Introduction

Economic losses caused by the abrasion and corrosion are considerable in the mechanical components and structures. Exploring superior wear-resistant and corrosion-resistant materials has been the permanently hot topic for researchers in the field of material science [1,2,3,4,5,6,7].

Cast alloys with high boron and low carbon (Fe–B alloys), consisting of metallic matrix (such as ferrite or pearlite) and hard boride (Fe2B), show two principal advantages over the most of wear and corrosion-resistant materials. On the one hand, the production cost for Fe–B alloys, e.g. raw materials, is relatively economical compared with traditional high-chromium cast iron. On the other hand, it is feasible to tailor the content of the boride and carbon in the metallic matrix so as to independently control the hardness of the alloy and metallic matrix based on the low solubility of boron in austenite and ferrite and poor dissolution ability of carbon into the crystal of Fe2B [8].Therefore, Fe–B alloy has been highly addressed as a potential candidate for wear- and corrosion-resistant material [9,10,11,12,13,14,15,16,17,18,19,20].

In the past few decades, modifying the microstructure and improving the wear, corrosion resistance have been the key goal in researches related to Fe–B alloys. Initially, Yi [19] and Zhang [18] found that Fe–B alloy exhibited comparable wear resistance with high-chromium cast iron. Subsequently, Ma [17] and Wang [16] investigated the erosion-corrosion behavior of Fe-3.5B alloy at elevated temperature in zinc melt, indicating that orientation and lamellar spacing of Fe2B had significant influence on the erosion–corrosion behavior of the alloy. By studying the microstructure, mechanical properties and oxidation behavior of Fe–B–C–Cr–Al alloys [14, 15], Lv et al. reported that Fe–3.08 wt% B alloy presented excellent oxidation resistance attributed to the inhibiting effect of the boride. Additionally, the author has also investigated the effects of chromium addition on the abrasive wear behaviors of Fe-3.0 B alloy in previous work [10, 12]. To sum up, all preceding studies draw an accordant conclusion that the hard boride (Fe2B) plays a dominant role in the corrosion- , wear- and oxidation-resistant performance.

In spite of the advantages of Fe–B alloys, however, Fe2B is in fact intrinsically brittle due to the weak B–B bond along [002] direction [21]. The lack of toughness of Fe2B is a well-known bottleneck that limits the widespread engineering application of Fe–B alloy. Nevertheless, very few works explored the effective ways to improve the toughness of Fe2B directly and shed light on the intrinsic mechanism. In this case, this work is to investigate the effects of chromium on the morphology and mechanical properties of Fe2B in Fe–3.0B alloy. The morphological evolution of Fe2B is quantitatively analyzed as a function of chromium content. Mechanical properties of Fe2B, especially the toughness, are systematically studied with the aid of nanoindentation technique. Furthermore, HRTEM and the first-principles calculation have been implemented to explain the underlying mechanism.

Materials and methods

Sample preparation

In this work, Fe-3.0B alloys with a series of chromium content (0, 1.0, 1.5, 2.0 and 2.5 wt%) were melt in a medium frequency induction furnace. To acquire the heat-treated microstructure, the five cast ingots were austenitized at 980°C and then quenched in oil. Subsequently, all samples were tempered at 220°C to eliminate the quenching stress. The chemical compositions of all samples are shown in Table 1.

Table 1 Chemical compositions of Fe-3.0B alloys with different chromium additions (wt%)
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The standard specimens for metallography and mechanical properties tests were sectioned from the lower part of the ingots using the electrical discharge machining (EDM) equipment. Specimens were carefully polished to a mirror finish using abrasive papers with varying meshes. To reveal the microstructure, the specimen was etched by 4 vol% nital.

Microstructure examination

Microstructure observation was conducted utilizing an optical microscopy (LEICA DMI 5000 M, OM) and a scanning electron microscopy (VEGAIIXMUINCA, SEM). Electron probe microanalysis (JXA-8230, EPMA) was used to analyze the chromium distribution in the alloy.

A high-resolution transmission electron microscope (JEM-2000F, HRTEM) was used to identify the distinct phases in the alloy. The experimental results were analyzed with the aid of the professional processing software (Gantan Digital Micrograph). The standard thin foil specimen for TEM examination was prepared by the initial mechanical grind and subsequent twin-jet electropolishing in solution of 5 vol% perchloric acid and 95% alcohol.

Nanomechanical tests

The nanomechanical properties of the boride were evaluated using a CSM Instruments nanoindenter (NANOVEA-NMT) equipped with a Berkovich-type diamond indenter. The typical load (P)–displacement (h) curve was obtained during the test by setting the maximum load as 80 mN, as shown in Fig. 1 [22,23,24]. Mechanical parameters, e.g. hardness (H) and elastic modulus (E), can be estimated from the P–h curves using Oliver and Pharr method [25, 26] and the following Eqs. (1), (2):

$$ H = \frac{{P_{\hbox{max} } }}{{A_{c} }} $$
(1)
$$ \frac{1}{{E_{r} }} = \frac{{1 - \nu^{2} }}{E} + \frac{{1 - \nu_{i}^{2} }}{{E_{i} }} $$
(2)

where Pmax is the maximum load; A c is the projected contact area between the indenter and specimen; E r is the reduced Young’s modulus of the specimen; E and E i , and ν and ν i denote the Young’s modulus and Poisson’s ratio for the specimen and the indenter, respectively. For diamond indenter tip, E i  = 1141 GPa and ν i  = 0.07 [23, 26]. For Fe2B crystal in this work, Poisson’s ratio ν = 0.388 [27]. To minimize the experimental errors, the ultimate value of hardness and modulus was determined by averaging at least five examinations, respectively.

Figure 1
figure 1

A typical load–displacement curve

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First-principles calculation

The first-principles calculation was carried out based on density functional theory. Ultrasoft pseudopotentials were used to describe the interactions of ionic core and valence electrons. Generalized gradient approximation (GGA) within PBE scheme was employed to evaluate exchange–correlation energy. A special k point sampling method proposed by Monkhorst–Pack was used for the energy integration in the first irreducible Brillouin zone [28], and the k point mesh was selected as 10 × 10 × 12. The kinetic energy cutoff 400 eV was used for plane wave expansions in reciprocal space. BFGS optimization method was used to find the ground state of Fe2B crystals in which both atom positions and lattice parameters were optimized simultaneously [27, 29]. Total energy changes were finally reduced less than 1.0 × 10−6 eV/atom, and Hellman–Feynman forces acting on atoms were converged less than 0.01 eV/Å.

Results and discussion

Effect of chromium on the microstructure of Fe-3.0B alloy and M2B

Figure 2 shows the SEM micrographs of the as-cast Fe-3.0B alloy. From the figures, it can be clearly found that 0Cr sample is composed of ferrite, pearlite and M2B (M representing for Fe or Cr) with various morphologies, e.g. typical fish-like, net-like M2B, rod-like M2B and cluster-like M2B. For 2Cr sample, only M2B and typical pearlite matrix appear in the view. By comparison, we can find that M2B grain tends to become visually coarse after chromium addition in Fe-3.0B alloy. In addition, ferrite in the metallic matrix gradually disappears with increasing the chromium addition. Considering the considerable hardenability of chromium, it is not difficult to understand the phenomenon of matrix phase transformation. During the solidification and cooling process, the continuous cooling transformation curve tends to move right after chromium addition, contributing to the improved hardenability of the alloy [30].

Figure 2
figure 2

SEM micrographs of the as-cast microstructure of Fe-3.0B alloys: a 0Cr; b 2.0Cr

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Volume fraction and morphology of M2B have been quantitatively characterized in the current research. Beforehand, the five groups of alloys were heat-treated in order to distinguish M2B from the matrix, which has been introduced elsewhere [12]. Equipped with optical microscope, a digital photograph processing software (DT2000) was used to statistically analyze the morphology and volume fraction of M2B, as shown in Table 2. According to the results, volume fraction of the boride fluctuates in an amplitude less than 1.58 vol% in all samples. In other words, chromium addition in Fe-3.0B alloy scarcely gives rise to a significant volume fraction variation of the boride. The result agrees well with previous report that the volume of boride is mainly affected by boron content in the alloy.

Table 2 Volume fraction of M2B in Fe-3.0B alloy (Vol%)
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Figure 3 presents the grain size histograms of M2B for all samples. The number density of fine borides (the equivalent cycle diameter less than 5 μm) firstly increases and then decreases with the increase in chromium addition while the area fraction of coarse M2B (the equivalent cycle diameter lager than 10 μm) has an opposite trend. Interestingly, the critical point for both variation trends locates on 2Cr sample. Accordingly, it can be deduced that chromium addition can hinder the continuous growth of M2B crystal grain, leading to the increased number of fine borides. Furthermore, the average grain area of M2B has been presented as a function of chromium content in Fig. 4. The average equivalent area (Ã) decreases firstly and then increases with the increase in chromium addition. Associating with the results in Fig. 3, it can be concluded that the variation of coarse M2B plays a key role in affecting the average grain size of M2B. However, the grain size variation is not very significant, with the largest difference not exceeding 7 μm2. Generally, the effect of chromium on grain size of M2B may be against some previous views. In the previous studies, chromium addition was deemed to be able to refine the structure of carbides and pearlite in Fe–C alloy [31,32,33]. Besides, Zhang [18] found that the morphology of the boride would become less continuous with chromium addition of 17.94 wt%. However, a common ground in these studies is that the chromium content is considerably high. Thus, some Cr–C compounds and Cr–B compounds may be precipitated in advance during the solidification and act as an initial crystal nucleus, contributing to the refinement of crystal grains.

Figure 3
figure 3

Distribution histograms of the equivalent circle diameter of the borides in Fe-3.0B alloys with different chromium contents

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Figure 4
figure 4

Average grain area and fractal dimension of the borides in Fe-3.0B alloys with different chromium contents

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The morphology of M2B has also been quantitatively characterized by a fractal dimension (D f ). In some cases, D f can be generally used to characterize the morphology of the second phase, such as carbide and graphite [30, 34, 35]. The fractal dimension can be calculated by area–perimeter method [34], as shown in Eq. (3):

$$ D_{f} = 2\lg L_{p} /\lg A $$
(3)

where A and L p is the is the area and the perimeter of borides, respectively.

As shown in Fig. 4, the fractal dimension of M2B rises firstly and then drops with the increment of chromium content, which is somewhat opposite to trend of the average grain size. The result is exactly accordant to the empirical view that fractal dimension has an opposite trend to the grain size [36]. On the other hand, the variation of D f is approximately opposite to that of coarse M2B in Fig. 3. So we can deduce that coarse M2B has an important influence on the fractal dimension (D f ). In general, the morphology tends to be globular as the fractal dimension (D f ) is close to 1 and vice versa. In this context, we can conclude that M2B grain may gradually change from slender-type to wide-block feature with chromium addition increasing from 1.0 to 2.5 wt%. Interestingly, this conclusion agrees well with the phenomenon of increasing coarse M2B in return.

Mechanical properties of M2B

Nanoindentation tests have been conducted on M2B grain to explore the effect of chromium on the mechanical properties. Figure 5 presents the load (P)–displacement (h) curves during indentation for each sample. No apparent displacement bursts can be found on the loading curves, indicating that the crack propagation and indentation size effect (ISE) during indenting process are negligible. As depicted from the inset in Fig. 5, the indentation by Berkovich indenter locates within M2B grain. According to Oliver–Pharr method [23,24,25,26, 37,38,39,40], the hardness and elastic modulus of M2B can be obtained from the P–h curves. As shown in Fig. 6, nanoindentation hardness of M2B varies slightly in an according order of magnitude (near 24 GPa) with the increase in chromium content. Compared with previous results of Vickers hardness [9, 11,12,13], the nanoindentation hardness appears to be larger. Generally, the hardness of material is supposed to decrease with the increase in testing load, so the result of hardness in current research is reasonable. On the other hand, the elastic modulus of M2B declines firstly and then increases slightly, within the range from 302.53 to 336.54 GPa. At chromium content of 1.5 wt%, the elastic modulus achieves its minimum value. And the evolution of elastic modulus of M2B is in accordance with the results of the first-principles calculation [27].

Figure 5
figure 5

The load–displacement curves of the borides in Fe-3.0B alloys with different chromium contents

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Fig. 6
figure 6

Hardness, elastic modulus and H/E r of the boride in Fe-3.0B alloys with different chromium contents

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Furthermore, the ratio of H–E r can be obtained accordingly. As shown in Fig. 6, H/E r of M2B increases firstly and then decreases, reaching the peak value of 0.092 at chromium content of 2.0 wt%. Previous studies have found that H/E r owns an approximately linear relationship with W e /W t (W e : the elastic work during the uploading process; W t : the total work during the indentation test) [22, 24]. In this context, the higher the H/E r of the boride, the higher the elastic recovery work. During the indentation process, elastic and plastic deformations simultaneously take place around and beneath the indenter. Unfortunately, M2B is such a brittle intermetallic that microcracks are bound to arise along with the deformation. Accordingly, part of the total work during the indenting process will be consumed to support the surface energy originating from the occurrence of microcracks. Consequently, the elastic work (W e ) to support the elastic recovery during the uploading process will decline. The more severe the phenomenon of microcracks, the less the elastic work. In other words, higher elastic work indicates better toughness of M2B. In view of the linear relationship between H/E r and elastic recovery, the H/E r can reflect the toughness of the boride to some extent. Thereby, it can be concluded that the toughness of M2B increases firstly and then decreases with increasing chromium content, obtaining the highest toughness at the chromium content of 2.0 wt%.

Toughening mechanism of chromium addition in M2B

In the current work, the tetragonal Fe2B with the I4/MCM space group has been selected to conduct the first-principles calculations [41]. As for (Fe, Cr)2B crystal structure, one of Fe atoms in the initial Fe2B crystal cell is replaced with one Cr atom. The crystal cells parameters and atomic positions have been fully optimized by performing the first-principles calculations. The lattice parameters of Fe2B have been determined to be a = b = 4.89 Å and c = 4.222 Å, while these of (Fe, Cr)2B to be a = b = 4.986 Å and c = 4.107 Å. With Cr atom being doped, the crystal lattice of Fe2B can be compressed in some degree along [002] direction and expanded a little transverse to [002] direction. In addition, population analysis results show that the average bond lengths of B–B are 2.11 and 1.94 Å for Fe2B and (Fe, Cr)2B, respectively.

Table 3 shows the binding energy and mechanical modulus of Fe2B and (Fe, Cr)2B. It can be found that Ebinding of M2B decreases slightly from − 105.934 to − 106.976 eV/Cell, which indicates that (Fe, Cr)2B may be more thermodynamically stable than the initial Fe2B. On the other hand, the elastic modulus of M2B ranges from 326.934 to 350.007 GPa, which is according to the experimental results of nanoindentation in Fig. 6. Furthermore, the ratio of bulk modulus and shear modulus (B/G) increases slightly, which indicates the toughness of M2B can be improved to some extent after Cr atom being doped [27].

Table 3 Binding energy and modulus of Fe2B and (Fe, Cr)2B
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Figure 7 exhibits the EPMA mapping of chromium distribution in 2Cr sample. Chromium concentration in M2B is evidently higher than the surrounding metallic matrix. According to Fig. 7b, the total area with chromium concentration ranging from 3.0 to 6.0 wt% reaches about 25.7 area %, which is approximately equal to the volume fraction of M2B in 2Cr sample. In this case, we can conclude that chromium tends to segregate in M2B after being added in Fe-3.0B alloy. A number of factors can be supposed to contribute to the segregation phenomenon. Firstly, due to the similar atom radius and electronegativity, iron atom in M2B can be effectively replaced by chromium. On the other hand, during solidification solute atoms are partitioned between the solid phase (S) and liquid phase (L) to either enrich or deplete region depending on the solute atom partition coefficient (K = C S /C L , where C S and C L are defined as the solute concentration in the S and L, respectively). With the partition coefficient being less than 1, chromium tends to segregate in the liquid contributing to a higher chromium content in the final liquid before eutectic reaction. Furthermore, chromium has strong affinity with boron, which also contributes to the chromium concentration in boride being higher than the matrix. From the comparison of the binding energy of M2B in Table 3, the possibility of chromium replacement can be explained thermodynamically. Taking all the factors above into consideration, it is reasonable for the segregation of chromium in M2B.

Figure 7
figure 7

Chromium distribution in Fe-3.0B alloy: a Heat-treated microstructure of 2Cr, b Mapping of chromium distribution

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Figure 8 shows the results of high-resolution transmission electron microscope (HRTEM) observation for 0Cr, 1Cr and 2Cr samples, respectively. Figure 8a1–c1 is the bright-field images combining with the corresponding selected area diffraction patterns (SADP) of 0Cr, 1Cr and 2Cr, respectively. For all samples, Fe-3.0B alloy is composed of smooth boride and rough metallic matrix. The matrix has been identified as martensite due to its typical body-centered cubic patterns in designated region A. For 0Cr sample, the SADP of M2B can be identified as the tetragonal lattice, revealing the typical lattice structure of Fe2B (indexed by ICSD#42530). From high-magnified micrograph of M2B in Fig. 8a2, the atomic arrangement is quite orderliness and no evident defects (e.g. dislocations, stacking faults) appear, which may be attributed to the considerable stiffness and elastic modulus of hard Fe2B. From the inverse Fourier-filtered (IFFT) image in Fig. 8a3, the crystal plane spacings of (211) and (110) can be measured to be 2.043 and 3.631 Å, respectively, according to the standard spacings of 2.013 and 3.613 Å. However, for 1 and 2Cr samples, M2B can be identified as the orthorhombic lattice structure, revealing to be (Fe, Cr)2B (indexed by ICSD#16554). From the IFFT images in Fig. 8b3 and c3, the spacings of (400) plane for 1 and 2Cr sample are 3.649 and 3.695 Å, respectively, being approximately equal to the theoretical value of 3.643 Å within the range of accidental error. Therefore, it can be concluded that the crystal lattice of Fe2B may transform from tetragonal to orthorhombic ((Fe, Cr)2B) lattice with chromium addition.

Figure 8
figure 8

HRTEM micrographs of the boride in 0Cr a, 1Cr b and 2Cr c sample: a1–c1 bright-field images and the SADPs; a2–c2 high-magnified micrographs of the boride; a3–c3 inverse Fourier-filtered images of the boride

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According to the first-principles calculation result, with fully structure optimization, the crystal lattice of M2B transforms from tetragonal (Fe8B4) to orthorhombic structure (Fe7CrB4) after chromium doped. This result is exactly accordant to the above experimental data. Furthermore, the initial B–B bond length along [002] has been shorted by about 8% as a result of the lattice evolution of M2B. Therefore, the inherently weak B–B bond is expected to be strengthened accordingly. In this context, the fracture toughness of Fe2B is supposed to be improved with the weakest chain being reinforced.

However, if the chromium addition exceeds the ideal limit, excessive chromium may dissolve into M2B generating excessive (Fe, Cr)2B crystal cell. In this case, large amounts of distorted cells (orthorhombic structure) will cause considerable defects in the whole M2B grain. In reverse, fracture toughness of the boride may turn to decrease. In this context, the decline of fracture toughness of M2B in 2.5Cr sample can be explained reasonably. In conclusion, appropriate chromium addition can help improve the fracture toughness of M2B by affecting the crystal lattice and strengthening the weak bond.

Conclusions

The morphology, mechanical properties and crystal lattice structure of M2B in Fe-3.0B alloys with different chromium additions have been investigated. The following conclusions can be drawn:

  1. (1)

    With increasing chromium addition, the average grain size of M2B (Ã) decreases firstly and then increases slightly, while the fractal dimension (D f ) has an opposite trend.

  2. (2)

    The hardness of M2B changes little while the elastic modulus decreases firstly and then increases with the increase in chromium addition; H/E r increases firstly and then decreases and reaches the maximum value at chromium addition of 2.0 wt%.

  3. (3)

    With chromium addition, M2B crystal tends to be more thermodynamically stable with the binding energy decreasing from − 105.934 to − 106.976 eV/cell; the elastic modulus and B/G can also be improved.

  4. (4)

    With chromium addition, the crystal lattice of Fe2B may transform from tetragonal to orthorhombic structure ((Fe, Cr)2B), contributing to shortening the length of B–B bond along [002] direction.