Modulating Hardness in Molybdenum Monoborides by Adjusting an

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Modulating Hardness in Molybdenum monoBorides by Adjusting Array of boron zigzag chain Qiang Tao, Yanli Chen, Min Lian, Chunhong Xu, Li Li, Xiaokang Feng, Xin Wang, Tian Cui, Weitao Zheng, and Pinwen Zhu Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.8b04154 • Publication Date (Web): 05 Dec 2018 Downloaded from http://pubs.acs.org on December 6, 2018

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Chemistry of Materials

Modulating Hardness in Molybdenum mono-Borides by Adjusting Array of boron zigzag chain Qiang Tao,† Yanli Chen,§ Min Lian,† Chunhong Xu,† Li Li,† Xiaokang Feng,† Xin Wang,† Tian Cui,† Weitao Zheng,*,†,‡ and Pinwen Zhu*,† †

State Key Laboratory of Superhard Materials, College of Physics, Jilin University,

2699 Qianjin Street, Changchun 130012, People’s Republic of China ‡

State Key Laboratory of Automotive Simulation and Control, Department of

Materials Science and Key Laboratory of Automobile Materials of MOF, Jilin University, 2699 Qianjin Street, Changchun 130012, People’s Republic of China §

Key Laboratory of Functional Materials Physics and Chemistry of the Ministry of

Education, Jilin Normal University, Changchun, People’s Republic of China

*Email: [email protected] Abstract Hardness is an essential but complex property in materials. Although it is generally accepted that high hardness is related to high covalent bonds density, the determinant of hardness is always conflicted. In order to break though the restriction of high density of covalent bonds, the low boron content transition metal borides (TMBs) are chosen to explore new way to enhance hardness. We fix the density of covalent bonds, and modulating the hardness by design perpendicular boron zigzag chain (Bzc) skeleton (pe-Bzcs) and parallel Bzc skeletons (pa-Bzcs) in α-MoB (I41/amd) and β-MoB (Cmcm). Utilizing pe-Bzcs in α-MoB to enhance shear modulus via less slip directions than pa-Bzcs. Pe-Bzcs generates higher grain boundary density in α-MoB than β-MoB to create nano polycrystal morphology under high pressure and high temperature (HPHT). Hence α-MoB has higher hardness (18.4 GPa) than β-MoB (12.2 GPa) attribute to higher shear modulus and higher density of

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grain boundary caused by pe-Bzcs. This work suggests a new opinion that modulating boron covalent bonds substructures is an effect way to enhance the hardness even in low-boron content TMBs. It is significant to design new hard or superhard functional materials. Introduction Hardness is a complex property, which correlate to electric density, chemical bonds, grain boundary density, and defect.1-3 The classical conception is that high density of covalent bonds in materials is prefer to generate high hardness.4-6 However, the opinion is controversial, especially in transition-metal borides (TMBs).7-9 In general, boron-rich compounds possess high covalent bonds density. But the hardness is not relative the covalent bonds density strictly in TMBs. For example, in W-B system, increasing boron content does not lead to higher mechanical strength in boron-rich tungsten borides.10 While, the low-boron content transition metal mono-borides (TMmBs) can also indicate high hardness. Such as WB (I41/amd) has the hardness convergence value at the range of 19.8~28.9 GPa (4.9 N),11 which is comparable with boron-rich TMBs in experimental results: WB3/WB4 (25.5 GPa), FeB4 (15.8 GPa) and CrB4 (23.3 GPa).8, 9, 12 Thus high covalent bonds density may not the unique factor to achieve high hardness in TMBs, and low-boron content TMBms may also generate high hardness. In order to uncover intrinsic hardness mechanism of TMmBs, and discover new method to increasing hardness without augment the density of covalent bonds, study the low-boron content phases of TMmBs is significant. Except increasing density of covalent bonds, skeleton of covalent bonds are important to regulate the hardness of TMBs.13 In TMmBs, boron atoms can form boron zigzag chain (Bzc) skeletons (Bzcs), but how the different arrays of Bzc influences the hardness in TMmBs is mysterious. To study the effect of Bzcs in TMmBs, two compounds with same transition metal but different arrays of Bzc is necessary. MoB is the most appropriate candidate, because MoB have two structures with diverse arrays of Bzc: α-MoB (I41/amd) and β-MoB (Cmcm).14 These two structures make it possible to exploring the hardness mechanism caused by one


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dimension (1D) covalent bonds boron skeleton, meanwhile, ignore the density of covalent bonds. Because α-MoB (I41/amd) and β-MoB (Cmcm) have same content of transition metal and boron atoms, which will result close electronic density, and then close compressibility, also the same covalent bonds density. Thus hardness distinction between α-MoB and β-MoB can reflect different electron transfer and different chemical combination caused by the diverse Bzcs arrays. Moreover, till to now, there is no report of single phase of β-MoB, attribute to α-MoB and β-MoB have very close formation enthalpy, mixture of α-MoB are prefer to exist in product of β-MoB.15, 16 Moreover, the intrinsic hardness value of MoB is still unclear, due to it is difficult to synthesize dense bulk MoB. Hence prepare single phase of MoB is meaningful to explore the structure and intrinsic properties. Besides, except density of covalent bonds, hardness is not only decided by inner factors of structure, but the density of grain boundary. Diverse arrays of Bzc may generate different grain growth rate. Thus, arrays of Bzc may be the key to control grain size in TMmBs. Different substructure of Bzcs may give rise to diverse morphology, which may results different density of grain boundary. According to Hall-Petch effect,17, 18 increasing density of grain boundary is an effective way to block dislocation slipping, and can enhance the mechanical properties. Such as WB synthesized by high pressure and high temperature (HPHT) indicates high hardness of 28.9 GPa under 4.9 N with average grain size about 20.8 nm.11, 19 Thus, study the growth mechanism and fabricate nano polycrystal of TMmBs is meaningful. While, generating nano-size grain bulk materials in TMmBs is hard to control. The reason is that high temperature is necessary to synthesize TMmBs,20 which will results the grain growth rapidly. Chemical method can proceed under lower temperature to synthesize nano-TMBs, but most resultants are powder.21-23 Preparing TMmBs bulk materials with nano-size grain by control the arrays of Bzc is meaningful not only to enhance hardness of TMmBs, but also to uncover the growth mechanism of Bzc in TMmBs. In this work, we fixed the covalent bonds density, designed different arrays of Bzc and different grain boundary density in MoB. So as to uncover the hardness



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mechanism of MoB, and find a new method to increase hardness of TMBs without augment covalent bonds density. α-MoB (I41/amd) and β-MoB (Cmcm) with nano-polycrystal morphology and nano-lamellar morphology were synthesized by HPHT. The growth mechanism of MoB is analysed. The reasons of hardness distinguish between α-MoB (I41/amd) and β-MoB (Cmcm) is uncovered via study the Bzc array and grain boundary density of nano-polycrstal. This work is not only meaningful to understand the growth and hardness mechanism of TMmBs, but also uncover a new conception to enhance hardness of TMBs. It is significant to search for new functional hard or superhard materials. Experimental The raw materials were powdery molybdenum (99.95%) and amorphous boron powder (99.9 %). The two powder were mixed with mole ratio of Mo : B=1 : 1.2 in agate mortar more than 3 h. The bit more boron is necessary to supplement the loss at mixing. And mixed powders were cold-pressed into cylindrical sample with 4 mm in-diameter and 3 mm in-height. The cubic anvil high pressure and high temperature (HPHT) apparatus (SPD-6×600) was used to synthesize MoB at pressure of 5.2 GPa and at temperature range of 1900 K~2600 K, the dwell time was 15 min. The phases of the as-synthesized samples were characterized by X-ray Diffraction (XRD) using Cu Kα (λ = 1.5404 Å) radiation in a Rigaku D/max-2500 as implemented in the GSAS program suit.24, 25 A JEM-2200FS Transmission Electron Microscope was used for Transmission Electron Microscope (TEM), and High Resolution Transmission Electron Microscope (HRTEM) observations. Synthesized sample was observed by Scanning Electron Microscopy (SEM FEI Magellan 400) to study the growth morphology. The Vickers hardness (HV) measurements were performed by Micro-Hardness Tester (HV-1000ZDT), the applied load P and HV were determined using eq 1: HV = 1854.4P/d2

(1)

Where d is the mean of the two diagonals of the indentation and the holding time under the peak load was 15 s.


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The calculations of elastic properties, density of states (DOS) and electron localization function (ELF) of MoB were carried out using the VASP code within the generalized gradient approximation (GGA) with the exchange-correlation functional of Perdew, Burke and Ernzerhof (PBE).26-28 The valence states of Mo and B are 4p64d55s1 and 2s22p1, respectively. A plane-wave cutoff of 500 eV and a dense Monkhorst-Pack grid with a reciprocal space resolution of 2π×0.03 Å-1 were chosen to ensure the total energies are less than 1 meV/atom.29 Elastic constants were calculated with the strain-stress method, based on which the mechanical properties, the bulk modulus B and shear modulus G were estimated via the Voigt-Reuss-Hill (VRH) approximations.30 Mulliken bond populations were calculated using a 2×2×1 supercell implemented in the CASTEP code.31 The ultra-soft Vanderbilt pseudo-potential (USPP) with GGA-PBE is chosen.32 The cutoff energy and k-mesh were the same as the setting in VASP calculations. Results and Discussion As reported, MoB have two structures: α-MoB (I41/amd) and β-MoB (Cmcm).14 In both structures, boron form 1D zigzag chains, the substructure unit can be regard as H layer (Fig 1). Bzc are parallel each other in H layer. And in H layer, Bzc separated by Mo atoms, the Mo atoms can form channel for Bzc. Moreover, Bzc are covered by two-tier of Mo atoms as sandwich structure in H layer. β-MoB (Cmcm) is only stacked with H layers with stacking order “H H H H”. And all of Bzc are parallel in β-MoB to form parallel Bzcs (pa-Bzcs). However, the stacking order is changed by insert K layers as “H K H K H” in α-MoB. Actually, the K layer has same atomic arrangement as H layer, but K layer are rotated of 90°on c axis when stacking in α-MoB. Hence, in α-MoB, Bzc in K layers are perpendicular to the Bzc in H layers, and can be regard as perpendicular Bzcs (pe-Bzcs). The different arrays of Bzc in MoB are very important to determine the synthesis, growth morphology, and physical properties. In order to confirm α-MoB and β-MoB are suitable to uncover the influence of Bzc array, chemical bonds are analyzed. Chemical bonds are essential to determine the intrinsic hardness of materials. In MoB, all of the covalent bonds, ionic bonds, and



metal bonds generate the complex combination. Structures of α-MoB and β-MoB are very close, the substructure unit (H/K layer) and content of Mo atoms are the same. Moreover, the metal bonds are the weakest bonds in the three chemical bonds. So the metal bonds cannot be the essential reason to decide hardness in MoB. Study the covalent bonds and ionic bonds in MoB are important. The populations are calculated to analysis the electron transfer between Mo and B, which can reflect the strength of ionic bonds. The charges transfer in α-MoB and β-MoB are the same, per Mo atom donates 0.46 e to per B atom in both α-MoB and β-MoB. Thus, the strength of Mo-B ionic bonds in α-MoB and β-MoB are the same. According to the density of states (DOS) in Fig S1, both α-MoB and β-MoB are metal, attribute to Mo 4d electrons occupancy the major orbit near the Fermi level. Since absence B 2p electrons occupancy at Fermi level, B and Mo are bare of orbital hybridization, which indicates there are no covalent bonds between Mo and B. Electron location functional (ELF) was calculated to analysis covalent bonds in MoB (Fig 2). Strong covalent bonds are formed in Bzc, due to electrons are located between boron atoms. Hence Bzc generates 1D covalent skeleton in MoB. The strength of covalent bonds are very close due to the B-B bonds length are close. So the strength of chemical bonds in α-MoB and β-MoB are very close. The major distinction is the arrangement of Bzc that may result different slip model in α-MoB and β-MoB. In α-MoB and β-MoB, structures prefer to slip along H/K plane with breaking the metal bonds, attribute to metal bond is the weakest bond. And under stronger shear deformation, the ionic bonds (Mo-B) can be bended or broken before covalent bonds (B-B), H/K layer will be destroyed by break Mo-B ionic bonds under strong shear deformation. Thus, β-MoB can glide not only along H plane but also glide in b axis direction which perpendicular to H plane (needn’t to broken B-B covalent bonds); But α-MoB only can be glide along H/K plane, B-B covalent bonds will be broken if slip along c axis (perpendicular to H/K plane). With this analysis, pe-Bzcs in α-MoB should have higher shear modulus than the pa-Bzcs in β-MoB, which may induce higher hardness in α-MoB. In order to confirm the inference that α-MoB has higher shear modulus than


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β-MoB, the elastic constants are calculated (Table 1). α-MoB and β-MoB indicate very close incompressibility bases on almost same bulk modulus (313 GPa and 311 GPa), which depend on electric density in structure. The shear modulus of α-MoB (205 GPa) is bit higher than β-MoB (194 GPa) as the inference. The higher shear modulus of α-MoB attribute to the Bzc in H layers are perpendicular to K layer, which enhance the structure by resist the glide along c axis direction under strong shear deformation. So with the calculated results, the α-MoB should has higher hardness than β-MoB by pe-Bzcs block slip in structure. We performed the experiments to generate different boron skeletons (pa-Bzcs and pe-Bzcs) in MoB. MoB are prepared by HPHT, the phases of synthesized samples are detected by XRD in Fig 3. Under 5.2 GPa, α-MoB is synthesized at 1900 K, the synthesized temperature is consistent with Mo-B system phase diagram.16 β-MoB appears at 2300 K with amounts of α-MoB mixture. The content of α-MoB is decreasing with increasing temperature. When temperature increases to 2600 K, α-MoB disappeared, and single phase of β-MoB is synthesized. α-MoB is a low temperature phase, and β-MoB is high temperature phase. Reflecting that α-MoB is the most stable phase in molybdenum mono-borides. β-MoB is a metastable phase, in accord with theoretical results that α-MoB has bit lower formation enthalpy than β-MoB.14 Besides, Bzc form “H K H K H” stacking sequence at low temperature, but form “H H H H” stacking sequence at high temperature more than 2300 K. That illustrates the arrangement of Bzc prefer to be more ordered at high temperature. To reconfirm the structures of MoB, the Rietveld refinement is performed (Fig S2). The crystal parameters are list in Table 1, which confirm that α-MoB has the space of I41/amd and β-MoB has the space of Cmcm. It is consistent with the results reported by Hasan et al.14-16 And Mo-Mo bonds length which connecting H-K or H-H layers are very close in α-MoB and β-MoB (2.856 Å and 2.859 Å), B-Mo bonds length is also close with 2.234 Å and 2.218 Å. But the Bzc in α-MoB and β-MoB is bit different with the B-B bonds length of 2.303 Å and 2.402 Å, respectively. And the Bzc angle is 66.1° and 66.7° in α-MoB and β-MoB, respectively. Thus the structures are very close in α-MoB and β-MoB that is consistent with theoretic results.



Bzc are combined by B-B covalent bonds, hence the boron chains can be consider as the skeletons in MoB. The different stacking sequence of Bzc may influence the mechanical properties in MoB. Uncover the hardness of MoB is necessary. Hardness results are shown in Fig 4, the hardness decrease with increasing the applied load in both α-MoB and β-MoB. The hardness of β-MoB is very close with α-MoB under low load (0.98 N). But the hardness value of β-MoB decreases faster than α-MoB when increasing the applied load. The convergence values are 18.4 GPa and 12.2 GPa under 4.9 N for α-MoB and β-MoB, respectively. Even though α-MoB indicates higher hardness convergence value than β-MoB, the hardness of β-MoB is very close with α-MoB under low load. That indicates α-MoB can maintain the ability to stand the indentor deformation even under high load, but β-MoB was generated more deformation with high load. Strong chemical bonds and high electric density is basic for the high intrinsic hardness. But except the intrinsic hardness, the material’s hardness can be enhanced by increase the density of grain boundary, which can obstruct the slip of dislocation. According to Hall-Petch effect,17, 18 the mechanical properties have improved in metal (nano Cu) and nonmetallic (nano-twinned diamond),1, 33 but rarely reports in alloy which content both metal and nonmetallic elements. So, study the morphology of MoB is important to further understand the hardness mechanism. The SEM of MoB is shown in Fig 5, Fig 5. (a) (d) are the surface of α-MoB and β-MoB with no modified. Moreover, β-MoB is composed by lamels, but not very clear in Fig 5. (d), and α-MoB is a dense material with no special morphology (Fig 5. (a)). To uncover the intrinsic morphology, α-MoB and β-MoB are treated by acid, which can eliminate the oxides on the surface of structure. The intrinsic morphology is shown in Fig 5. (b), (e). α-MoB has nano polycrystal morphology (Fig S3), and β-MoB is lamellar morphology obviously. The statistic results of particle size are shown in Fig 5. (c), (f). α-MoB has very small average size 18 nm, β-MoB has average lamel’s thickness 60 nm, but the size of lamel in β-MoB is bigger than 10 µm. HRTEM was performed to confirm the morphology of MoB (Fig 6, Fig 7). In α-MoB, TEM results reconfirmed the structure is polycrystal with crystal size small


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than 20 nm (Fig 6 (a)). And stacking faults in α-MoB can results (103) rotation about 29°(Fig 6 (b)). Defect and stacking faults are always found in α-MoB (Fig S4. (a)), which may due to the pe-Bzcs. The Fourier Transform results (Fig S4. (b), (c)) indicate the zone axis is , which illustrates the crystal is difficult growth regular in c direction, but form much of stacking faults. Except stacking faults, dislocation also can be found in α-MoB (Fig S5). In β-MoB, the lamels are stacked, and the grain boundaries are clear in Fig 7. (a), (b), (e). The zone axis is obtained by Fourier Transform in HRTEM (Fig 7. (c), (d)). Thus the lamels prefer to growth along [100] and [001] direction. That is consistent with Periodic Bond Chain (PBC),34-36 because B-B covalent bonds is strongest bonds in [001] direction, and Mo-B ionic bonds is second stronger bonds in [100] direction, but Mo-Mo metal bonds is weakest bonds in [001] direction. The distinguishing of growth rate in different direction results the lamellar morphology in β-MoB. And the extremely high synthesized temperature (2600 K) make the grain growth rapid, which inducing big lamellar size (more than 10 µm). In both of α-MoB and β-MoB, the size of polycrystal is related to the arrays of Bzc. According to the grain morphology, α-MoB has much higher grain boundary density than β-MoB. Except the intrinsic hardness which is related to structure and chemical bonds, the hardness can be enhanced by higher grain boundary density as Hall-Petch effect,17, 18 the equation obeys： !

𝐻𝑉 = 𝐻! + 𝐾𝑑 !!

(2)

H0 is the intrinsic hardness of single crystal, d is grain size, and K is a constant depend on the ability of hardness increasing rate with decreasing of grain size.37 The equation is on the base of sphere nano polycrystal. According to sphere area πr2, the density of grain boundary can be wrote as: 𝜌=

!

(3)

!! !

ρ represent density of grain boundary. V represent unit volume, r is sphere radius, d=2r. So the Hall-Petch effect equation depend on the grain boundary density turn into:



!

𝐻𝑉 = 𝐻! + 𝐾 ∙ 2

! !

∙

!

!

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! !

(4)

!"

In lamellar morphology, the ρ=V/S, S=2(l·m+l·n+m·n), S is the area of lamellar, l, m, n represent length, width, height, respectively. Combine these with equation (4), the Hall-Petch effect equation for lamellar nano polycrystal turn into: !

𝐻𝑉 = 𝐻! + 𝐾 ∙ 2

! !

!

∙

! !∙!!!∙!!!∙! !! !

(5)

In order to estimate the influence of hardness caused by grain size, assume the H0 of α-MoB and β-MoB are the same, and assume that K is one sixth of c-BN (K=126 GPa nm1/2 in c-BN).37 So the increment of hardness caused by grain size in α-MoB and β-MoB can be estimated by the equation: !

!!

!

∆𝐻 = 𝐻𝑉!!!"# − 𝐻𝑉!!!"# = 𝐾 𝑑! − 2

! !

!

∙

! !∙!!!∙!!!∙! !! !

(6)

d1 (18 nm) and l, m, n (60nm, 60 nm, 10 µm) represent the polycrystal size of α-MoB and β-MoB, respectively. With equation (6), the hardness increment resulted by grain size is about 4.6 GPa. So the hardness increasing in α-MoB not only cause by shear modulus, but also more than half of increment contributed by increasing the grain boundary density. With these results, the hardness of α-MoB is not only enhanced by intrinsic mechanical property (higher shear modulus), but also attribute to the higher grain boundary density. Moreover, the higher grain boundary density cannot take effect under low load, but enhancing hardness under high load obviously. Because with increasing the applied load, the content of grain boundary is increasing, more grain boundary can resist the glide of dislocation more obviously. Therefore, in order to design high hardness in TMmBs, the intersectional array of Bzc is preferred. The intersectional array of Bzc in TMmBs will not only increase the shear modulus, but also enhance the isotropy mechanical properties. And the intersectional array of Bzc will also conduced to generate high density of grain boundary to enhance hardness. So the suitable intersectional array of Bzc can also cause effect for hardness, which may comparable with boron rich phases of 2D boron skeleton or even 3D boron skeleton.


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On the other side, the electrical resistivity is tested in both MoB. α-MoB indicates the electrical resistivity is 1.6×10-6 Ω·m, and β-MoB indicates the electrical resistivity is 1.1×10-7 Ω·m. According to the results of DOS (Fig S1), both structure are metal and has close DOS in Fermi Level, hence the higher electrical resistivity in α-MoB may attribute to much of electron scattering by high density of grain boundary. The different arrangement of Bzc cause different morphology, which not only enhance the hardness of MoB, but also modulate the electrical properties. Enhancing hardness by modulate the array of boron skeleton is effective way to adjust the mechanical property of TMBs, and also a new way to find high hardness or even superhard functional materials in TMBs. Conclusions In summary, α-MoB and β-MoB are synthesized by HPHT, and it is first time to obtain the single phase of β-MoB bulk material. Forming different morphology in α-MoB (nano-polycrystal) and β-MoB (nano-lamellar polycrystal) attribute to diverse pe-Bzcs and pa-Bzcs. The hardness of α-MoB and β-MoB are 18.4 GPa and 12.2 GPa, respectively. Higher hardness of α-MoB attribute to different arrangement of Bzc results higher shear modulus, and higher grain boundary density which resists the glide of dislocation. Thus conclude the new conception that increasing the density of covalent bonds is not the only way to enhance the hardness in TMBs, modulating the covalent bonds array and grain boundary density also can generate high hardness in low boron content TMBs. With high content of transition metals, the low boron content TMBs may exhibit varied functions, which will be a kind of promising functional hard material. So, we suggest two approaches to enhance the hardness of TMmBs, i) by various arrays of Bzc to modulate the shear modulus and isotropic mechanical properties; ii) regulating the growth rate by diverse arrays of Bzc to increase the density of grain boundary. This work is significant to design new hard or superhard functional materials in TMBs. Supporting Information



Calculated PDOS results, pattern of Rietveld refinement, SEM image, HRTEM image (PDF) Acknowledgements The authors acknowledge funding supports from the National Natural Science Foundation of China (No.21601062), and China postdoctoral Science Foundation (No.2016M601374). Reference (1) Huang, Q.; Yu, D. L.; Xu, B.; Hu, W. T.; Ma, Y. M.; Wang, Y. B.; Zhao, Z. S.; Wen, B.; He, J. L.; Liu, Z. Y.; Tian, Y. J., Nanotwinned diamond with unprecedented hardness and stability. Nature 2014, 510, (7504), 250-253. (2) Mansouri Tehrani, A.; Brgoch, J., Impact of Vacancies on the Mechanical Properties of Ultraincompressible, Hard Rhenium Subnitrides: Re2N and Re3N. Chem. Mater. 2017, 29, (6), 2542-2549. (3) Šimůnek, A., How to estimate hardness of crystals on a pocket calculator. Phys. Rev. B 2007, 75, (17). (4) Wang, M.; Li, Y. W.; Cui, T.; Ma, Y. M.; Zou, G. T., Origin of hardness in WB4 and its implications for ReB4, TaB4, MoB4, TcB4, and OsB4. Appl. Phys. Lett. 2008, 93, (10), 101905. (5) Gu, Q. F.; Krauss, G.; Steurer, W., Transition Metal Borides: Superhard versus Ultra-incompressible. Adv. Mater. 2008, 20, (19), 3620-3626. (6) Kaner, R. B., Gilman, J. J.; Tolbert S. H, Designing Superhard Materials. Science 2005, 308, (5726), 1268-1269. (7) Li, B.; Sun, H.; Chen, C. F., First-principles calculation of the indentation strength of FeB4. Phys. Rev. B 2014, 90, (1), 014106. (8) Wang, Q. Q.; He, J. L.; Hu, W. T.; Zhao, Z. S.; Zhang, C.; Luo, K.; Lü, Y. F.; Hao, C. X.; Lü, W. M.; Liu, Z. Y.; Yu, D. L.; Tian, Y. J.; Xu, B., Is orthorhombic iron tetraboride superhard? Journal of Materiomics 2015, 1, (1), 45-51. (9) Knappschneider, A.; Litterscheid, C.; Dzivenko, D.; Kurzman, J. A.; Seshadri, R.; Wagner, N.; Beck, J.; Riedel, R.; Albert, B., Possible Superhardness of CrB4. Inorg. Chem. 2013, 52, (2), 540-542. (10) Li, Q.; Zhou, D.; Zheng, W. T.; Ma, Y. M.; Chen, C. F., Anomalous Stress Response of Ultrahard WBn Compounds. Phys. Rev. Lett. 2015, 115, (18), 185502. (11) Chen, Y.; He, D. W.; Qin, J. Q.; Kou, Z. L.; Bi, Y., Ultrasonic and hardness measurements for ultrahigh pressure prepared WB ceramics. Int. J. of Refract. Met. Hard Mater 2011, 29, (2), 329-331. (12) Tao, Q.; Zheng, D. F.; Zhao, X. P.; Chen, Y. L.; Li, Q.; Li, Q.; Wang, C. C.; Cui, T.; Ma, Y. M.; Wang, X.; Zhu, P. W., Exploring Hardness and the Distorted sp2 Hybridization of B–B Bonds in WB3. Chem. Mater. 2014, 26, (18), 5297-5302. (13) Zhong, M. M.; Kuang, X. Y.; Wang, Z. H.; Shao, P.; Ding, L. P.; Huang, X. F.,


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Phase Stability, Physical Properties, and Hardness of Transition-Metal Diborides MB2 (M = Tc, W, Re, and Os): First-Principles Investigations. J. Phys. Chem. C 2013, 117, (20), 10643-10652. (14) Zhang, M. G.; Wang, H.; Wang, H. B.; Cui, T.; Ma, Y. M., Structural Modifications and Mechanical Properties of Molybdenum Borides from First Principles. J. Phys. Chem. C 2010, 114, 6722–6725. (15) Yang, G.; Kun, H. Z.; Xu, X. L.; Gang, X., Formation of Molybdenum Boride Cermet Coating by the Detonation Spray Process. J. Therm. Spray Technol. 2001, 10, (3), 456-460. (16) Çamurlu, H. E., Preparation of single phase molybdenum boride. J. Alloys Compd. 2011, 509, (17), 5431-5436. (17) Petch, N. J., The cleavage strength of polycrystals. J. Iron Steel Inst. 1953, 174, 25-28. (18) Hall, E. O., The Deformation and Ageing of Mild Steel: III Discussion of Results. Proc. Phys. Soc. B 1951, 64, 747-753. (19) Chen, Y.; He, D. W.; Qin, J. Q.; Kou, Z. L.; Wang, S. M.; Wang, J. H., Ultrahigh-pressure densification of nanocrystalline WB ceramics. J. Mater. Res. 2010, 25, (4), 637-640. (20) Sarma, B.; Ravi Chandran, K. S., Accelerated kinetics of surface hardening by diffusion near phase transition temperature: Mechanism of growth of boride layers on titanium. Acta Mater. 2011, 59, (10), 4216-4228. (21) Portehault, D.; Devi, S.; Patricia B.; Gervais,C.; Giordano, C.; Sanchez, C.; Antonietti, M., A General Solution Route toward Metal Boride Nanocrystals. Angew. Chem. Int. Ed. 2011, 50, 3262-3265. (22) Akgün, B.; Çamurlu, H. E.; Topkaya, Y.; Sevinç, N., Mechanochemical and volume combustion synthesis of ZrB2. Int. J. Refract. Met. and Hard Mater 2011, 29, (5), 601-607. (23) Shi, L.; Gu, Y. L.; Chen, L. Y.; Yang, Z. H.; Ma, J. H.; Qian, Y. T., Low-temperature synthesis of nanocrystalline vanadium diboride. Mater. Lett. 2004, 58, (22-23), 2890-2892. (24) Rieveld, H. M., A Profile Refinement Method for Nuclear and Magnetic Structures. J. Appl. Cryst. 1969, 2, 65. (25) Toby, B. H., EXPGUI, a graphical user interface for GSAS. J. Appl. Cryst. 2001, 34, 210-213. (26) Kresse, G.; Futhmüller, J., Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Computational Materials Science 1996, 6, 15-50. (27) Kresse, G.; Futhmüller, J., Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169-11186. (28) Perdew, John P.; Kieron, B., Ernzerhof, M., Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865-3868. (29)Monkhorst, H. J.; Pack, J. D., Special points for Brillouin-zone integrations. Phys. Rev. B 1976, 13, (12), 5188-5192. (30) Hill, R., The Elastic Behaviour of a Crystalline Aggregate. Proc. Phys. Soc. A



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1952, 65, 349-354. (31) Segall, M. D.; Philip, J. D. L.; Probert, M. J.; Pickard, C. J.; Hasnip, P. J.; Clark, S. J.; Payne, M. C., First-principles simulation: ideas, illustrations and the CASTEP code. J. Phys. Condens. Matter 2002, 14, 2717-2744. (32) Vanderbilt, D., Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys. Rev. B 1990, 41, (11), 7892-7895. (33) Li, X. Y.; Wei, Y. J.; Lu, L.; Lu, K.; Gao, H. J., Dislocation nucleation governed softening and maximum strength in nano-twinned metals. Nature 2010, 464, (7290), 877-880. (34) Hartman, P.; Perdok, W. G., On the Relations Between Structure and Morphology of Crystals.I. Acta Cryst. 1955, 8, 49-52. (35) Hartman, P.; Perdok, W. G., On the Relations Between Structure and Morphology of Crystals.II. Acta Cryst. 1955, 8, 521-524. (36) Hartman, P.; Bennema, P., The attachment energy as a habit controlling factor. J. Cryst. Growth 1980, 49, 145-156. (37) Dubrovinskaia, N.; Solozhenko, V. L.; Miyajima, N.; Dmitriev, V.; Kurakevych, O. O.; Dubrovinsky, L., Superhard nanocomposite of dense polymorphs of boron nitride: Noncarbon material has reached diamond hardness. Appl. Phys. Lett. 2007, 90, (10), 101912. Table 1 The calculated MoB Elastic Constants Cij, Bulk Modulus B, Shear Modulus G, Young’s Modulus E, and experimental Vickers hardness Hvexp (in units of GPa) Compounds

C11

C22

C33

C44

C55

C66

C12

C13

C23

B

G

Hvexp

Reference

α-MoB (I41/amd)

561

561

554

212

212

239

199

186

186

313

205

18.4

Present

α-MoB (I41/amd)

574

574

564

222

222

242

203

198

198

324

210

β-MoB (Cmcm)

520

521

556

202

232

211

207

195

196

311

194

β-MoB (Cmcm)

546

539

572

209

240

212

219

194

211

324

199

a represents reference 14 Table 2 Structure parameters from the final Rietveld refinement Compounds

α-MoB

β-MoB

Crystal system

tetragonal

orthorhombic

Space group

I41/amd (141)

Cmcm (63)

a/Å

3.118

3.142

b/Å

3.118

8.481

c/Å

16.936

3.077

Atoms position

Wyckoff (x y z)

Wyckoff (x y z)

Mo(1)

8e (0 0 0.1962)

4c(0 0.1425 0.25)

B(1)

8e (0 0 0.3249)

4c(0 0.3912 0.25)


a 12.2

Present a

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Residuals

Rwp: 0.1252;

Rwp: 0.1130;

Rp: 0.0963;

Rp: 0.0873;

Rf2: 0.034

Rf2: 0.1087

χ2: 1.338

χ2: 1.314



Figure 1. (a) The structure of α-MoB with stacking sequence of “H K H K H”, (b) The structure of β-MoB with stacking sequence of “H H H H”.


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Figure 2. The Electron Localization Function (ELF) of MoB, (a) is α-MoB, (b) is β-MoB. The blue atoms represent boron atoms, the orange atoms represent molybdenum atoms.



Figure 3. The XRD results of synthesized samples, under 5.2 GPa, 1900 K~2600 K, dwell time is 15 min. the solid rhombus represent α-MoB, and the hollow rhombus represent β-MoB.


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Figure 4. Vickers hardness of MoB. The applied load is 0.98 N, 1.96 N, 2.94 N, and 4.9 N; The holding time under the peak load is 15s.



Figure 5. SEM results of MoB, (a) (d) represent the surface of α-MoB and β-MoB, respectively (with no modified), (b) (e) represent the surface after treated by acid of α-MoB and β-MoB, respectively. (c) (f) distribution of lamellar thickness of α-MoB and β-MoB, respectively. The total of 400 policrystal and 400 lamels were measured to determine the lamellar thickness distribution.


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Figure 6. (a) TEM of α-MoB, GB represent grain boundary. (b) HRTEM of α-MoB, GB represent grain boundary, SFs represent stacking faults. Lattice plane (103) rotation was uncovered in HRTEM.



Figure 7. HRTEM results of β-MoB, (a) HRTEM of β-MoB, GB represent grain boundary. (b) (e) is larger images of white dashed box A and B in (a), respectively. (c) Fourier Transform of HRTEM in white dashed box in (b). (d) Simulate results in zone axis of , which is consistent with (c).


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TOC graphic


Modulating Hardness in Molybdenum Monoborides by Adjusting an

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