Synthesis, Crystal Structure, and Compressibilities of Mn3−xIr5B2+x (0≤x≤0.5) and Mn2IrB2

Abstract The new ternary transition metal borides Mn3‐xIr5B2+x (0≤x≤0.5) and Mn2IrB2 were synthesized from the elements under high temperature and high‐pressure/high‐temperature conditions. Both phases can be synthesized as powder samples in a radio‐frequency furnace in argon atmosphere. High‐pressure/high‐temperature conditions were used to grow single‐crystals. The phases represent the first ternary compounds within the system Mn–Ir–B. Mn3−xIr5B2+x (0≤x≤0.5) crystallizes in the Ti3Co5B2 structure type (P4/mbm; no. 127) with parameters a=9.332(1), c=2.896(2) Å, and Z=2. Mn2IrB2 crystallizes in the β‐Cr2IrB2 crystal structure type (Cmcm; no. 63) with parameters a=3.135(3), b=9.859(5), c=13.220(3) Å, and Z=8. The compositions of both compounds were confirmed by EDX measurements and the compressibility was determined experimentally for Mn3−xIr5B2+x and by DFT calculations for Mn2IrB2.


Introduction
Metal boridesd isplay av ariety of very interesting physical properties such as ah igh hardness( ReB 2 ,W B 4 ,F eB 4 ,I rB 1. 35 ), [1] low compressibility (OsB 2 ,R e 7 B 3 ), [2] magnetic properties (Nd 2 Fe 14 B), [3] high transition temperature into as uperconducting state (MgB 2 ), [4] and av ery high electron emissivity (LaB 6 ). [5] Most boridesc an be synthesized at ambient pressure and are therefore relatively inexpensive and easily accessible, which makes them interesting materials for industrial usage. [1a,b, 6] Very few compounds exhibit such ah uge structuralv arietya sb orides do, which can be seen from the existence of more than 1000 binary and ternary borides that crystallize in over 150 different structure types. [7] The discovery of superconducting MgB 2 below 39 Ki n2 001 by Nagamatsu et al. [4] led to at remendousi nterest in borides within the scientific community.
Even before the discovery of the superconductivity of MgB 2 , some borides such as Ru 7 B 3 and Mo 2 IrB 2 were known to be superconducting at very low temperatures. [8] The compound Mo 2 IrB 2 was first synthesized and characterized by Rogl et al. in 1972 and the superconductivity was detected af ew years later by Vandendberg et al. [8a, 9] Since then only few other borides, such as Cr 2 IrB 2 and Mo 2 OsB 2 ,w eref ound to crystallize in the same crystal structure. [10] Kotzott et al. revisited the crystal structure of Cr 2 IrB 2 in 2007 and weres uccessful in synthesizing b-Cr 2 IrB 2 ,w hich crystallizes in as tructure type similart ot hat of Mo 2 IrB 2 . [11] Here, we report the synthesis of Mn 2 IrB 2 ,r epresenting the first ternary Mn-Ir-B compound and the second known phase adopting the b-Cr 2 IrB 2 structure type. We furthermore synthesized Mn 3Àx Ir 5 B 2 + x (0 x 0.5), as econd phase within the system Mn-Ir-B that crystallizes in the Ti 3 Co 5 B 2 structure type. The Ti 3 Co 5 B 2 structure type (ing eneral A 3 T 5 B 2 ), which was first described by Kuz'ma et al. in 1971, and including related structures, such as the quaternary substitution variant with the general formula of A 2 MT 5 B 2 ,i so ne of the most common structure types within metal-rich borides. [12] In the quaternary variant, the "Ti" position is split into two different crystallographic sites with different coordinations: ap entagonal-prismatic "A"-position and at etragonal-prismatic coordinated "M"-position. Within the quaternary variant, the atoms occupying the "M"positiona re usuallys mallert han those occupying the "A"-position. The "T"-position is preferentially occupiedb yavalence electron-rich transition metal such as Co, Rh, or Ir.T he occupation of the "M"-position with am agnetically active element (e.g. Cr,M n, Fe, Co, Ni)l eads to compounds with notable magnetic properties such as ferromagnetism in Sc 2 MnIr 5 B 2 ,a nti-ferromagnetism in Sc 2 FeIr 5 B 2 ,o rm eta-magnetism in Sc 2 MnRh 5 B 2 . [13] Due to the huge variety of possible elements occupying the variousp ositions, over 60 compounds are known to adopt the crystal structure of the aristotype or the quaternary and quinary variants, respectively. [12][13][14] Despite its importance,u pt onow only eight ternary compounds crystallizing in the Ti 3 Co 5 B 2 type are known. [15] With the successful synthesis of Mn 3Àx Ir 5 B 2 + x (0 x 0.5), an ew ternary member with am agnetic active element (Mn) at the important "M" position can be added to the important family of compounds crystallizing in the Ti 3 Co 5 B 2 structure type.

Results and Discussion
Crystal structure of Mn 2 IrB 2 Mn 2 IrB 2 is the first known ternary phase within the system Mn-Ir-B. According to the systematic extinctions, the orthorhombic, centrosymmetric space group Cmcm was derived for Mn 2 IrB 2 .T he dimensions of the unit cell are a = 3.135(3), b = 9.859(5), c = 13.220(3) ,a nd V = 408.57(4) 3 with Z = 8f ormula units. The compound is isotypic to b-Cr 2 IrB 2 [11] with Mn occupying the Cr positions. The refinement with free occupancy factors showedt hat one crystallographic site (Mn3) is not entirely occupied by manganese atoms, but depictsapartial substitutiono f% 7(2) %o ft he manganese atoms by iridium atoms. As the atomic radii of iridium (1.35 )a nd manganese (1.40 )a re similar,s uch ap artial substitution can be expected. [16] The boron atoms form aB 4 chain that can be interpreted as af ragment of ah exagon (Figure 1). The chain consists of two different boron atoms with an interatomic distance of 1.808(2) for B1ÀB1 and 1.813(9) for B1ÀB2. The B2-B1-B1 angle within the chain amounts to 112.2(3)8 which is relatively close to the ideal 1208 angle within ah exagon. Six metal atoms in the form of at rigonal BM 6 prism ( Figure 2) coordinate the boron atoms, whereas there are two different kinds of BM 6 prisms. Six Mn atoms build up the trigonal prisms, which coordinate the two B1 atoms in the center of the chain, whereas four Mn and two Ir atoms form the two prisms, which coordinate the B2 atoms at the end of the chain fragments ( Figure 1 and 2). The B1ÀMn distance within the B1Mn 6 prisms range from 2.227(4)-2.283(5) ,b eing capped by the two neighboring Ba toms (B1 and B2) and by one Ir atom (B1ÀIr1:2 .244(6) ) ( Figure 1). The interatomic distances within the B2M 6 prisms range from 2.264(5)-2.283(5) for B2ÀMn and 2.213(4) for B2ÀIr.T he complete buildingu nit can also be described as four trigonal BM 6 prisms interconnectedb yt heir rectangular sides arranged in a" cis"g eometry.T he unit cell contains four of these BM 6 units, where two are orientated with the "open" side of the chain fragment upwards and the other two units downwards ( Figure 3).
The b-Cr 2 IrB 2 structure type is closely relatedt ot he well-known Mo 2 IrB 2 -type. The main difference is the arrangemento ft he B 4 chain fragment. Whereas in the b-Cr 2 IrB 2 type the chain can be seen as af ragment of ah exagon (Figure 1), in the Mo 2 IrB 2 type the B 4 unit represents af ragment of az ig-zag boron chain. The interatomic distances between the atoms in Mn 2 IrB 2 and in b-Cr 2 IrB 2 are very similar, which was expected as the only difference is the substitution from the chromium atomsb ym anganese atoms both being of similar size. [9,11] Crystals tructure of Mn 3À Àx Ir 5 B 2 + + x (0 x 0.5) The new compound Mn 3Àx Ir 5 B 2 + x (0 x 0.5) represents the second known ternary phase within the system Mn-Ir-B.F rom the systematic extinctions, the tetragonal space group P4/mbm (no. 127) was derived. The dimensions of the unit cell are a = 9.332(1) and c = 2.896(2) with V = 252.19(2) 3 . Mn 3Àx Ir 5 B 2 + x (0 x 0.5) is isostructural to Ti 3 Co 5 B 2 ,w hich was first described by Kuz'ma et al. in 1971. [12a] The structure determinationr evealed that the Wyckoff-position 2a is as ubjecto f substitutional disorder between Mn (55(5) %) andB(45(5) %) atoms. In order to indicate the phase width, the phase is labelled as Mn 3Àx Ir 5 B 2 + x (0 x 0.5). The structure is built up by alternating layers (ABAB) consisting either of iridium atoms or of manganese and boron atoms (Figure4). By stackingt he iridium layers in the c-direction, columns of face-sharing trigonal,    Figure 5). The boron and manganese atoms reside within these different channels. The trigonal iridium prisms are centered by the boron atoms with the boron-iridiumd istance ranging from 2. 16(1)t o2 .18(1) .T he BIr 6 prisms within one columns hare their rectangular faces with pentagonal MnIr 10 polyhedra of the neighboring channel and furthermore one common Ir2-Ir2 edge with another columno fBIr 6 prisms, leading to ac olumno fe dge-sharing trigonal prisms ( Figure 6). Eight iridium atoms form ac uboid with edge lengths of 2.882(1) and 2.900(1) and coordinatet he Mn/B atoms at the 2a site with an IrÀMn/B distance of 2.506(1) .F urther manganese atoms (Mn2) reside within the center of pentagonali ridium prisms with as ide length ranging from 2.773(1)-2.900(1) and angles rangingf rom 108.1(2)-116. 9(1)8 for the base face of the pentagonal prism. Three of the rectangularf aces are sharedw ith the trigonal BIr 6 prisms and two with the neighboringt etragonal MnIr 8 cuboid.
Due to the mixed Mn/B site at the Wyckoff position 2a,M n and Ba toms occupy the "Ti" position, whereas the Wyckoff position 4g is exclusivelyoccupied by Mn atoms. The different occupation of the two "Ti-positions" is well established in compoundso ft he Ti 3 Co 5 B 2 structure-typef amily such as in Ti 2.4(2) Co 5.6(2) B 2 or Sc 2 MnIr 5 B 2 . [13, 15b] The substitution of the metal atom at the 2a site by much smallerb oron atoms was first observedb yF okwa et al. in Ti 3Àx Ru 5Ày Ir y B 2 + x (0 x 1a nd 1 y 3). [17] The interaction between the magnetically active atoms (manganese) on this positioni sd ecisive for the excellent magnetic properties of the isostructural compounds. [13, 14c,f, 15b]

Elemental analysis
Numerous crystals for both phases were investigated with the focus on the Mn:Ir ratio, as the detection of boron is impossible. Mn 2 IrB 2 shows ar atio of 67.9 AE 0.9 atom %M na nd 32.1 AE 0.9 atom %I ra nd for Mn 3Àx Ir 5 B 2 + x (0 x 0.5) ar atio of 35.1 AE 1.8 atom %M na nd 64.9 AE 1.8 atom %I rw as observed. Both ratios are similart ot he ratios obtained by the single-crystal structure determination.A st he metal ratios of both phases differ by few atomic percentc ompared to the single-crystal structure solution,t he exact formula shouldb eM n 2 AE x Ir AE x B 2 (x 0.1) and Mn 3Àx Ir 5 B 2 + x (0 x 0.5) to indicatet he phase width.

Compressibility
In the pressure regime up to 37 GPa, Mn 3Àx Ir 5 B 2 + x (0 x 0.5) shows no structuralp hase transition. The bulk modulus is B 0 (Mn 3Àx Ir 5 B 2 + x (0 x 0.5), 3rd order) = 209(10)GPa, with ap ressure derivative B' = 7.8(1.8). Restraining B' to the value 4g ives B 0 (Mn 3Àx Ir 5 B 2 + x (0 x 0.5), 2nd order) = 246(6) GPa. The individuall attice parameters showa nisotropic behavior as the pressurei ncreases,s hown by the c lattice parameter becoming more incompressible,w hich is reasonable regarding the fact that the atomic layers are stacked in the c-direction (Figure 7). As ummary of the compressibilities of the phases is given in Ta ble 1, and the pressured ependence of the unit cell parameters is listed in Ta ble S5 (Supporting Information). Due to metrological difficulties,t he compressibility of Mn 2 IrB 2 could not be obtainede xperimentally but could be determined from DFT calculations ( Figure 8).

DFT calculations
DFT calculations were performed on af ully ordered structure of Mn 2 IrB 2 ,n eglecting the partial substitution of Mn atoms by Ir atoms. The pressure dependence of the lattice parameters was calculatedu pt oam aximum pressure of 50 GPa. Fitting the DFT data by at hird order Birch-Murnaghan (BM EOS) yielded B 0 (Mn 2 IrB 2 ,3 rd order,D FT) = 304(2) GPa with ap ressure derivative B' = 4.4 (2).Asecond order fit gives B 0 (Mn 2 IrB 2 , 2nd order,D FT) = 309(2). The calculations showedn oi ndications of as tructuralc hange upon compression.The anisotropic behavior of the individuall attice parameters remained unchanged over the entire pressure, with a being most compressible ( Figure 8). As ummary of the compressibilities of the phases is given in Table 1a nd the pressure dependenceo ft he  unit cell parameters is listed in Table S6.

Conclusions
With the synthesis of Mn 2 IrB 2 and Mn 3Àx Ir 5 B 2 + x (0 x 0.5), we have synthesized the first two ternary boridesc ontaining manganesea nd iridium.B oth phases can be synthesized by hightemperature techniquesb ut high-temperature/high-pressure conditions wereu sed to improve the quality of the single crystals. Mn 2 IrB 2 represents the second phase crystallizing within the b-Cr 2 IrB 2 structuret ype, whereas Mn 3Àx Ir 5 B 2 + x (0 x 0.5) crystallizes in the well-known Ti 3 Co 5 B 2 type, with aM n/B mixed site. Within the new compound, the important "M"-position, which is responsible for many outstanding magnetic properties of othersp hases with the Ti 3 Co 5 B 2 type, is occupied with a magnetically active element (Mn). Due to the extremelyl ow scattering crosss ectiono fb oron in comparison with iridium and manganese for X-rays, it is practically impossible to reliably determine the exact occupation of the boron atoms solely based on X-ray diffraction data. Therefore, EDX measurements were carriedo ut to specifyt he existingp hase width. Compared to relatedb inaryi ridium and manganese boridess uch as b-Ir 4 B 5 (B 0 ,3 rd order, = 249(3) GPa), Ir 5 B 4 (B 0 ,3 rd order, = 304(6) GPa) andM nB 4 (B 0 ,3 rd order, = 254(9) GPa), Mn 3Àx Ir 5 B 2 + x (0 x 0.5) shows ah igher compressibility (B 0 ,3 rd order, = 209(10) GPa). The DFT calculations for Mn 2 IrB 2 indicate that its compressibility (B 0 ,3 rd order,D FT = 304(2)GPa) is lower than the compressibility of MnB 4 and comparable to iridium borides, whereby it needs to be confirmed by experiment. [18] Both bulk moduli are in between the bulk modulus for elemental iridium (B 0 ,3 rd order, = 326(3) GPa) and elemental manganese (120 GPa) but do not reach the high bulk moduli of the rheniumoro smium borides. [2,19] The existence of an ew,m anganese-containing phase crystallizingi nt he Ti 3 Co 5 B 2 structure type should stimulate further research, especially focusingo nt he magnetic properties of the new compounds.

Experimental Section
Synthesis Manganese (99.95 %p urity,C hemPur,K arlsruhe, Germany), iridium (99.9 + %p urity,C hemPur,K arlsruhe, Germany) and amorphous boron (95 + %p urity,G oodfellow,C ambridge, England) were used as starting materials in am olar ratio of 2:1:2f or Mn 2 IrB 2 and of 1:2:2f or Mn 3Àx Ir 5 B 2 + x (0 x 0.5). The reaction mixtures were finely ground in an agate mortar and afterwards inserted into crucibles made from hexagonal boron nitride (HeBoSint P100, Henze BNP GmbH, Kempten, Germany). The boron nitride crucibles were placed in tungsten crucibles (Plansee Metall GmbH, Reutte, Austria) and heated in ar adio frequency furnace (TruHeat HF 5010, Hüt-   tinger Elektronik GmbH + CO. KG, Freiburg, Germany) under Ar atmosphere. [20] For the synthesis of Mn 2 IrB 2 ,t he furnace was first heated to 1200 8Cw ithin one hour,m aintained at 1200 8Cf or four hours, then the temperature was lowered to 1000 8Cw ithin 10 hours, and finally quenched to room temperature by switching off the furnace. The synthesis of Mn 3 Ir 5 B 2 required at emperature of 1400 8C, which was then held for 12 hours before switching off the furnace. Both compounds were obtained as off blackish powders, but no single-crystals with an adequate quality and size for single-crystal X-ray diffraction analyses could be synthesized.
With the aim to improve the crystal size and quality,h igh-pressure/ high-temperature syntheses were carried out. Therefore, the finely grounded educts were inserted in ah exagonal boron nitride (He-BoSint P100, Henze BNP GmbH, Kempten, Germany) container, which was then inserted into a1 4/8 high-pressure assembly.I tw as compressed to 10 GPa within four hours by ah igh-pressure device consisting of ah ydraulic 1000 tp ress (mavo press LPR 1000-400/ 50, Max Voggenreiter GmbH, Mainleus, Germany) and aW alkertype module (Max Voggenreiter GmbH) with eight tungsten carbide cubes (HA-7 %Co, Hawedia, Marklkofen, Germany). The mixture was heated from ambient temperature to 1100 8Cw ithin 5min. The temperature was held for 45 minutes and afterwards reduced to 700 8Ci n4 5minutes. For the syntheses of both phases, the same synthesis program can be used. After decompression, the samples were isolated from the surrounding assembly parts by mechanical separation. This method led to the formation of singlecrystals of Mn 2 IrB 2 and Mn 3Àx Ir 5 B 2 + x (0 x 0.5) with dimensions of up to 0.040 mm and 0.015 mm, respectively.Amore detailed description of this setup can be found in the literature. [21] High-pressure X-ray diffraction For high-pressure experiments, Boehler-Almax type diamond anvil cells were used. [22] The cells were loaded with Ne as pressure-transmitting medium. Samples were placed in holes of 110-130 mmi n diameter,which were drilled by ac ustom-built laser lathe in pre-indented Re gaskets (40-50 mmi nt hickness). The pressure was determined using the ruby fluorescence method. [23] Synchrotron Xray diffraction experiments at high pressures were performed at the beamline P02.2 of the PETRA III synchrotron (DESY,H amburg, Germany). The diffraction patterns were acquired with aP erkinElmer XRD1621 detector at aw avelength of 0.2902 ,w ith beams focused to 1.5 2.3 mmF WHM by Kirkpatrick-Baez mirrors. AC eO 2 standard and an Enstatite single-crystal standard were used to determine the sample-to-detector distance and for detector calibration during the experiments. [24] The diffraction patterns were corrected and integrated using the FIT2D and DIOPTAS software packages. [25] Crystal structure analysis The powder X-ray diffraction patterns were obtained in transmission geometry from flat samples of the products. The measurements were carried out using aS TOES TADI Pp owder diffractometer equipped with Mo Ka1 radiation (Ge(111)m onochromator l = 0.7093 )i nt he 2q range of 2.0-60.38 with as tep size of 0.0158 for both phases. As ad etector,asilicon microstrip solid-state detector (Dectris Mythen 1K)w as employed. For Mn 3Àx Ir 5 B 2 + x (0 x 0.5), a Rietveld analysis was carried out, which is shown in Figure S1 in Supporting Information. Most of the reflections can be assigned to Mn 3Àx Ir 5 B 2 + x (0 x 0.5), however,af ew reflections (e.g. at 18.38, 20.38,a nd 21.58)c ould not be assigned to any known phase. Next to the non-assignable reflections and those of Mn 3Àx Ir 5 B 2 + x (0 x 0.5), the pattern exhibits ab road amorphous halo at low 2q that is due to unreacted amorphous boron. The reflection of the (110)lattice plane at 6.68 cannot be detected as it is too weak compared to the amorphous halo in this range. The lattice parameters of Mn 3Àx Ir 5 B 2 + x (0 x 0.5) shown in Ta ble 2w ere obtained through a Rietveld analysis of the powder pattern using the program TOPAS. [26] The powder pattern of Mn 2 IrB 2 exhibits further reflections, which cannot be assigned to any known phase within the system Mn-Ir-B. These reflections show that at least one further unknown compound was synthesized as as ide-product during this synthesis. Due to the amount of non-assignable reflections, aR ietveld refinement was unsuccessful and the measured powder pattern of Mn 2 IrB 2 was just visually compared to the theoretical pattern (Figure S2).
Small single crystals of Mn 2 IrB 2 were selected by mechanical fragmentation using ap olarization microscope. AB ruker D8 Quest Kappa diffractometer with Mo Ka radiation (l = 0. 71073 )w as used to collect the single-crystal intensity data at room temperature. A multiscan absorption correction (SADABS-2014) [27] was applied to the intensity data sets. The structure solution and parameter refinement (full matrix-least-squares against F 2 )w ere performed by using the SHELX-13 software suite with anisotropic displacement parameters for all atoms. [28] According to the systematic extinctions, the orthorhombic space group Cmcm (no. 63) was derived for Mn 2 IrB 2 .T he GOF of 1.235 as well as the value of R1 = 0.0250 for 640 unique reflections with I ! 2s(I)a re indicative of as uccess- ful refinement. To ensure that no symmetry operations were missing, the final solution was checked with PLATON. [29] All relevant details of the data collection and the refinement are listed in Ta ble 3, the positional parameters are listed in Ta ble S1 (Supporting Information), and the important bond lengths are listed in Ta ble S2. The program Diamond [30] was used for the graphical representation (Figure 1-6) of both structures.
For Mn 3Àx Ir 5 B 2 + x (0 x 0.5), single-crystal diffraction data were collected using crystals placed in diamond anvil cells. The data were collected by performing w-scans in 0.58 steps, with an integration time of 1s econd. Ap latinum foil of proper thickness was used as an absorber in order not to oversaturate am ajority of reflections. The CrysAlis program was used to reduce and integrate the data. As tandard enstatite crystal was measured beforehand, in order to determine the instrumental parameters. The space group determination and solution of the crystal structure were done with SHELXT, [28b] the crystal structure refinement was done with Jana2006. [31] The crystal structure solution and refinement was performed in space group P4/mbm. Upon crystal structure solution, the positions of Mn and Ir atoms were found. The SHELXT algorithms were not able to determine the positions of the much lighter Ba toms;these were taken from DFT calculations. The formula of the resulting compound was Mn 3 Ir 5 B 2 and resultant structure was found to be isostructural to Ti 3 Co 5 B 2 . [32] No observed reflections violated the extinctions of the space group P4/mbm. The correctness of the crystal structure solution was furthermore checked by carrying out aR ietveld refinement of the measured powder diffraction pattern. It clearly emphasizes the assumption of P4/mbm being the correct space group ( Figure S2). Additionally,the DFT calculations also suggest that the structure description in the space group P4/mbm is the correct one. The structure refinement in the space group P4/mbm based on the single-crystal data showed that the isotropic displacement parameter of the Mn1 atom was four times larger than that of the Mn2 atom. This suggested that the model with the formula Mn 3 Ir 5 B 2 overestimates the electron density at the Mn1 site. In the next step, the data was refined with a partial substitution of the Mn1 site with Ba toms. The final refinement showed that such am odel fits very well to the data, further lowering the factor R obs and yielding reasonable atomic displacement parameters. The final formula was found to be Mn 3Àx Ir 5 B 2 + x with x = 0.45 (5). This model was again confirmed by the Rietveld refinement of the powder diffraction data.

Elemental analysis
Crystals of both phases were semi-quantitatively investigated by the use of aJ EOL JSM-6010LVs canning electron microscope with a Quantax (Bruker,B illerica, USA) energy dispersive system (EDX) for element identification. An acceleration voltage of 15 kV was used for small fragments of the sample, which were mounted on carbon pads on ac harge reducing sample holder.S uitable regions of the crystals were selected for the measurement points.

Determination of the compressibility
The compressibilities were determined by investigating the dependence of the unit cell parameters upon compression. The unit cell parameters were obtained by analyzing the single-crystal data. The data were fitted using at hird order Birch-Murnaghan (BM) equation of state [33] using the EosFit software package. [34] In Equation (1), p is the pressure, V 0 is the reference volume at ambient conditions, V is the unit cell volume at the respective pressure and B 0 is the bulk modulus. In the second order BM equation of state, B 0 0 is constrained to 4.
Density functional theory In order to obtain ab etter understanding of the structure-property relations of the synthesized compounds, we performed density functional theory (DFT) calculations employing the CASTEP [35] code. This code implements the Kohn-Sham DFT based on ap lane wave basis set in conjunction with pseudopotentials. The plane wave basis set is unbiased (as it is not atom-centered) and does not suffer from basis set superposition errors in comparison to atom- Table 3. Crystal data and structure refinementofM n 2 IrB 2 (standard deviations in parentheses). centered analogues. It also makes converged results straightforward to obtain in practice, as the convergence is controlled by a single adjustable parameter,t he plane wave cut-off, which was set to 580 eV.A ll pseudopotentials were ultrasoft and were generated using the PBE-GGA to allow for af ully consistent treatment of the core and valence electrons. [36] Brillouin zone integrals were performed by using Monkhorst-Pack grids with spacings of less than 0.020 A À1 between individual grid points. As imultaneous optimization of the unit cell parameters and internal coordinates was performed in the way that forces were converged to 0.005 eVA À1 and the stress residual was 0.005 GPa. Elastic stiffness coefficients were derived by stress-strain calculations.