On the constitution and thermodynamic modeling of the phase diagrams Nb-Mn and Ta-Mn

The constitution of the two phase diagrams Nb-Mn and Ta-Mn has been determined from light optical and transmission and scanning electron microscopy (LOM, TEM and SEM) with energy dispersive (EDX) as well as wavelength dispersive (WDX) X-ray spectroscopy, X-ray powder (XPD) and single crystal diffraction (XSCD), differential thermal analysis (DTA) and/or differential scanning calorimetry (DSC). The Laves phases NbMn2 and TaMn2 are the only binary compounds in these systems. High-temperature differential thermal analyses revealed congruent melting for NbMn2 with Tm(NbMn2) = 1515 ± 15 °C, whereas TaMn2 melts incongruently with Tm(TaMn2) = 1797 ± 40 °C close to a depleted peritectic reaction. Both Laves phases engage in eutectic reactions l ↔ (Mn) + Nb(Ta)Mn2 (Teut = 1220 ± 10 °C at 4.9 at% Nb and Teut = 1234 ± 10 °C at 0.7 at% Ta, respectively). NbMn2 also forms a eutectic with (Nb): l ↔ (Nb) + NbMn2 at Teut = 1493 ± 15 °C and 53.2 at% Nb. Mn shows remarkably large maximum solid solubilities of 19.4 at% Mn in (Nb) as well as of 21.3 at% Mn in (Ta). Detailed atom site distribution has been established for the Laves phases by means of temperature dependent X-ray single crystal data (both C14 MgZn2-type). Combined data from XPD, EDX/WDX and SEM microstructure indicate that for both Laves phases extended homogeneity regions exist: Nb1+xMn2−x (62.5–73.0 at% Mn at 950°C: −0.19≤x≤0.125) and Ta1+xMn2−x (59.5–68.5 at % Mn: −0.055≤x≤0.215). Density functional theory (DFT) calculations favor Nb(Ta)/Mn antisite occupation rather than defects. The phases, “NbMn” and “TaMn”, adopted earlier in the literature as binary system inherent compounds, were shown (TEM, WDX electron microprobe data and X-ray Rietveld refinements) to be oxygen stabilized phases of the Ti4Ni2O type (so-called eta(η)-phases) with modified Nb(Ta)/Mn site substitution to comply with the formula Nb(Ta)3−xMn3+xO1−y (defect η-W3Fe3C-type). From magnetic susceptibility and magnetization measurements, both oxide stabilized eta phases η-Nb3Mn3O1−y and η-Ta3Mn3O1−y were found to order ferromagnetically below Tc ~ 77 K, but the Laves phases NbMn2, TaMn2 reveal weakly temperature dependent paramagnetism. No trace of the rhombohedral μ-phase (W6Fe7-type) has been encountered in our investigation of the two binary phase diagrams. Thermodynamic and transport properties (specific heat, electrical resistivity and magnetic susceptibility/magnetization) classify the Laves phases with metallic behavior whilst mechanical properties (elastic moduli from DFT and nanoindentation as well as hardness and thermal expansion) group both Laves phases among rather hard and brittle intermetallics. Based on (i) the experimentally derived constitution of the Nb-Mn and Ta-Mn systems, and https://doi.org/10.1016/j.jallcom.2021.158715 0925-8388/© 2021 The Authors. Published by Elsevier B.V. CC_BY_4.0 ☆ The paper is dedicated to Prof. Dr. Wolfgang Jeitschko, in memoriam. ]]]] ]]]]]] ⁎ Corresponding author. E-mail address: peter.franz.rogl@univie.ac.at (P. Rogl). 1 Current address: Institute of Solid State Physics, TU-Wien, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria. Journal of Alloys and Compounds 865 (2021) 158715


Introduction
In diverse technological applications Nb, Ta and Mn are playing an important role such as for instance: (i) additions of Mn are able to increase the yield strength of Ti-Nb-Ta-Mn alloy foams for biomedical implants [1,2], (ii) niobium-manganese composite electrodes were found to be more suitable in supercapacitors than niobium electrodes [3]; (iii) Mn, Nb and boron additions maximize strength and toughness in martensitic micro-alloyed steels for heavy-duty engine connecting rods [4]; facilitate the production of seamless steel tubes [5]; Ta increases the pitting corrosion in super duplex stainless steels forming (Ta,Mn) -oxysulfide [6], and (iv) Hatano [7] studied the counteracting effects of Nb and Mn on microstructure and toughness for 590 MPa class low carbon bainitic steels. Nb(Ta)or Mn-doping has been employed to improve the thermoelectric behavior of perovskite manganites [8,9], of NbFe 2−x Mn x Al Heusler alloys [10] and of higher manganese silicides (Nowotny chimney ladder structures) [11].
Although the knowledge of phase diagrams and thermodynamic properties is essential in defining processing conditions for optimal engineering properties, reliable phase diagram information on the basic binary systems Nb-Mn and Ta-Mn is still scarce. For a detailed summary of the experimental findings, see the compilation of binary phase diagrams in Massalski [12]. The limited experimental data available within the partial phase diagram Nb-Mn concern the region around the Laves phase (50-80 at% Mn [13]) and the Mn-rich liquidus/solidus, which has been derived from thermal analysis in the region from 88 to 100 at% Mn [14]. Interestingly the investigation of the system Nb-Mn-B at 800 °C revealed a binary NbMn phase at 45-50 at% Mn (structure undetermined, W 6 Fe 7 -type assumed [15]). Such a phase was later but unknowingly accounted for as a μ-phase (Nb 6 Mn 7 ) in the thermodynamic modeling of the Nb-Mn binary as part of the Nb-Fe-Mn system [16].
From the phase diagram of the Ta-Mn system hitherto only the region from 67 to 100 at% Mn has been experimentally derived [17] with some additional data on the hardness of the TaMn 2 -Laves phase [13]. Being unaware of an experimental diagram, Kaufman [18] produced a first thermodynamic calculation of the entire phase diagram Ta-Mn using structure-insensitive heat of formation data derived from Miedema's model [19] and early ab initio data by Colinet [20]: besides TaMn 2 , also a compound TaMn was shown to exist. However, the Gibbs energies of phases were not based on standard SGTE unary data [21]. Although experimental data are only available for the Mn-rich part and the type and temperature of melting of TaMn 2 remained unclear [17], thermodynamic modeling of the entire phase diagram was performed by C. Wang et al. [22] resulting in a Mn-rich and a Ta-rich eutectic besides congruently melting TaMn 2 (T m = 1670 °C). A phase "TaMn" was not considered.
The Laves phases in both systems received more attention: from high-temperature direct synthesis calorimetry measurements Meschel et al. [23] claimed a standard enthalpy of formation for NbMn 2 of −31.2 ± 8.1 kJ/mol.f.u. and −43.5 ± 7.5 kJ/mol.f.u. for TaMn 2 . This experimental value for NbMn 2 , however, appears significantly lower than the Δ 298 H f° = −45.05 ± 3.64 kJ/mol.f.u. extracted from drop isoperibolic calorimetry in a Ni bath [24], which proved to be consistent with a density functional theory (DFT) calculation by Yan et al. [24], who arrived at −46.5 kJ/mol.f.u. These values compare well with older ab initio data by Colinet [20]), which were evaluated within a tight-binding scheme for the d band -an approximate model calculation to estimate the enthalpies of formation not dealing with structure and magnetic effects. More recent ab initio calculations of Yan et al. on NbMn 2 also provided an eDOS (from which a gamma value of γ = 10.5 mJ/mol.K 2 is derived), as well as a full set of elastic moduli [24] (for details see Section 4.4. Hardness and mechanical properties).
With respect to (a) the absence of reliable phase diagram data in both systems Nb-Mn and Ta-Mn as well as (b) concerning the inconsistencies on the existence of the phases "Nb 7 Mn 6 " and "TaMn", and (c) inconsistencies in the heat of formation and the lack of physical property data for the Laves phases, the aim of the present paper is manifold: (i) to check on the crystal structure, the formation and stability of the system inherent phases particularly on the "NbMn" (Nb 7 Mn 6 ) and "TaMn" phases, (ii) to establish reliable phase relations for the entire phase diagrams Nb-Mn and Ta-Mn, (iii) to provide physical property data for a detailed characterization of the Laves phases, (iv) to calculate via ab initio methods the energy of formation of the Laves phases, and (v) to check on the DFT stability of the "Nb(Ta)Mn" phases (particularly on η-Ta 3 Mn 3 O 1−x ), as well as (vi) to provide a reliable set of thermodynamic data via CALPHAD modeling of both systems.

Synthesis and characterization of physical properties
The starting materials were of a minimal purity of 99.9 mass%: Ta and Nb in the form of ingot, foil or wire from Goodfellow, UK, and electrolytically deposited Mn platelets (>99.95%, Alfa Aesar, D), which were surface cleaned in concentrated HNO 3 immediately prior to use. Sample specimens (1-2 g each) were prepared from elemental pieces by either argon arc melting on a water-cooled copper hearth or on a water-cooled Hukin crucible of a high frequency (HF) furnace in Ti-gettered argon. To ensure homogenization, all alloys were re-melted several times. A slight excess of Mn was used to allow for evaporation during fusion in order to keep the total mass loss of the sample after melting below 0.5 mass%. Each alloy was weighed carefully after melting and, if necessary, Mn was added until the nominal composition was achieved after final melting. Due to the high differences in the melting points of Nb(Ta) and Mn in combination with the high vapor pressure of Mn, some of the specimens after melting and annealing still turned out to be inhomogeneous. Therefore, alloy specimens with more than 90% Mn and a total weight of 2 g were prepared from well blended powder mixtures, which were compacted in steel dies (Φ = 10 mm, without lubricant) at a pressure of 50 kg/cm 2 (~5 MPa). Nb(Ta) powders of 99.9 mass% were purchased from Sigma-Aldrich, D; Mn powder was obtained from clean Mn-pieces freshly crushed in a WC mortar (see above).
A part of each sample (within an Al 2 O 3 crucible) was sealed in a silica capsule under 280 mbar Ar and heat-treated at 950 °C for about 120 h and quenched. At maximum annealing temperature the Ar-pressure inside the silica capsule reached about 1 bar and efficiently suppressed Mn-evaporation. For annealing at 750 °C, 700 °C and 650 °C the ampullae were kept at temperature for 1 month.
X-ray powder diffraction (XPD) data from as-cast and annealed alloys were collected employing a Guinier-Huber image plate system with monochromated Fe K α1 or Cu K α1 radiation (8°≤2θ≤100°). Precise lattice parameters were calculated by least-squares fits to the indexed θ-values with Ge as internal standard (a Ge = 0.5657906 nm). Rietveld refinements were made with the FULLPROF program [25]. Single crystals (SC) were mechanically isolated from a crushed alloy. Inspection on an AXS D8-GADDS texture goniometer assured high crystal quality, unit cell dimensions and Laue symmetry of the single crystal specimens prior to X-ray intensity data collection on a four-circle APEX II diffractometer equipped with a CCD area detector and an Incoatec Microfocus Source IμS (30 W, multilayer mirror, Mo-K α ; λ = 0.071069 nm; detector distance of 3 cm; full sphere; 2°≤2θ ≤72°). Whereas the SC of TaMn 2 was studied at room temperature (RT), for NbMn 2 we collected X-ray data at four temperatures: 100 K, 150 K, 200 K and 300 K, cooled by a continuous stream of nitrogen gas enclosing the crystal at preset temperature. Besides the general treatment of absorption effects using the multi-scan technique (SADABS; redundancy of integrated reflections >8) [26], no individual absorption correction was necessary because of the rather regular crystal shape and small dimensions of the investigated specimens (40 × 45 × 60 µm³). The crystal structure was solved applying direct methods (Program SHELXS-97) and refined against F 2 (Program SHELXL-97-2) within the programs OSCAIL or WINGX [27]. Finally, the crystal structure was standardized with the program Structure Tidy [28].
All as-cast and annealed samples were ground on SiC papers and polished with Al 2 O 3 powders (down to 0.3 µm) via standard procedures and have been examined by light optical metallography (LOM) and scanning electron microscopy (SEM). The microstructure and chemical composition of the alloys were analyzed by SEM on a Zeiss Supra 55 VP equipped with an energy dispersive X-ray (EDX) detector operated at 20 kV. The non-metal content in oxygen/nitrogen/carbon stabilized impurity phases was determined from wavelength dispersive X-ray (WDX) analyses in a Jeol JSM-6460 scanning electron microscope operated at 20 kV equipped with an Oxford Instruments microanalyser using Nb/Ta-L α , Mn-K α , O-K α , C-K α , Ν-K α and Si-K α radiation and spectrometer crystals LiF (for Mn), PET (Nb/Ta), LSM60 (O, C) and LSM80N (N) (PET = Pentaerythritol, LSM60 = W-Si superlattice, LSM80N = Ni-C superlattice). Quantitative evaluation of compositions was performed with the INCA -software [29].
Thin lamellae (lateral dimensions about 10 × 7 µm 2 ) for the TEM study were prepared from the Ta45Mn55 alloy after long annealing (2 months at 1000 °C) using a focused ion beam (FIB) technique in a TESCAN LYRA 3 XMU FEG/SEM×FIB scanning electron microscope. A Philips CM12 transmission electron microscope operated at 120 kV was used namely in diffraction mode.
Electrical resistivity was measured from 4.2 K to room temperature in a conventional 4 He cryostat, relying on an in-house equipment (error <3%). The specific resistance was obtained via a dc fourpoint technique using a Lake Shore Resistance Bridge 370 AC.
For specific heat measurements, we employed a Quantum Design PPMS in the temperature range from 2 to 300 K using Apiezon-N grease to ensure a good thermal contact between sample and sample platform. Temperature and field dependent magnetization data were collected at temperatures ranging from 3 to 298 K using a 6T CRY-OGENIC SQUID magnetometer. Temperature dependent ac susceptibility measurements were carried out from 4.2 to 150 K with a revised Lakeshore 7000 AC Susceptometer [30], applying an ac field with an RMS amplitude of 400 A/m and a frequency of 200 Hz.
Thermal expansion from 4.2 K to 300 K was measured in a miniature capacitance dilatometer, using the tilted plate principle [31].
Three different types of equipment served to obtain hardness data (HV): (i) a microhardness tester, AD Paar MHT-4 mounted on a Zeiss Axioplan optical microscope, employing loads of 0.1, 0.5, 1, 1.5 and 2 N, applying a rate of 0.1 N s −1 and a loading time of 10 s, referred to as HV static, (ii) a microindenter MHT4 with a Zeiss microscope, referred to as HV dynamic (MI), using loads of 0.1, 0.5, 1, 1.5, 2, 3, 5 N and a rate of 0.1 N s −1 providing in parallel to HV the Young's modulus, E, from the indentation experiments, using the Poisson's ratio ν (ν = 0.36 was taken from DFT calculations for NbMn 2 [32]) and (iii) a nanoindenter ASMEC Unat with QCSM module (Vickers Hardness Test V1, ISO 14577 standard method), referred to as HV dynamic (NI), measuring the indentations (at least 30 imprints per load and sample) with a load of 100 mN, a load rate of 100 mN/20s, an unloading rate of 10 mN/15s and providing in addition the Young's modulus for a given ν. To evaluate the hardness data of (i), the diagonal length, 2ℓ is measured and HV is calculated according to: with F as indentation load. To get reliable results, at least 10 different impressions per load were evaluated and the error was calculated.
The error for (ii) and (iii) was about 5%.

Differential thermal analysis (DTA) and differential scanning calorimetry (DSC) measurements
DTA and DSC measurements were performed on annealed samples in a Netzsch STA 409 CD/3/403/5/G apparatus within sealed quartz and/or Al 2 O 3 crucibles, respectively, under a stream of 6 N argon. Sealed quartz ampules were used to prevent evaporation of volatile Mn from the samples during the measurement (technique discussed, e.g. in [33]). The equipment was calibrated in the temperature range from room temperature to 1400 °C against pure metal standards supplied by Netzsch with the accuracy to be within ± 1 °C. The measurements were performed at heating and cooling rates of 10 K/min for which the best signals vs. their separation were found. As a negligible influence of Mn evaporation on measured data was found and consistency between DTA and DSC data was observed, the DSC technique allowing measurement up to 1400 °C was preferred. Sample specimens, for which melting was anticipated above 1400 °C, were measured in Al 2 O 3 and/or ZrO 2 crucibles covered by a thin sprayed-on layer of Y 2 O 3 under high purity argon (6 N) at a heating rate of 15 K/min in either a DTA Setaram SETSYS 18 TM , a 3D DSC Setaram MHTC Line 96, or a DTA NETZSCH STA 449 F3 Jupiter.

DFT stability calculations
The ab initio calculations were performed using the Vienna ab initio Simulation Package (VASP) [34,35] within the framework of DFT. The pseudopotentials were constructed according to the projector augmented wave method [36,37], where the Perdew, Burke and Ernzerhof approximation was used to treat the exchange-correlation term [38,39]. The valence state configuration for the construction of the pseudopotentials included the 3d and 4s states for Mn, 4p, 5s, 4d for Nb, 6s, 5d for Ta and 2s, 2p for O. In case of the configurations NbMn 2 , Nb 2 Mn, TaMn 2 , and Ta 2 Mn of the C14 Laves phase, the optimization calculations were made with the ferrimagnetic (FIM) arrangement of magnetic moments (here, the magnetic moments of Nb and Ta have opposite direction and smaller values than those of Mn), as this arrangement of magnetic moments is more stable in comparison with the nonmagnetic (NM) arrangement [40]. The cut-off energy restricting the number of plane waves in the basis set was 550 eV for TaMn 2 , Ta 2 Mn, Ta 3 Mn 3 , Ta 48 Mn 48 O 8 , Ta 48 Mn 48 O and the corresponding pure elements, i.e. body-centered tetragonal Mn (bct, being equivalent to face-centered tetragonal), body-centered cubic (bcc) Ta and the dimolecule of oxygen. For NbMn 2 and Nb 2 Mn, bcc Nb and bct Mn (used for the evaluation of energies of formation in the Nb-Mn system), a cut-off value was set at 650 eV. Here, the bct structure corresponds to the bcc one with the c lattice parameter shorter than a and b. The convergence tests of total energies with respect to the number of k-points showed that the 21 × 21 × 21 k-point grid in the irreducible part of the Brillouin zone is optimal for TaMn 2 and Ta 2 Mn, whilst a grid 13 × 13 × 7 is appropriate for NbMn 2 and 23 × 23 × 13 for Nb 2 Mn. For Ta 3 Mn 3 , Ta 48 Mn 48 O 8 and Ta 48 Mn 48 O, the k-point grid was 6 × 6 × 6. For pure elements, the grid of k-points 31 × 31 × 31 was used for bcc Ta and 19 × 19 × 19 for bct Mn, both in the Ta-Mn system, and the grid 35 × 35 × 37 and 29 × 29 × 29 were used for bct Mn and bcc Nb in the Nb-Mn system. For oxygen, the k-point grid was 8 × 8 × 8. This resulted in well-converged total energies and equilibrium structural parameters, i.e. lattice parameters and internal atomic positions.
The energies of formation were calculated as the difference between the DFT total energy of the corresponding compounds and the weighted ratio of total energies of pure elements in their standard element reference (SER) states, i.e. αMn, bcc Nb, bcc Ta and O 2 . In order to avoid the ab initio calculation of the complex magnetic structure of αMn, we used the total energy of the bct Mn structure with an antiferromagnetic arrangement (antiparallel orientation of magnetic moments) plus the total energy difference between α and bct Mn (1.82 kJ/mol), as calculated by Chen et al. [41], to evaluate the total energy of the SER state of αMn.

CALPHAD modeling
For thermodynamic and phase diagram calculations as well as for optimization of thermodynamic parameters based on the CALPHAD method, the Pandat software package [42] was used. Thermodynamic modeling of phases existing in the binary systems Nb-Mn and Ta-Mn relies on the well-known Compound Energy Formalism (CEF) enabling us to respect the real crystallographic structure of a phase by means of a sublattice description [43]. For the thermodynamic description of elements i in the phase ϕ, the commonly used polynomial form was applied: where A, B, C, D n and n (typically equal to 2, 3, and −1) are constants characteristic for the particular structure of the element i in a given temperature interval in Kelvin [21]. The Gibbs energy of a given ternary phase ϕ is here expressed as a sum of several contributions: where G m ref is the reference level of the molar Gibbs energy of a given phase ϕ, G m means Gibbs energy of formation, G m id describes the molar Gibbs energy of ideal mixing of components (nonstoichiometric case) and G m ex is the molar excess Gibbs energy describing a non-ideal behavior of components due to their mutual interactions [44].
The Gibbs energy of formation of the phase ϕ is expressed by the equation which is used for the description of the Gibbs energies of compounds. The value of ΔH was based on DFT values of energy of formation of the phase and optimized on phase equilibrium data, similarly as ΔS. The lattice stabilities of metastable or unstable phases are calculated from first-principles now; this idea was presented first in 2001 in papers [45,46]. For the description of solubilities of components in phases, the substitutional model of the Compound Energy Formalism (CEF) Eq. (3) is used. The formula for ideal mixing: and the Redlich-Kister polynomial for excess contribution from interaction of components to the Gibbs energy: are used. In Eqs. (5) and (6) x i , x j , are the molar fractions of components and n is the summation index for parameters L, which may be temperature dependent.

Crystal structure of the Laves phases NbMn 2 and TaMn 2
Both Laves phases NbMn 2 and TaMn 2 are known to crystallize with the hexagonal MgZn 2 -type structure (C14-type). A summary of all XPD data available in the literature can be found in the compilation by P. Villars and K. Cenzual [47], however, recent single crystal X-ray work on NbMn 2 and Nb 0.87 Mn 2.13 (Nb29Mn71 at%) by D. Grüner [48] was not included (details will be discussed below). So far, no detailed single crystal structure determination has been published for TaMn 2 .
For the present work, small single crystals were broken from arc melted alloys with the stoichiometric nominal composition {Nb,Ta} Mn 2 . The X-ray intensity patterns in both cases were fully indexed and were unambiguously consistent with hexagonal symmetry with space group P6 3 /mmc and lattice parameters: a = 0.48898(1) nm, c = 0.79970(1) nm for the Nb-crystal and slightly smaller values a = 0.48708(1) nm and c = 0.79718(1) nm for the Ta-crystal. Structure solution by direct methods yielded a fully ordered atom arrangement of MgZn 2 -type for NbMn 2 , whereas a minor but significant random distribution of 0.96(1) Mn1 + 0.04 Ta1 in the 2a site was observed for Ta(Ta x Mn 1−x ) 2 (x = 0.01). The refinements with anisotropic atom displacement parameters (ADPs) converged to R F2 = 0.0110 with residual electron densities smaller than ± 0.51 e -/10 −3 nm 3 for NbMn 2 (at RT) and R F2 = 0.0244 with residual electron densities < ± 2.40 e -/10 −3 nm 3 for Ta(Ta x Mn 1−x ) 2 ; x = 0.01, respectively. Crystallographic data for both single crystals are summarized in Tables 1 and 2. Interatomic distances are shown in Fig. 1 for Ta(Ta x Mn 1−x ) 2 with 0.2970 ≤ d Ta-Ta ≤0.2990 nm, 0.2848 ≤ d Ta-Mn ≤0.2858 nm, 0.2360 ≤ d Mn-Mn ≤ 0.2510 nm and are rather consistent with the sum of CN12 metal atom radii (R Nb = 0.1468 nm, R Ta = 0.1467 nm and R Mn = 0.1304 nm [49]). Whereas distances Ta-Ta are slightly longer than the sum of radii, distances Mn-Mn for site 6h are shorter by about 10% and for Mn-Mn (2a to 6h) are shorter by about 5% indicating a strong Mn-Mn interaction. Such a behavior is also inherent to NbMn 2 . Our room temperature atom parameters for NbMn 2 are essentially consistent with the findings of Grüner [48], although his atom parameters are slightly higher and his lattice parameters are somewhat lower.
Evaluation of the temperature dependent X-ray single crystal intensity data sets in Table 2 clearly document that NbMn 2 adopts the MgZn 2 -Laves type at all the four temperatures measured, namely: 100 K, 150 K, 200 K and 300 K. In combination with XPD data up to the melting point we observe that no phase transition appears within the entire temperature interval (100-1788 K). TaMn 2 displays analogous behavior (298-2070 K).
The temperature dependence of the lattice parameters of NbMn 2 for the temperature range from 100 to 300 K, as depicted in Fig. 2 (top), shows a rather smooth variation within ~2 permille. Fig. 2 (middle) denotes the variation with T of the atom parameters in the various Wyckoff sites for NbMn 2 . Although the z parameter of the Nb-atoms in 4f seems to constantly rise with temperature, the x parameter of the Mn-atoms in the 6h site passes through a maximum at 150 K. Fig. 2 (bottom) (100-300 K) portraits the temperature dependence of the interatomic distances in NbMn 2 , which merely reflects the variation of lattice parameters in combination with the atom parameter variation vs. T. Consequently, all distances between Mn atoms rise rather monotonically with temperature within 2 permille. For the evaluation of the Debye temperature from the temperature dependent ADPs see Section 4.2. Specific heat.
In this context, it is interesting to note that D. Grüner [47] observed a weak 2a×2a×2c superstructure of the MgZn 2 -type on polycrystalline residues, which were extracted by diluted HCl from arc melted Mn-rich alloys Nb10Mn90 (in at%), sealed in Nb-vessels and annealed at 1100 °C. No structural details were reported, but it was said that single crystals Nb 0.87 Mn 2.13 (Nb29Mn71 at%), extracted in the same way from Mn-rich alloys, did not show any superstructure reflections and clearly revealed isotypism with the MgZn 2type. The random distribution of (3.48Nb+0.52Mn) in the 4f-sites in the Mn-rich single crystal Nb 0.87 Mn 2.13 [48] is in line with random distributions of (0.1Nb+1.9Mn) in the 2a sites and (0.22Nb+5.78Mn) in the 6h sites for the Nb-rich alloy Nb 1.08 Mn 1.92 (Rietveld refinement data in Table 2). It should be mentioned here, that our XPD neither in Nb-Mn nor the Ta-Mn system detected any superstructure reflections.

The oxygen-stabilized phases "NbMn" (^ Nb 3 Mn 3 O 1-y ) and "TaMn" (^ Ta 3−x Mn 3+x O 1-y )
Our recent attempts to get a phase-pure compound NbMn 2 [24], revealed that in Nb-rich samples small amounts of a second compound richer in Nb caused the appearance of weak ferromagnetism. EDX measurements yielded a phase composition close to NbMn. Further experiments gave clear hints that the percentage of this phase in Nb-Mn and also in Ta-Mn alloys increases with the non-metal impurity content (from WDX predominantly oxygen, no nitrogen, no carbon) in the raw elements (such as Mn or Nb/Ta-powder). Therefore, the new secondary phase was concluded to be an impurity stabilized ternary phase. Indeed, painstaking attempts to reduce the oxygen-level of the starting ingot materials as well as in the preparation (melting under high purity argon, handling materials exclusively in a <3 ppm (O+H 2 O) glove box system) were finally successful yielding phase pure and paramagnetic Laves phases NbMn 2 [24] and TaMn 2 (this work). Laves phase samples without any traceable amounts of the magnetic phase have been obtained with an addition of 1-2 mass% of lanthanum metal as an internal oxygen getter obviously capturing the oxygen and forming a "nonmagnetic" LaMn x O y phase, which did not disturb the magnetic characterization of the Laves phases (see below Section 4.1 Susceptibility).
In this paper we adopted a "dirty way" to increase the amount of this impurity stabilized phase by melting powder compacts in the region Nb to NbMn (and Ta to TaMn) in an argon arc-melter with intermittent crushing the buttons in air and adding Mn to compensate fusion losses. Various oxygen contents were introduced by adding proper amounts of MnO 2 or Nb 2 O 5 and Ta 2 O 5 . In a few cases, we also tried to start from fine powder compacts that were reacted in a sealed quartz tube for 3 × 36 h at 950 °C with intermittent crushing in air and re-compacting. Although the new phase formed in larger quantities, we were unable to synthesize a single-phase sample in both systems. The spectra usually contained the Laves phase as the dominant phase and the "impurity phase" in addition.
At this stage, a series of selected area electron diffraction (SAED) patterns in Fig. 3 were obtained via TEM from thin lamellae prepared in SEM by FIB from the white phase in the cast alloy Ta50Mn50, which was annealed for 2 months at 1000 °C. Their analyses prompted a face-centered cubic (fcc) lattice with a lattice parameter a ~ 1.12 nm (averaged from a set of axes, [ ). On the basis of this information, the indexation of the X-ray powder intensity pattern of the new phases in both systems was successful. A search for the structure type in crystal databases such as in Pearson's Crystal Data [47] and in ICSD [50], employing fcc crystal symmetry with a range of lattice parameters a = 1.13 ± 0.1 nm prompted directly the CdNi-type (of HfMn), which in fact is an occupation variant of the Ti 2 Ni-type (eta(η)-phase).
The mode of atom site occupation and filling the octahedral voids in the various composition variants of the so-called η-phases deriving from the parent Ti 2 Ni-type was already extensively discussed by Rogl et al. [51]. Referring to this analysis, the phases Nb~1Mn~1O y and Ta~1Mn~1O y have to be classified as a filled metal host lattice structure where the manganese atoms in 16c of space group Fd3m (origin at center of symmetry) fill the centers of metal icosahedra (each formed by six Nb(Ta)/Mn atoms from the sites 48f and 32e) yielding a formula Nb(Ta)~3Mn~3O y . Generally in eta-phases, nonmetal atoms such as C, N or O are assumed to occupy the octahedral voids in 16d, but may also enter a second set of octahedral voids in Wyckoff site 8b (⅜,⅜,⅜). It may be noted here that Wyckoff site 8b changes to site 8a (⅛,⅛,⅛) in the non-standardized structure (using Fd3m with the origin at −43m). We used this standardized starting model for Rietveld refinements to elucidate the final atom distribution in the novel compounds Nb~1Mn~1O y and Ta~1Mn~1O y . As the situation is quite similar for both systems Nb(Ta)-Mn, we may further on focus here on the alloys from the Ta-Mn system. Table 1 Structural data for Ta(Ta x Mn 1−x ) 2 (x = 0.01) from X-ray single crystal measurement at 300 K. Partially ordered MgZn 2 -type; space group P6 3 /mmc; No. 194; structure standardized with program Structure Tidy [28]. Anisotropic atomic displacement parameters U ij in [ Rietveld refinement of an arc melted alloy Ta43Mn57 (see Fig. 4) clearly showed that the composition of the new phases appears close to a ratio (Nb,Ta):Mn ~ 1:1 rather than to a ratio (Nb,Ta):Mn ~ 4:2 such as is typical for many oxygen-stabilized compounds deriving from the Ti 2 Ni-type (Ti 4 Ni 2 O) (eta(η)-phase; for representatives see Pearson's Crystal Data [47]). Although the hexagonal Laves phase Ta 0.9 Mn 2.1 (MgZn 2 -type) with 85 vol% is the dominant phase in the X-ray powder diffraction pattern, the secondary phase of this pattern can clearly be indexed on an fcc lattice (a = 1.14546(1) nm), fully consistent with the structure model discussed above. The results of the refinement are listed in Table 3. These results reveal only slight deviations from a full atom order with a random atom distribution of (43.6 Ta+4.4 Mn) atoms in the 48f site, (1.0 Ta+31.0 Mn) atoms in the 32e site and exclusively Mn in the 16c site. Interestingly the refinement refuses any oxygen in the Wyckoff sites 8a and 8b but readily accepts 5.34 O atoms in the 16d site of the space group Fd3m (origin at center). From this atom distribution, we arrive at a chemical formula Ta Fig. 3 in the JEMS software [52,53]) are fully consistent with the observed patterns. It should be mentioned here that the appearance of oxygen exclusively in Wyckoff site 16d rules out the structure type of W 6 Fe 6 C (where the nonmetal atom only enters the 8b site but leaves the 16d site empty). Table 2 Structural data for NbMn 2 from X-ray single crystal measurement at four different temperatures. Partially ordered MgZn 2 -type; space group P6 3 /mmc; No. 194; origin at center; structure standardized with program Structure Tidy [28]. Anisotropic atomic displacement parameters U ij in [ (1)  After annealing at 950 °C for 4 days the XPD pattern of the cast alloy Ta43Mn57 has changed, i.e. besides the Laves phase as the dominant phase, we now encounter two of the fcc eta-phases in the SEM analysis as well as from Rietveld refinement (see Table 3). Interestingly the Laves phase (~81 vol%) appears practically stoichiometric but with slightly lower lattice parameters. The secondary phases can both be described with the W 3 Fe 3 C-type but contain rather small contents of oxygen: Ta 2.84 Mn 3.16 O 0.23 (14 vol%, a = 1.14088(1) nm) and Ta 3.01 Mn 2.99 O 0.13 (4 vol%, a = 1.12859(2) nm). Random distributions of Ta/Mn atoms only appear in the 48f site and are of smaller extent, therefore the formulae are close to full order; the main difference is the oxygen content reflected also by the different unit cell dimensions. It is unclear if the sample reveals a transition state to final equilibrium or if the two eta-phases are equilibrium phases of the Ta-Mn-O system.
The ferromagnetic impurity phase, which appeared in small quantities during the attempts to prepare single phase NbMn 2 was equally well described by a W 3 Fe 3 C-type eta-phase (for details see the Rietveld refinement of alloy Nb40Mn60, annealed at 900 °C, in Table 3 and Fig. S1 of Supplementary Material). Rietveld and EDX analyses agree on a formula Nb 2.86 Mn 3.14 O 0.31 (Nb 3−x Mn 3+x O y ; x = 0.14, y ~ 0.69) with a lattice parameter a = 1.13415(2) nm.
Finally, a search for representatives of the W 3 Fe 3 C type in Pearson's Crystal Data [47] indeed revealed the eta-phase Ta 3 Mn 3 O, as reported by Schönberg [54]. Although Schönberg investigated the Ta-Mn-O system (<50 at% O), he was unable to obtain the eta-phase in a pure condition but rather "in the presence of fairly large amounts of other phases". However, neither the Ta-Mn-O phase equilibria nor a structure refinement of the eta-phase have been given; only the range of lattice parameters was listed from 1.115 to 1.118 nm [54], which, however, is much smaller than the unit cells derived from our samples. Interestingly, Schönberg's investigation of the Ta-Mn-N system [55] did not yield any η-phase, in contrast to findings of Holleck et al. [56], who was able to synthesize both eta-nitrides: Nb 3.5 Mn 2.5 N (a = 1.142 nm) and Ta 3 Mn 3 N (a = 1.135 nm). Here it should be emphasized that our WDX test on N in our eta-phases was always negative.
The formation of eta-phases in Ta-Mn alloys can be best seen in Fig. 5 from an HF melted alloy TaMn 2 , prepared from Ta-foil and pieces of Mn. The evaluation of the microstructure by means of SEM-EDX and WDX revealed a partially melted Ta-foil surrounded by liquid Mn, which solidified in layers of eta-phases and finally the Laves phase (for details see Fig. 5).

Constitution of the systems Nb-Mn and Ta-Mn
In order to provide a thorough constitutional basis for proper thermodynamic modeling, we have started with DTA/DSC investigations. As the hitherto known information suggested melting temperatures for the sections T -TMn 2 (T = Nb,Ta) above 1400 °C, we applied high-temperature DTA with Al 2 O 3 and/or Y 2 O 3 -surface coated ZrO 2 crucibles from which we defined the following characteristics: congruent melting of NbMn 2 at T m (NbMn 2 ) = 1515 ± 15 °C, incongruent melting for TaMn 2 at T m (TaMn 2 ) = 1797 ± 40 °C and a practically identical melting temperature for alloy Ta40Mn60, whereas alloy NbMn displayed large primary dendrites of NbMn 2 and a eutectic ℓ = (Nb) + NbMn 2 at T eut. = 1493 ± 15 °C. Some of the high-temperature DTA runs are summarized in Fig. S2 and Fig. S3 of Supplementary Material. This information on the liquidus curves, complemented by SEM micrographs and EDX/WDX analyses (see Fig. 6 and Tables 4 and 5), confirmed (i) congruent melting for NbMn 2 (Svechnikov et al. gave T m = 1500 °C [13]) and (ii) a rather depleted peritectic melting of TaMn 2 at 1797 °C, consistent with (a) the note of Savitskii et al. that TaMn 2 "melts above 1670 °C" [17] and (b) Svechnikov [13], who simply listed (without comment) the melting of TaMn 2 at 1800 °C. It should be emphasized, that in none of our samples from both systems (Nb-Mn and Ta-Mn) we observed any trace of the rhombohedral μ-phase (W 6 Fe 7 -type; space group R m 3 ; hex. axes: a ~ 0.47 nm, c ~ 2.58 nm). Therefore, and from the discussion (i) in Section 3.2. on the oxygen stabilized eta-phases as well as (ii) on the DFT-instability of eta-Ta 3 Mn 3 , (iii) the Rietveld refinements for the alloys Nb40Mn60 (as-cast after anneal at 900 °C) and Ta43Mn57 (as-cast and after anneal at 1000 °C), and (iv) the Structure parameters for NbMn 2 in the temperature range from 100 to 300 K (from X-ray single crystal data, Table 2). Top: thermal expansion of the lattice parameters; middle: atom parameters for the various Wyckoff sites; bottom: interatomic distances. The distance d Mn2-2Mn2 = 0.25130 nm (towards the neighboring unit cell) at 300 K with almost no variation is not shown here. solidification microstructures in Fig. 6f (Nb-Mn) and Fig. 6l (Ta-Mn), we may safely exclude the phases "NbMn" [16] and "TaMn" [18] from the corresponding binary phase diagrams.
Whilst the homogeneity regions of the two Laves phases will be treated below, the maximum solubility of Mn in (Nb) and (Ta), as derived from the cast alloys and the alloys from DTA (see also the microstructures in Fig. 6 and Tables 4 and 5) were 19.4 at% Mn in (Nb) and even 21.3 at% Mn in (Ta). In addition, it should be mentioned that for the (Nb/Ta)-rich part of the phase diagrams, DTA did not reveal any transformations from RT to the melting.
Conventional DTA (alloys sealed in quartz) and DSC (Al 2 O 3 -crucibles under argon) were chosen to elucidate the Mn-rich part of the phase diagrams, for which liquidus temperatures were all expected to reside below 1250 °C. Whereas the cast alloy Nb5Mn95 turned out to be fully eutectic (T eut = 1220 ± 10 °C), the situation is less straightforward in the system Ta-Mn revealing an almost depleted eutectic at about 0.7 at% Ta ((δ-Mn) + TaMn 2 at T eut = 1234 ± 10 °C) (see Fig. 6). The maximal solid solubility of (Nb) and (Ta) in δ-Mn appears to be small and is about 0.5 at% Mn for both Nb and Ta. In contrast to that, Hellawell [14] (on the basis of microstructures, TA and XPD data; but no EPMA) reported the eutectic at 3.6 at% Nb (1224 °C) and a maximum solubility of 2.4 at% Nb in δ-Mn, a value which in view of our investigations (see Fig. 6a and Table 4) seems to be exaggerated. In contrast to our findings, the data for the Ta-Mn system by Savitskii [17] exclude δ-Mn from the eutectic, which was claimed at 2.6 at% Ta at 1175 °C and formed by (γ-Mn) + TaMn  Although the higher transition temperatures are alike, the lower two transition temperatures in the compilation from A. Dinsdale [21] (thermodynamic data of unary phases) show a discrepancy as high as about 20 °C (707 °C and 1087 °C).
EXD and WDX data inferred that for both phase diagrams the solubilities of the T-metal are below ~0.8 at% T for all modifications except for (γMn) and (αMn), the latter yielding a significant increase of its T-solubility close to its peritectoid decomposition on heating (see Fig. 6 and Tables 4 and 5), hand in hand with a pronounced increase of the (αMn) to (βMn) transformation temperature on solution (for details see the phase diagrams below in Figs. 8 and 9). It should be mentioned here, that also Savitskii et al. [17] from thermal analyses concluded a peritectoid decomposition on heating of (αMn) at ~1.5 at% Ta and 750 °C, quite similar to our DTA and EPMA data. DTA/DSC curves for selected Mn-rich alloys are presented in Fig. S4 and Fig. S5 of Supplementary Material.

The homogeneity regions of the Laves phases NbMn 2 and TaMn 2
The experimentally derived homogeneity region of the Laves phase Nb 1+x Mn 2−x (62.5-73.0 at% Mn at 950 °C: −0.19 ≤x≤ 0.125) (see Fig. 7a) is fairly consistent with the reports by Drys [   also used by Gupta et al. [59] for the Nb-Mn-Ni system at 1000 °C. Our study of the lattice parameters confirmed the homogeneity region obtained from EDX measurements within a small margin of ± 0.5 at% Mn (see Fig. 7a). A similarly wide homogeneity region was found from XPD for Ta 1+x Mn 2−x (59.5-68.5 at% Mn for 900 °C and cast alloys: −0.055 ≤x ≤ 0.215; see Fig. 7b), which is fairly consistent with the EPMA values.
At this point, it should be emphasized that both systems Nb-Mn and Ta-Mn are characterized by only one binary compound, a Laves phase with MgZn 2 -type without any other structure modifications in the entire composition/temperature range of existence. For NbMn 2 this has been proven by temperature dependent XPD (4.2-300 K), Xray SC diffractometry from 100 to 300 K and by XPD up to the melting range on quenched alloys. Fig. 7a and b display the lattice parameters of Nb 1+x Mn 2−x and Ta 1+x Mn 2−x as a function of composition and for a set of temperatures. For comparison, all data available in the literature are plotted (taken from [47]), although many of them lack a defined composition and can only be placed at stoichiometric TMn 2 . It is interesting to see that the width of the homogeneity region Nb 1+x Mn 2−x is practically invariant from 950 °C to the melting range: − 0.19 ≤ x ≤ 0.125. Similar behavior is also encountered for Ta 1+x Mn 2−x .
From the energetics of point defect formation in a DFT supercell approach for the large homogeneity region of the ZrMn 2 Laves phase, Chen et al. [41] clearly derived that antisite occupation is more favorable than vacancy formation. Particularly the low energy for Mn at Zr sites infers a broad nonstoichiometry range toward the Mn-rich side and with increasing temperature the minimum of the free energy of the Laves phase is shifted toward Mn-richer compositions (at 32.8 at% Zr) concomitant with the occurrence of the congruent melting point not at the stoichiometric but at a slightly Mn-richer composition [41]. Similar arguments may also hold for both Laves phases NbMn 2 and TaMn 2 .

DFT stability of intermetallic phases
The ab initio calculated equilibrium lattice parameters for the FIM arrangement of the various configurations of C14 Laves phases are provided below. This type of magnetic arrangement was chosen, as it shows to be the most stable (a detailed study of this topic can be found in Ref. [40]). The lattice parameters of NbMn 2 (a = 0.48087 nm, c = 0.79061 nm) and TaMn 2 (a = 0.47899 nm, c = 0.78874 nm) agree Table 3 XPD Rietveld refinement (room temperature data) for alloys Nb40Mn60 (as-cast after anneal at 900 °C) and Ta43Mn57 (as-cast and after anneal at 1000 °C); theta range 14 ≤ 2Θ≤ 95°); all structures standardized with program Structure Tidy [28]. Isotropic atomic displacement parameters B iso in [ [20]). However, taking C14-TaMn 2 and pure bcc Ta as reference states, the eta-phase becomes unstable by 6.95 kJ/mol at. This explains why this phase has not been observed in the Ta-Mn binary system. Inserting one atom of O in the 8a site (Ta 48 Mn 48 O) resulted in the energy of formation of − 9.94 kJ/mol at. with respect to SER states. Although this value suggests a stabilizing influence compared to SER states, it is even smaller than the value for Ta 3 Mn 3 , indicating that this structure will be also unstable when the Laves phase is present (by 6.85 kJ/mol at. with respect to the weighted ratio of bcc Ta, O 2 and C14-TaMn 2 ). Furthermore, we also investigated the energy of formation of etaphase containing one O atom in the 8b sublattice with respect to the SER states, which resulted in the value of −14.97 kJ/mol at. This value proves that the O atoms prefer the 8b sublattice to 8a and makes the structure only slightly unstable with respect to the weighted ratio of bcc Ta, O 2 and C14-TaMn 2 by 1.83 kJ/mol at. Hence, it can be suggested that this structure could become stable at higher temperatures. On the other hand, the addition of 8 atoms of O to the 16d sublattice  arrangement and magnetism) is much more complex and deserves more attention, which will be paid to it in the forthcoming publication [40], where, among other things, the stabilization effect of O in the eta-phase will be discussed in detail.

Thermodynamic modeling of the systems Nb-Mn and Ta-Mn
The experimental phase diagrams of the systems Nb-Mn and Ta-Mn, as presented in Figs. 8 and 9, form the basis for our thermodynamic modeling backed by the DFT calculated energies of formation of different configurations of the Laves phases NbMn 2 and TaMn 2 (Chapter 3.4). Thermodynamic data for pure elements were taken from [21]. Parameters for CAPHAD calculations of phase diagrams of Nb-Mn and Ta-Mn systems as the result of modeling are given in Table 6 and phase diagrams are drawn in Fig. 10 and Fig. 11. A comparison of the experimentally derived and thermodynamically calculated details on the invariant equilibria, as presented in Tables S1 and S2 in Supplementary Material, shows a convincing agreement; in addition also the databases (tdb files) for the calculation of the phase diagrams of both systems are listed in Supplementary Material (Tables S3 and S4).

Physical properties of the Laves phases NbMn 2 and TaMn 2
As usual for samples within a homogeneity region, we have to emphasize that certain physical properties as well as their temperature dependencies are highly variable and sample dependent. This section covers only the single-phase compounds NbMn 2 (Nb34Mn66 in at%) and TaMn 2 (Ta33Mn67) close to their stoichiometric 1:2 composition.

Susceptibility
The temperature dependent dc magnetic susceptibility, = X(T) M/H(T), of single-phase NbMn 2 (Nb34Mn66) and TaMn 2 (Ta33Mn67) shown in Fig. 12 was measured with an applied field of 3 T and reveals paramagnetic behavior of both compounds. Considering the obviously dominant, weakly temperature dependent Pauli paramagnetic component, we analyze these data in terms of a Pauli component, where a is the leading coefficient of a Sommerfeld expansion, superimposed by a Curie-Weiss component, χ CW (T) = C/(Tθ p ) due to paramagnetic impurities, which are expected to arise from Mn-atoms located at Nb-or Tasites [62]. The corresponding fits of the measured magnetic susceptibilities χ exp (T) = χ P (T) + χ CW (T) are shown as solid lines. For the Pauli components of the magnetic susceptibility we obtain χ 0 = 1.73 × 10 −3 emu/mol and = × a 3.05 10 K 6 2 for NbMn 2 as well as χ 0 = 1.37 × 10 −3 emu/mol and a = 2.44 × 10 −6 K −2 for TaMn 2 . The Curie-Weiss components are characterized by a rather small Curie constant C = 0.0032 emuK/mol and paramagnetic Weiss temperature θ p = −2.3 K for NbMn 2 (thus, indicating a relatively small number of localized Mn-moments, i.e. a small fraction of Nb-sites being occupied by Mn-atoms) and roughly a factor seven larger C = 0.021 emuK/ mol and θ p = −20 K for TaMn 2 (i.e., suggesting a correspondingly larger fraction of Ta-sites being occupied by Mn-atoms in this sample). We emphasize, that in particular the magnitudes of the Curie-Weiss components of the magnetic susceptibility of these Laves phase compounds are highly variable and sample dependent, when varying the stoichiometry within their homogeneity region.
The insert of Fig. 12 (upper panel) displays the dc magnetic susceptibility of a NbMn 2 sample containing η-phase and Fig. 12 (lower panel) displays ac susceptibility data of NbMn 2 and TaMn 2 samples with an intentionally higher fraction of eta-phases Nb 3 Mn 3 O 1−y and Ta 3 Mn 3 O 1−y , respectively. These data reveal a pronounced ferromagnetic contribution of the Nb 3 Mn 3 O 1−y and Ta 3 Mn 3 O 1−y impurity phases, both with a Curie temperature T C ~ 77 K. The latter contribution has been verified, at least qualitatively, to scale with the relative fraction of the η-phase.

Specific heat
Specific heat data of NbMn 2 (Nb34Mn66) and TaMn 2 (Ta33Mn67), presented as C/T vs T in Fig. 13, reveal moderately enhanced Sommerfeld-like, roughly T-linear, specific contributions with γ ~ 33(1) mJ/mol.K 2 for NbMn 2 and γ ~ 28(1) mJ/mol.K 2 for TaMn 2 at temperatures below 10 K. The relative magnitudes of these two Sommerfeld coefficients conform reasonably well with the relative magnitudes of the corresponding Pauli susceptibilities χ 0 of NbMn 2 and TaMn 2 (see above). There are moderate, but nonetheless obvious deviations from the expected γT + βT 3 behavior of simple paramagnetic metals: in C/T vs. T of TaMn 2 there is a small hump centered at around 4-5 K and for NbMn 2 a rather moderate lowtemperature upturn in C/T is observed. These behaviors obviously relate to magnetic contributions due to weakly interacting paramagnetic moments (i.e., due to the Curie-Weiss-type paramagnetic susceptibility component discussed above), which we attribute to anti-site Mn-atoms at Nb(Ta)-sites. The latter proposal is motivated by a strong increase of such magnetic low-temperature contributions for Mn-richer samples formed within the homogeneity region of these Laves phases and will be analyzed in a separate paper. The admixture of magnetic contributions at low temperatures impedes an unambiguous evaluation of the low-temperature Debye temperature of these compounds for which we can provide only rough estimates of about 430 K for NbMn 2 and 370 K for TaMn 2 , which we obtain from the analysis of the phonon contributions in a (C − γT)/T 3 versus log(4.93 T) plot, shown as an insert in Fig. 13. The corresponding Debye functions representing the acoustic phonon spectral weight are displayed as solid lines in this graph. The observed excess contributions at lowest temperatures up to the first local minimum of the experimental data in this graph (at T ~ 7 K for NbMn 2 and T ~ 10 K for TaMn 2 ) are attributed to primarily originate from interactions among diluted localized magnetic moments, whereas excess Table 6 Parameters for calculations of phase equilibria in the Nb-Mn and Ta-Mn systems. contributions observed above the local minima of the experimental data are due to the obviously expected phonon contributions related to the optical phonon spectral weight. The corresponding local maxima of the experimental data, thus, refer to distinct maxima in the optical phonon spectral weight [63,64] at around θ E ~ 120 K for NbMn 2 and θ E ~ 160 K for TaMn 2 .

Mn-Nb phase diagram
As far as the θ D = 430 K of NbMn 2 is concerned, the value derived from C/T vs T fits quite well to an analysis of atom vibrations extracted from the atom displacement parameters as a function of temperature (θ D = 398 K, from temperature dependent X-ray single crystal data; see Fig. 14). Similarly, the extracted Sommerfeld constant γ ~ 33 mJ/mol.K 2 might appear somewhat higher than the DFT value of γ = 10.5 mJ/mol.K 2 derived from DFT calculations [24].

Electrical resistivity
The electrical resistivities, ρ(T), as presented in Fig. 15 for both compounds NbMn 2 (Nb34Mn66 at%) and TaMn 2 (Ta33Mn67 at%), display metallic behavior in the measured temperature range (4-300 K), which (considering the above magnetic susceptibility and specific heat results) are expected to essentially result from electrondefect, electron-phonon, electron-electron and electron-paramagnon scattering. In order to qualitatively analyze these experimental data, we assign a tentative estimate of the electron-defect and electron-phonon scattering contributions as ρ(T) = ρ 0 + ρ BG (T) (see Eq. (7); BG is the Bloch-Grüneisen relation), displayed as dashed lines in Fig. 15, where we make use of the above estimates of the Debye temperatures of these compounds from their specific heat data.
θ D stands for the Debye temperature and R is a temperature independent electron-phonon interaction constant. Subtracting these estimated ρ 0 + ρ BG (T) contributions from the totally measured electrical resistivities, ρ(T), we obtain a rough estimate of electron-electron and electron-paramagnon scattering contributions, Δρ(T) = ρ(T) -[ρ 0 + ρ BG (T)], displayed in Fig. 16, which appear to be rather similar for NbMn 2 and TaMn 2 despite of their almost one order of magnitude different residual resistivity values of ρ 0 = 26 µΩcm versus 220 µΩcm, respectively. When analyzing the temperature dependence of Δρ(T) for T < 35 K by a simple power law fit Δρ(T) = aT n , we obtain exponents n close to three, i.e. clearly different values from a trivially expected ρ el (T) ∝ T 2 . The initially larger contribution Δρ(T) of TaMn 2 , as compared to NbMn 2 , obviously relates to its larger Curie-Weiss component of the magnetic susceptibility (see above). We have  to emphasize that the magnitude of the residual resistivity as well as the low-temperature power law exponent n of these Laves phase compounds are highly variable and sample dependent, in particular when varying the stoichiometry of these compounds within the homogeneity region.

Hardness and mechanical properties
The results of the hardness measurements are presented in Fig. 17. For NbMn 2 (Nb36Mn64 at%) as well as for TaMn 2 (Ta35Mn65 at%), static and dynamic (MI) hardness is decreasing with increasing loads and level out for F ≥ 1 N resulting for NbMn 2 in a static HV 0.1 = 823 and in a dynamic hardness (MI) value HV 0.1 = 735. For TaMn 2 the respective values are slightly higher with HV 0.1 (stat) = 900 and HV 0.1 (dyn) = 815, respectively. Dynamic hardness values are lower than the static ones, which is not unusual, because in case of the static hardness measurement the imprint shrinks as soon as the load is withdrawn, whereas the dynamic hardness is evaluated during the impression. The dynamic hardness values, measured with the nanoindenter, with HV 0.01 = 724.7 ± 46.6 for NbMn 2 and HV 0.01 = 815.9 ± 73.3 for TaMn 2 are in good agreement with those measured with the microindenter (for all hardness data, also converted into GPa see Table 8). Whereas Savitskii's hardness data for TaMn 2 (720 kg/mm 2 at a load of 100 g [17]) are close to our values, Svechnikov et al. [13] arrived at slightly higher values (at a 100 g load): 1020 kg/mm 2 for TaMn 2 and 1040-1250 kg/mm 2 across the homogeneity region of NbMn 2 .
The Young's moduli, E, dependent on the applied force, and evaluated with the Poisson's ratio of ν = 0.36 (from DFT calculations for NbMn 2 [32]), are displayed in Fig. 18. E is load dependent and decreasing with increasing load, flattening out for forces F ≥ 1.5 N and reaching E = 203 GPa for NbMn 2 and E = 232 GPa for TaMn 2 . Both values are in very good agreement with E = 203.4 ± 15 GPa and   E = 233.9 ± 16 GPa, respectively, evaluated from the nanoindenter measurements as well as with the DFT value E H = 197 calculated for NbMn 2 [32] (for details see Table 7).
For the calculations of the bulk modulus, B, and the shear modulus, G, the following equations were applied: The results for TaMn 2 , B ~ 277 GPa, G ~ 86 GPa, are slightly higher than those for NbMn 2 with B ~ 242 GPa, G ~ 75 GPa (for details see Table 7). This bulk modulus value for NbMn 2 is fairly consistent with the values obtained from DFT calculations of a previous work of the authors [24] with B ~ 250 GPa for the paramagnetic and B = 200-220 GPa for ferromagnetic and antiferromagnetic NbMn 2 .
According to the criterion of Pugh [65] that materials with < G/B 1.75 are brittle, both compounds NbMn 2 and TaMn 2 with = G/B 0.309 classify as brittle.
For isotropic compounds, it is possible to determine the Debye temperature, θ D from the sound velocity, using Anderson's Eq.
Fracture toughness is a measure of the resistance of a material to crack propagation. As can be seen in the insert of Fig. 17, cracks were produced from the imprint, from which we calculate the indentation fracture toughness K IC using Eq. (11): where E is the Young's modulus, HV is the hardness, F is the indentation load, c is the radial crack length from the center of the Vickers indentation and β is a function of the indenter angle, which for Vickers indentation is β = 0.016 (4). The indentation fracture toughness usually is substituted for fracture toughness in case of brittle materials, or for samples not big enough to qualify for the standard methods to determine fracture toughness (like the Chevron Notched Flexure Specimen method, the Single-Edge Precracked Beam method or the sharp 'V′ notch beam method). The results are   almost alike to those of measured fracture toughness data. Evaluating many crack lengths for various loads from static and dynamic hardness imprints, yields a K IC = 1.1 ± 0.5 MPa m 1/2 for NbMn 2 and K IC = 1.5 ± 0.2 MPa m 1/2 for TaMn 2 . From σ ≈ E 1/2 a rough estimation of the fracture strength can be derived, which reveals for NbMn 2 σ ≈ 14 GPa 1/2 and for TaMn 2 σ ≈ 15 GPa 1/2 . Thermal expansion of NbMn 2 was measured in the temperature range of 4.2-300 K (Fig. 19). The corresponding T ( ) 0 vs. T curve shows a strictly linear behavior above 150 K. Consequently, a linear fit in the temperature range of 150-300 K reveals a thermal expansion coefficient α = 10.9 × 10 −6 Κ −1 . Besides extracting the thermal expansion coefficient, the semi-classical treatment by Mukherjee et al. [67] was applied to analyze the thermal expansion as a function of temperature, taking into account the Debye model for acoustic phonons and the Einstein approximation for the optical modes.
The length change T ( ) 0 is given by: where δ is the electronic contribution to the average lattice displacement, θ D is the Debye temperature, θ E is the Einstein temperature, and p is the average number of phonon branches actually excited over the temperature range. G, F, c, and g are further material dependent constants. The Debye and Einstein temperature, extracted via a least-squares fit to the experimental data were θ D = 413 K and θ E = 87 K, with θ D in very good agreement with the data gained via elastic moduli and electrical resistivity.

Summary/conclusion
Based on a detailed re-investigation, the constitution of the two phase diagrams Nb-Mn and Ta-Mn has been established from 600 °C to the melting range: the systems are characterized by MgZn 2 -type Laves phases (C14), which are the only binary compounds in these systems but reveal extended homogeneity regions (each including the stoichiometric composition): Nb 1+x Mn 2−x (62.5-73.0 at% Mn at 950 °C: −0.19 ≤ x ≤ 0.125) and Ta 1+x Mn 2−x (59.5-68.5 at% Table 7 Elastic constants c ij for NbMn 2 (all in GPa; density d = 8.15 g/cm 3 ) and for TaMn 2 (d = 11.86 g/cm 3 ; c 66 = (c 11 -c 12 )/2); shear modulus G; bulk modulus B; Young's modulus E; subscripts V, R, H refer to Voigt, Reuss limits and Hill average; Poisson's ratio ν; mean sound velocity vm in ms −1 ; Debye temperature θ D in K; references (t.w. = this work); values in cursive script were completed in this work from the C ij matrix of the author [24,32]. a For paramagnetic C14-type; # data extracted from microindentation and nanoindentation measurements. Mn: −0.055 ≤ x ≤ 0.215). About 20 samples have been prepared in each system, mainly by arc-or high frequency melting elemental ingots, in some cases also cold compacted powder blends. The investigation of the constitution comprised light optical and transmission and scanning electron microscopy (TEM and SEM) with energy dispersive (EDX) as well as wavelength dispersive (WDX) Xray spectroscopy, X-ray powder (XPD) and single crystal (XSCD) diffraction, differential thermal analysis (DTA) and/or differential scanning calorimetry (DSC). Whereas NbMn 2 melts congruently at T m (NbMn 2 ) = 1515 ± 15 °C, TaMn 2 melts incongruently with T m (TaMn 2 ) = 1797 ± 40 °C close to a depleted peritectic reaction. Both Laves phases engage in eutectic reactions with manganese: ℓ ↔ (Mn) + TMn 2 (T eut = 1220 ± 10 °C at 4.9 at% Nb and T eut = 1234 ± 10 °C at 0.7 at% Ta, respectively). NbMn 2 also forms a eutectic with (Nb): ℓ ↔ (Nb) + NbMn 2 at T eut = 1493 ± 15 °C at 53.2 at% Nb. In both systems, Mn reveals remarkably large maximum solid solubilities (at the reaction isotherms 1493 °C (Nb) and 1797 °C for (Ta)): 19.4 at% Mn in (Nb) and 21.3 at% Mn in (Ta).
Detailed investigation (SEM-WDX, TEM, Rietveld-XPD) on the stability and structure of the phases, "NbMn" and "TaMn", adopted earlier in the literature as binary system inherent compounds, clearly revealed these phases to be oxygen-stabilized adopting the Ti 4 Ni 2 O type (so-called eta(η)-phases) with modified Nb(Ta)/Mn site substitution to comply with the formula Nb(Ta) 3−x Mn 3+y O 1−y (W 3 Fe 3 C-type). We also emphasize that no hints were found in our analyses for the existence of a μ-phase Nb 6 Mn 7 or Ta 6 Mn 7 (W 6 Fe 7type; space group R3m). Magnetic susceptibility and magnetization measurements documented that both eta-phases η-Nb 3 Mn 3 O 1−y and η-Ta 3 Mn 3 O 1−y are ferromagnetic below T c ~ 77 K, whereas the Laves phases NbMn 2 , TaMn 2 are temperature independent paramagnetic. Furthermore, our DFT calculations define instability of the eta-phase Ta 3 Mn 3 within the binary system (with respect to the weighted ratio of the C14 Laves phase TaMn 2 and pure bcc Ta). Additionally, the ab initio calculations confirmed (i) the stabilizing effect of oxygen on the eta-phase and (ii) the preference of oxygen atoms for sublattices in the sequence 16d (W 3 Fe 3 C-type)> 8b> 8a (W 6 Fe 6 C-type) in space group Fd3m.
The experimentally derived constitution of the Nb-Mn and Ta-Mn systems served as the basis for CALPHAD calculations resulting in a complete set of optimized thermodynamic data for each system. The CALPHAD optimization was supported by DFT calculated heats of formation of various configurations of the C14 Laves phases.

CRediT authorship contribution statement
All authors have contributed equally to the work.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.