Experimental and Theoretical Investigations of Out-of-Plane Ordered Nanolaminate Transition Metal Borides: M4CrSiB2 (M = Mo, W, Nb)

We report the synthesis of three out-of-plane chemically ordered quaternary transition metal borides (o-MAB phases) of the chemical formula M4CrSiB2 (M = Mo, W, Nb). The addition of these phases to the recently discovered o-MAB phase Ti4MoSiB2 shows that this is indeed a new family of chemically ordered atomic laminates. Furthermore, our results expand the attainable chemistry of the traditional M5SiB2 MAB phases to also include Cr. The crystal structure and chemical ordering of the produced materials were investigated using high-resolution scanning transmission electron microscopy and X-ray diffraction by applying Rietveld refinement. Additionally, calculations based on density functional theory were performed to investigate the Cr preference for occupying the minority 4c Wyckoff site, thereby inducing chemical order.


INTRODUCTION
Transition metal carbides and borides are known for their technological importance as electrically conductive refractories with high hardness. 1,2 When interleaved by A-group elements such as Al or Si, they form atomically layered structures combining both ceramic and metallic properties. The ternary transition metal carbides mainly form the so called MAX phases, with the general formula M n+1 AX n , where M is the transition metal and X is C and/or N arranged in a hexagonal structure of P6 3 /mmc symmetry. 3 Ternary transition metal borides, on the other hand, come in different structures and chemical formulae, such as the orthorhombic structures M n+1 AB 2n (n = 1−3), 4,5 MAB 6 and M 4 AB 4 , 7 the hexagonal structure M 2 AB 2 , 8 and the tetragonal M 5 AB 2 (T2). 9 Most of the MAB phases have Al as the A element 10 except for the hexagonal M 2 AB 2 (Ti 2 InB 2 ) 11 and the tetragonal M 5 AB 2 , also called T2 phases, (Mn 5 SiB 2 and Fe 5 SiB 2 ). 12 In 1957, the first two members of the T2 phases, Mo 5 SiB 2 and W 5 SiB 2 , were reported by Nowotny et al. 9 followed by the discovery of Fe 5 SiB 2 and Mn 5 SiB 2 in 1960. 13 More recently, interest in T2 phases has been reignited for their chemical variety, where the M element can be Mo, Mn, Fe, Cr, W, Ta, Co, and Nb, while the A element can be Si, S, P, and Ge. 9, 13−19 This has enabled them to possess various attractive properties such as high oxidation resistance, 20 near isotropic thermal expansion, 21 and excellent elastic properties 22 in addition to magnetic 14 and superconductive properties. 19 To expand the chemistry of the MAB phase family and include more transition metals, several attempts have been made to synthesize quaternary MAB with two M elements as solid solutions. Hirt et al. 23 studied the effect of Co substitution on the magnetic properties of Fe 2 AlB 2 . They reached up to 15 atom % Co in (Fe 1−x Co x ) 2 AlB 2 using spark plasma sintering, which decreased the Curie temperature from 290 to about 200 K, rendering it as a promising magnetocaloric material. Chai et al. 24 studied the magnetic properties of the (Fe 1−x Mn x ) 2 AlB 2 system. Furthermore, Hanner et al. 25 reported the synthesis of quaternary solid solutions of (Mn 1−x Cr x ) 2 AlB 2 and (Mn 1−x Cr x ) 3 AlB 4 phases, while Okada et al. synthesized the quaternary solid solutions (Cr 1−x Mo x )-AlB and (W 1−x Mo x )AlB. 26 Chemical ordering in MAB phase alloys has until recently not been reported. Inspired by the discoveries of chemical ordering in MAX phases, in the form of both in-plane ordering, i-MAX, 27 and out-of-plane ordering, o-MAX, 28 evidence was presented for a family of quaternary metal borides with inplane chemical ordering, i-MAB. 29 In particular, it was found that adding Sc or Y as the M element in Mo 2 AlB 2 , for a ratio of Mo to Sc/Y of 2:1, induces in-plane ordering in the form of Mo 4/3 M′ 2/3 AlB 2 , where M′ is Sc or Y. 30 By selectively etching Al and Sc/Y from the i-MAB phase, the first two-dimensional metal boride was discovered as single sheets of Mo 4/3 B 2−x T z (boridene). 30,31 Similarly, by adding Ti to Mo 5 SiB 2 (a T2 phase) in a ratio of Ti:Mo equal to 4:1, out-of-plane chemical ordering was established, creating the o-MAB phase Ti 4 MoSiB 2 , 32 while using the molten salt (ZnCl 2 ) method resulted in the conversion of Ti 4 MoSiB 2 to single sheets of 2D TiO x Cl y . 32 Recently, a systematic theoretical approach was implemented by Dahlqvist et al. 33 to predict the stability of o-MAB phases in the form of M 4 M′AB 2 with M from Groups 3 to 9 and A = Al, Si, P, Ga, Ge. Guided by this and previous work, 32,33 we present herein the synthesis and characterization of three novel o-MAB phases: Mo 4 CrSiB 2 , W 4 CrSiB 2 , and Nb 4 CrSiB 2 , overcoming the challenge of including Cr in Sibased T2 MAB phases. Chemical ordering is confirmed, and Cr is found to reside in Wyckoff position 4c. These findings are discussed in the light of results from density functional theory (DFT) calculations.

Materials and Synthesis Parameters.
Synthesis conditions and parameters are presented in detail in the SI. In short, all phases were synthesized by mixing their corresponding elemental powders (See Table S1) with the ratio of the desired phases, then cold pressed and placed in alumina crucibles and inserted in an alumina tube furnace. The holding temperature and time were 1700°C and 60 min, respectively. Specific synthesis details for all phases are listed in Table  S2. After furnace cooling, the sintered samples were crushed into powders using a mortar and pestle followed by sieving through a 450mesh sieve.
2.2. Characterization Techniques. The structure and weight percentage of the phases present in the produced samples were characterized using X-ray diffraction (XRD) of the powders, by filling a groove of dimensions 20 x 20 x 1 mm 2 in a glass holder. The measurements were conducted using a PANalytical diffractometer equipped with a Cu K α radiation source (step size = 0.0084°2θ and time per step = 32 s). The divergence slits and receiving slit of 1/2°a nd 5 mm, respectively, were used along with a Ni beta filter. To obtain the structural parameters and weight percentages of the phases in a sample, Rietveld refinement of the XRD pattern was performed using FullProf. code 34,35 using peak shape pseudo-Voigt #7. The refined parameters were: five background parameters, scale factors (from which the phases' weight percentage was obtained), lattice parameters, X and Y profile parameters, and atomic positions for all the phases, in addition to the global isotropic thermal displacement parameter and asymmetry parameters (the asymmetry parameters are used for asymmetry correction when the peak shapes: pseudo-Voigt #5 or #7 are used, the parameters are four independent asymmetry correction coefficients) for the major phases. The dependency of M (Mo, W or Nb)/Cr site mixing on the refinement was assessed by evaluating χ 2 for 25, 50, and 75% occupancy on each crystallographic metal site, and the obtained results were only used if the refinement reduced χ 2 by at least 10% compared to 100% occupancy. If not, site mixing was allowed, and the occupancies were fixed during the refinement.
The microstructure and chemical composition were obtained by scanning electron microscopy, (SEM) (LEO 1550), combined with energy dispersive X-ray spectrometry (EDX). The EDX measurements were acquired from at least 15 particles, all containing M, Cr, and Si in a ratio close to 4:1:1, respectively. Particles that have a stoichiometry close to the secondary phases identified by the XRD Rietveld refinement were excluded. To resolve the atomic structure and ordering of the out-of-plane ordered phases, high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) imaging and EDX analysis were performed using the Linkoping's double-corrected FEI Titan 3 (S)TEM electron microscope operated at 300 kV. Selected area electron diffraction (SAED) patterns were recorded using a FEI Tecnai G2 TEM operated at 200 kV. The HAADF signal intensity of the atomic columns in the HAADF-STEM images are considered as directly interpretable scaling with the atomic number (∼Z 1.7 ). 36 2.3. Computational Details. The computational bonding analysis was performed using the theory of crystal orbital Hamilton population (COHP) as implemented in LOBSTER. 37−41 The analyzed structures were relaxed using DFT 42,43 as implemented in the Vienna ab-initio simulation package (VASP), 44−47 using the Perdew−Burke−Ernzerhof functional. 48 An energy cutoff of 400 eV was used for the plane wave expansion, and the structures were sampled with a k-point density of at least 0.1 Å −1 , corresponding to kpoint meshes of 12 × 12 × 7 or 11 × 11 × 6 for the different structures, depending on the specific cell parameters. The atomic positions were relaxed until a force convergence of 0.005 eV Å −1 was reached, and the total electronic energy was within 10 −6 eV per atom. The projected augmented-wave method 49,50 was used for treating the core-electrons, with semicore p-and s-electrons considered as valence electrons for the transition metals Cr, Mo, Nb, and W. Including the semicore electrons resulted in a smaller charge spilling when mapping the electron density obtained from VASP in a plane wave basis to the localized atomic wavefunctions needed for the COHP analysis.

RESULTS AND DISCUSSION
The ternary T2 phases, M 5 AB 2 , have a tetragonal crystal structure of I4/mcm symmetry, where the M element occupies two Wyckoff sites, 16l and 4c. The transformation of the M 5 AB 2 phases into the out-of-plane ordered M 4 M′AB 2 leads to the occupation of M and M′ at Wyckoff site 16l and 4c, respectively. Such chemical ordering of the major transition metal (M) and minor transition metal (M′ = Cr) can be verified experimentally using high-resolution STEM imaging, from the zone axis [100] and from the atoms marked with a yellow cross from zone axes [110] and [111], shown in Figure  1. Any observed contrast between the M and Cr atoms in the STEM images can then be linked to the atomic mass differences between the two metals, as the atomic columns along these zone axes have the same number of corresponding atoms in them.
The structure of Mo 4 CrSiB 2 is shown in the STEM images in Figure 2a  Inorganic Chemistry pubs.acs.org/IC Article images. A potential explanation as to why M in M 5 SiB 2 can be replaced by Cr at the minority site 4c but not at the majority site 16l, is presented below in the theory section. The crystal structure, obtained from the refinement of the XRD data ( Figure 2c and Table 1) and overlaid on both STEM images, shows an identical atomic arrangement. Furthermore, the SAED shown in the insets of Figure 2a,b confirms the T2 tetragonal structure of I4/mcm symmetry of the Mo 4 CrSiB 2 . SEM images showing the morphology of Mo 4 CrSiB 2 particles are found in Figure S1a. The chemical composition obtained from EDX in SEM (Table S3) and EDX in TEM (Table S4) is consistent with the following relative elemental atomic percentages: Mo = 68, 70 at. %, Cr = 15, 14 at. %, and Si = 17, 16 at. %, respectively, which are close to the ideal molar ratio of 4:1:1.
The XRD pattern shown as black cross symbols in Figure 2c is obtained from a sample with initial elemental ratios corresponding to a stoichiometry of Mo 4 CrSiB 2 . The red line together with the blue line represent the calculated pattern obtained from the Rietveld refinement analysis, and the difference between the experimental and calculated XRD patterns, respectively. The major phase in the sample was found to be Mo 4 CrSiB 2 of ≈98.4 wt %, together with a small amount of Mo 2 B 5 and CrB 2 . The lattice parameters a and c, calculated from the refinement, were 5.939(5) and 11.016(4) Å, respectively. These values are in agreement (within 1%) with those calculated theoretically as listed in Table S6. It is worth noting that according to the Rietveld refinement, there is a site mixing at the 4c site, in other words there is ∼20% occupancy of Mo in the Cr occupied site. However, Mo atoms occupy 100% of the 16l site. A comparison to the other o-MAB phases as well as the ternary counterparts is found below. The detailed refinement results are found in Tables 1, S2, and S5.
The STEM images of W 4 CrSiB 2 and Nb 4 CrSiB 2 are depicted in Figure 3a, Figure 3a and S2b, respectively) show the ordering of W and Cr atoms, as W is brighter (heavier) than Cr. The crystal structure overlaid on the STEM images ( Figure  3a) and the SAEDs shown as insets in Figure S2a,b confirm the T2 tetragonal structure with I4/mcm symmetry of the W 4 CrSiB 2 phase. Similar observations made for W 4 CrSiB 2 and Mo 4 CrSiB 2 may be correlated to Mo and W being in the same group (VI) in the periodic table of elements, i.e., having a similar valence electron configuration.
The morphology of the W 4 CrSiB 2 particles is shown in the SEM image in Figure S1b. The average relative atomic percentages of W, Cr, and Si, obtained from SEM−EDX on individual particles (tabulated in Table S3) were found to be 70, 16, and 14 at.%, respectively. These values are close to the ideal molar ratios of 4:1:1 for W:Cr:Si, respectively. The XRD pattern for the sample with initial elemental ratios corresponding to the stoichiometry of W 4 CrSiB 2 is shown in Figure 3b for a selected 2θ range and in Figure S2c for the full 2θ range. The black cross symbols, red line, and blue line represent the obtained XRD pattern, the calculated pattern obtained from the Rietveld refinement analysis, and the difference between them, respectively. According to the refinement, the sample contains ≈90 wt % of the main phase, W 4 CrSiB 2 , while the rest belongs to the binary phases W 2 B, Cr 2 B 3 and Cr 5 B 3 . The obtained lattice parameters, a = 5.942(3) Å and c = 10.948(3) Å, are within 1.3% of the theoretically predicted value in Table  S6. A comparison to the other o-MAB phases as well as the ternary counterparts is found below. Further refinement results are tabulated in Tables 1, S2, and S5.    100] orientation shows the chemical ordering of Nb and Cr atoms, evident from the difference in brightness that corresponds to the difference in atomic mass. The crystal structure along with the atomic arrangement are shown by the schematic structure overlaid on both STEM images. It should be noted that Nb is an element in group V of the periodic table of elements, and as such has a different valence electron configuration compared to Mo and W. Still, it is found in the chemically ordered structure of an o-MAB phase, just like W 4 CrSiB 2 and Mo 4 CrSiB 2 . Being in the same period as Mo (the majority element of a highly stable o-MAB phase, see above), one can expect a size of Nb being suitable for occupation of the majority site 16l, just like for Mo.
The morphology of Nb 4 CrSiB 2 is shown in the SEM image presented in Figure S1c. The relative amount of Nb:Cr:Si, obtained from SEM−EDX, corresponds to 67, 17, and 16 atom %, respectively, and is shown in Table S3. Once again, these values closely match the ideal 4:1:1 molar ratios of Nb:Cr:Si in Nb 4 CrSiB 2 , respectively. Figure 3d shows the measured XRD pattern (black cross symbols) of the sample resulting from the initial elemental ratios of 4:1:1:2 for Nb:Cr:Si:B, respectively, together with the calculated patterned produced from the Rietveld refinement analysis (red line), and the difference between them shown as a blue line. The weight percentage of the desired phase, Nb 4 CrSiB 2 , was ≈68 wt % and the remainder was comprised of the phases CrB 2 , Nb 2 Cr 4 Si 5 , Cr 3 B 4 , and NbB. The a and c lattice parameters obtained from the refinement are 6.109(1) and 11.547(2) Å, respectively, and these values are within 1% of the theoretically predicted values shown in Table S6. The XRD pattern of the full 2θ range along with its refinement can be found in Figure S3c and the detailed results of the refinement are found in Tables 1, S2, and S5.
Both lattice parameters a and c (Table S5) increase as the size of the major transition metal, M, increases, going from the smaller atoms Mo and W to the larger Nb. In addition, when comparing the lattice parameters, a and c (Table S5) of the o-MAB phases Mo 4 CrSiB 2 , W 4 CrSiB 2 , and Nb 4 CrSiB 2 , with their ternary counterparts, Mo 5 SiB 2 , W 5 SiB 2 , and Nb 5 SiB 2 , a noticeable reduction of the lattice parameters is shown for the o-MAB phases due to the replacement of M in Wyckoff position 4c with a smaller element, Cr. Although the ternary Cr 5 SiB 2 is theoretically predicted to be unstable, 33 this work clearly shows the possibility to incorporate Cr in ternary T2 phases when the A element is Si and the occupied site is 4c, to form out-of-plane chemically ordered phases with the chemical formula M 4 CrSiB 2 (M = Mo, W, Nb).
To better understand why M in M 5 SiB 2 can be replaced by Cr at the minority site 4c but not at the majority site 16l, a computational bonding analysis of the COHP was performed for the 24 shortest bonds in each of the structures M 5 SiB 2 ,  The COHP of a bond can be described as an energy-weighted DOS-contribution from that specific bond and thus indicate bonding and antibonding states as a function of energy. By integration of the COHP up to the Fermi level, a measure of the bond strength is obtained. A direct comparison of integrated COHP (iCOHP) values between different structures should be done carefully, and the analysis has here been used only to get a qualitative understanding of the bonding characteristics in the different structures. In addition to the structures listed above, the binary and ternary T2 structures Cr 5 B 3 , Cr 4 WB 3 , and W 4 CrB 3 (i.e., phases of an equivalent structure but different stoichiometry) have also been studied for comparison. Out of these, Cr 5 B 3 and W 4 CrB 3 have been realized experimentally, 51,52 i.e., also in the latter system Cr will reside on the minority site with Mo at the majority site, although the structure with full Cr population, Cr 5 B 3 , is stable. The resulting total iCOHP values for the 12 shortest bonds of the different structures are shown in Figure S4, with experimentally verified phases marked by a diamond shape. It can be seen that the iCOHP of the various bonds are affected by substitution of Cr at both the 4c and 16l sites in different ways for different bonds. The most considerable effect of the substitution is seen in the interactions between the majority sites 16l, shown in Figure S4h−l, which increases substantially, for a few bonds by ∼100%, by substitution of Cr for Mo, Nb, or W at the 16l site. This implies that the bonding between the 16l sites is highly important for stability. Considering the additional phases Cr 5 B 3 , Cr 4 WB 3 and W 4 CrB 3 , a similar trend is seen, with the main difference that Cr 5 B 3 and Cr 4 WB 3 , out of which the former is stable, has a considerably larger iCOHP for the 16l−16l interactions compared to the Cr 4 MSiB 2 phases.
In Figure 4a, the relative contribution of the 16l−16l interactions to the total iCOHP is shown for the different phases. By considering the relative contribution to the total iCOHP rather than the partial iCOHP directly, discrepancies that might be caused by the different structures having different elemental species is avoided. However, a clear trend can still be seen where the 16l−16l contributions are consistently larger for all the experimentally verified phases than for the seemingly unstable phases. Figure 4b shows the bond lengths of the 16l−16l bonds in the six T2 phases with the smallest contributions from the 16l−16l interactions. These all have Cr populating the 16l−16l sites, and out of these Cr 5 B 3 , shown in dark gray diamonds, is the only experimentally verified phase, and also the phase with the shortest bond lengths. Along with the T2 phases, one of the competing phases, Cr 3 Si, 32 is also shown for comparison. It can be seen that this phase has even shorter Cr−Cr bonds. This implies that for the T2 phases with Cr at the 16l site, the Cr−Cr bonds becomes too long and therefore too weak to make the structure energetically favorable.

CONCLUSIONS
Herein, we report the synthesis and characterization of three chemically ordered Cr-based T2 MAB phases, establishing outof-plane ordered MAB phases (o-MAB) as a family of materials. Clear evidence for out-of-plane ordering in Mo 4 CrSiB 2 , W 4 CrSiB 2 , and Nb 4 CrSiB 2 is shown through STEM analysis. The relative elemental ratios of M (M = Mo, W, Nb), Cr, and Si for the three phases, measured by EDX, show a ratio close to the ideal molar ratio of 4:1:1. The crystal structure and weight percentage of phases found in the samples synthesized from the ideal molar ratio 4:1:1:2 of M 4 CrSiB 2 were obtained from the Rietveld refinement of the samples' XRD patterns. The three samples show the desired phase to be the main phase of an approximate weight percentage of 98 wt % (Mo 4 CrSiB 2 ), 90 wt % (W 4 CrSiB 2 ), and 68 wt % (Nb 4 CrSiB 2 ).
We also present a computational bonding analysis of the herein reported MAB structures along with the related T2 structures M 5 SiB 2 , Cr 4 MSiB 2 , and Cr 5 SiB 2 . This analysis shows that the 16l−16l bonds are consistently stronger in the experimentally verified structures than in the hypothetical Cr 4 MSiB 2 and Cr 5 SiB 2 . Further comparisons with the experimentally verified T2 phase Cr 5 B 3 show that the Cr−Cr bonds are both stronger and shorter in Cr 5 B 3 than in Cr 4 MSiB 2 and Cr 5 SiB 2 , implying the increased length of the Cr−Cr bonds in Cr 4 MSiB 2 and Cr 5 SiB 2 is rendering these phases energetically unfavorable.
The results presented herein show the incorporation of a new element, Cr, in the ternary T2 MAB phase where A is Si. The study also sheds further light on the structural requirements for the T2 phase to be stable. This opens the door for expanding the chemistry of the T2 family further, which in turn could enhance the property space toward, e.g., Cr-based magnetism and corrosion resistance, while also adding new potential precursors for synthesizing novel 2D materials.