The Influence of the Third Element on Nano-Mechanical Properties of Iron Borides FeB and Fe2B Formed in Fe-B-X (X = C, Cr, Mn, V, W, Mn + V) Alloys

In this study, the influence of alloying elements on the mechanical properties of iron borides FeB and Fe2B formed in Fe-B-X (X = C, Cr, Mn, V, W, Mn + V) alloys were evaluated using instrumented indentation measurement. The microstructural characterization of the alloys was performed by means of X-ray diffraction and scanning electron microscope equipped with an energy dispersive X-ray analyzer. The fraction of the phases present in the alloys was determined either by the lever rule or by image analysis. The hardest and stiffest FeB formed in Fe-B-X (X = C, Cr, Mn) alloys was observed in the Fe-B-Cr alloys, where indentation hardness of HIT = 26.9 ± 1.4 GPa and indentation modulus of EIT = 486 ± 22 GPa were determined. The highest hardness of Fe2B was determined in the presence of tungsten as an alloying element, HIT = 20.8 ± 0.9 GPa. The lowest indentation hardness is measured in manganese alloyed FeB and Fe2B. In both FeB and Fe2B, an indentation size effect was observed, showing a decrease of hardness with increasing indentation depth.


Introduction
Owning to their characteristics, i.e., high hardness, thermal stability, high wear and corrosion resistance, metal borides are considered a perspective option where the operational conditions demand for improved performance, reliability, safety and increased service life of various engineering components [1]. For example, the use of metal borides as protective coatings is one technological area of considerable practical importance in the case of both ferrous and non-ferrous alloys [2]. The surface modification of the materials is achieved by formation of a dual layer FeB + Fe 2 B or a monophase Fe 2 B layer by high-temperature diffusion of boron atoms (boronizing process) [3]. As such, these materials are utilized, for example, in the production of forging and stamping dies used in the manufacturing industry or valves, bearings and other production tubing system components used in the oil and gas industry [4,5]. Equally important is the application of boron for hardness enhancement through alloying, where the borides formed are utilized as hard reinforcing phases, e.g., boron alloyed tool steels [6,7], and high-boron white cast irons [8][9][10][11][12], etc.
Numerous information on FeB and Fe 2 B borides can be obtained from boronizing processes research, where these borides have been of primary interest. Available studies on mechanical and tribological properties of boride layers vouch for their advantages over other surface hardening The volume fraction of the identified phases in alloys Fe-B-C, Fe-B-Cr, Fe-B-W, and Fe-B-Mn-V was determined by image analysis. The volume fraction was derived from the area fraction. Namely, the area fraction can be considered as equivalent to the volume fraction under the assumption of homogenous and isotropic materials. Image analysis was done using the open-source scientific processing program ImageJ/Fiji [47]. The volume fraction of the identified phases present in Fe-B-Mn and Fe-B-V alloys was calculated using the lever rule. For this purpose, experimentally determined chemical composition values for the phases of interest and the overall composition of the alloys were used as input data, followed by conversion from mole percent to volume percent. Information on phases' molar volume are taken from Repovský et al. [39]. The determined volume fractions are given in Table 2.
For the nanoindentation testing, the sectioned alloys were mounted using the compression thermosetting molding technique, and then they were ground and polished-flat. In addition, a final automatic polishing step was used to ensure a smooth top surface. Using crystal-bond hot-melt thermoplastic polymer, the alloys were mounted on aluminum sample disks, and then installed into a sample holder. Nanoindentation experiments were performed using Nano Indenter G200 produced by MTS Nano Instruments equipped with a Berkovich-type diamond indenter. Poisson's ratio (ν) of 0.3 is used, for both FeB (MB) and Fe 2 B (M 2 B) phases, assuming a quasi-isotropic behavior. Measurements were done using both single loading-unloading indentation and continuous stiffness measurement (CSM) methods. The latter was applied to study the indentation size effect (ISE). In both cases, an indentation depth-controlled method was used with a maximum depth of 500 nm. On average, 25 indentation tests were carried out on FeB and/or Fe 2 B phase for determining the indentation hardness and modulus of the alloys. In addition, 10 depth-controlled indentation tests to a maximum depth of 500 nm were performed with an aim to inspect for the presence of indentation size effect (ISE). The area function of the indenter tip was calibrated using fused silica preceding the indentation tests.

Phase Composition and Microstructure
Sixteen equilibrated ternary Fe-B-X (X = C, Cr, Mn, V, W) alloys and one equilibrated quaternary Fe-B-Mn-V alloy were investigated in this study. The microstructures of the investigated alloys are shown in Figure 1. Alloys' phase composition is given in Table 1.
Two-phase microstructure was identifiable in eight of the investigated ternary alloys. The rest of the ternary alloys were characterized by three-phase microstructure. Three-phase microstructure is also observed in the quaternary Fe-B-Mn-V alloy. In the majority of alloys, both FeB (MB) and  (Figure 1a,b,e,f). Whilst, in alloys 82 Fe-9 B-9 Mn and 50 Fe-41 B-9 V (alloy 13), only Fe 2 B is observed (Figure 1h,m).
Although, FeB and Fe 2 B phases are present in various shapes and dimensions, still, in most of the alloys, phases of 10 µm in diameter are easily identifiable (Figure 1). Iron borides relevant crystallographic structure information are as follows: FeB (Pearson symbol-oP8, Proto-type FeB, Space group Pnma) and Fe 2 B (Pearson symbol-tI12, Proto-type CuAl 2 , Space group-I4/mcm) [48].
The determined phase fractions of the investigated alloys are shown in Table 2. Values calculated by image analysis are consistent with location of the individual alloys in phase equilibrium regions of the corresponding phase diagrams. The lever rule method is essentially based on the location of the alloy in the phase equilibrium fields, so that the values calculated by this method are, of course, in accordance with it. The iron borides dissolve the third element (in case of the quaternary alloy, also the fourth element) in greater or lesser amounts in all investigated alloys. The amount of the third element dissolved in FeB and Fe 2 B phases in the investigated ternary alloys and the dissolved amount of vanadium and manganese in iron borides in investigated quaternary alloy are given in Table 1.  (Figure 1q). The matrix consists of light gray M2B phase. The dark gray phase embedded in the matrix is identified as V3B4. V3B4 is surrounded by MB phase. Here, vanadium and manganese are both dissolved in iron borides M2B and MB. Additional information about Fe-B-Mn-V quaternary can be obtained from Homolová et al. [42]. A segmented image of the microstructure of alloy 17 used for phase fraction calculation is given in Figure 3. The different colored segments are obtained using the image analysis technique and represent different phases, as labeled in Figure 3. The M2B phase is the predominant phase, occupying 71.28 vol.% of the Fe-B-Mn-V alloy microstructure (Table 2).    (Table 2). However, it should be noted that the given phase fraction for graphite, when present in the alloy, is overestimated at an expanse of B 4 C, Fe 2 B, and FeB phases, since it is very difficult to distinguish the border between graphite and these other phases.  Table 2). In alloy 50 Fe-40 B-10 Cr, the FeB phase (dark gray) is present, together with light gray Fe 2 B phase, each characterized with relatively high chromium solubility of 8 at.% and 16 at.%, respectively (Table 1, Figure 1g).  (Table 1). Additional information for Fe-B-Mn alloys are given in the studies by Repovsky et al. [39] and Kirkovska et al. [49].

Fe-B-V Alloys
Two Fe-B-V alloys were investigated in this study, alloy 13 (50 Fe-41 B-9 V annealing conditions 1353 K/1440 h) and alloy 14 (50 Fe-41 B-9 V annealing conditions 903 K/4560 h) (Figure 1m,n). The phase fraction analysis shows that Fe 2 B phase takes up the biggest portion of the microstructure, 76.7% and 63.8%, for alloys 13 and 14, respectively ( Table 2). In alloy 13, the large dark grey plates of V 3 B 4 are embedded in light gray Fe 2 B matrix ( Figure 1m). The dendrite-like structure identified as V 3 B 4 (darkest color) is surrounded by FeB phase (medium color), embedded in the (light gray) Fe 2 B matrix in alloy 14 ( Figure 1n).

Fe-B-W Alloys
Two Fe-B-W alloys (Figure 1o,p) were investigated in the present study. X-ray analysis results confirm the existence of FeB and Fe 2 B ( Figure 2). The experimentally determined equilibrium composition of the phases present in these alloys, using energy-dispersive X-ray spectroscopy (EDX/EDS) coupled with published Fe-B-W phase diagram studies [48], indicate the existence of W 2 FeB 2 for the unidentified picks. Hence, a three-phase microstructure consisting of FeB + Fe 2 B + W 2 FeB 2 was identified. With long-term annealing at the higher temperature (1323 K), the FeB phase appears more refined (Figure 1o,p). Also, with long-term annealing, the phase fraction of W 2 FeB 2 ternary boride increases slightly, alongside FeB phase, at the expense of Fe 2 B phase ( Table 2).    [42]. A segmented image of the microstructure of alloy 17 used for phase fraction calculation is given in Figure 3. The different colored segments are obtained using the image analysis technique and represent different phases, as labeled in Figure 3. The M 2 B phase is the predominant phase, occupying 71.28 vol.% of the Fe-B-Mn-V alloy microstructure (Table 2).

Hardness and Modulus of FeB and Fe2B Borides
The average hardness and indentation modulus of both FeB and Fe2B phase are given in Table  3

Hardness and Modulus of FeB and Fe 2 B Borides
The average hardness and indentation modulus of both FeB and Fe 2 B phase are given in Table 3.      For the manganese alloyed Fe2B annealed at 873 K, only a slight increase in hardness is observed with higher amounts of manganese dissolved (Figure 6a). For the Fe2B formed in Fe-B-Mn alloys annealed at 1223 K, the decrease in hardness at 11 at.% Mn dissolved is followed by a hardness increase at 43 at.% Mn dissolved (Figure 6b). Fe2B indentation modulus for the Fe-B-Mn alloys annealed at 1223 K shows the same behavior. For the Fe2B in Fe-B-Mn alloys annealed at 873 K, the indentation modulus is lower at higher manganese content. Nonetheless, when probing phases during nanoindentation testing as a part of a multiphase material, it must be accounted for the possible influences of the surrounding phases/matrix. The extrinsic influences on nanoindentation measurement depend on, for example, the amount of the surrounding phases in the microstructure, and/or their proximity to the indented phase.
In these alloys, FeB and Fe2B phases are found in different combinations both with harder phases, e.g., V3B4, CrB2, CrB4, Cr3B4, B, and B4C, and/or softer, e.g., γ-Fe and graphite, as surrounding phases. Herein, in an attempt to minimize the influence of the surrounding phases, the diameters (d) of the phases measured were carefully chosen at d > 10 μm, and distance of about one-indent diameter was kept from the phase border during testing. Hence, for the alloys used in this study, the extrinsic effects can be considered minimized, although it cannot be claimed that they are eliminated  (Figure 5b). In a like manner, the indentation hardness of FeB containing manganese is higher at lower amounts of dissolved manganese (Figure 5c,d).

FeB indentation modulus shows the same behavior as the indentation hardness for the Fe-B-Cr and Fe-B-Mn alloys.
For the manganese alloyed Fe 2 B annealed at 873 K, only a slight increase in hardness is observed with higher amounts of manganese dissolved (Figure 6a). For the Fe 2 B formed in Fe-B-Mn alloys annealed at 1223 K, the decrease in hardness at 11 at.% Mn dissolved is followed by a hardness increase at 43 at.% Mn dissolved (Figure 6b). Fe 2 B indentation modulus for the Fe-B-Mn alloys annealed at 1223 K shows the same behavior. For the Fe 2 B in Fe-B-Mn alloys annealed at 873 K, the indentation modulus is lower at higher manganese content. Nonetheless, when probing phases during nanoindentation testing as a part of a multiphase material, it must be accounted for the possible influences of the surrounding phases/matrix. The extrinsic influences on nanoindentation measurement depend on, for example, the amount of the surrounding phases in the microstructure, and/or their proximity to the indented phase.
In these alloys, FeB and Fe 2 B phases are found in different combinations both with harder phases, e.g., V 3 B 4 , CrB 2 , CrB 4 , Cr 3 B 4 , B, and B 4 C, and/or softer, e.g., γ-Fe and graphite, as surrounding phases. Herein, in an attempt to minimize the influence of the surrounding phases, the diameters (d) of the phases measured were carefully chosen at d > 10 µm, and distance of about one-indent diameter was kept from the phase border during testing. Hence, for the alloys used in this study, the extrinsic effects can be considered minimized, although it cannot be claimed that they are eliminated entirely. On the contrary, the indentation hardness and modulus of Fe 2 B boride formed in the 82 Fe-9 B-9 Mn alloy and FeB in the 39.7 Fe-33 B-27.3 C alloy are probably underestimated due the extrinsic influences of the softer γ-Fe matrix and Fe 2 B phase, respectively.
The relationship between amount of alloying and indentation hardness of alloys grouped by equal chemical composition is given in Figure 7. A trend of lower hardness at higher alloying content is observed, with exception to the Fe 2 B phase in alloy group 51 Fe-39 B-10 Mn. The differences between alloys in a group are within standard deviation at lower amounts of alloying content, and the difference within alloy group increases with increases in alloying content. The anomalous behavior in 51 Fe-39 B-10 Mn alloys cannot be claimed as inherent to the material and can be an outcome of the nanoindentation measurement process. In general, the hardness of materials is primarily related to the mobility of dislocations [55]. However, at a more fundamental level, intrinsic hardness modification has been successfully linked to electronic structure effects induced by the alloying elements [56]. In the literature, the understanding of the underlying mechanism of electronic mechanical properties modification imposes a challenge, and its investigation is beyond the scope of this study. Herein, the measured indentation hardness is linked to a parameter called valence electron concentration (VEC) that has been used as an indicator for electronic modification of mechanical properties. The aim is to assess any possible relation of the VEC parameter to the nanoindentation hardness measured in this study.
The valence electron concentration (VEC) is defined as the number of valence electrons per In general, the hardness of materials is primarily related to the mobility of dislocations [55]. However, at a more fundamental level, intrinsic hardness modification has been successfully linked to electronic structure effects induced by the alloying elements [56]. In the literature, the understanding of the underlying mechanism of electronic mechanical properties modification imposes a challenge, and its investigation is beyond the scope of this study. Herein, the measured indentation hardness is linked to a parameter called valence electron concentration (VEC) that has been used as an indicator for electronic modification of mechanical properties. The aim is to assess any possible relation of the VEC parameter to the nanoindentation hardness measured in this study.
The valence electron concentration (VEC) is defined as the number of valence electrons per formula unit [57]. VEC is calculated as given in Ge et al. [58]. The following valence electron numbers are used: 3 (B), 8 (Fe), 4 (C), 6 (Cr), 7 (Mn), 5 (V), and 6 (W), in determining VEC [59]. The calculation was done using the borides chemical composition as given in Table 1. VEC and indentation hardness for the Fe 2 B and FeB are given in the map in Figure 8. The map shows strong partitioning between the different phases, i.e., FeB and Fe 2 B. The typical values for single element alloyed FeB in these alloys are between 5.07 VEC to maximum 5.53 VEC, and for the Fe 2 B are in between mininum 6.07 VEC and maximum 6.36 VEC. Comparing FeB and Fe 2 B, the indentation hardness shows a decreasing trend with increasing VEC. This is due to the fact that with increasing VEC, the 'metallic' character of the materials increases, which could result in easier slip on a given slip system or the activation of more systems.

Indentation Size Effect
In the investigated alloys, an indentation size effect (decreasing hardness with indentation depth) in FeB and Fe2B was observed. Indentation hardness (HIT) and indentation modulus (EIT) for the FeB and Fe2B phase as a function of indentation depth (h) for chosen alloys are visualized in Figures 9 and 10 (the different colored curves represent an individual indentation measurement). In the case of the Fe 2 B phase formed in the quaternary 45 Fe-40 B-5 Mn-10 V alloy, the map shows that the synergistic effect of Mn and V (alloying content of Mn = 5 at.% and V = 3 at.%), results in VEC = 6.16, and the measured indentation hardness is 18.1 ± 1.2 GPa. Although the boride structure type is the hardness determinant and in comparison to only manganese alloyed Fe 2 B, there is unclear disposition (because of the wider range of measured hardness data), the influences caused by the different elements are viable; since, in the presence of both manganese and vanadium, the indentation hardness is lower compared to only vanadium alloyed borides, i.e., 19.2 ± 0.6 GPa (alloy 13), 19.0 ± 0.6 GPa (alloy 14).
Further, even though some clustering of hardness values at the same VEC is present, a strong tendency is not observable. Among the groups of alloys mentioned above, i.e., alloys with the same alloying element and heat-treated at the same temperature, i.e., FeB in 17 Fe-65 B-18 Cr and 50 Fe-40 B-10 Cr, FeB in manganese alloys annealed at 873 K, and FeB in manganese alloys annealed at 1223 K, as well as alloy groups that have the same chemical composition and/or phase composition, i.e., FeB in 51 Fe-39 B-10 Mn, Fe 2 B in 50 Fe-41 B-9 V, and Fe 2 B in 22 Fe-39 B-39 Mn, Fe 2 B in manganese alloys annealed at 1223 K the VEC vs. H IT map shows that primarily lower hardness is observed at lower VEC values. However, this tendency is partially substantiated, i.e., it is not observed for the rest of the alloy groups where lower hardness is present at higher VEC values. For the C alloyed FeB annealed at 1173 K, alloy group 22 Fe-39 B-39 Mn, and manganese alloys annealed at 873 K, no relation can be discerned. The empirical relations between indentation hardness and VEC parameter obtained in this study can be used as orientation points for hardness estimation of similar borides.

Indentation Size Effect
In the investigated alloys, an indentation size effect (decreasing hardness with indentation depth) in FeB and Fe 2 B was observed. Indentation hardness (H IT ) and indentation modulus (E IT ) for the FeB and Indentation hardness vs. depth plots show that after reaching peak value (at approximately 50-100 nm), the indentation hardness decreases monotonically with increasing depth (Figure 9). The ISE for the FeB phase is most pronounced in the 50 Fe-40 B-10 Cr alloy, and for the Fe2B phase, in alloy 50 Fe-41 B-9 V (alloy 14). The ISE is more pronounced for Fe2B phase compared to FeB phase ( Figure  9). Indentation modulus vs. depth plots show an initial increase to a maximum value followed by a subsequent decrease up to a constant value ( Figure 10). The constant modulus indicates that intrinsic materials' properties were measured.
The change of indentation hardness (HIT) and indentation modulus (EIT) at different depth intervals (h = 100-200 nm, h = 200-300 nm, h = 300-400 nm, h = 400-500 nm) for the FeB and Fe2B phase is visualized in Figure 11. Indentation hardness vs. depth plots show that after reaching peak value (at approximately 50-100 nm), the indentation hardness decreases monotonically with increasing depth (Figure 9). The ISE for the FeB phase is most pronounced in the 50 Fe-40 B-10 Cr alloy, and for the Fe 2 B phase, in alloy 50 Fe-41 B-9 V (alloy 14). The ISE is more pronounced for Fe 2 B phase compared to FeB phase ( Figure 9). Indentation modulus vs. depth plots show an initial increase to a maximum value followed by a subsequent decrease up to a constant value ( Figure 10). The constant modulus indicates that intrinsic materials' properties were measured.
The change of indentation hardness (H IT ) and indentation modulus (E IT ) at different depth intervals (h = 100-200 nm, h = 200-300 nm, h = 300-400 nm, h = 400-500 nm) for the FeB and Fe 2 B phase is visualized in Figure 11.
Indentation size effect is a well-known phenomenon in indentation testing and various mechanisms have been identified as responsible for ISEs, such as dislocations, cracking, phase transformations, surface effects, etc. [60]. In the case of crystalline metals, the dislocation-based mechanisms are identified as the dominant underlying mechanisms of ISE [60]. The Nix and Gao model [61] is an established model used to estimate hardness based on the dislocation-based behavior as a prevailing mechanism influencing ISEs. Observed slip lines and linear details (steps) in the FeB phase in alloys 50 Fe-40 B-10 Cr ( Figure 12) signify a dislocation-based deformation behavior. Dislocation-based deformation for the Fe 2 B was also reported by Lentz et al. [29]. Indentation size effect is a well-known phenomenon in indentation testing and various mechanisms have been identified as responsible for ISEs, such as dislocations, cracking, phase transformations, surface effects, etc. [60]. In the case of crystalline metals, the dislocation-based mechanisms are identified as the dominant underlying mechanisms of ISE [60]. The Nix and Gao model [61] is an established model used to estimate hardness based on the dislocation-based behavior as a prevailing mechanism influencing ISEs. Observed slip lines and linear details (steps) in the FeB phase in alloys 50 Fe-40 B-10 Cr ( Figure 12) signify a dislocation-based deformation behavior. Dislocation-based deformation for the Fe2B was also reported by Lentz et al. [29]. Thus, the Nix and Gao model has been applied to calculate the hardness at infinite indentation depth or true hardness (H0) of both FeB and Fe2B phases. The calculated true hardness (H0) based on the Nix-Gao model is given in Table 4.  Indentation size effect is a well-known phenomenon in indentation testing and various mechanisms have been identified as responsible for ISEs, such as dislocations, cracking, phase transformations, surface effects, etc. [60]. In the case of crystalline metals, the dislocation-based mechanisms are identified as the dominant underlying mechanisms of ISE [60]. The Nix and Gao model [61] is an established model used to estimate hardness based on the dislocation-based behavior as a prevailing mechanism influencing ISEs. Observed slip lines and linear details (steps) in the FeB phase in alloys 50 Fe-40 B-10 Cr ( Figure 12) signify a dislocation-based deformation behavior. Dislocation-based deformation for the Fe2B was also reported by Lentz et al. [29]. Thus, the Nix and Gao model has been applied to calculate the hardness at infinite indentation depth or true hardness (H0) of both FeB and Fe2B phases. The calculated true hardness (H0) based on the Nix-Gao model is given in Table 4.  Thus, the Nix and Gao model has been applied to calculate the hardness at infinite indentation depth or true hardness (H 0 ) of both FeB and Fe 2 B phases. The calculated true hardness (H 0 ) based on the Nix-Gao model is given in Table 4. The model was fitted to data for indentation depth >100 nm ( Figure 13). The HIT 2 vs. h −1 plot showed good fit of the Nix-Gao model for both FeB and Fe2B phases. However, as one can see, the plots for FeB and Fe2B phase show linear behavior at larger depths, but the linearity does not extend to smaller depths (h < approximately 150 nm). In the literature, this behavior has been interpreted as bilinear and considered as an indicator of change in the prevailing ISE mechanism at smaller depths [60,62].

Conclusions
In this study, the influence of the third element dissolved in FeB and Fe2B phases formed in different Fe-B-X (X = C, Cr, Mn, V, W, Mn + V) systems has been characterized by nanoindentation. The results of this study can be outlined as follows: (1) The determined indentation hardness under the influence of different amounts and type of alloying elements showed the highest hardness of FeB formed in Fe-B-X (X = C, Cr, Mn) systems in the presence of Cr as an alloying element with a hardness value of HIT = 26.9 ± 1.4 GPa. The highest hardness in the Fe2B was measured in the presence of W additions HIT = 20.8 ± 0.9 GPa. The lowest hardness in both alloys was determined in Mn alloyed FeB and Fe2B. (2) The highest hardness for FeB boride was measured at VEC = 5.28, and for the Fe2B boride, at VEC = 6.368. Comparison between FeB and Fe2B showed, overall, that the indentation hardness decreases with increasing VEC, which is associated with the increase of the 'metallic' character of the materials and easier slip on a given slip system or the activation of more systems.

Conclusions
In this study, the influence of the third element dissolved in FeB and Fe 2 B phases formed in different Fe-B-X (X = C, Cr, Mn, V, W, Mn + V) systems has been characterized by nanoindentation. The results of this study can be outlined as follows: (1) The determined indentation hardness under the influence of different amounts and type of alloying elements showed the highest hardness of FeB formed in Fe-B-X (X = C, Cr, Mn) systems in the presence of Cr as an alloying element with a hardness value of H IT = 26.9 ± 1.4 GPa. The highest hardness in the Fe 2 B was measured in the presence of W additions H IT = 20.8 ± 0.9 GPa. The lowest hardness in both alloys was determined in Mn alloyed FeB and Fe 2 B. (2) The highest hardness for FeB boride was measured at VEC = 5.28, and for the Fe 2 B boride, at VEC = 6.368. Comparison between FeB and Fe 2 B showed, overall, that the indentation hardness decreases with increasing VEC, which is associated with the increase of the 'metallic' character of the materials and easier slip on a given slip system or the activation of more systems.

Conflicts of Interest:
The authors declare no conflict of interest.