Anisotropic thermal expansions of select layered ternary transition metal borides: MoAlB, Cr₂AlB₂, Mn₂AlB₂, and Fe₂AlB₂

Transition metal borides are attractive because of their high hardness values, high melting points, performance in extreme high-temperature environments, good thermal and electrical conductivities, and, in the some cases, magnetic properties, which has led to exploration of their applications in coatings and as catalysts.^1–4 Many of these properties can be traced to the strong boron (B) covalent framework and the metal sublattice. The ternary transition metal borides M₂AlB₂ (M = Cr, Mn, Fe) and MAlB (M = Mo, W) were discovered between the 1960s and 1990s.^5–8 In 2015, Ade and Hillebrecht⁹ dubbed them the “MAB phases” because their atomically laminated structures resemble those of the ternary carbides and nitrides M_n+1AX_n phases, or MAX, where M is an early transition metal, A is mostly a group 13 or 14 element from the periodic table (such as Al, Si, and Ga), X is C and/or N, and n = 1, 2, or 3.¹⁰ Recently, the MAB phases MoAlB and Fe₂AlB₂ have generated interest for their promising high-temperature oxidation and magnetocaloric properties, respectively.^11,12

The ternaries M₂AlB₂ and MAlB crystallize in the Cmmm and Cmcm space groups, respectively. In the M₂AlB₂ phases, the M-B sublattice is interlayered by a single Al layer [Fig. 1(a)]; in MAlB, two Al layers are present [Fig. 1(b)]. Another important structural feature that looms large in this work is the B–B chains. In the ternaries, the zig-zag B–B chains run along the a-direction and c-direction for the M₂AlB₂ and MAlB phases, respectively [Figs. 1(a) and 1(b)]. When the structure of the binary boride CrB (space group Cmcm) [Fig. 1(c)] is compared to its ternary counterparts, it is clear that the M-B sublattices of the latter are nearly identical to M-B blocks of CrB, but intercalated with Al. The shortest B–B and M–M bonds distances in CrB and Cr₂AlB₂ are nearly identical (see Table S1 in the supplementary material).

The binaries MnB and FeB crystallize in the space group Pnma, even though the non-standard space group Pbnm can also be found in the literature. When compared to CrB, both structures are characterized by one dimensional zig-zag chains of B-atoms, with a slightly different arrangement of the BM₆ trigonal prisms [Figs. 1(c) and 1(d)] than CrB. Kanaizuka previously described how the FeB-type structure can be obtained from the CrB-type structure.¹³ The binary boride MoB has two polymorphs:¹⁴ a high temperature orthorhombic β-MoB (space group Cmcm) which is isostructural with CrB, and a low temperature tetragonal α-MoB (space group I4₁/amd), where the B–B chains’ directions alternate in the a or b directions in each subsequent MB block [Fig. 1(e)]. Thus, slight differences exist between the various monoborides and the MAB phases, but the B–B zig-zag chains, with trigonal prismatic coordination by the M atoms around the constituent B atoms, are a shared structural feature among them all.

Before comparing the coefficients of thermal expansion (CTE) of the ternaries and corresponding binaries, it is important to point out that variations in the nomenclatures of the crystallographic axes can render comparisons confusing. For example, in MnB and FeB, the stacking direction can be considered to be along the c-axis, whereas in CrB, it is the b-axis [cf. Figs. 1(c) and 1(d) and Table I]. To solve this problem, henceforth, we refer to the expansion directions not by their crystallographic axes, but rather by their bonding arrangements. More specifically, the CTEs in the directions perpendicular (α_⊥) and parallel (α_//) to the B–B chains, and the CTEs along the stacking direction (α_st) are reported in Table II and discussed below. The links between these directions and the crystallographic axes for each compound are shown in Table I.

The thermal expansions along the different axes of MoB were reported by Zhao et al.²⁰ from room temperature (RT) to 1273 K, though a deviation from linearity at intermediate temperatures was observed during heating. Linear CTEs, determined by dilatometry, have been reported for bulk CrB²¹ (8.9 × 10⁻⁶ K⁻¹), MnB²² (5.1 × 10⁻⁶ K⁻¹), and FeB²³ (12 × 10⁻⁶ K⁻¹). Kanaizuka²⁴ reported on the evolution of the lattice parameters and unit cell volumes of CrB, MnB, and FeB from RT to 1000 K. The thermal expansions of CrB along the a and b axes were not reported, which is why they were measured herein.

Only quite recently were the CTEs of a few MAB phases reported by dilatometry or X-ray diffraction (XRD) measurements. Dense, polycrystalline MoAlB samples, with ∼9 vol. % intermetallic and Al₂O₃, were found to have a CTE of 9.5 × 10⁻⁶ K⁻¹ up to 1373 K.¹⁸ The CTE of dense, polycrystalline Mn₂AlB₂ samples, with ∼10 vol. % intermetallics, was measured up to 1173 K by thermo-mechanical analysis (TMA) and found to have a significantly higher CTE of 18.6 × 10⁻⁶ K⁻¹.²⁵ The temperature dependences of the lattice parameters of Fe₂AlB₂, below RT, were calculated by Lewis et al.²⁶ from XRD data. A contraction of the c parameter and an expansion of a and b upon heating from 200 K to 293 K was observed, resulting in a limited volume contraction and a calculated volumetric CTE of 4.4 × 10⁻⁶ K⁻¹. However, as this temperature range includes the effects of magnetostriction, these values may not be valid at higher temperatures. Cedervall et al. observed similar trends for the lattice parameters for temperatures below 295 K.²⁷ 

While the thermal properties of MAX phases have been extensively studied,^15,16 much less experimental and theoretical work has been carried out so far on the MAB phases.^17–19 However, such knowledge is essential from both a scientific point of view as well as a practical one. A systematic study of thermal expansions along the different crystallographic axes is scientifically useful because it sheds light on the relative bond strengths and their anharmonicities. From a practical point of view, such information is crucial if these solids are ever to be used in industrial applications at elevated temperatures.

Herein, in situ powder X-ray diffraction (XRD) patterns were collected as a function of temperature, from RT to 1273 K under a nitrogen (N₂) or argon (Ar) atmosphere. The resulting diffractograms were analyzed using Le Bail’s method to calculate the changes in lattice parameters with temperature of MoAlB, Cr₂AlB₂, Mn₂AlB₂, and Fe₂AlB₂ powders. The CTEs of CrB powders were also measured.

The ternaries, MoAlB, Fe₂AlB₂, and Cr₂AlB₂, were synthesized according to our previous report.²⁸ Powders of MoB (>99%, <38 μm, Alfa Aesar, Ward Hill, MA, USA), FeB (98%, <20 μm, Alfa Aesar), or CrB (MP Biomedicals, <38 μm) were ball milled with Al (99.5%, <44 μm Alfa Aesar, Ward Hill, MA, USA) in a 1:1.3 or 2:1.5 atomic ratio for MoAlB and M₂AlB₂ (M = Cr, Fe), respectively. The mixed powders were cold-pressed and heated under flowing Ar in a tube furnace to 1173 K for Cr₂AlB₂ and to 1273 K for Fe₂AlB₂ and MoAlB and held at these temperatures for 15 h. Powders of Mn₂AlB₂ were synthesized by ball milled Mn (Alfa Aesar, 99.3%, <44 μm), Al (Alfa Aesar, 99.5%, <44 μm), and B (Alfa Aesar, 98%, amorphous and crystalline, <44 μm) powders in a 2:1.5:2 atomic ratio and cold-pressed in a steel die using a load that corresponded to a stress of 100 MPa. The resulting pellets were then heated, under flowing Ar in a tube furnace, to 1293 K, at a heating rate of 4 °C/min and held at this temperature for 15 h, followed by furnace cooling. Powders were obtained by drilling the reacted porous pellets. For Fe₂AlB₂, the powders were immersed in 2M hydrochloric acid for 10 min to dissolve the Al₁₃Fe₄ impurities (Fig. S1 in the supplementary material). The weight loss with this process was 63%, which means that a fraction of Fe₂AlB₂ was also dissolved. Attempts to dissolve the intermetallic impurities in the Mn₂AlB₂ powders were unsuccessful due to equally fast dissolution of the ternary. Single-phase CrB (HC Starck, Grade B) powder was tested as-received.

To investigate the stability of Fe₂AlB₂ in N₂, powders were heated in a tube furnace to 1273 K, for 2 h, under flowing N₂. XRD patterns of the resulting powders were then obtained.

High-temperature XRD patterns were acquired on MoAlB, Mn₂AlB₂, Fe₂AlB₂, and CrB powders and on a pressed pellet of Cr₂AlB₂, using a Rigaku SmartLab powder diffractometer setup in the Bragg-Brentano geometry in the 20–155° 2θ range using a 0.01° step size and a speed of 3°/min. XRD patterns were acquired at RT, 323 K and every 100 K and 200 K in the 373–1273 K temperature range on heating and cooling, respectively. A heating stage (Anton Paar DHS1100) was used with a static N₂ gas atmosphere enclosed in a hemispherical graphite dome. Only the 29–80° 2θ range is shown in Fig. 2 for clarity (the graphite dome induced a large peak centered at 28.5° 2θ). At ≈973 K, the XRD patterns of the CrB sample degraded noticeably to the point that the data could not be processed after 973 K or during cooling. This sample, in contrast to all others, was noticeably cracked and distorted after the measurement. Measurements were also performed on standard α-Al₂O₃ (NIST SRM1976a) to check the accuracy of our temperature. The results obtained are consistent with the literature (see Fig. S2 in the supplementary material).²⁹ Profile refinement using the Le Bail method was carried out on the XRD diffractograms using the JANA2006 program.³⁰ The background was estimated using a Legendre polynomial and the following parameters were refined: overall zero-shift, background parameters, lattice parameters, and peak shape parameters.

All powders tested were predominantly single phase (Fig. 2). Rietveld refinement of the Cr₂AlB₂ sample evidenced ≈14 vol. % CrB impurities; the Mn₂AlB₂ powders contained Al₆Mn, Al₄Mn, and Al₂O₃ impurities at 1, 12, and 2 vol. %, respectively. The HCl-treated Fe₂AlB₂ powders used for the measurements contained ≈6 vol. % Al₂O₃ impurities. The MoAlB sample contained some Al₃Mo and Al₅Mo impurities (below 1 vol. %). Because we used XRD and the impurity content in the powders was relatively low, the presence of these impurities should not affect any of our conclusions.

Figures 3(a)–3(e) summarize the temperature dependences of the lattice parameters—on both heating (open red symbols) and cooling (solid blue symbols)—and the unit cell volumes for MoAlB, Cr₂AlB₂, Mn₂AlB₂, Fe₂AlB₂, and CrB, respectively. The CrB results of Kanaizuka²⁴ are included (open green symbols) in Fig. 3(e). The lattice parameters and unit cell volumes at each temperature can be found in Tables S2–S6 in the supplementary material, together with the linear fits of the data (Figs. S3–S8 in the supplementary material).

The resulting CTEs, obtained by linear least-squares fitting of the results, are summarized in Table II. To compare the results obtained here with bulk dilatometric measurements, the normalized unit cell volume is plotted as a function of temperature during heating and the slope was divided by three to yield

where V₀ is the unit cell volume at 673 K for Mn₂AlB₂ and RT for the other compounds. The CTEs along the three principal crystallographic directions are defined as

where l is a, b, or c and l₀ is the value at 673 K for Mn₂AlB₂ and at RT for the other compounds.

The maximum degree of anisotropy is defined here as

where α_av is the average value of α_a, α_b, and α_c.

Of the four ternaries, the CTEs of MoAlB are the most isotropic [see Fig. 3(a) and Table II]. They are also the lowest, which is consistent with the fact that this compound is the most thermally stable^19,25,31,32 among the ternaries. There is no hysteresis between the results obtained on heating and cooling, and the CTE values reported (Table II) are valid in the 308 K to 1273 K temperature range. When α_vol is compared to α_dila in Table II, it is clear that the latter is larger. This discrepancy may be partially accounted for by the fact that the sample used for dilatometry contained Al₃Mo and Al₈Mo₃ intermetallic phases that would raise the CTE of the bulk sample.¹⁸ This is a reasonable assumption considering that Al₃Mo, as well as aluminides of high-melting-point 3d and 4d transition metals, generally have CTEs of >10⁻⁵ K⁻¹.^33–36 

At ≈8.8 × 10⁻⁶ K⁻¹ and 8.4 × 10⁻⁶ K⁻¹, respectively, α_// and α_st are comparable [Fig. 3(b)]. For reasons discussed below, α_⊥, at ≈14 × 10⁻⁶ K⁻¹, is significantly higher. Upon cooling, new peaks, not belonging to Cr₂AlB₂, were observed and matched to those of chromium nitride (CrN) and a second unknown phase. Despite the appearance of these extra peaks, no hysteresis between the results obtained on heating and cooling was observed [Fig. 3(b)]. The CTE values reported (Table II) are, again, valid for the 308 K to 1273 K temperature range.

Of the four ternaries, the response of Mn₂AlB₂ is unique [Fig. 3(c)]. Because of a magnetic transition close to RT,³⁷ a contraction in b is observed in the 308 K to 373 K temperature range. The average CTE values reported in Table II are thus only valid in the 673 K–1273 K temperature range, wherein the unit cell volume and all the lattice parameters increase roughly linearly with temperature. In the 373 K –1273 K range, the temperature dependencies of b and c are non-linear and well-described by Eqs. (4) and (5)

At ≈22.1 × 10⁻⁶ K⁻¹, α_⊥ is almost 3 times larger than α_st and twice as large as α_// (Table II). This anomalously high α_⊥ value is the main reason that, at 14.0 × 10⁻⁶ K⁻¹, α_vol for this compound is the highest among the MAB phases. When considering the whole temperature range measured, α_vol increases slightly to 15.5 × 10⁻⁶ K⁻¹. As high as the latter value is, it is still lower than the value of 18.6 × 10⁻⁶ K⁻¹ obtained by dilatometry for this compound.²⁵ Here again, and most probably for the same reasons as for MoAlB, viz. presence of impurities (Al-rich Al-Mn intermetallics), α_vol < α_dila (Table II).

At some point between 873 K and 973 K, Fe₂AlB₂ decomposed as evidenced by the emergence of peaks originating from FeB. This result was somewhat surprising since recent work showed that Fe₂AlB₂ is stable under argon (Ar) to temperatures of at least ∼1460 K.^19,32 To confirm this result, we heated Fe₂AlB₂ powders to 1273 K for 2 h under flowing N₂. XRD of the resulting powder (Fig. 4) indicated the total conversion of the ternary to FeB and AlN, with a few small peaks associated with α-Al₂O₃. It follows that Fe₂AlB₂ becomes unstable in N₂ at temperatures below 1273 K. Based on these results, the following reaction most probably occurs at ≈900 K:

Because the in-situ XRD measurements were done under a static N₂ atmosphere, the rate of decomposition of Fe₂AlB₂ was limited relative to the N₂ annealing experiment. This decomposition, however, most probably explains both the hysteresis observed on cooling [Fig. 3(d)] as well as the deviation from linearity of the measured lattice parameters at temperatures >773 K. Thus, the CTE values reported in Table II are only valid in the 308 K to 773 K temperature range. Acquisitions were also carried out under Ar, but for reasons that are not clear the sample also decomposed noticeably starting from 873 K and the data could not be processed above that temperature. However, the data below 873 K acquired under Ar are in good agreement with the ones obtained under N₂ (Fig. S8 and Table S7 in the supplementary material).

The results obtained in this work, together with Kanaizuka’s, for CrB,²⁴ are plotted in Fig. 3(e). The agreement between the two sets of results is quite good for the c parameter (for reasons that are not clear, only the evolution of c is given in Ref. 24). Our unit cell volume expansion, is slightly lower than previous results [compare green and red symbols in Fig. 3(e) (iii)] but comparable to the value obtained by dilatometry obtained by Shigematsu et al.²¹ 

The following discussion is predicated on the premise that stronger bonds expand less than weaker ones. In the MAB phases, there are three sets of bonds that are likely to play an important role in determining the CTE values in the various crystallographic directions: (i) the strong B–B chains, parallel to a for M₂AlB₂ and parallel to c for MoAlB; (ii) the M–A bonds along the stacking direction b, and (iii) the M–M bonds along the b-direction.

Based on the results shown in Table II, MoAlB stands apart in a number of ways. It has the lowest CTE and is the most isotropic. The maximum degree of anisotropy, as defined by Eq. (3), is 27%. Further, α_⊥ and α_// are quite comparable indeed, and both are lower than α_st. The empirical trends of the axial CTEs of Fe₂AlB₂ are analogous to those of MoAlB in that α_st is the highest. Thus, it can be grouped with MoAlB despite their different structures. At 37%, the maximum degree of anisotropy is also relatively low.

Cr₂AlB₂, Mn₂AlB₂ and, interestingly, CrB, can be grouped together. For these compounds, α_st is the lowest. Moreover, α_⊥ is significantly higher than α_//. In Mn₂AlB₂, α_⊥ is 22.1 × 10⁻⁶ K⁻¹. These results suggest that the strengthening of the M–A bonds along the stacking direction, comes at the expense of the M–M bonds normal to the B–B chains. While α_⊥ is not the highest among the three directions for Fe₂AlB₂, as it is for Cr₂AlB₂ and Mn₂AlB₂, the general the trend α_⊥ > α_// prevails for all the M₂AlB₂ phases.

When compared to the MAX phases, wherein the vast majority expand the most along the stacking c direction,^15,38,39 the MAB phases show more variability. The reasons for such wide variations in CTEs along the various directions are to be found in the intricacies of the bonding between the different atoms. Based on the simple assumption that stiffer bonds would expand less, in some cases, density functional theory (DFT) calculations of elastic constant can shed light on the matter. Table III lists the elastic constants (c_ij) calculated by DFT reported in the literature for MoAlB, Mn₂AlB₂, Cr₂AlB₂, and Fe₂AlB₂. Based on the DFT-calculated c_ij values, the order of the CTE values from high to low should be: MoAlB > Fe₂AlB₂ > Mn₂AlB₂ ≈ Cr₂AlB₂. The actual order determined herein, on the other hand, also from high to low, is Mn₂AlB₂ > Cr₂AlB₂ ≈ Fe₂AlB₂ > MoAlB. It follows that there is no correlation between the DFT-calculated elastic constants and the CTEs measured. The same is true if individual c_ij values are considered. For example, based on the results shown in Table II, by far the lowest c_ij for Mn₂AlB₂ should be c₃₃ (i.e., along c where the expansion is 22 × 10⁻⁶ K⁻¹). This is not the case in Table III.

These observations suggest that (i) the DFT calculations are missing a crucial component such as magnetic, or other, interactions, (ii) the anharmonic terms are quite important and cannot be ignored, and/or (iii) our crystals are highly defective. Clearly more work needs to be carried out to reconcile some of the discrepancies outlined here.

As noted above, further insight can be gleaned from comparing the CTEs of the ternaries and corresponding binaries. The evolution of lattice parameters with temperature from the work of Kanaizuka²⁴ on MnB and FeB is plotted in Fig. 5 and the CTEs can be found in Table II. Except for MoAlB and α-MoB, the lowest expansion occurs along the strong covalent B–B chains (α_//) for all the binaries and ternaries studied.

Somewhat surprisingly, given their respective melting points (α-MoB = 2623 K, while the decomposition temperature of MoAlB is significantly lower and peritectic at 1700 K³¹), the α_vol of both compounds are quite comparable. Indeed, α_vol for MoAlB and MoB are 7.3 × 10⁻⁶ K⁻¹ and 7.7 × 10⁻⁶ K⁻¹. This suggests that intercalating the binary with two Al layers does not reduce the bond strengths significantly. At about 26%, the anisotropies are also almost identical. This is quite remarkable since MoAlB comprises Al–Al bonds [see Fig. 1(b)], that are typically not considered strong bonds. This result, in turn, implies considerable covalent character to that bond. The fact that the shortest Al–Al distances in elemental Al and MoAlB are, respectively, 0.2863 nm and 0.2657 nm lends validity to this conjecture. It is worth noting here that the α-MoB structure is unique since, in this case, the B–B chains run in two alternating and orthogonal directions [see Fig. 1(e)]. The fact that the chains in MoAlB only run one way, and yet the CTEs are comparable, is again a testament to the strengths of the bonds in the ternary.

α_⊥ for CrB and Cr₂AlB₂ (12.9 × 10⁻⁶ K⁻¹ vs. 13.9 × 10⁻⁶ K⁻¹) are not too different. Similarly, the values of α_// for CrB and Cr₂AlB₂ (8.6 × 10⁻⁶ K⁻¹ vs. 8.8 × 10⁻⁶ K⁻¹) are within 2% of each other. Conversely, α_st for the ternary (8.4 × 10⁻⁶ K⁻¹) is 56% greater than the binary (5.4 × 10⁻⁶ K⁻¹). These results imply that, as a first approximation, the Cr–Cr bonds in CrB along the stacking direction, are stronger than the Cr–Al bonds in the ternary [cf. Figs. 1(a) and 1(c)]. The introduction of Al in the CrB structure therefore only seems to significantly affect the thermal expansion along the stacking direction. Note that in the absence of the Al-layers, viz., CrB, the M–M and the M–B bonds along the stacking direction are exceptionally strong and appear to significantly weaken the M–M bonds normal to the B–B chains, as manifested by an α_⊥ of 12.9 × 10⁻⁶ K⁻¹ in CrB.

At 11.4 × 10⁻⁶ K⁻¹, α_// for the ternary is roughly twice that of the binary (5.6 × 10⁻⁶ K⁻¹). Lastly, α_⊥ for MnB and Mn₂AlB₂ are 14.9 × 10⁻⁶ K⁻¹ vs. 22.1 × 10⁻⁶ K⁻¹. In this case, the introduction of Al does make a significant difference in the various CTEs. Note that this comparison is valid above 673 K where the variation of the lattice parameters is linear [Figs. 3(b) and 5(a)].

For this pair, neither α_vol (≈10 × 10⁻⁶ K⁻¹) nor the maximum anisotropies are too different. What is somewhat surprising is that α_// for the binary is greater than the ternary, in which Al layers exist. Interestingly, the distorted stacking of the BM₆ trigonal prisms in MnB and FeB, relative to the ternaries and CrB, does not change the fact that α_// > α_⊥ for the binary/ternary pairs.

From a technological point of view, large CTE anisotropies could be problematic if they result in large thermal residual stresses during thermal cycling. Based on the results shown in Table II, it is unlikely that Cr₂AlB₂ or especially Mn₂AlB₂ will prove to be immune to thermal cycling, especially if the grains are large. Nonetheless, the CTE values of Cr₂AlB₂ and Mn₂AlB₂ are quite high relative to many engineering ceramics, which lowers their CTE mismatch with many alloys. Similarly, the anisotropy of CrB, a candidate for anti-wear coatings, may also prove detrimental. On the other hand, MoAlB is more isotropic, which is fortuitous since it currently not only possesses the highest MAB decomposition temperature but also forms a protective alumina layer when heated in air.¹¹ 

In situ XRD patterns of MoAlB, Cr₂AlB₂, Mn₂AlB₂, Fe₂AlB₂, and CrB powders were collected as a function of temperature. The lattice parameters, calculated from Le Bail analysis of the diffractograms, were used to calculate the CTEs along the different crystallographic axes. These compounds fell into two groups. In the first group—MoAlB and Fe₂AlB₂—the anisotropies were mild, with the differences between the lowest and highest expansions of 27% and 37%, respectively. In those compounds, expansion was highest along the stacking direction.

For the second group, Cr₂AlB₂, Mn₂AlB₂, and CrB, the maximum anisotropies were 53%, 100%, and 87%, respectively, and expansion normal to the direction of the B–B chains was the highest. At 22 × 10⁻⁶ K⁻¹, α_⊥ for Mn₂AlB₂ was the highest measured in this work. Analysis of our results suggests that there are significant differences in bond strengths between these MAB phases, despite their structural and chemical similarities. These differences are currently not captured by DFT calculations.

See supplementary material for the comparison of select interatomic distances in binary monoborides and MAB phases, additional XRD patterns on Fe₂AlB₂ before and after treatment with HCl, and data on α-Al₂O₃ and lattice parameters for every compound studied with the linear fits.

This work was funded by the National Science Foundation (DMREF 1729335). The authors acknowledge Yoshito Soda for the translation of Japanese articles, and Dr. Maxim Sokol at Drexel University for fruitful discussions.