat exceeds the ideal atomic moment 7.0 µB. The reason can be the exchange polarization of non-f states. The Curie-Weiss behavior in the paramagnetic range can be modelled using peff. = 8.4 µB/f.u. and θp = 13 K (Figure 9.), the latter being consistent with the ferromagnetic interactions. The heat-capacity of EuAu5In measured in 0, 0.5, 1, 2, and 5 T shows a λ-type anomaly, indicating the second-order transition at TC, which is smeared out and entropy shifted to higher temperatures with applied magnetic field (Figure 1). No other anomalies are observed. As in EuCu5In, due to large magnetic contribution to specific heat, it is not possible to accurately determine the coefficient of electronic specific heat, γ, from the Cp/T vs. T2 plot. The magnetocaloric effect in EuAu5In was calculated using the heat-capacity data (Figure 1). It is typical for a ferromagnetic second-order transition. The magnetic entropy change scales with H2/3. For ∆H = 0-5 T magnetic field change the maximum magnetic entropy change is -6.3 mJ/g K and the maximum adiabatic temperature change is 5 K (at TC = 13 K). These values indicate a moderate magnetocaloric effect in EuAu5In. It size is positively affected by high multiplicity of the paramagnetic state just above TC (due to crystal electric field absent), giving high entropy, R·ln(15), released by disordering.

Electronic Structures of the EuT5In (T = Cu, Ag, Cu) Compounds. The spin-polarized Density of States (DOS) and the Crystal Orbital Hamilton Population (COHP) of the EuT5In (T = Cu, Ag, Au) compounds were examined to identify the origins of the magnetic ordering 16 ACS Paragon Plus Environment

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phenomena and the structural preferences for these materials. It has been clearly demonstrated recently49 that a redistribution of the electron density around the Fermi level during the first order magnetic transitions may result in a formation of covalent bonds. The latter strongly reduce the magnetic moment of a magnetic element involved in bonding being the reason for the enhanced magnetocaloric effect. In other words electronic contributions due to DOS change at EF strongly influence crystallographic and magnetic behavior. Corroborating the predictions evolved from the comparisons of the total energies for diverse magnetic EuT5In (T = Cu, “Au”) models, the examination of the temperature dependent magnetization of EuCu5In and EuAu5In indicate antiferromagnetic and ferromagnetic ground states, respectively, for which the DOS will be discussed in the following. In addition to the analysis of the spinpolarized DOS curves for EuT5In (T = Cu, “Au”), the spin-polarized DOS will be evaluated for an “EuAg5In”-In1 Theor. model with an antiferromagnetic state that is indicated by a paramagnetic-antiferromagnetic transition at 6 K (see Physical Properties). In the cases of EuT5In (T = Ag, Au), the spin-polarized band structure calculations will be inspected in detail for the “EuAg5In”-In1 Theor. and the “EuAu5In”-I models, since the model corresponding to the lowest total energy represents the most preferable crystal structure to be compared to the experimentally determined one for intermetallic compounds with disordered positions.83 To reveal the influence of the local site and bond energies on the preferences to adopt a certain structure type within the EuT5In series, the (chemical) bonding analyses was completed based on the integrated values of the −COHP curves (ICOHP) for diverse “EuT5In” (T = Cu, Au) models. Densities of States (DOS). The spin-polarized DOS curves (Figure 13) of EuT5In (T = Cu, “Ag”, “Au”) resemble antiferromagnetic ground states for EuCu5In and “EuAg5In”-In1 Theor. and a ferromagnetic state for the gold-containing structure for the reason that the “spin-up” and “spin-down” contributions for the Cu- and Ag-containing structures superimpose, which is not the case for the “EuAu5In”-I model. The significant differences between the “spin-up” and the “spin-down” DOS in “EuAu5In”-I stem from the bands arising from the Eu-4f atomic orbitals (AOs), which, accordingly, may be regarded as the origin of the magnetic response for this structure. The Eu-4f bands exhibit relatively small dispersions leading to sharp peaks at 3.03 eV, 2.61 eV and 3.95 eV in the DOS of EuCu5In, “EuAg5In”In1 Teor. and “EuAu5In”-I, respectively. Such small dispersions of the Eu-4f bands in the electronic structures of EuT5In (T = Cu, “Ag”, “Au”) mean that the Eu-4f can be considered as localized (core-like) states that play a subordinate role in the overall bonding of these models. The theoretical magnetic moments of 6.92 µB/Eu for EuCu5In and of 6.87 µB/Eu for 17 ACS Paragon Plus Environment


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“EuAu5In”-I are indicative of a divalent character for europium with a half-filled 4f7-shell (L = 0, J = S = 7/2), which was also identified from the magnetization data of EuT5In (T = Cu, Au; gJ = 7 µB/atom; see Physical Properties). An additional examination of the spinpolarized DOS curves for EuT5In (T = Cu, “Ag”, “Au”) reveals that the states near and below the Fermi level, EF, originate primarily from the T-d AOs with minor contributions from the Eu-d and the In-p AOs. Close inspections of the DOS regions at and in the vicinity of the strong peaks that are largely composed of the Eu-4f states disclose the presence of Eu-d states, which can hybridize with the Eu-4f states to promote the magnetic interactions via conducting electrons between the europium atoms. The magnitudes of the total energy differences between the FM and the AFM models – 4.6 meV/f.u. for EuCu5In and 4.1 meV/f.u. for “EuAu4In2” (see Structural and Site Preferences in the EuT5In Series) – suggest that the spins of the Eu-4f electrons can be reoriented with slight efforts. Indeed, the field-dependent magnetization data of EuCu5In indicate a metamagnetic-like transition for fields higher than 1.8 T, while the heat capacity data of EuAu5In point to the likely presence of a Fermi-liquid behavior for this compound. The locations of the Fermi levels, EF, close to local minima of pseudogaps in the spin-polarized DOS curves of EuT5In (T = Cu, “Ag”, “Au”) are indicative of an electronically favorable situation for these materials. From the comparison of the calculated densities for “EuAu5In”-rh and “EuAu5In”-I it is clear that a tetragonal structure of EuAu5In appears to be preferred due to geometrical reasons (see Structural and Site Preferences in the EuT5In Series); yet, there is no evidence of any geometrical factors controlling the structural preferences for the Cucontaining compound. To examine the presence of electronic instabilities as causes for the formation of a given structure, we also inspected the DOS regions at the Fermi level for the “EuCu5In”-I model (“EuAu5In”-I-type (P4mm; no. 99)) in a non-magnetic regime (Figure S9). Because EF in “EuCu5In”-I falls in a pseudogap, an electronically favorable situation is indicated for this structure. Another factor, which significantly influences the electronic structure and total energy for a given material and, hence, could produce the large difference between the total energies of EuCu5In and “EuCu5In”-I (Table 3), is the bond energy arising from the contacts in a given atomic environment type.1 To evaluate the impact of the local (chemical) bonding on the electronic structures of EuCu5In and “EuCu5In”-I, we followed up with a (chemical) bonding analysis for both models. In addition to EuCu5In and “EuCu5In”-I, we also examined the −COHP curves and their respective integrated values (Table 5) for the “EuT5In” models (T = Ag, Au) that correspond to the lowest total energies.


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Bonding Analyses. A (chemical) bonding analysis for EuCu5In, the “EuCu5In”-I model and the models of “EuT5In” (T = Ag, Au) that correspond to the lowest total energies (i.e. “EuAg5In”-In1 Theor, and “EuAu5In”-I, -III, -IV) was accomplished based on the Crystal Orbital Hamilton Population (COHP) curves and their respective integrated values. The TBLMTO-ASA code was used for the –COHP computations (see Computational Details), in which the Eu 4f states were treated as core-like states as suggested by the spin-polarized band structure calculations (see above). A direct comparison of the –ICOHP values for EuCu5In and the diverse “EuT5In” models (T = Cu, Ag, Au) cannot be made, as the electrostatic potential is set to an arbitrary “zero” energy in each DFT-based computation. Because the relative position of this “zero” energy varies from system to system,58,108 it is inapt to compare –ICOHP values of different compounds without any reference energy across all systems; however, projecting the –ICOHP values, weighted by the bond frequencies of the nearest neighbor interactions, as percentages of the total bonding capabilities has been demonstrated to be a powerful means to identify bonding differences between unlike materials.28,71,73,109 In the following, the –COHP curves will be exemplarily described for EuCu5In and the models of “EuAg5In”-In1 Teor. and “EuAu5In”-I, for which the spin-polarized DOS curves were inspected in detail in the previous section. The –COHP curves for EuCu5In, “EuAg5In”In1 Teor. and “EuAu5In”-I exhibit strong T−T and T-In bonding interactions below the Fermi level (Figure 13). For the Cu-containing species, the homoatomic Cu−Cu interactions first change from bonding to antibonding states at −4.51 eV and, then, from antibonding to bonding states at −3.10 eV. The Cu−Cu –ICOHP/bond values range between 0.7151 eV/bond and 0.4348 eV/bond, hence, showing a net bonding character, and contribute 36.87 % to the total bonding capabilities (Table 5). The antibonding character of the homoatomic Cu−Cu contacts originates from the closed-shell (d10-d10) interactions, while hybridizations of the Cu 3d orbitals with the 4s and 4p AOs outweigh the repulsive d10-d10 interactions into bonding interactions.110-112 Note that the Cu−Cu and Cu−In interactions in the rhombohedral EuCu5In show nearly similar percentage contributions to the total bonding capabilities (Table 5), whereas the percentage shares of the heteroatomic Cu−In interactions in the tetragonal “EuCu5In”-I model are larger than those corresponding to the Cu−Cu interactions. A comparison of the average –ICOHP values for the diverse bonds in the tetragonal “EuCu5In”I reveals that the Cu−Cu interactions show less bonding character relative to Cu−In contacts in view of the fact that each “EuCu5In”-I unit cell comprises more Cu−Cu (32) than Cu−In (20) contacts; however, in the rhombohedral EuCu5In, the difference between the average – ICOHP/Bond values for the Cu−Cu and Cu−In interactions is much smaller than that in the 19 ACS Paragon Plus Environment


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tetragonal “EuCu5In”-I. This outcome implies that the rhombohedral EuCu5In structure gains significant stability from the driving force to maximize overall bonding and, hence, is preferred rather than the tetragonal structure. For the tetragonal “EuAu5In”-I model, the Au−Au interactions change from bonding to antibonding states at −3.81 eV and remain nonbonding between −1.60 eV and the Fermi level (Figure 13). Although the occupation of antibonding states at such energies may infer a less bonding attribute of the Au−Au interactions relative to the other, heteroatomic contacts, yet, the Au−Au –ICOHP values indicate a net bonding character (Table 5). Note that the Au−Au –ICOHP values scale in the same range or are even larger than those of the Au−In separations for all inspected “EuAu5In” models, i.e. “EuAu5In”-I, “EuAu5In”-III, “EuAu5In”IV. Since the homoatomic Au−Au contacts exhibit higher bond frequencies than the heteroatomic Au−In separations in all inspected “EuAu5In” models (Figure S4), there are larger relative contributions from the Au−Au interactions to the total bonding capabilities than from the heteroatomic Au−In bonds. The shares of the diverse interactions to the bonding capabilities in the “EuAu5In” models are in stark contrast to those obtained for the “EuCu5In”-I model, in which the largest fraction stems from the strong, heteroatomic Cu−In contacts. This result indicates that the “EuAu5In” models comprise both “strong” Au−Au and Au−In interactions and reflects recent investigations28 on the site and structural preferences of YbAl4Mo2-type29 compounds, which also demonstrated the tendency of these materials to adopt the structure with the maximal number of the contacts providing the largest bond energies. The antibonding character of the Au−Au interactions originates from the repulsion of the Au-d states;113 however, the magnitudes of the Au−Au –ICOHP values evidence the bonding character of these strong homoatomic interactions providing the largest percentages to the total bonding capabilities in contrast to the Cu−Cu states in “EuCu5In”-I. Important aspects that have to be recapitulated in the presence of homoatomic Au−Au bonds are the typical contraction of the Au-6s orbitals and, based on that, the existence of dispersion effects as attractive interactions between the d10 shells.10,31 The magnitudes of the Ag−Ag –ICOHP values in the “EuAg5In”-In1 Theor. model scale in the same range as those of the heteroatomic Ag−In interactions (Table 5); yet, the percentage contributions to the total bonding capabilities arising from the homoatomic Ag−Ag states are larger than those from the overlap populations between the Ag−In separations because of the increased bond frequencies from the Ag−In to the Ag−Ag contacts (Table S3). The magnitudes of the Eu−In and the T−Eu (T = Cu, Ag or Au) –ICOHP values in all inspected models are smaller than those of the T−T and T−In interactions (Table 5) and, 20 ACS Paragon Plus Environment

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hence, point to a less bonding character for these interactions relative to the T−In and T−T states – a feature typically observed for europium-containing, polar intermetallic phases.28,61,83

Conclusions. First-principles-based methods have been employed to forecast the structural preferences and the magnetic ground states for EuT5In (T = Cu, Au). The comparisons of the total energies, which were evaluated for diverse EuT5In (T = Cu, Au) models adopting different structure types and magnetic states, revealed the lowest total energies for the EuT5In (T = Cu, Au) crystal and magnetic structures that were also determined experimentally based on singlecrystal X-ray diffraction experiments and physical properties measurements, respectively. EuCu5In is isostructural with the previously reported EuNi5In26 and undergoes a paramagnetic-antiferromagnetic transition at 12 K, while EuAu5In crystallizes with the YbMo2Al4-type29 and is a ferromagnet below 13 K. Nevertheless, this procedure is rather restricted in its ability to predict the complex nature of the magnetic structure for the rhombohedral EuCu5In, for which its unusual MCE correlates well with the complex magnetic structure. A broader quantumchemical screening involving more parameters to identify the most favorable structrural models and compositions is still required to probe the potential of new materials for large MCEs. Examinations of the spin-polarized DOS curves for EuCu5In suggest that the magnetic interactions between the europium atoms are promoted by the capability of the Eu-d states to hybridize with Eu-4f AOs. Geometrical and (chemical) bonding analyses were accomplished for “EuT5In” models (T = Cu, Au) that adopt the EuNi5In-type26 as well as the YbMo2Al4-type29 to reveal the causes for the preferences to crystallize with a particular type of structure. From these analyses it is clear that the tetragonal structure is preferred for EuAu5In due to geometrical reasons (“optimal packing of atoms”), while the rhombohedral structure is favored for EuCu5In because of the driving force to maximize overall bonding. In addition to EuT5In (T = Cu, Au) the crystal structure, the physical properties and the electronic band structure were also examined for the EuAg5In compound. Because the clear assignments of indium and silver to the diverse crystallographic sites were set hurdles in the solutions and the refinements of the single-crystal X-ray intensity data sets, the total energies of diverse “EuAg5In” models were evaluated and compared to reveal the electronically most favorable crystal structure for this material. In summary, the examinations on EuT5In (T = Cu, Ag, Au) demonstrate the strength of the computational approach to screen for the structure models with the lowest total energy, 21 ACS Paragon Plus Environment


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which acknowledges the subtle interplay between the attempts to optimize geometrical factors and to maximize overall bonding. In doing so, the (electronically) most favorable structure of a material with a complex magnetic structure and an unusual MCE behavior was identified for the rhombohedral EuCu5In. A further research focused on the effects of chemical pressure produced by doping parent compounds with third party elements is required to predict the structural preferences. At the same time, the study of partial substitution of non-magnetic transition metal positions within the same structure might help to better understand the nature of magnetic ordering and magnetocaloric effect in EuCu5In and EuAu5In as well as to improve given physical properties.

Supporting Information. Lists of atomic displacement parameters for I, II and III; SEM image of the surface for and EDX spectrum of a sample of III; representations and total energies of the “EuAu5In” models -I to -VI; representation of the magnetic structure for an antiferromagnetic model of EuCu5In; site- and orbital-projected, spin-polarized DOS curves for EuCu5In, “EuAg5In”-In1 Theor. and “EuAu5In”-I; DOS and projected DOS curves for the “EuCu5In”-I model; tables with distances, multiplicities and –ICOHP/bond for selected interactions in EuCu5In, “EuCu5In”-I, “EuAg5In”-In1 Teor., “EuAu5In”-I, “EuAu5In”-III, “EuAu5In”-IV; tables with optimized (VASP) structure and atomic parameters for the “EuCu5In”-I, “EuAg5In”-In1 Teor., “EuAu5In”-I, “EuAu5In”-II, “EuAu5In”-III, “EuAu5In”IV, “EuAu5In”-V, “EuAu5In”-VI and “EuAu5In”-rh models; crystallographic information of I, II and III in CIF form. This material is available via the internet.

Corresponding Author. E-mail: [email protected]

Acknowledgments. This research was supported in part by Grant Agency of the Czech Republic under the grant No. P204/12/0285 and International Vesengard Fund (I.B. and L.H. sample and manuscript preparation, measurement of the physical properties), the Critical Materials Institute (CMI), an Energy Innovation Hub of the U. S. Department of Energy (DOE), the Office of Energy Efficiency and Renewable Energy, Advanced Manufacturing Office (A.V.M. and V.S., crystallographic analysis, sample and manuscript preparation), the Office of the Basic Energy Sciences, Materials Sciences Division of the U.S. DOE (A.V.M., S.S., V.S. conducting 22 ACS Paragon Plus Environment

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research, data analyses, quantum chemical computations and manuscript preparation; V.K.P. and Ya.M., measurements of the physical properties and manuscript preparation) and the Department of Materials Science and Engineering at Iowa State University (A.V.M. and S.S., sample and manuscript preparation). Ames Laboratory is operated for U.S. DOE by Iowa State University under Contract No. DE-AC02-07CH11358. The technical support of JEOL USA, Inc. (D. Guarrera) with the acquisitions of the surface image and the EDX spectrum is gratefully acknowledged.



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