Interstitial-Boron Solution Strengthened WB 3+x
Xiyue Cheng, Wei Zhang, Xing-Qiu Chen, Haiyang Niu, Peitao Liu, Kui Du, Gang Liu, Dianzhong Li, Hui-Ming Cheng, Hengqiang Ye, Yiyi Li
aa r X i v : . [ c ond - m a t . m t r l - s c i ] S e p Interstitial-Boron Solution Strengthened WB x Xiyue Cheng , Wei Zhang , , Xing-Qiu Chen , ∗ Haiyang Niu , Peitao Liu , KuiDu , , † Gang Liu , Dianzhong Li , Hui-Ming Cheng , Hengqiang Ye , and Yiyi Li Shenyang National Laboratory for Materials Science, Institute of Metal Research,Chinese Academy of Sciences, Shenyang 110016, China and Beijing National Center for Electron Microscopy, Tsinghua University, Beijing 100084, China (Dated: September 1, 2018)By means of variable-composition evolutionary algorithm coupled with density functional theoryand in combination with aberration-corrected high-resolution transmission electron microscopy ex-periments, we have studied and characterized the composition, structure and hardness propertiesof WB x ( x < andnon-stoichiometric WB x both crystallizing in the metastable hP
16 ( P / mmc ) structure. Nosigns for the formation of the highly debated WB (both hP
20 and hP
10) phases were found. Ourresults rationalize the seemingly contradictory high-pressure experimental findings and suggest thatthe interstitial boron atom is located in the tungsten layer and vertically interconnect with fourboron atoms, thus forming a typical three-center boron net with the upper and lower boron layersin a three-dimensional covalent network, which thereby strengthen the hardness.
PACS numbers: 71.20.Lp, 71.23.Ft, 76.60.-k, 61.43.Bn
Typical ultrahard or superhard materials [1–3] (i.e.,diamond, c -B CN, c -BN, γ -B [4, 5] and most recentlysynthesized nanotwinned c -BN [6]) would require three-dimensional (3D) bonding networks commonly consist-ing of high densities of strong covalent bonds, atomicconstituents and valence electrons as well as nano-scalegrains. Currently, the most powerful way to yield thehigh densities of these factors is the synthesis under highpressure conditions. However, in recent years transi-tion metal borides (OsB , ReB , CrB , and FeB , etc[7–15]) have attracted extensive interests because of su-perior mechanical properties and ambient-condition syn-thesis without the need of high pressure, although theirhardness is not as hard as superhardness.Among those borides, the W-B system has attractedparticular attention since the report [16] on WB witha measured superhardnees, H v of about 46.3 GPa, un-der the loading force of 0.49 N, as the highest mea-sured hardness among those borides mentioned above.Although the superhardness of WB has been again con-firmed experimentally [17] and interpreted theoretically[18] based on the widely accepted hP structure[16, 17, 19, 20], several subsequent first-principles cal-culations denied its existence [21–23]. This structure isneither thermodynamically [21] nor dynamically [22] sta-ble, and also not superhard [24] ( H v = 6.5 GPa accordingto a recently proposed hardness model [25, 26]). Instead,those first-principles calculations [21–23] suggested thatthe experimentally attributed WB [17, 27, 28] should becharacterized as a hP phase.Given the fact that the theoretically proposed hP [21–23] is thermodynamically and mechanically sta-ble, and its XRD pattern matches well the experimentallyobserved ones [17, 19], there seems no reason to suspectthe reliability of its composition and structure. However,it is highly surprising that four recent high-pressure ex- perimental findings of this phase [16, 28–30] yielded con-flicting tendency of the pressure dependence normalized c / a ratio. The more striking fact is that none of themagrees with the theoretically derived pressure-dependent c / a ratio [31] of hP . Therefore, this tungstenboride still needs further clarification.Within this context, by combining first-principles cal-culations [32, 33] (unless otherwise mentioned, all cal-culations have been performed with the Perdew-Burke-Ernzerh generalized gradient approximation (GGA-typePBE) [34]), variable-composition evolutionary algorithmsearch as implemented recently in USPEX [35, 36] and theaberration-corrected images of high resolution transmis-sion electron microscopy (
Ac-HRTEM ) (method detailsrefers to Supporting information), we have confirmed theexistence of WB x ( x < hP ) and denied the formation of the exten-sively debated boride of hP [17, 27, 28]. The pre-viously experimentally attributed WB is indeed WB x .The results uncovered that the structure can be regardedas a defective hP one but with a certain propor-tion x of extra interstitial boron locating in the tungstenatomic layers. Varying x , the normalized c / a ratio ratio-nalized four puzzling high-pressure experimental findings[16, 28–30]. Importantly, our results revealed that the in-terstitial boron solution highlights an effect of strength-ening (hardening) to the mechanical property of WB x because of the appearance of the 3D covalent frameworkinduced by boron solution from the ideal 2D boron sheetsin hP .The USPEX searched results are compiled in Fig. 1(details refer to Supporting information and Figure S1).Although the
USPEX found a lowest-enthalpy hP (MoB -type, Fig. 1(c)) in accordance with four recentlytheoretical results [14, 23, 37, 38], its enthalpy of for-mation lies about 2.3 meV/atom above the hR FIG. 1: (color online) (a) The derived GGA-type PBE en-thalpies of formation predicted by variable-composition evo-lutionary computations for the WB -B system (more detailsrefer to Supporting information). Every square represents anindividual structure and the most stable ground state phases(solid circles) are connected to a convex hull. Hollow circlesdenote metastable phases above the convex hull. In panels(b) and (c),the crystal structures of WB : (b) the previouslyexperimental attributed structure ( hP
20) and (c) the USPEXsearched ground state phase ( hP : (d,h) hR
24, (e,i) hP
16, (f,j) hP hP ↔ α -B tieline of the convex hull, suggesting its insta-bility at T = 0 K. In addition, the experimentally at-tributed hP phase (Fig. 1(b)) is confirmed tobe definitely unstable because its enthalpy is positive,much higher than the convex hull. Therefore, we ex-cluded the existence of WB at the ground state. At WB composition, the USPEX searches demonstrated that thestability of WB is highly robust at the ground state(Fig. 1(a)). The results suggest that WB has a lowest-enthalpy hR
24 ( R m ) structure agreeing with the recentresults [23, 38] and has three metastable phases (Fig.1(d - g)), hP
16 ( P /mmc )[21–23], hP P m hP P m
2) with little energy deviations. Their opti-mized lattice parameters are compiled in supporting in-formation, Table S3. These four lattices have been con-firmed dynamically stable by the derived phonon disper-sions without any imaginary frequencies, as illustrated
FIG. 2: (color online) (a-c) Experimental electron diffraction(ED) patterns along the [1010], [1121]and [2241] directions,respectively. (d) The experimental X-ray diffraction data;reflections of the ideal hP and hP are indi-cated by vertical bars. Right inset in (d) shows an SEM im-age of annealed sample. Note that amorphous boron couldnot be distinguished by the XRD pattern. Besides, the 26.4 ◦ peak origins from SiO which was ground by the much harderWB x in the preparation of the x-ray diffraction powder us-ing an agate mortar and pestle. in Fig. 1(j - m). From the phonon densities of states,we further derived the temperature-dependent Gibbs freeenergies by also including zero-point energies and staticDFT energies among these phases (Fig. 1(c)), reveal-ing a phase transition from the ground state hR to the metastable hP phase above 659 K. In or-der to elucidate the impact of the exchange-correlationfunctional on phase transition, we further employed thelocalized density approximation (LDA) potential [39] andfound consistently this phase transition above 678 K(Supporting information, Figure S2).To clarify these theoretical results, we further mea-sured XRD patterns of the powder sample annealed for144 hours at 1523 K (details refer to Supporting infor-mation). As illustrated in Fig. 2(d), the
XRD patternuncovers the mixture of WB and WB x . Furthermore,from the SEM image (see, insert of Fig. 2d), the den-drite of WB and WB x can be identified, whereas thedark contrasting part is amorphous boron which can notbe detectable by XRD. It is clear that the XRD patternof WB indicates a hP
12 (WB -type) phase, in goodagreement with the previous experimental characteriza-tion [10]. The XRD pattern of WB x has been foundin accordance with the reported ones [17, 27, 28] and isexactly same with the theoretically proposed metastable hP phase, rather than its ground state hR phase. This fact can be interpreted well, since our FIG. 3: (color online)The Ac-HRTEM character-ization of the superhardWB x . (a) The projec-tion along the [1120] di-rection of the hP [16, 17, 27, 28]. (b) The Ac-HRTEM morphology witha 10 nm dimension. (c) and(h) The projections alongthe [1120] and [0001] direc-tions of hP , respec-tively. (d,e,f) and (i,j,k)The Ac-HRTEM imageswith the 1 nm dimensionprojected along the [1120]and [0001] directions ofdefective WB x , respec-tively. (g and l) the pro-jections of the structuralmodel along the [1120] and[0001] directions of defec-tive WB x , respectively. annealed temperature of 1523 K is much higher than ourestimated temperature (659 K (GGA) and 678 K (LDA))of phase transition (Fig. 1(c)). Furthermore, the electrondiffraction ED images (Fig. 2(a-c)) and the XRD pattern(Fig. 2d) evidence a hexagonal structure of WB x withthe lattice parameters of a = 5.2055 ˚A , c = 6.3348 ˚A andthe axial ratio c/a = 1.2169, agreeing well with the pre-viously reported data [17, 27, 28]. Moreover, the Vickershardness of the polycrystal sample of WB x was mea-sured to be 36.7 GPa under a loading force of 1N, whichis comparable to the reported values (31.8 GPa under 1.2N [16] and 38.3 GPa under 1N [17]). FIG. 4: (color online) The 2 × × hP , (b) non-stoichiometric WB x , and (c)the partial isosurface of the ELF (with an isovalue of 0.65)projected along the [1120] of WB x , mainly illustrating thethree-center covalent boron net as marked by the dashed line. Because boron is a weak electronic scatterer, it is im-possible to refine the accurate structure of WB x from XRD patterns of powder samples. However, the
Ac-HRTEM image [40] provides a powerful tool to directly (calc.)(calc.)(calc.)(calc.)(calc.)
FIG. 5: (color online) The calculated pressure dependence ofthe normalized c / a ratio of WB x (0 < x < visualize the light mass elements (i.e., oxygen and boron)with the minimum resolution length of about 0.8 ˚A (Sup-porting information). Figure 3b shows the Ac-HRTEM morphology of WB x and boundaries between the darkand bright regions can be clearly identified as markedby the dashed curves. The Ac-HRTEM images with the1nm dimension of Fig. 3(d,e,f) were selected along the[1120] projection, while Fig. 3(i,j,k) corresponds to thesame region along the [0001] projection. Interestingly,Fig. 3d and 3i perfectly match the theoretical projec-tions (Fig. 3c and 3h) along the same directions ofthe hP , confirming the existence of the stoichio-metric hP . For the [1120] projection of hP , between any two dense boron lines there exists atungsten-atom line, which consists of a repeated unit ofevery two tungsten atoms separated by a void. However,what out of our expectation is that the voids are partiallyoccupied in the WB /WB x boundary (see arrows inFig. 3e) and fully occupied in Fig. 3f (see dashed hol-low circles). We further identify that these voids shouldbe occupied by extra boron atoms, rather than tung-sten atoms. If the tungsten atom occupies these voids,the extra peaks would be expected to appear from theXRD patterns in Fig. 2d. As further evidence, the extraatoms can be also found in the Ac-HRTEM images in Fig.3j and 3k projected along the [0001] direction. The factreflects well the occurrence of the new composition ofWB x , which shares, accordingly, the same hexagonalstructure with the hP . In other words, WB x can be considered as defective hP in which theextra x boron atoms occupy the interstitial sites in thetungsten layers. Moreover, the previously experimentallyattributed hP [17, 27, 28] have been absolutelyexcluded, because no any boron pairs (as illustrated inFig. 3a projected along its [1120] direction) can be iden-tified in the Ac-HRTEM images (Fig. 3(d-f)).We further performed a series of first-principles com-putational experiments to analyze the exact position ofthe interstitial boron atoms within a 2 × × hP (Fig. 4a). According to the Ac-HRTEM im-ages, the interstitial boron atoms are placed in the samelayers of tungsten atoms but deviated from all tungstenatoms if viewed from the [0001] direction. After the re-laxation, these interstitial boron atoms still locate in thelayers of tungsten atoms but now each interstitial boronbinds four nearest boron atoms, equivalently, from its up-per and lower boron hexagonal rings, as shown in Fig. 4b.These positions nicely agree with our
Ac-HRTEM images(Fig. 3f and 3k). In fact, there exists sixteen equivalentinterstitial sites in this supercell, determining that themaximum x would be 0.5. To keep the full agreementwith the experimental Ac-HRTEM results in Fig. 3f and3k, at least eight interstitial sites (namely, WB . ) haveto be occupied by boron. Therefore, the x content in theboundary region in Fig. 3e and 3j should be below 0.25.Figure 3g and 3l illustrate the projections along the [1120]and [0001] directions for WB . , in agreement with the Ac-HRTEM images (e.g., Fig 3f and 3k)). In addition, itcan be seen that the
Ac-HRTEM images of WB x along[1120] and [0001] directions are well consistent with thesimulated images (Supporting information, Figure S3) ofthe proposed structural model.Another compelling support to the defective WB x is the normalized pressure dependent c / a ratio (Fig. 5).In agreement with the reported results by Zang et. al. [31], the stoichiometric hP exhibits a large neg- ative pressure dependence. However, with increasing x ,the pressure dependence is substantially elevated. As aresult, this behavior interprets well the apparently con-tradictory results from four recent high pressure measure-ments. It can be seen that with x = 0.343 the theoreticaltrend is similar to that of the experimental observations[29, 30] whereas with x = 0.375 the normalized c / a ratioremains nearly unchanged in the pressure region consid-ered here, which again agrees well with another exper-imental findings [16]. When x reaches its maximum of0.5, the normalized c / a ratio rises significantly from 1 to1.0115 with increasing pressure up to 45 GPa, matchingthe experimental observation by Xie et al [28], althoughour theoretical trend does not reproduce the experimen-tally observed quick drop by less than 1 from 45 GPa to60 GPa.Mechanically, upon different conditions (temperatureand pressure) of synthesis a certain proportion of intersti-tial boron atom diffuses in the space featured by any twoideal 2D boron sheets (Fig. 4a) in hP . This kindof boron solution contributes an extrinsic component tothe superhardness and strengths of WB x due to theformation of 3D covalent network through the connectionof the three-center covalent boron nets as highlighted bydashed lines in Fig. 4c. Our results demonstrated thatthe interstitial boron atoms in a solid solution way areconsidered as an efficient routine to tune the mechanicalproperties (hardness) of transition-metallic borides. Thefindings highlight a promising factor utilizing the con-cept of solid solution [27] to design superhard materials,besides our widely recognized manipulations of covalentbonds, valence electrons and atomic constituents as wellas nano-scale grains. In addition, despite of a good levelof maturity of structural searches for materials discovery,those successful methods ( USPEX [35, 36],
AIRSS [41],
MAISE [42],
CALYPSO [23], and
AFLOW [15], etc) mayneed further algorithm implementations on the search ofthis class of defective or non-stoichiometric structures.Finally, our detailed theoretical and experimental stud-ies of this tungsten boride demonstrate that the composi-tions and structures of many reportedly known transitionmetal borides need to be further investigated in-depth us-ing advanced techniques coupled with the art-of-the-statefirst-principles calculations, in terms of the characteriza-tion difficulties of boron atoms.
Acknowledgements
We are grateful for the usefuldiscussions with Artem Oganov and Qiang Zhu and forthe experimental synthesis with Jiaqi Wang and ShiLiu. This work was supported by the “Hundred TalentsProject” of the Chinese Academy of Sciences and fromNSFC of China (Grand Numbers: 51074151, 51174188,51171188) as well as Beijing Supercomputing Center ofCAS (including its Shenyang branch) and Vienna Scien-tific Clusters. This work made use of the resources of theBeijing National Center for Electron Microscopy. ∗ Corresponding author:[email protected] † Corresponding author:[email protected][1] Kaner, R. B.; Gilman, J. J.; Tolbert, S. H.
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