Understanding How Bonding Controls Strength Anisotropy in Hard

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Understanding How Bonding Controls Strength Anisotropy in Hard Materials by Comparing the High Pressure Behavior of Orthorhombic and Tetragonal Tungsten Monoboride Jialin Lei, Michael Tyrone Yeung, Paul J. Robinson, Reza Mohammadi, Christopher L Turner, Jinyuan Yan, Abby Kavner, Anastassia N. Alexandrova, Richard B. Kaner, and Sarah H. Tolbert J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b11478 • Publication Date (Web): 13 Feb 2018 Downloaded from http://pubs.acs.org on February 27, 2018

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The Journal of Physical Chemistry

Understanding How Bonding Controls Strength Anisotropy in Hard Materials by Comparing the High Pressure Behavior of Orthorhombic and Tetragonal Tungsten Monoboride Jialin Lei,† Michael T. Yeung,† Paul J. Robinson,† Reza Mohammadi,§ Christopher L. Turner,† Jinyuan Yan,║ Abby Kavner, Anastassia N. Alexandrova,*,†,┴ Richard B. Kaner,*,†,‡,┴ and Sarah H. Tolbert*,†,‡,┴ †

Department of Chemistry and Biochemistry, UCLA, Los Angeles, California, 90095-1569 USA Department of Materials Science and Engineering, UCLA, Los Angeles, California, 90095 USA § Department of Mechanical & Nuclear Engineering, Virginia Commonwealth University, Richmond, Virginia 23284, USA ┴ California NanoSystems Institute (CNSI), UCLA, Los Angeles, California, 90095 USA ║ Advanced Light Source, Lawrence Berkeley National Lab, Berkeley, California 94720, USA Department of Earth and Space Sciences, UCLA, Los Angeles, California, 90095 USA ‡

*

Corresponding Authors: [email protected], [email protected], [email protected]

Abstract In this work, we investigate the high pressure behavior of the stabilized high-temperature (HT) orthorhombic phase of WB using radial X-ray diffraction in a diamond-anvil cell at room temperature. The experiments were performed under non-hydrostatic compression up to 52 GPa. For comparison, the low temperature (LT) tetragonal phase of WB was also compressed nonhydrostatically to 36 GPa to explore structurally-induced changes to its mechanical properties. Although our microindentation hardness tests indicate that the HT WB possesses slightly higher hardness, synchrotron-based high-pressure compression data yield significant distinct incompressibilities. The ambient pressure bulk modulus of the HT phase of WB is 341 ± 5 GPa obtained by using the second order Birch-Murnaghan equation-of-state, while for the LT phase of WB the incompressibility increased to 381 ± 3 GPa. The elastically-supported differential stress was measured in a lattice specific manner and analyzed by using lattice strain theory. Greater strength anisotropy was observed in the HT WB phase, compared to the LT materials. DFT energy shift calculations indicate that W-B bonds, rather than B-B bonds are responsible for the latticedependent mechanical properties.

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Introduction As the world’s hardest natural material, diamond has surprisingly limited applications in cutting and drilling, since it reacts with ferrous materials to form brittle carbides. 1,2 With an increasing demand for diamond replacements, many superhard materials have been discovered with both good chemical stability as well as high hardness, including rhenium diboride (ReB2), and cubic boron nitride (c-BN). 3,4,5 Unfortunately, synthetic requirements for c-BN (i.e. high pressure and high temperature) lead to high costs, limiting its use. Similarly, use of ReB2 is limited because it contains an expensive platinum group metal. Tungsten tetraboride (WB4) has emerged as a less expensive superhard material. WB4 has a Vickers hardness that reaches 43.3±2.9 GPa6,7 under an applied load of 0.49 N and a bulk modulus of 324±3 GPa.8 Its high hardness results from the high valence electron density of tungsten and short strong covalent bonds introduced by boron. However, it is still a challenge to make phase pure WB4. As a thermodynamically unfavorable phase, WB4 cannot be made by high temperature arc melting unless the W:B molar ratio is kept at 1:12. 9 The WB4 samples prepared in this way are therefore not stoichiometric, but rather a composite of WB4 and crystalline boron, which introduces unwanted non-uniformity.10,11 Lower borides of transition metals may offer a solution to the stoichiometry problem if superhard phases can be found. In particular, consider tungsten monoboride (WB), with a tungstentungsten bond distance of 2.8 Å that is comparable to pure tungsten metal (2.7 Å). This similarity with pure tungsten suggests a stronger metallic character than any of the previously mentioned borides, bringing with it the ductility and electrical conductivity typically found in conventional metals. Tungsten monoboride possesses two distinct phases with a B:W molar ratio of 1:1,12 one orthorhombic high temperature (HT) phase and one tetragonal low temperature (LT) phase with a 2


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transition temperature of 2170 °C.13 Both of these phases share the same alternating BCC tungsten bilayer/boron chain superstructure, but differ in the arrangement of the boron atoms. In the LTtetragonal phase, the boron chains alternate to form perpendicular arrays, but in the HTorthorhombic phase, the boron chains are all aligned along the c-axis and this is responsible for the subtle orthorhombic distortion (Fig. 1). It has been reported that LT tetragonal WB is an ultraincompressible material14 with a bulk modulus of 428 – 452 GPa15,16 and a maximum differential stress of 14 GPa, suggesting it could be a potential candidate for a superhard material. However, due to the synthetic challenges in stabilizing a high temperature phase, no high pressure study has yet been carried out on the HT-orthorhombic phase of WB. Fortunately, in our recent study,17 it has been demonstrated that by doping a small amount of Ta into WB, the HT orthorhombic phase of WB can be stabilized at room temperature. According to our Vickers micro-indentation hardness measurement reported previously, the hardness of HT-orthorhombic WB (35.5 ±2.5 GPa) is higher than the hardness of LT-tetragonal WB (31 ± 3.0 GPa), a result that is not obvious from the differences in crystal structure, particularly if one postulates that the network of B-B bonds should dominate the hardness.17 In that case, the more isotropic network in the LT WB would be expected to result in a harder material. Moreover, the elastic deformation behavior such as bulk modulus and crystal lattice strain response to an applied non-hydrostatic stress of this new metallic metal boride have not been characterized. Most importantly, the ability to examine two different tungsten monoboride phases that differ only in the arrangement of the boron chains should provide an excellent model system to understand the extent to which boron chain dimensionality controls lattice deformations. Here, synchrotron-based angle dispersive X-ray diffraction (XRD) experiments in a radial geometry using a diamond anvil cell (DAC) 18 were performed to examine the volumetric 3



deformations and anisotropic lattice deformations of orthorhombic and tetragonal WB under uniaxial applied pressures up to 52 GPa and 36 GPa, respectively. While the anisotropic stress condition in the DAC during compression in the radial experimental geometry,19,20,21 is different to that under an indenter’s tip in a micro-indentation hardness test,22 there are enough similarities that this data can provide insights for understanding the microscopic response of a crystal lattice to differential stress and thus to understanding the macroscopic response to an applied load. Additionally, radial XRD enables us to make in situ observations of deformation behavior in a lattice specific manner as a function of pressure.

Experimental procedure Orthorhombic and tetragonal WB were synthesized by arc melting. Tungsten powder and boron powder with a 1:1 molar ratio were mixed together followed by pressing into pellets. Subsequently, the pellets were arc melted and cooled in argon gas. More synthetic details can be found in Ref. 17. In order to stabilize the HT-orthorhombic phase of WB at room temperature, 5 at.% Ta was added because TaB is known to crystallizes in the orthorhombic structure. Tetragonal WB and orthorhombic stabilized WB pellets were then crushed and ground with a Plattner’s-style hardened tool-steel mortar and pestle set (Humboldt Mfg., Model H-17270). The fine powder (50 GPa. If we assume that t reflects the lower bound of the yield strength, then these results are consistent with our micro-indentation hardness measurements. Finally, computational studies were used to understand the remarkably high hardness and differential strain observed in these materials, despite their low boron content. The results indicate that for tungsten monoborides, W-B bonds contribute the most to the strength of the material and it is the W-B bonding network that needs to be optimized to increase strength. While lower borides, like WB, are not as hard as higher borides like WB4, research on lower borides may allow us to optimize the interplay between hardness and brittleness by understanding what controls the available slip systems and how to correlate those features to various bonding motifs.

Supporting information (Figure S1) Representative 2D caked diffraction patterns for HT WB collected at 2 GPa and 52 GPa, plotted as a function of azimuth angle and diffraction angle; (Figure S2) Fractional lattice constants as a function of pressure for HT WB and LT WB; (Figure S3) Plots of normalized pressure versus Eulerian strain for the linear incompressibility of each lattice constants for HT WB and LT WB; (Table SI.) Compression Data for HT WB; (Table S2) TABLE S2. Compression Data for LT WB.

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ACKNOWLEDGMENTS The authors thank M. Kunz and A. MacDowell for technical support at the Lawrence Berkeley National Laboratory (LBNL) beamline 12.2.2. We also thank Professor H.-R. Wenk for equipment support. This work was funded by the National Science Foundation under Grants DMR-1506860 (S.H.T. and R.B.K.), CAREER Award CHE1351968 (A.N.A.), and DGE-0654431 (M.T.Y.). Radial diffraction experiments were performed at the Advanced Light Source, beamline 12.2.2 (LBNL). The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02- 05CH11231. Partial support for the operation of ALS beamline 12.2.2 is provided by COMPRES, the Consortium for Materials Properties Research in Earth Sciences under NSF Cooperative Agreement EAR 1606856.

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Captions FIG. 1. Representative synchrotron X-ray diffraction patterns for (a) the HT phase of WB and (b) the LT phase WB with increasing pressure. Pt diffraction can also been seen, and was included for in situ pressure calibration. The crystal structures of orthorhombic HT WB and tetragonal LT WB are shown in parts (c) and (d), respectively. FIG. 2. Selected d-spacings vs. pressure collected at  = 54.7° for HT WB and LT WB. Error bars that are smaller than the size of the symbols have been omitted. Lattice planes were chosen for analysis to define all unique unit cell axes. FIG. 3. Linearized plots of d-spacings for (a) HT WB and (b) LT WB as a function of φ angle at the highest pressure. The solid lines are the best linear fit to the data. FIG. 4. Part (a) shows the ratio of the differential stress to the aggregate shear modulus (t(hkl)/G) for HT WB (black) and LT WB (red). Part (b) shows the evolution of peak broadening for the (020) plane of HT WB and the equivalent (004) plane of LT WB. FIG. 5. Differential stress (t) as a function of pressure for selected lattice planes of HT WB (a) and LT WB (b) under the Reuss (iso-stress) condition (open symbol) and the Voigt (iso-strain) condition (closed symbol). The crystal structure of orthorhombic HT WB looking down the c axis and the a axis is shown in parts (c) and (d), respectively. The bicolor sticks in these figures denote the W-B bonds. FIG. 6. Part (a) shows calculated DFT energy changes for HT WB in response to a range of shearing distortions. Part (b) shows relevant bonding structures of the solid. FIG. 7. Variation of the average differential stress with pressure for HT WB, LT WB, and selected other representative superhard materials. FIG. 8. Evolution of unit cell volume for HT WB (a) and LT WB (b) as a function of pressure under non-hydrostatic compression. The volume was measured at 54.7°. Fits (red lines) correspond to the second order Birch-Murnaghan equation-of-state. The insets show the BirchMurnaghan equation-of-state for WB replotted in terms of normalized pressure and Eulerian strain. The straight line yields the ambient pressure bulk modulus.

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Figures:

FIG. 1.

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FIG. 2.

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FIG. 3. 26


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FIG. 4.

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FIG. 5.

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FIG. 6.

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FIG. 7.

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FIG. 8.

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Understanding How Bonding Controls Strength Anisotropy in Hard

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