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Structural, mechanical properties and fracture mechanism of RuB1.1 Yong Pan,a,b Weiming Guanb and Weitao Zheng*a Polycrystalline RuB1.1 has been prepared by using an arc-melting method and its structure and mechanical properties including elastic modulus, hardness and fracture behavior have been characterized. Also, the electronic structure and bond characteristics for this compound have been investigated by first-principles calculations. The lattice parameters of RuB1.1 have been precisely determined by a Rietveld refinement. First-principles calculations show that this compound has a high bulk modulus and a big Poisson’s ratio compared to RuB2. The measured hardness of ∼10.6 GPa for RuB1.1 is three times lower than the theoretical value. This low hardness can be attributed to bond characteristics such as the bonding state and orientation, and fracture mechanism, in which the features of the Ru–B bonds plays an important

Received 26th September 2013, Accepted 10th December 2013

role in the hardness. We found that there is an isosceles triangle bonding state including the B–B and

DOI: 10.1039/c3dt52675e

Ru–B bonds, and the two-dimensionally inclined Ru–B bonds along the a–b plane weaken the hardness and C33. The scanning electron microscopy images show that this RuB1.1 compound exhibits a twinning

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fracture, and this fracture model is also confirmed by first-principle calculations.

Introduction Since ReB2, with a hardness of about 48 GPa under a lower applied load (0.49 N),1 was successfully synthesized by using an arc-melting method, the transition metal borides (TMBs) as potential superhard materials have attracted much attention due to their higher hardness, higher bulk modulus and ultraincompressibility, etc. So far, numerous TMBs such as OsB2,2 IrB1.1,3,4 RhB1.1,5 RuB2,6,7 WB48 and CrB49,10 have been synthesized and studied in recent years. Theoretical calculations show that the high hardness of these TMBs originates from the strong B–B covalent bonds and TM–B bonds because of the hybridization between TM-d states and B-2p states. However, the hardness of these TMBs is generally lower than 40 GPa (the superhard materials’ requirement: Hv ≥ 40 GPa).11,12 Therefore, exploring the nature of hardness is very necessary and of interest in order to obtain very hard TMBs. In the past years, many studies on these TMBs have focussed on the relationship between hardness and bond states, structure and composition.13–17 However, the determining factors for hardness are very complex. The hardness of a solid is related not only to the intrinsic factors such as

a

Department of Materials Science, Key Laboratory of Automobile Materials of MOE and State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012, PR China. E-mail: [email protected]; Fax: +86-431-85168246; Tel: +86-431-85168246 b State Key Laboratory of Advanced Technologies for Comprehensive Utilization of Platinum Metals, Kunming 650106, PR China

5168 | Dalton Trans., 2014, 43, 5168–5174

electronic structure, covalent bond and structural type, etc. but also to external conditions such as deformation, defects and fracture behavior, etc. In nature, the hardness of a material is a measure of the energy needed to shear deformation, that is, to break the shear band. Shear deformation gives rise to the fracture and influences the hardness. Therefore, the fracture model also plays an important role in hardness. Unfortunately, this relationship between hardness and fracture behavior for TMBs has not yet been investigated either theoretically or experimentally. Recently, Rau et al. reported that the measured hardness of a ruthenium boride film was about 49 GPa compared to pure RuB2.18,19 They found that this high hardness derives from the microstructure which is composed of two ruthenium boride phases: Ru2B3 (main phase) and RuB2 (second phase). However, so far, the crystal structure and mechanical properties including elastic modulus, hardness, as well as electronic structure have been studied in detail only for RuB2, while those for other ruthenium borides such as RuB1.1, Ru2B3, Ru7B3 have not been reported yet. In order to reveal the nature of hardness and to search for new hard materials, in this paper, the polycrystalline RuB1.1 is successful prepared by using an arc-melting method, and its structural and mechanical properties including elastic modulus, fracture, and hardness are characterized. The structural stability and the nature of hardness are explored by using a first-principles approach. To the best of our knowledge, the structural information and the fracture mechanism of RuB1.1 are first reported here.

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Experimental section A polycrystalline sample of RuB1.1 in this paper was prepared by using an arc-melting method. A mixture of ruthenium powder (∼200 mesh, purity > 99.95%) and crystalline boron powder with a molar ratio of 1 : 1.3 was used in order to compensate for the evaporative loss of boron during the synthesis. These powders were carefully mixed in an agate mortar with the addition of acetone to facilitate close mixing. After the mixing procedure, the mixture was cold pressed into a block. Following, these samples were prepared by arc-melting with a water-cooled copper hearth under a high purity argon atmosphere. The pressure inside the chamber was about 1 × 10−3 Pa during the synthesis. For the melting process, an accelerating voltage of 380 V and an emission current of 80 A were used. The blocks were melted three times (each melting was performed after the repositioning of the pellet upside-down), so as to ensure the completeness of the reaction. The arc-melted samples were analyzed by Powder X-ray diffraction. The powder X-ray diffraction (XRD) patterns were obtained using a Panalytical XPert Pro powder diffractometer (Cu Kα radiation, λ = 1.54184 Å) with an X-ray tube operating at 8 kW (40 kV, 200 mA). The diffraction patterns were collected in the range of 20°–90° for 12 h. The morphological and structural characterizations of these samples were carried out by using scanning electron microscopy (SEM). The microhardness measurements were performed by means of a Leica VMHT apparatus equipped with a standard Vickers diamond microindenter. The speed of loading was 5 × 10−6 ms−1, and the time under the peak load was 20 s. Indentations were made by applying 5 loads, ranging from 0.98 N to 9.8 N. Before the loading, these samples were encased in a slow-curing epoxy resin and a preliminary polishing was carried out in order to obtain a mirror finish. The measured Vickers hardness (Hv) was determined by the Load stress P and the arithmetic mean of the two diagonals of the indentation d. The equation of Vickers micro-hardness is given by: H v ¼ 1854:4p=d 2

ð1Þ

the structural optimization, no symmetry and no restrictions were constrained for the unit-cell shape, volume and atomic position. The structural relaxation was stopped until the total energy, the max force, and the max displacement were less than 1 × 10−5 eV per atom, 0.001 eV Å−1 and 0.001 Å, respectively.

Results and discussion Structural information The X-ray diffraction pattern of RuB1.1 is shown in Fig. 1, from which the RuB1.1 possesses a hexagonal crystal structure ˉm2, no: 187, a = b = 2.852 Å, c = 2.855 Å, V = (space group: P6 3 20.104 Å ), and the strongest peak from (100) appears at 36°. Unfortunately, the atomic coordinates cannot currently be determined. As we know, Rietveld refinement of powder diffraction data gives insight into the peaks, lattice parameters and atomic coordinates of an unknown crystal structure. To attain a high quality of structural information, the structure of RuB1.1 was refined by the Rietveld method.25 At ground state and zero pressure, the lattice parameters were determined to be a = b = 2.860 Å and c = 2.846 Å after a Rietveld refinement of the data (see Fig. 2). The refined lattice parameters, a-axis is overestimated by 0.28% and the c-axis is underestimated by 0.31%, respectively, indicate that the calculated refinement results are in good agreement with the experimental data. The calculated Wyckoff sites of atomic coordinates and atomic occupancy are listed in Table 1. The hexagonal structure of RuB1.1 is shown in Fig. 2, wherein the B atom locates at the octahedral interstitial site (OIS) and each B atom is surrounded by six Ru atoms, which can be viewed as alternate stacked Ru and B layers along the a-direction. The calculated lattice parameters by first-principles are: a = b = 2.821 Å and c = 2.819 Å for LDA, and a = b = 2.864 Å and c = 2.853 Å in the case of GGA. Obviously, the calculated lattice parameters by GGA are in excellent agreement with the refinement results and experimental values. It is worth mentioning that there are two kinds of bond states: the Ru–B bond (main bonds, 86%) and B–B covalent bond (secondary bonds,

First-principles calculations ˉm2, no: 187), RuB1.1 has a hexagonal structure (space group: P6 with lattice parameters a = b = 2.852 Å, and c = 2.855 Å.20 The structural stability and electronic structure analyses were performed by using CASTEP code.21 To compare our calculation results, the exchange-correlation function was taken into account through the local density approximation (LDA)22 with Ceperley–Alder (CA-PZ) and general gradient approximation (GGA)23 with Perdew–Burke–Ernzerhof (PBE), respectively. The interactions between ions and electrons were described using the Vanderbilt ultrasoft pseudopotential.24 A plane-wave basis set for the electron wave function with a cut-off energy of 360 eV was used. Integration in the brillouin zone was performed using the special k-point generated with 17 × 17 × 17. During

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Fig. 1

X-ray powder diffraction pattern of RuB1.1.

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equilibrium state (V = 20.999 Å3) displays a low negative total energy with a minimum value of about −1.420 eV per atom. The excellent agreement between the theoretical calculations and the experimental results for this hexagonal structure gives strong support to the validity of the current refined structure. Mechanical properties

Fig. 2 The structure of RuB1.1. Ru and B atoms are in blue and gray, respectively.

Table 1

The calculated atomic coordinates of RuB1.1

Atom

Wyckoff

x

y

z

Ru B

1a 1f

0 0.6667

0 0.3333

0 0.500

14%). Moreover, the nearest neighbor distance of the B–B covalent bond is 2.819 Å, which is slightly bigger than the corresponding bonds of other borides.26 However, the nearest neighbor distance of the Ru–B bond (2.153 Å) is in good agreement with the previous calculated results (2.210 Å).27 We found that the bond length of the Ru–B bond is shorter than that of the B–B covalent bond and the bond number for the former is more than the latter, indicating that the Ru–B bond plays an important role in the intrinsic hardness for this RuB1.1 structure. In order to estimate the structural stability, RuB1.1 in a relaxed atomic position was calculated by using a firstprinciples approach. The calculated total energy as a function of volume is shown in Fig. 3. We observe that RuB1.1 at

The elastic properties of a material are very important because they determine the mechanical stability, strength, hardness and ductile or brittleness behavior, etc. Therefore, the elastic properties of RuB1.1 should be first investigated here. The calculated elastic constants of RuB1.1 are listed in Table 2. Regardless of LDA or GGA, the calculated elastic constants of RuB1.1 satisfy the Born stability criteria, meaning that the mechanical stability is at the ground state. The elastic constants, C11 and C33, indicate deformation along the a-direction and c-direction, respectively (see Fig. 2). The general trend is, the larger the values of C11 and C33, the higher the resistance to deformation along the a-direction and c-direction. It is worth noticing that the applied load plane for Vickers hardness is in the a–c plane and the direction of applied load is the b-direction. Therefore, C33 represents the depth of indentation, and a large C33 may be responsible for the high hardness. For example, the C33 of ReB2 is about of 1023 GPa, which is very close to the C11 of diamond.28 As shown in Table 2, the value of C33 is bigger than C11 whether LDA or GGA, which is consistent with other borides. In addition, the C33 of RuB1.1 is slight bigger than for RuB2.29 According to the Pugh rule,30 either ductile or brittle behavior of a solid is estimated by its B/G ratio (B: bulk modulus, G: shear modulus). A low G means a low resistance to shear deformation, and hence ductility; while a low 1/B indicates a low resistance to fracture, and hence brittleness. The critical value of B/G which separates ductile and brittle material has been found to be 1.75. If B/G > 1.75, a material behaves in a ductile manner, while if B/G < 1.75, a material behaves in a brittle manner. In fact, the value of B/G ratio indirectly determines the hardness of a solid. The general trend is, the lower the B/G ratio, the higher the hardness for a material. For example, the B/G ratio of diamond is only about 0.826.31,32 To estimate the micro-hardness (Hv) of RuB1.1, the equation for hardness can be described as: Hv ¼

ð1  2σÞE 6ð1 þ σÞ

ð2Þ

The calculated bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, B/G ratio and hardness of RuB1.1 within LDA and GGA are listed in Table 3. The calculated bulk modulus of RuB1.1 is bigger than that of RuB2 whether LDA or Table 2

The elastic constants Cij (in GPa) of RuB1.1 by LDA and GGA

Phase RuB1.1 Fig. 3

Calculated total energy of RuB1.1 as a function of volume.

5170 | Dalton Trans., 2014, 43, 5168–5174

LDA GGA

C11

C12

C13

C33

C44

C66

595 541

211 173

179 158

798 722

184 162

192 184

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Table 3 The calculated bulk modulus B (in GPa), shear modulus G (in GPa), Young’s modulus E (in GPa), Poisson’s ratio σ, B/G ratio and micro-hardness Hv (in GPa) for ruthenium borides

B

G

E

σ

B/G

Hv

Hexp

LDA GGA

346 307

203 186

509 464

0.255 0.248

1.704 1.651

33.2 31.2

10.6

LDA29 GGA29

319 293

198 191

0.253 0.238

1.611 1.576

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Phase RuB1.1 RuB RuB2

GGA. However, the shear modulus of RuB1.1 by LDA is bigger than for RuB2 in contrast to the shear modulus for the former by GGA being lower than the latter, implying that RuB1.1 has a stronger resistance to shape deformation. On the other hand, the Poisson’s ratio is indicative of the degree of directionality for covalent bonding. As seen in Table 3, the calculated Poisson’s ratio of RuB1.1 is slight bigger than that of RuB2. Obviously, RuB1.1 has weak bond covalency. This is not surprising as the boride-rich region has more covalent bonding compared to the boride-poor region. This is demonstrated by the calculated B/G ratio because the B/G ratio of RuB2 is lower than that of RuB1.1. The measured hardness of RuB1.1 as a function of load is presented in Fig. 4. Indentations were made with five loads ranging from 0.98 N to 9.8 N. For the Vickers hardness measurement, Latini et al. pointed out that there is a linear relationship between the hardness and applied load for TMBs. The bigger the applied load is, the lower the hardness of a material is. However, Fig. 4 shows that the average measured hardness of RuB1.1 is very similar regardless of low or high loads. That is to say, the average hardness of RuB1.1 is not affected by applied load. Moreover, the micro-hardness of RuB1.1 is lower than RuB2, and is higher than RuB, which is consistent with the bond covalency, i.e. the boron-rich or boron-poor regions. In addition, we note that the elastic constant C33 and bulk modulus of RuB1.1 are bigger than that of RuB2 in contrast to the hardness of the former being lower than that of the latter. At the same time, the calculated microhardness of RuB1.1 is about three times larger than the experimental value. These results indicate that the hardness of

8.033 14.533

RuB1.1 is not determined by its elastic modulus, and may be influenced by other factors such as bond feature or fracture mechanism (the discussion will be given below). The discrepancy in hardness of the TMBs can be ascribed to their bond states. Previous reports have shown that the hardness of a boron-rich boride is higher than a boron-poor boride because the boron-rich boride has more covalent bonds. For a covalent or ionic crystal, the bond strength can be estimated by Gao’s hardness model. Based on this model, the calculated bond strength of a B–B covalent bond is stronger than a TM–B bond. Therefore, either shear deformation or fracture of RuB1.1 easily occurs along the weak Ru–B bonds. For TMBs, the orientation of bonds also plays an important role in hardness because it is directly involved in the direction of shear fracture. In a covalent or ionic crystal, the shear deformation mainly depends on the force needed to shear planes. As the force reaches the critical value, the shear deformation occurs along the direction of the weak bonds, resulting in a plastic deformation or fracture. Therefore, the shear deformation or hardness of a material is strongly affected by the orientation of the bonds.34,35 For example, previous results have shown that the calculated shear modulus of ReB2 with an orthorhombic structure (288 GPa by LDA) is lower than that of a hexagonal structure (313 GPa by LDA).36 One of the reasons for this is that the orientation of the Re–B bond for the former is different to that of the latter. For an orthorhombic structure, the two-dimensional Re–B bonds are parallel to the a–c plane, which is the loading plane. The hardness of ReB2 with this structure is mainly determined by the bond strength of the Re–B bonds. However, for a hexagonal structure, not only the Re–B bonds, but also the B–B covalent bonds are parallel to the a–c plane, and hence the bond strength of the strong B–B bonds, rather than the weak Re–B bonds, plays a key role in resistance to the deformation under loading. As shown in Fig. 2, the stacking sequence of Ru and B layers for RuB1.1 with a hexagonal structure is ABABABAB… along the crystallographic a-direction, and the main Ru–B bonds are distributed in the a–c plane. When force is loaded on RuB1.1, the weak Ru–B bonds are more easily ruptured compared to the strong B–B covalent bonds. Therefore, we conclude that the hardness of RuB1.1 is determined by not only the bond strength but also the orientation of the Ru–B bonds. Electronic structure

Fig. 4

The average measured hardness of RuB1.1 as a function of load.

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To gain an insight into the origin of hardness and bond characteristics, the density of state (DOS) of RuB1.1 was

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Bond characteristics

Fig. 5

Total and partial density of states (DOS) of RuB1.1.

calculated and is presented in Fig. 5, the black vertical dashed line represents the Fermi level (EF). As shown in Fig. 5, the DOS profile of RuB1.1 from the bottom to −7.35 eV is composed of B-2s states and Ru-4d states. From −7.35 eV to EF, the valence states are mixed Ru-4d and B-2p hybridized states. The Ru-4d states, B-2p states and partial B-2s states dominate in the range of EF ∼ 10 eV. This DOS profile indicates that there is strong hybridization between the Ru-4d and B-2p states so as to form Ru–B bonds along the d–p direction. On the other hand, the B-2p states stretch into the B-2s states from the bottom to −7.35 eV, meaning that B–B covalent bonds are formed in RuB1.1. However, the main peak positions of B-2s states and 2p states for RuB1.1 are different to ReB2.37 The detachment of the main peak of the B atom (B-2s state at −8.37 eV and B-2p state at −6.10 eV) indicates that electron transferral between Ru and B atoms is more than between B and B atoms, and thus numerous Ru–B bonds are formed.

Fig. 6

The bond features of RuB1.1 are shown in Fig. 6. Fig. 6(a) presents the contour plots of difference charge density on the (100) plane, from which the B atoms occupy the center of the octahedral interstitial site as well as the fourfold-coordinated positions, and form a large number of Ru–B bonds. We note that the inclination of the Ru–B bonds and B–B covalent bond form an isosceles triangle, in which the Ru–B bonds form two sides, while the B–B covalent bond forms the base. Therefore, this inclination of Ru–B bonds in the a–b plane may weaken the hybridization between the Ru and B atoms, and decrease the hardness and C33. The distribution of the isosceles triangle bonding state as a two dimension plane for RuB1.1 is depicted in Fig. 6(b). It can be seen that the directional Ru–B bonds form the shear lips along the a–b plane. However, the B–B covalent bonds along the a-direction form the mountain peak, which is observed in the image of zone A (see Fig. 7(a)). When the applied load is very large, the weak Ru–B bonds as shear lips are ruptured, which is indicated by arrows in Fig. 6(b). Therefore, we conclude that the ruption of Ru–B bonds forms the twinning fracture along the a–b plane. Fracture behavior In order to reveal the relationship between hardness and bond ruption, the morphological and microstructural characterization of the fractured surface of RuB1.1 are presented in Fig. 7. The plain view SEM images are shown with a 500× to 2000× magnification, in which the particle size is between 100 μm and 20 μm. As seen in Fig. 7(a), the fracture surface and cleavage plane are easily observed. The fractured surface consists of cleavage facets as well as a lamellar structure. It is worth noticing that two major zones with the same fracture model can be recognized by mountain peak A. At the same tine, the

The features of bond states, (a) the difference charge density contour plots of RuB1.1 in (100) plane and (b) the bond characteristics of RuB1.1.

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Fig. 7

Paper

SEM micrographs of the fractured surface of RuB1.1; (a) fracture model and (b) lamellar structure.

fracture morphology with zone C is similar to zone B. Therefore, we suggest that a twinning fracture is the typical fracture mechanism for this compound. Fig. 7(b) is the SEM image with a large magnification of zone B. It is apparent that zone B is characterized by a lamellar structure, and the fractured surface is rather flat. It must be noted that the visible crack region, observed by arrow D, may be the origin of fracture and lowest hardness. For RuB1.1, the plastic deformation originates from the weak Ru–B shear bands under applied load, and numerous shear bands at the tip of the main crack are formed along the crack propagation direction. The crack propagation remains in the deformable direction of the initial fracture region, which is similar to the shear lips. Under applied load, the onset of the Ru–B shear band coalescence begins and the crack propagation direction changes when the dilapidated Ru–B bonds meet the strong B–B covalent bonds. Then, the profuse B–B shear bands, as mountain peak A, form in this boride (see Fig. 7(a)). The mountain peak A separates the grain matrix into several stripe areas, corresponding to the lamellar structure, as shown in Fig. 7(b).

Conclusion RuB1.1 with a hexagonal structure can be obtained by using an arc-melting method. From the Rietveld method, the refined structural parameters are: a = b = 2.860 Å, c = 2.846 Å, which are in good agreement with experimental values and first-principles results. Based on first-principles, the calculated average hardness of RuB1.1 is three times bigger than the experimental results, and the hardness of RuB1.1 is bigger than RuB and lower than RuB2. Moreover, the first-principles calculations show that RuB1.1 has a high bulk modulus and big Poisson’s ratio, the calculated B/G ratio is close to 1.75, indicating that RuB1.1 has fewer covalent bonds and a lower hardness compared to RuB2. The lower hardness originates from the bonding state and orientation. We found that there is an isosceles triangle bonding state including a B–B covalent bond and Ru–B bonds, in which the Ru–B bonds are two sides, while the B–B covalent bond is the base. Although the bond

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strength of the B–B covalent bond is stronger than that of the Ru–B bonds, the Ru–B bonds play an important role in the hardness of RuB1.1. The Ru–B bonding state along the a–b plane results in a shear fracture and reduces the hardness, which was demonstrated experimentally. The SEM images show that twinning fracture is the typical fracture mechanism in RuB1.1 and the fracture feature with a lamellar structure is in excellent agreement with the theoretical calculation results.

Acknowledgements This work was supported by the National Natural Science Foundation of China (grant no. 50525204, 50832001 and 50902057) and the important project of Nature Science Foundation of Yunnan (no. 2009CD134).

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Structural, mechanical properties and fracture mechanism of RuB(1.1).

Polycrystalline RuB(1.1) has been prepared by using an arc-melting method and its structure and mechanical properties including elastic modulus, hardn...
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