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Origin of Superhardness in Metallic Tungsten Monoboride

A dissertation submitted in partial satisfaction of the

requirements for the degree Doctor of Philosophy

in Chemistry

Michael Tyrone Yeung

2016

Michael Tyrone Yeung

2016

ABSTRACT OF THE DISSERTATION

Origin of Superhardness in Metallic Tungsten Monoboride

Michael Tyrone Yeung

Doctor of Philosophy in Chemistry

University of California, Los Angeles, 2016

Professor Richard B. Kaner, Chair

Conventional superhard materials (Vicker’s hardness Hv ≥ 40 GPa) are typically found in highly covalent systems such as diamond and cubic boron nitride. Here, we demonstrate that even materials dominated by metallic bonding can be made to be superhard. A solid solution between tungsten monoboride and tantalum monoboride, i.e. W1-xTaxB, produces a material that is both superhard (Hv = 42.8 ± 2.6 GPa) and ultra-incompressible (bulk modulus = 337 ± 3 GPa).

Note that this new superhard material is derived from two non-superhard parents. The hardness of W1-xTaxB increases linearly with increasing tantalum concentration up to 50%, strongly suggesting that the increased hardness comes from solid-solution hardening of the metallic bilayer. Further evidence for this hypothesis comes from high-pressure radial diffraction.

Tantalum-substituted tungsten monoboride represents the newest superhard member in the tungsten-boron system.

Next, we demonstrate that the superhard metal W0.5Ta0.5B can be prepared as nanowires through flux growth. The primary focus of superhard materials development has relied on chemical tuning of the crystal structure. While these intrinsic effects are invaluable, there is a strong possibility that hardness can be dramatically enhanced using extrinsic effects. The aspect ratios of the nanowires are controlled by the concentration of boride in molten aluminum, and the nanowires grow along the boron-boron chains, confirmed via electron diffraction. This morphology inherently results from the crystal habit of borides and can inspire the development of other nanostructured materials.

Finally, we study the role of inorganic crystal structure towards surface area through the model system, tungsten trioxide. High surface area in h-WO3 has been verified from the intracrystalline tunnels. This bottom-up approach differs from conventional top-down templating-type methods. The 3.67 Å diameter tunnels are characterized by low-pressure CO2 adsorption isotherms with non-local density functional theory fitting, transmission electron microscopy, and thermal gravimetric analysis. These open and rigid tunnels absorb H+ and Li+, but not Na+ in aqueous electrolytes without inducing a phase transformation, accessing both internal and external active sites. Moreover, these tunnel structures demonstrate high specific pseudocapacitance and good stability in an H2SO4 aqueous electrolyte. Thus, the high surface area created from 3.67 Å diameter tunnels in h-WO3 shows potential applications in electrochemical energy storage, selective ion transfer and selective gas adsorption.

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The dissertation of Michael Tyrone Yeung is approved.

Xiangfeng Duan

Qibing Pei

Richard B. Kaner, Committee Chair

University of California, Los Angeles

2016

Table of Contents

Title of Dissertation i

Abstract of Dissertation ii

List of Figures vi

Acknowledgements vii

Vita x

Chapter 1 1

Chapter 2 12

Chapter 3 42

Chapter 4 58

Chapter 5 79

Chapter 6 92

Conclusions 119

List of Figures

Figure 1: The techniques for measuring hardness 2

Figure 2: Schematic of a diamond anvil cell 6

Figure 3: Design rules for superhard metals 16

Figure 4: Rhenium Diboride 19

Figure 5: Hardness of Rhenium Diboride 21

Figure 6: Tungsten Tetraboride 23

Figure 7: Chromium and Manganese Tetraboride 26

Figure 8: Rhenium nitrides 32

Figure 9: Materials Characterization of W1-xTaxB 47

Figure 10: Grain size of W1-xTaxB 50

Figure 11: Hardness of W1-xTaxB 51

Figure 12: Differential strain of W1-xTaxB 54

Figure 13: Incompressibility of W1-xTaxB 56

Figure 14: TGA of W1-xTaxB 58

Figure 15: Electrical resistance vs temperature of W1-xTaxB 59

Figure 16: pXRD of nanostructured W1-xTaxB 66

Figure 17: SEM micrographs of nanostructured W1-xTaxB 69

Figure 18: TEM micrographs of nanostructured W1-xTaxB 71

Figure 19: Growth direction of nanostructured W1-xTaxB 72

Figure 20: Hierarchical Assembly of W1-xTaxB Nanowires 73

Figure 21: Crystal Structure of WO3 94

Figure 22: Characterization of h-WO3 96

Figure 23: BET Isotherms of WO3 98

Figure 24: Thermogravimetric Analysis of WO3 100

Figure 25: Powder X-Ray diffraction of WO3 103

Figure 26: Volumetric Capacitance 104

Figure 27: Cyclic Voltammograms before and after acid washing 105

Figure 28: Electrochemicstry Characterizations 106

Figure 29: Cyclic Voltammograms at different scan rates 108

Figure 30: Cyclic Performance 111

Figure 31: Specific Capacitance 112

Figure 32: Nyquist plots 113

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Acknowledgements

There are advisors in the world who trust their students. These few believe in doing the best things for their students, and more importantly, they are there to lend their students a hand should their students fall. There is no question that Ric is one of these advisors. Throughout my graduate career, I have been given the freedom to study the most interesting of topics, and the freedom to dictate my experiments. Whenever I failed, Ric was always there to pick me off the ground, dust me off, and send me off on my merry way. Quite frankly, I would not have done as well as I could had it not been for my boss (and probably would have amounted to nothing without him). I cannot thank Ric enough for trusting me throughout these years.

I would like to extend a deep debt of gratitude to the Old Guard of the Kaner Lab.

Whenever I was about to do something stupid, Jessica would be there to stop me. She is one of my good friends in lab, and she has always ensured that I did the right thing no matter how difficult the problem may be. I will always remember the lighthearted approach you took to things, and…the K-jokes….ugh. She is the best the Kaner lab has to offer in both pure talent and character, and I am very fortunate to have overlapped with her. She will best all of us one day.

And Reza, you were the one that sent me on my path; had it not been for my good friend, I would have been working on a dead project. You’ve also spent hours giving me advice on everything. I remember the late nights in lab we spent, XRD-ing those damn samples. To Jessica and Reza, I owe and thank you two immensely for fixing me both inside and outside of lab.

Sergey is a man of his word, and I very much admire that. He and I were forced to do our oral exams together, and that lead to a great understanding between him and I. Danny and I have struggled together, and without him it would have been much more difficult.

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To the New Guard of the Kaner Lab, it was my great pleasure to have served with you guys. I value the friendship I have with Cheng-Wei, and I see the drive and the intellect that he possesses. The fact that only he and I were in lab on New Year’s should have already been enough to say how impressive he will be. Also, he routinely beats me in any of our bets and competitions (I’ll beat him one day, I might have to cheat to do so). Jialin, thank you for all the discussions and arguments we had. Georgiy is the next hope the Kaner lab has to offer, and he will be better than all previous superhard members. By far he is one of the smartest people I have ever met, and he is incredibly dedicated. We spent hours in the Ben Wu lab poking a “that’s nice” sample while discussing all manners of things. Wanmei always prodded me throughout my graduate career, ensuring that I had the most difficult time and contributing extensively to my drinking problem (I’m joking). She created some of the most interesting encounters in lab which led me here today, thank you Wanmei. Rebecca and I are often the only people in lab sometimes.

She would hit me with a stick whenever I was not productive. Maybe if I can take her around wherever I go in life, I’ll stay focused from fear of SMACK SMACK SMACK.

Finally, to the grad students I hang out with outside of research. I thank Chain for saving my @#$ during that superacid misadventure. Logan has made my life infinitely more interesting from all the adventures on the side. Bootsie has served as my foil and my lawyer for many a litigation (he is also one of the smartest people I have ever met). Erik’s sharp wit has stung me many a times in the campaign. Abraham and I have spent many dinners arguing about Fate.

Renato may be the only vegetarian I have met that can handedly beat the $%#@ out of me.

Matthew, you ruined my campaign sometimes with your perception (I hope you are proud of yourself). Prof Lin and Prof Jung, you guys were the ones that made me me.

I would like to say I did this by my own ability, but I didn’t. Thank you all.

Chapter 1 and 2 is split from the following reference: Michael T. Yeung, Reza Mohammadi,

Richard B. Kaner. “Ultraincompressible, Superhard Materials” Annual Reviews of Materials

Research 2016, 46 (1) Link

Chapter 5 is abridged from the following reference: Georgiy Akopov, Michael T. Yeung;

“Rediscovering the Crystal Chemistry of Borides” Under Review, Advanced Materials

Chapter 4 is from the following reference: Michael T. Yeung, Jialin Lei, Reza Mohammadi,

Christopher L. Turner, Yue Wang, Sarah H Tolbert, Richard B Kaner. “Superhard Monoborides:

Hardness Enhancement Through Alloying in W(1-x)Ta(x)B” Accepted Advanced Materials

Chapter 5 is from the follow reference: Michael T. Yeung, Georgiy Akopov, Reza Mohammadi,

Richard B. Kaner; “Superhard W0.5Ta0.5B Nanowires Prepared at Ambient Pressure” Under

Review, Applied Physics Letters

Chapter 6 is from the following reference: Wanmei Sun, Michael T. Yeung, Andrew T. Lech,

Cheng-Wei Lin, Chain Lee, Tianqi Li, Xiangfeng Duan, Jun Zhou, Richard B. Kaner. “High

Surface Area Tunnels in Hexagonal WO3” Nano Letters 2015, 15 (7), 4834-4838

Vita

2006- 2010 Bachelors of Science, Chemistry

University of California, Los Angeles

2010- Philosophy of Science, Inorganic Chemistry

University of California, Los Angeles

Publications

1. Jialin Lei, Michael T. Yeung, Paul J. Robinson, Reza Mohammadi, Christopher L. Turner,

Anastasia Alexandrova, Richard B. Kaner, Abby Kavner, and Sarah H. Tolbert. “Volumetric

deformation and strength anisotropy of high temperature phase tungsten monoboride under

nonhydrostatic compression to 52 GPa” Manuscript in preparation

2. Georgiy Akopov*, Zachary C. Sobell*, Michael T. Yeung, Richard B. Kaner; “Stabilization

of GdfB12 in Zr1-xGdxB12 Under Ambient Pressure” Manuscript in Preparation

* These authors contributed equally

3. Georgiy Akopov*, Michael T. Yeung*; “Rediscovering the Crystal Chemistry of Borides”

Under Review, Advanced Materials

* These authors contributed equally

4. Michael T. Yeung, Georgiy Akopov, Reza Mohammadi, Richard B. Kaner; “Superhard

W0.5Ta0.5B Nanowires Prepared at Ambient Pressure” Under Review, Applied Physics Letters

5. Georgiy Akopov, Michael T. Yeung, Zachary C. Sobell, Christopher L. Turner, Richard B.

Kaner. “Superhard Mixed Transition Metal Dodecaborides” Accepted, Chemistry of

Materials

6. Robert S. Jordan, Yue Wang, Ryan D. McCurdy, Michael T. Yeung, Kristofer L. Marsh,

Saeed I Khan, Richard B. Kaner, Yves Rubin. “Synthesis of Graphene Nanoribbons via the

Topochemical Polymerization and Subsequent Aromatization of a Diacetylene Precursor”

Chem 2016, 1, 78-90 Link

7. Georgiy Akopov, Michael T. Yeung, Christopher L. Turner, Reza Mohammadi, and Richard

B. Kaner. “Extrinsic Hardening of Superhard Tungsten Tetraboride Alloys with Group IV

Transition Metals” Journal of the American Chemical Society 2016, 138, 5714-5721 Link

8. Georgiy Akopov, Michael T. Yeung, Christopher L. Turner, Rebecca L. Li, and Richard B.

Kaner. “Stabilization of HfB12 in Y1-xHfxB12 Under Ambient Pressure” Inorganic Chemistry,

2016 Link

9. Michael T. Yeung, Jialin Lei, Reza Mohammadi, Christopher L. Turner, Yue Wang, Abby

Kavner, Sarah H Tolbert, Richard B Kaner. “Superhard Monoborides: Hardness

Enhancement Through Alloying in W(1-x)Ta(x)B” Accepted Advanced Materials

10. Michael T. Yeung, Reza Mohammadi, Richard B. Kaner. “Ultraincompressible, Superhard

Materials” Annual Reviews of Materials Research 2016, 46 (1) Link

11. Wanmei Sun, Michael T. Yeung, Andrew T. Lech, Cheng-Wei Lin, Chain Lee, Tianqi Li,

Xiangfeng Duan, Jun Zhou, Richard B. Kaner. “High Surface Area Tunnels in Hexagonal

WO3” Nano Letters 2015, 15 (7), 4834-4838 Link

12. Reza Mohammadi, Andrew Lech, Miao Xie, Beth Weaver, Michael T. Yeung, Sarah Tolbert,

Richard Kaner. "Tungsten tetraboride, an inexpensive superhard material" Proceedings of

the National Academy of Sciences 2011, 108 ( 27) 10958-10962 Link

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Chapter 1

All superhard materials are also ultra-incompressible, and this can be rationalized by understanding hardness measurements. Since at least 300 B.C.E., humanity has measured hardness by scratching one stone with another, with the harder stone left unblemished and the softer one scored1. About two thousand years later, this technique evolved into the standardized

Moh’s scale of hardness, with soft materials like talc rated as 1 and superhard diamond rated at

10. Today, hardness is quantified by impinging a sample with a diamond indenter and then correlating the size of that indent to a hardness value. For Vickers hardness2, the width of the resulting indent can be used to quantify the hardness, with materials possessing a Vickers hardness greater than 40 GPa defined as superhard. Each of the aforementioned techniques relies on an applied concentration of force. A material will begin to elastically deform, and beyond the elastic limits, the material will suffer plastic deformation. These plastic deformations are visualized as scratches and/or indents. While the fundamentals behind hardness measurements over the years have remained the same, the techniques have become more refined (Figure 1).

A high bulk modulus (K0 > 300 GPa) helps resist surface damage. As seen in naturally occurring minerals, all hard materials, such as sapphire (Al2O3), and silicon carbide (SiC), have a high bulk modulus (i.e. they’re quite incompressible), while superhard materials, such as diamond, have even higher values. However, while all superhard materials are ultra- incompressible, not all ultra-incompressible materials are superhard. For example, zirconium

3 oxide (K0 = 444 GPa) and hafnium oxide (K0 = 340 GPa) are quite incompressible possessing a bulk modulus higher than many of the materials listed in this review, yet they are not superhard.

Figure 1: The techniques for measuring hardness still rely on surface deformation. A) Vickers indentation hardness on rhenium diboride shows that it is harder than 40 GPa at a load 0.49 N and therefore crosses the superhard threshold. B) As further evidence of its superhard nature, rhenium diboride readily scratches diamond. C) Indentation of rhenium diboride along the softest axis and d) the hardest axis. From 4. Reprinted with permission from AAAS.

Regardless, the importance of incompressibility has dictated design rules for creating new materials in the superhard field, i.e. going beyond what nature has provided. Since then, the field has blossomed and there have been several new superhard compositions that follow new design parameters.

Furthermore, superhard materials can be used in a number of exciting applications owing to their superior mechanical properties with the superhard materials market projected to reach

$20 billion during the next five years5. These materials may find many industrial applications as high-performance cutting tools and wear protective coatings6, 7. Currently, there are only two commercially relevant superhard materials – diamond and cubic boron nitride. While diamond can be used to cut through rock, it cannot be used to cut steel due to a chemical reaction that forms iron carbide. Instead, cubic boron nitride is used to cut and mill ferrous metals8. In some ways, it is remarkable that humanity has achieved so much in terms of industrial machining, drilling, and polishing, relying on just two high-end compositions.

Other excellent reviews and perspectives on the design and applications of incompressible and superhard materials can be found in references 7-13.9-15 In this review, we focus on how microscopic structure and bonding relates to macroscopic mechanical properties.

This will be accomplished by examining several recently discovered materials, notably borides, nitrides, and oxides. From this we will propose new parameters by which to judge superhard materials.

Measuring Hardness

As noted earlier, the measurement of hardness relies on the quantification of plastic deformation on the surface of a material. Plastic deformations can be visualized as scratches or

3 indents. Nowadays, one of the most common techniques for measuring hardness is through

Vickers indentation hardness ( ). Here, a pyramidal indenter, made of diamond (the hardest material known), depresses a polished surface with a specified applied force. After indentation, a diamond imprint is dug into the surface. The lengths of the diagonals are then imputed into the following equation:

[1]

where P is the applied load in Newtons and d is the average of the diagonals in microns. For

Vickers hardness, the threshold for defining a superhard material is ≥ 40 GPa. There are other indentation methods, most notably Knoop indentation hardness16 which also uses a diamond indenter. Here, the indenter takes on the shape of an elongated rhombus, with a cross-sectional ratio of 1:7.

Nanoindentation is another commonly used characterization technique for hardness17, focused on samples with small volumes. Like the other indentation techniques, nanoindentation also uses a diamond indenter except here a Berkovich tip in the shape of a trigonal pyramid is replaced with a square pyramid. Furthermore, while Vickers indentation hardness measures the width of the indents, nanoindentation measures the depth of penetration, which is used to calculate hardness.

The shear modulus contributes significantly towards the hardness of a material, and this is understandable in light of the geometry used to measure indentation hardness. Because the force on the indenter should be orthogonal to the surface, a high degree of shear force is generated in the material from the sloping sides of the indenter. Once the elastic limits are reached, the material will plastically deform resulting in an indent. As such, there have been many excellent correlations between the shear modulus of a bulk material and its hardness.

However, the bulk modulus of a material also contributes to high hardness, as this force is also resisted by the material’s incompressibility. It should be noted that while indentation measurements quantify plastic deformations, these plastic deformations are at elastic limits

(which is why high moduli are usually correlative).

Measuring Incompressibility

For superhard materials, the bulk modulus is measured at high pressures (upwards of 50

GPa) through diffraction in a diamond anvil cell (Figure 2). From the diffraction under various loads, the lattice parameters are obtained and from the lattice parameters, the deformation of the unit cell. Incompressibility is often determined using the Birch-Murnaghan equation of state

(Equation 2):

[2]

where P is the applied load, K0 is the isothermal room-temperature bulk modulus, V is the deformed unit cell volume, V0 is the un-deformed unit cell volume, and K0’ is the derivative of

18, 19 the K0 with respect to P. Here, K0’is fixed to 4 .

Deformations in a diamond anvil cell can provide additional insights beyond the bulk modulus. For example, the diffraction spectra can reveal an axis-dependency of the deformations. Combining these results with knowledge of the crystal structure leads to an understanding of what makes a superhard material incompressible, a more advanced interpretation than the simple quantification from valence electron density. In the following section, we will compare incompressibility results with crystal structures and show that bonding does indeed play a significant role in incompressibility. Note that the measurement of shear

Figure 2: A typical setup of a diamond anvil cell used to measure lattice deformations under high pressures (109).

6 modulus is considerably more involved, and requires sophisticated techniques such as Brillion

Spectroscopy20-22.

Traditional and Theoretical Hard Covalent Materials

The traditional hard covalent materials are silicon nitride, Si3N4 (Hv = 21 GPa), alumina,

Al2O3 (Hv = 22 GPa), silicon carbide, SiC (Hv = 28 GPa) and boron carbide, B4C (Hv = 30

23 GPa) . Diamond is superhard (Hv > 80 GPa) and will be described in detail in the next section.

These materials consist entirely of main group elements, and, not surprisingly, they are comprised of directional covalent bonds. Furthermore, each of the aforementioned materials possesses a completely different crystal structure, which reflects on the complexities behind hard materials. Alumina crystallizes in a trigonal structure; beta silicon nitride in a hexagonal structure; silicon carbide in hexagonal and cubic polymorphs, with the cubic polymorph resembling that of diamond; and boron carbide, due to the presence of boron, forms polyhedra.

Because these bonds are directional, meaning their electron density is geometrically localized, it is energy intensive to break these bonds and this results in a high shear modulus for each of these materials. The bulk moduli for alumina (K0 = 246 GPa), silicon nitride (K0 = 249 GPa), silicon carbide (K0 = 226 GPa), and boron carbide (K0 = 247 GPa) are appreciable.

The incompressibility of covalent compounds is largely related to the ionicity between the constituents and the bond length. For example, in zinc blende structures, the bulk modulus fits the following empirical formula (Equation 3):

[3]

7 where K0 is the room-temperature bulk modulus, λ is the ionicity (i.e. for group 4 elements λ = 0, for III-IV compounds λ = 1, etc.), and d is the bond length24. From this simple formulation, a whole series of theoretical compounds have been predicted that should be ultra-incompressible and also may be superhard24. In particular carbon nitride, which would have the same crystal structure as silicon nitride, but with significantly shorter bonds, should have a significantly higher incompressibility. Indeed, the predicted bulk modulus of β-C3N4 reaches 427 GPa, which places this theoretical carbon nitride phase as one of the most incompressible materials.

Unfortunately, β-C3N4 is one of the more difficult materials to synthesize as the high volatility of nitrogen requires the synthesis to be conducted under extreme conditions e.g. shock compression25 or thin film techniques26-30. While nanoindentation of thin films have suggested

27 that β-C3N4 may be quite hard , this has not been confirmed with bulk materials. In fact, the enormous amount of research devoted to this compound should serve as a cautionary tale of why ultra-incompressibility is a necessary, but insufficient condition for superhardness. Early reports conflating incompressibility with hardness may have exacerbated the confusion31.

References

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6. Cook, M. W.; Bossom, P. K. International Journal of Refractory Metals and Hard

Materials 2000, 18, (2–3), 147-152.

7. Faure, C.; Hänni, W.; Schmutz, C. J.; Gervanoni, M. Diamond and Related Materials

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9. Abukhshim, N. A.; Mativenga, P. T.; Sheikh, M. A. International Journal of Machine

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10. Brookes, K. A. Metal Powder Report 1995, 50, (12), 22-28.

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12. Gilman, J. J.; Cumberland, R. W.; Kaner, R. B. International Journal of Refractory

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B. Advanced Materials 2009, 21, (42), 4284-4286.

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Chapter 2

Diamond is the hardest single-phase material known to humanity, with a Vickers

1 hardness ranging from Hv = 60 – 150 GPa, depending on the type and quality . Analogously, isostructural cubic boron nitride, where each carbon-carbon bond is replaced with an isoelectronic boron-nitrogen bond, is also superhard with values ranging from Hv = 45 – 80

GPa1. Further development of these superhard materials has led ever increasing hardness values,

2 with nanotwinned cubic boron nitride exceeding Hv = 100 GPa and nanotwinned diamond

3 reported to reach upwards of Hv = 200 GPa (five times the threshold for superhard materials!).

Diamond’s high strength makes it an extremely attractive material in the laboratory. As noted earlier, diamond is often used in diamond anvil cells (hence the name), where diamonds with flatted tips can withstand up to 2 million atmospheres of pressure generated in a small tabletop device4. The high pressures generated from diamond anvil cells allow for the exploration of many new properties. For example, metallic iodine5-7 and even metallic xenon8-10, a noble gas, have been created in diamond anvil cells. Metallic hydrogen, which is thought to exist in the core of Jupiter and other celestial bodies, may have even been synthesized in a diamond anvil cell11-14. While this is not without controversy15-17, it demonstrates the incredible strength of diamond. Under much lower pressures, the high strength of diamond helps sulfur18, iron metal19, and cuprates20 to superconduct, with the latter reaching the current record superconducting transition temperature of 165 K21. Unfortunately, diamond is a difficult/expensive substance to synthesize as it requires high pressures and temperatures that mimic the conditions deep within the earth’s mantle22, 23.

The origin of diamond’s high hardness can be found in its crystal structure. First, diamond has the highest atomic density of any bulk material which is reflected in its high

3 24 valence electron density (upwards of 0.705 electrons/Å ), and high incompressibility (K0 = 438

- 446 GPa). Second, diamond also possesses a high density of short covalent bonds, and this prevents dislocations and results in a high shear modulus (578 GPa)25

Inspired by diamond, in 2005 we proposed two parameters to create new superhard materials.

These are:

1. Begin with a high valence electron dense metal, most commonly found in the third row

transition metal block (e.g. osmium, rhenium, tungsten) to mimic the incompressibility of

diamond.

2. Introduce short covalent bonds to prevent dislocations by adding in first row main group

elements (e.g. boron, carbon, nitrogen or oxygen). This will mimic the high shear

modulus of diamond.

These diamond simulants comprised of transition metals have demonstrated superior mechanical strength. More importantly, these materials, while refractory, can be synthesized in bulk under ambient pressure. This ease-of-synthesis has allowed for the development of novel, metallic superhard materials.

Unlike the traditional covalent hard materials, it is much more difficult to predict the hardness and incompressibility of these new materials simply because the structure and bonding is much more complex. Furthermore, the high number of electrons in the metal atoms makes computational predictions difficult. As such, the focus of this review will now turn to the intricacies between structure, bonding, hardness and incompressibility in this new generation of

13 ultra-incompressible, superhard materials. In this way, we hope to explain why these metallic materials exhibit such prodigious mechanical properties from a microscopic perspective.

Osmium and Osmium Diboride

By itself, osmium metal, which crystallizes in a hexagonal close packed lattice, is ultra- incompressible. It therefore has a very high bulk modulus, with values ranging from K0 = 395

26 27 GPa as reported by Takemura , to K0 = 411 GPa as described by Occelli et al. , to possibly

28 even K0 = 462 GPa as published by Cynn et al. (suggesting that elemental osmium may be stiffer than even diamond). The high bulk modulus can be attributed to osmium’s high bulk density (22.5 g/cm3) that leads to a high electron density (0.572 electrons/Å3), so that these

3 values approach that of diamond (K0 = 442 GPa and 0.705 electrons/Å , respectively). Despite its incompressibility, osmium metal is over 20 times softer than diamond simply because the metallic planes in osmium can readily slip, while the covalent bonding in diamond is directional and much more resistant to the movement of dislocations. This can be remedied by adding short covalent bonds into osmium to yield osmium diboride. Unlike diamond, most metal borides can be synthesized under ambient pressure, and osmium diboride is no exception. Direct reaction from the elements at 1000°C yields OsB2 along with a couple other osmium borides, so X-ray pure osmium diboride was originally prepared by a metathesis reaction between OsCl3 and MgB2

29 . However, when balancing the reactants in the metathesis reaction to produce the salt MgCl2, excess boron always remained in the OsB2 product. Since the excess boron favors OsB2, direct reactions can be carried out simply by adding a small excess of boron29. This product was used to determine hardness and bulk modulus. Finally, direct fusion of the elements in an arc melter with a slight excess of boron also yields X-ray pure ingots30, 31.

Inspection of the crystal structure reveals the dominant bonding behind each axis.

Osmium diboride (OsB2) crystallizes in an orthorhombic unit cell (Pmmm). The metal atoms are arranged in a hexagonal close packed lattice, and the boron is arrayed into a six atom, boat-like configuration along the basal plane32. The boron boats bond along the a-axis, with the boron- boron bond lengths varying between 1.8717 Å and 1.8202 Å at ambient pressure33. Another way of visualizing the structure of osmium diboride is to realize that the osmium atoms roughly retain the same hexagonal close packed structure as osmium metal, except with puckered boron sheets separating every two osmium layers (Figure 3A). Because of the similarities in the positions of the metal atoms in osmium metal and osmium diboride, a rough understanding of the role of the osmium-boron and boron-boron bonds can be ascertained by comparing the lattice compression data. Both the a-axis and the c-axis reflect different bond character, with the a-axis reflecting more covalent, boron-boron bonds, while the c-axis is comprised solely of osmium-boron bonds.

Unfortunately, osmium diboride is not superhard. Under a load of 0.49 N, osmium diboride reaches a Vickers hardness Hv of ~27 GPa. Of course, this hardness is considerably higher than that of elemental osmium (Hv = 4 GPa) and OsB2 is capable of scratching sapphire (Al2O3) ranked 9 out of 10 on the Moh’s hardness scale. Yet, this hardness is considerably less than that of a superhard material (Hv ≥ 40 GPa). The weak link in the structure appears to be the bilayer of osmium atoms. Metallic bonds are easier to break than covalent bonds, and this bilayer acts as a slip plane that facilitates plastic deformation, resulting in lower hardness. Additionally, the boron-boron bonds in OsB2 are in a boat-like configuration, which means longer boron-boron distances than in a chair-like configuration that exists in ReB2, for example.

Osmium diboride retains the ultra-incompressibility comparable to osmium (K0 = 365 –

395 GPa) yet has become hard enough to scratch sapphire (Fig. 3B). Not surprisingly, the

Figure 3: A) Osmium diboride can be thought of as an osmium metal lattice, with puckered boron layers inserted between every two layers of osmium. B) While not superhard, osmium diboride can readily scratch sapphire. C) The c-axis of osmium diboride, comprised mainly of osmium-boron bonds, is slightly stiffer than diamond. Reprinted with permission from 29.

16 respective axes exhibit different degrees of incompressibility. As seen from the fractional lattice

29 parameters (Fig. 3), the c-axis of OsB2 is slightly stiffer than diamond, while the a- and b- axis are lower. Because the osmium-boron bonds are almost directly aligned with the c-axis, the electrostatic repulsions between osmium and boron likely will result in a stiffer c-axis (Fig. 3C).

Unfortunately, the crystal structure of osmium diboride is highly anisotropic, and because the a- and b-axes yield more easily, the overall bulk modulus (K0 = 365 – 390 GPa) drops to below that of elemental osmium. Despite the drop, the addition of boron to osmium has raised its Vickers hardness by 5-fold34. Perhaps more isotropic borides could result in higher volumetric incompressibility.

Of course, another way of tuning the bulk modulus is to change the electron density, and this can be readily accomplished through solid solution hardening. Ruthenium diboride should form a solid solution with osmium diboride according to the Hume-Rothery rules: ruthenium has a similar valence, electronegativity, and atomic radius when compared to osmium. Furthermore, osmium diboride crystallizes in the same phase as ruthenium monoboride. Not surprisingly, Os(1- x)Ru(x)B2 forms a full range of solid solutions; however, ruthenium may not be a good choice of substituent for osmium since both osmium and ruthenium have the same valence.

Correspondingly, the valence electron density for osmium diboride (0.512 electrons/Å3) and ruthenium diboride (0.521 electrons/Å3) are comparable. While the solid solutions between the two do indeed follow Vegard’s law, the difference in bulk modulus between the two parents is nearly 23%30. This discrepancy was hypothesized to originate from the higher number of core electrons in osmium relative to ruthenium. Regardless, solid solutions are an excellent route towards changing the incompressibility of a material.

Rhenium Diboride and Isostructural Analogues

According to the Periodic Table, to the left of osmium is rhenium, and as such, rhenium should have nearly as high of a bulk modulus as osmium. Indeed, the bulk modulus of rhenium is

35, 36 roughly K0 = 360 GPa . Rhenium also has the added benefit of being far more cost effective than osmium. Both of their respective diborides crystallize into a layered structure of metal and puckered boron. However, their similarities end there: rhenium diboride (P63/mmc) has 1 sheet of metals in the metal layer, while osmium diboride has 2, and the puckered boron sheets in rhenium diboride are in a chair configuration, while in osmium diboride the puckered boron sheets are in a boat configuration. Here again, the metal maintains its hexagonal AB-type stacking in the diboride except with layers of boron distributed between each and every layer32.

This different packing order results in a different bonding arrangement, with osmium diboride forming polyhedra resembling distorted trigonal trapezohedrons, while rhenium diboride forms polyhedra resembling more isotropic trigonal prisms (Fig. 4A). The different bonding arrangements are reflected in the symmetry of the unit cell, as rhenium diboride is tetragonal.

Because rhenium diboride is thermodynamically stable, it can be prepared under ambient pressure. Rhenium diboride can be synthesized by: i. a metathesis reaction between ReCl3 and

MgB2, ii. directly by heating the elements in a furnace under an inert atmosphere, or iii. by fusing the elements in an arc melter37. Single crystals can also be prepared via flux growth38.

Furthermore, thin films can be prepared via pulsed laser deposition, with the mechanical properties of the thin films approximating that of the bulk material39.

Unlike osmium diboride, rhenium diboride does not possess a simple metallic slip plane.

However, as rhenium diboride is still a layered structure, there is nevertheless a possibility that the basal plane can act as a slip plane. Regardless, rhenium diboride has been shown to be

Figure 4: A) Similar to osmium diboride, rhenium diboride possesses a layered structure.

However, unlike osmium diboride, rhenium diboride does not have a simple metallic slip plane.

B) Since the c-axis in rhenium diboride is comprised entirely of rhenium-boron bonds, it is actually slightly stiffer than diamond. From 37. Reprinted with permission from AAAS.

19 superhard with a Vickers Hardness of 48 GPa under a load of 0.49 N37; this is hard enough to scratch diamond40. Under high load (4.9 N), the hardness drops to 30.1 GPa; this is known as the indentation size effect37.

The difference between superhard metals such as rhenium diboride and conventional covalent superhard materials such as diamond can be rationalized by examining the bonding. In diamond, the electron density is localized in the covalent bonds, and this is why covalent bonding is known to be directional. For superhard metals, the electron density behaves more as a fluid, owing to the fact that it is metallic. Under higher loads, the electron density experiences a greater volumetric deformation41. This unique behavior between superhard metals and traditional diamond demonstrates that a new perspective and a new playing field can be found in superhard transition metal borides.

Furthermore, the bulk modulus of rhenium diboride (K0 = 360 GPa) matches that of incompressible rhenium metal (K0 = 360 GPa). Fractional lattice parameters with respect to pressure suggest that the c-axis of rhenium diboride is the stiffest, and like osmium diboride, it is comparable to that of diamond. Qualitative hardness measurements on a polycrystalline ingot

(using backscattered scanning electron microscopy to confirm the crystallite orientation) have shown that the c- axis is indeed harder, demonstrating the necessary role of incompressibility in creating superhard materials (Fig. 1C and 1D). More quantitative hardness measurements with single crystals have shown that the c-axis is roughly 10% harder than the a- and b-axes38, in good agreement with the fractional lattice parameters (Fig. 5). From rhenium diboride, a ternary solid solution can be made by substituting equal parts osmium and tungsten for rhenium to create

Os0.5W0.5B2 which is isoelectronic with ReB2. Because the bonding, valence electron count, and

Figure 5: Superhard metals usually possess anisotropic crystal structures and mechanical properties. Here, single crystals of rhenium diboride were prepared and indented on different facets, demonstrating that the c-axis, i.e. the axis along the rhenium-boron bonds, is the hardest38.

21 structure are retained, it is not surprising that the hardness and incompressibility of Os0.5W0.5B2 is essentially the same as that of ReB2.

Tungsten Tetraboride

While rhenium is less prohibitively expensive than osmium, the cost of rhenium per gram is still nearly half that of gold40. Therefore, we continued moving left of rhenium in the Periodic

Table to tungsten, which is quite cost-effective. More importantly, the valence electron density of tungsten tetraboride, 0.484 electrons/Å3 matches that of rhenium diboride. However, unlike rhenium diboride, tungsten tetraboride possesses a significantly larger number of covalent bonds in its unit cell. This is due to the fact that there are now 4 equivalents of boron for every metal atom, rather than two. Indeed, the crystal structure of tungsten tetraboride is different than that of many of the previously studied borides simply because of the high boron content. In particular, the boron forms defective covalent cuboctahedra42. Tungsten tetraboride is considerably more distorted from a layered structure than osmium diboride, and as such should possess even fewer slip planes (Fig. 6A). A comparison can be made between the most incompressible material currently known, i.e. diamond, and tungsten tetraboride. The latter also possesses an extended covalent framework, but with missing boron atoms at some vertices of the cuboctahedra.

Synthesis of bulk tungsten tetraboride is almost exclusively done via arc melting43, 44, while thin films can be prepared via pulsed laser deposition45.

As there is now less metal-boron bonding, the incompressibility of tungsten tetraboride

46 drops to K0 = 326 GPa . Because the metal-boron bonds are not completely aligned with any axis, none of the axes are as stiff as diamond (Fig. 6C)43. At about 42 GPa, tungsten tetraboride undergoes a structural transformation and becomes even more anisotropic, which can be

Figure 6: A) Crystal structure of tungsten tetraboride. Note the extensive boron-boron bonding between the layers; this leads to an extended covalent framework of boron. B) Vickers hardness of tungsten tetraboride shows that it is superhard. C) The axes of tungsten tetraboride are less stiff than diamond 43. D) Solid solutions prevent a structural transformation of tungsten tetraboride normally observed at ~42 GPa. Figure 6A is from 42, Copyright 2015 National

Chemical Society.

23 observed by a change in the c/a ratio. It is likely that this structural transformation is a result of tungsten tetraboride attempting to re-optimize bonding at extremely high levels of compression.

Interestingly, this structural transformation disappears in solid solutions47 (Fig. 6D). The a-axis of W0.93Ta0.02Cr0.05B4 becomes stiffer than pristine WB4, and this suggests that the type of bonding in the solid solutions differs from that of pristine WB4. Thus, the incompressibility results demonstrate that while valence electron density offers an estimate of incompressibility, the fact that tungsten tetraboride and rhenium diboride have the same valence electron density, yet their bulk moduli differ by 34 GPa demonstrates that bonding and structure also play important roles in incompressibility.

While the crystal structure of tungsten tetraboride is not conducive to an incompressibility approaching diamond, its covalent network prevents shear and results in high hardness. By itself, pristine tungsten tetraboride reaches 43.3 GPa at a load of 0.5 N (Fig. 6B).

Through dispersion hardening with 1 at.% rhenium, tungsten tetraboride reaches 50 GPa, higher than pure rhenium diboride (48 GPa under a load of 0.49 N)44. To further increase the hardness, solid solutions were investigated with Mn, Ta, and Cr47; these metals are not fully soluble in the tungsten tetraboride lattice since there exists no equivalent borides with comparable structures.

At low concentrations of substituents, an electronic contribution is believed to come into effect and the hardness increases. An optimized ternary solid solution has been developed, i.e. W-

0.93Ta0.02Cr0.05B4, which achieves a hardness of roughly 57 GPa (under a load of 0.49 N) and is the hardest metal known to date. Furthermore, radial diffraction of tungsten tetraboride solid solutions suggests that it is a combination of both doping effects on the band structure and size mismatch that is responsible for this increase in hardness48.

Chromium and Manganese Tetraboride

Chromium tetraboride crystallizes in an orthorhombic unit cell49, 50. Similar to tungsten tetraboride, chromium tetraboride possesses a 3-D boron network, but unlike tungsten tetraboride, the boron polyhedra are different with no planar boron sheets present. Instead, chromium is enclosed in distorted hexagonal boron prisms; it is thus closer to the puckered boron

51 boat-like sheets found in OsB2 (Fig. 7) . Regardless, there should be no slip planes and chromium tetraboride should be resistant to shear. Chromium tetraboride was theoretically predicted to be superhard in 201152. Since then, there have been several theoretical papers that have been both for 49, 53, 54 and against55 the original claim. This disparate response reflects on the difficulty of theory to make predictions with such a complex crystal system; chromium tetraboride possesses a multitude of different bonds and is therefore a difficult system to model.

Single crystals of chromium tetraboride with high quality have been prepared via vapor transport with iodine51. Polycrystalline samples can be prepared by annealing from the elements49 or through hot-pressing56. Vickers hardness on single crystals have shown that

50 chromium tetraboride is reasonably hard, reaching Hv = 26 GPa at 0.98 N load . The polycrystalline material reaches 44 GPa at 0.49 N and 36 GPa at 0.96 N56, suggesting that chromium tetraboride may be superhard. The differences between single crystal and polycrystalline hardness values are probably due to extrinsic effects such as grain size hardening.

Bulk modulus reported for chromium tetraboride is only 232 GPa, which is considerably lower than computational results for bulk modulus57. While theory claimed that the b-axis should be the stiffest and more incompressible than diamond, experiments did confirm that the b-axis is indeed the most incompressible, but not stiffer than diamond.

Figure 7: The crystal structure of chromium tetraboride (left) and manganese tetraboride (right)

58.

A series of solid solutions were made between chromium tetraboride and manganese tetraboride58. Both chromium tetraboride and manganese tetraboride possess the same covalent boron network. In manganese tetraboride, however, the manganese tends to bond with itself and form dimers, which somewhat distorts the structure59.

Computationally Predicted Superhard Phases Seeking Experimental Confirmation

The development of superhard and incompressible phases has spurred the interests of many research groups. Most notably, theorists have joined experimentalists in the search for new ultra-strong materials. While the theoretical results have often been conflicting (as seen with chromium tetraboride), theorists have brought many new insights into superhard, ultra- incompressible phases; some of which have provided guidance in this review.

Tungsten tetraboride was shown experimentally to be a superhard material, and this inspired theoretical analysis. Most notably, the computational results for tungsten tetraboride matched the experimental results quite well60. Beyond tungsten tetraboride, a series of other metal tetraborides with the tungsten tetraboride structure were theorized to be superhard and ultra-incompressible, including rhenium tetraboride (Hv = 50.3 – 54.4 GPa, K0 = 303.7 – 331.3

GPa), tantalum tetraboride (Hv = 40.1 – 46.7 GPa, K0 = 272.9 – 301.9 GPa), molybdenum tetraboride (Hv = 42.1 – 46.2 GPa, K0 = 275.7 – 310.4 GPa), and osmium tetraboride (Hv = 46.2

– 48.5 GPa, K0 = 285.1 – 317.0 GPa). These materials have the same origin of strength as tungsten tetraboride (as discussed earlier), but these materials have yet to be synthesized.

Furthermore, computation has also been used to study the thermodynamic stability of several compounds, most notably in the tungsten-boron system61.

In particular, there has been a great deal of focus on tungsten triboride. Both tungsten tetraboride and tungsten triboride have the same positions for the tungsten atoms, but differ in their boron content and arrangements. Tungsten triboride is based on an AlB2-type structure with

62-64 a focus on planar boron sheets . As tungsten triboride is based on AlB2, it will have a slip plane and it has been computationally confirmed to be softer65-67. On the other hand, tungsten tetraboride is based on the MB12 dodecaboride-type structure with strong boron bonds between sheets. Tungsten triboride may be the more thermodynamically stable phase, but experimentally,

42, 44 we have been working with tungsten tetraboride (W:B ratio ~ WB4.2) . That being said, because of the differences in bonding between the similar tungsten triboride and tungsten tetraboride, it would be interesting to see how the incompressibility and hardness is affected in the lower boride.

More Isotropic, Incompressible Materials, and Slip Planes

As of now, we have been suggesting that metal – main group element bonds are largely responsible for high stiffness and ultra-incompressibility. In osmium diboride, the c-axis, parallel to the osmium-boron bonds, was found to be stiffer than diamond, and the same with rhenium diboride. Unfortunately, the other axes do not possess metal-boron bonds and are more pliable than diamond. As such, an isotropic material comprised mostly of metal – main group element bonds should ideally possess a high incompressibility. However, many of the isotropic materials containing metal main group element bonds are hard, but not superhard, and this is likely due to the higher number of slip planes. There is a balance that must be maintained between forming metal – main group element bonds to achieve a high bulk modulus, and limiting the formation of

28 slip planes to achieve a high shear modulus. Until this can be optimized, the compounds discussed in the next section will remain only hard.

Tungsten Carbide

While tungsten carbide is not superhard, it is one of the most commonly used materials

68 1 for cutting tools . While it is only fairly hard (Hv = 13-25 ), it is one of the most incompressible

69 materials with a bulk modulus of K0 = 421 GPa in bulk and a reported K0 = 452 GPa in nanocrystalline form70. Because tungsten carbide has interstitial carbon, it maximizes the electrostatic repulsion between metal atoms and carbon, and this leads to its high incompressibility. If anything, tungsten carbide demonstrates that while ultra-incompressibility is important for superhard materials, by itself it cannot confer high hardness. Inspection of the crystal structure reveals that the interstitial carbon sits in a hexagonal close packed structure of tungsten atoms. Hexagonal close packed structures are generally known to be soft, and the interstitial carbon helps pin some of the dislocations, thus explaining why tungsten carbide is hard. That being said, tungsten carbide is quite brittle so that any improvements in its shear modulus could significantly improve the mechanical properties of this industrially relevant carbide. Currently binders such as cobalt are added to improve ductility but this comes at the cost of hardness.

Other Osmium Compounds

Because the incompressibility of a material is closely tied with the metal, a trend follows that more metal rich compounds should have higher incompressibilities. Os2B3 is more

43 incompressible that OsB2, with its bulk modulus (K0 = 443 GPa) approaching that of diamond .

Osmium monoboride, which crystallizes in a WC-type structure with interstitial boron, surpasses both diamond and osmium metal with K0 = 453 GPa. The high incompressibility of osmium monoboride can be rationalized through its highly isotropic structure that maximizes its electrostatic repulsions (as seen in the c-axis of osmium diboride). However, neither of these compounds are superhard, as OsB and Os2B3 exhibit hardness values of only 14.4 GPa and 21.8

GPa (under an applied load of 0.49 N) , respectively.

Besides boron, other first row main group elements (e.g. carbon and nitrogen) can also be used to introduce short covalent bonds into osmium, and this should prevent the movement of

32, 71 dislocations and increase hardness. Osmium nitrides (OsN2 and OsN4) and osmium carbides

72, 73 (OsC2 and Os2C3) have been suggested to be ultra-incompressible. Both of these compounds rely on the high electron density from osmium metal and the short covalent bonds introduced by the main group element. However, experimental results have yet to be seen, largely owing to the high pressures required to synthesize these nitrides.

Rhenium Nitrides

Because of the high volatility of nitrogen, it is difficult to synthesize rhenium nitrides74,

75. By using diamond anvil cells, high temperatures, and pressures upwards of 31 GPa, two new rhenium nitrides (Re3N and Re2N) have been synthesized and are stable upon returning to ambient conditions76. Both of these compounds are based on the hexagonal structure of rhenium metal, with the intercalation of nitrogen disrupting some of the stacking. Interestingly, the trends differ from what is seen in the borides; these nitrides show increasing incompressibility with

35, 36 decreasing metal content, such that pure rhenium metal possesses K0 = 360 GPa , for Re3N

K0 = 395 GPa, and for Re2N K0 = 401 GPa. This unique behavior can be rationalized by

30 comparing the bonding between the borides and the nitrides. As seen in the aforementioned osmium diboride and rhenium diboride, the presence of metal-boron bonds results in high electrostatic repulsion, and the axis that aligns with these bonds usually becomes stiffer than diamond. However, because of boron’s propensity to catenate, there will also be boron-boron bonds, and the axes that correspond with those bonds are shown to be more compressible. In these novel rhenium nitrides, the nitrogen occupies what can be best described as an interstitial position, which results in a high density of metal-nitrogen bonds and no nitrogen-nitrogen bonds.

Not surprisingly, computational modeling of higher rhenium nitrides show that nitrogen begins to catenate (Fig. 8). Correspondingly, the computational bulk modulus begins to drop, with Re3N2 at K0 = 379 GPa, ReN2 at K0 = 376 GPa, ReN3 at K0 = 330 GPa, and unstable ReN4

77 at K0 = 528 GPa . Experimental results suggest that for MoS2-type ReN2, synthesized via a metathesis reaction under high pressure, the bulk modulus does indeed drop, falling to 173

GPa78. While the increasing nitrogen concentration results in lower incompressibility, likely due to the increasing number of nitrogen-nitrogen bonds, the addition of more directional covalent bonding should result in enhanced hardness. Of the aforementioned higher rhenium nitrides, the hardness is predicted to increase, with rhenium metal at 15.49 GPa, Re3N at 17.26 GPa, Re2N at

14.98 GPa, Re3N2 at 19.63 GPa, ReN2 at 19.86 GPa, ReN3 at 29.51 GPa, and unstable ReN4 nearly superhard at 38.72 GPa77. In all, rhenium nitrides are a very interesting system for future study, and any progress towards lowering the difficult synthetic requirements would greatly facilitate experimental understanding of this system.

Figure 8: The crystal structures of A) rhenium metal, B) Re3N, C) Re2N, D) Re3N2, E) ReN2, F)

ReN3, and E) unstable ReN4. Reprinted by permission from Macmillan Publishers Ltd: Scientific

Molybdenum Nitrides

By itself, elemental molybdenum possesses a BCC structure with a bulk modulus of 267

GPa. With the insertion of one equivalent of nitrogen to yield Mo2N, the bulk modulus increases to 301 GPa ostensibly due to the added molybdenum-nitrogen bonding. To further increase its incompressibility, more nitrogen must be added. Interestingly, MoN crystallizes in the same crystal structure as tungsten carbide, and its bulk modulus reaches 345 GPa79. Again, due to the high volatility of nitrogen, molybdenum nitrides must be synthesized under high pressure usually in a diamond anvil cell; in this case, laser heating was used to help anneal the sample into the correct phase.

Chromium Nitride

Chromium nitride (CrN) crystallizes in a rock salt structure with each chromium atom sitting in an octahedral site and equidistant from each nitrogen. The bulk modulus of chromium nitride was reported to reach 361 GPa80, which places it within the range of rhenium diboride and osmium diboride. This is surprising given than chromium metal is not as incompressible as elemental rhenium or osmium, suggesting that nitrogen plays a key role in raising the bulk modulus. However, chromium nitride undergoes a phase transition to an orthorhombic structure above ~1 GPa of applied pressure, and as such the high incompressibility only exists under 1

GPa of applied pressure; under ambient pressure the bulk modulus drops to 243 GPa. Chromium nitride is also not particularly hard with a Vickers hardness of only ~16 GPa, which may be due to its transient incompressibility. However, promising clues show that metal – main group element bonds can lead to high incompressibility without relying on an incompressible metal.

Conclusions

It is no coincidence that virtually all superhard materials are also ultra-incompressible.

The parameters used previously to explain ultra-incompressible and superhard materials were adequate: materials are incompressible if they have a high valence electron density, and materials are superhard if they are both incompressible and have bonds that prevent shear. These parameters worked well for traditional superhard materials such as diamond and boron nitride, but started to become frayed when dealing with superhard metals. It is time to refine these models with more parameters that reflect the complexities of structure and bonding. In particular, we feel that the following parameters should also be considered:

1) The metal – main group element bonds that lead to high stiffness through their respective

direction; highly incompressible materials will be found in materials that maximize metal

– main group element bonds.

2) Avoid materials with slip planes, as they allow for deformations.

Thus, the development of hard materials, which started over two millennia ago, provides fertile ground for new discoveries.

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Chapter 3

There are very few compounds that can challenge the diversity of the crystal chemistry found in borides. Owing to boron’s propensity to catenate, boron compounds primarily exhibit bonding motifs possessing extended covalent networks. Combined with boron’s preference to form only three covalent bonds (an exception to the octet rule), borides crystallize with complex polyhedra, notably octahedra, pentagonal bipyramids, trigonal dodecahedra, double-capped square antiprisms, cuboctahedra, and icosahedra.1 These covalent networks encompass a plethora of structure forms ranging from 1-D chains to 2-D sheets to 3-D networks.

With such a wide variety of structures (a quick survey of the Inorganic Crystal Structure

Database counts 1253 entries for binary boron compounds!), it is surprising that the applications of borides have been quite limited despite a great deal of fundamental research. If anything, the rich crystal chemistry found in borides could well provide the right tool for almost any application. The interplay between metals and the boron results in even more varied material’s properties, many of which can be tuned via chemistry. Thus, the aim of this review is to reintroduce to the scientific community the developments in boride crystal chemistry over the past 60 years. We tie structures to material properties, and furthermore.

This review builds on several previous excellent works discussing crystal structure1, mechanical properties2, magnetic properties3 and chemistry4.

SELECT APPLICATIONS AND PROPERTIES OF METAL BORIDES

The variations in the structure and bonding of metal borides not surprisingly results in a diverse multitude of properties. What is surprising, though, is that the commercial applications of borides are limited. Here a short compilation of properties and potential applications is provided, which we hope will inspire further research into metal borides.

1. CATALYSIS

Since the 1960’s, metal boride powders have been used as catalysts for a variety of organic reactions, most notably hydrogenations and reductions5. Because metal borides catalytically hydrolyze borohydride in water, they have also found uses in fuel cells as the hydrogen generator. Traditionally prepared by precipitation of metal salts with sodium borohydride6, the nature of these catalytic borides were not fully understood until recently. As these borides are synthesized in solution at low temperatures, the resulting structure is amorphous. Annealing the

7 precipitates of borides above 300 °C transforms the disordered structure into crystalline Ni3B .

Unfortunately, the disorder obscures the role of boron toward catalytic activity; ostensibly, the high metal content is responsible for the catalytic activity. More recently, it has been hypothesized that boron may provide a stabilizing role against sintering. Computational studies have shown that the presence of strong boron-metal bonds lowers the chance of grain growth, thus preserving the surface area at high temperatures8.

2. MAGNETIC PROPERTIES

While it is more interesting to discuss the role of extended boron networks (i.e. boron chains, sheets, etc.) on material properties, the role of boron in stabilizing the structures of functional structures must not be overlooked. These boron-stabilized structures usually contain isolated

43 boron atoms due to low boron concentration, and thus lack an extended boron network. As there is no extended boron network, the bulk of material properties stem from the other elements that make up the majority of the stoichiometry. This is particularly relevant for magnetic materials as only in a compound do borides exhibit significant magnetism9.

The strongest permanent magnets, knows as neodymium magnets are of the composition

10–12 Nd2Fe14B , and possess very high remnant magnetization. Thus, these rare earth magnets find uses in hard drives, speakers, electric motors, and any other applications that require a strong magnetic field. Ostensibly, the magnetism originates from the ferromagnetic elements iron and neodymium. The contribution of the boron towards the enhanced magnetism comes from the crystallographic arrangement. In Nd2Fe14B, boron coordinates to 6 iron atoms to form a trigonal prism, which is a common motif found in isolated boron metalloids13. This in turn aligns the magnetic moments of iron along the c-axis, resulting in strong magnetic anisotropy. Contrast this

11 with another rare earth magnet, SmCo5, which possesses a somewhat similar trigonal structure , but requires a higher rare earth to transition metal ratio. Perhaps not surprisingly, the contribution of magnetism from the alignment of iron around boron suggests that the rare earth element may not be required, and this has led to the development of iron nitrides, where the nitrogen sits in a similar position to boron.

Aside from rare earth neodymium magnets, there are other magnetic borides. A more thorough review has been written by Bucher3, so here only the magnetic properties will be listed briefly. It is noted that Co2B (Tc = 429 K), Co3B (Tc = 747 K), FeB (Tc = 598 K), Fe2B (Tc = 1013 K),

MnB (Tc = 573 K), MnB2 (Tc = 157 K), and Mn3B4 (Tc = 392 K) all exhibit ferromagnetism.

Beyond transition metals, many rare earth borides exhibit ferromagnetism; however, unlike the transition metals, the ferromagnetism is less robust and results in a lower Tc, as TbB2 (Tc = 151

K), DyB2 (Tc = 55 K), ErB2 (Tc = 16 K), and HoB2 (Tc = 15 K) each crystallize in an AlB2-type structure, with all the rare earth metal spins aligned along the basal plane14. As one moves from

2-D boron sheets to 3-D boron networks of hexaborides and dodecaborides9, one soon finds more antiferromagnetic ordering with CeB6 (TN = 23 K), PrB6 (TN = 7 K), NdB6 (TN = 8.6 K),

GdB6 (TN = 18 K), TbB6 (TN = 23 K), DyB6 (TN = 21.5 K), HoB6 (TN = 9 K), HoB6 (TN = 6.5 K),

ErB6 (TN = 6.5 K), and TmB6 (TN = 4.2 K). For hexaborides, the antiferromagnetic ordering stems from the coupling between the conduction band and the 4f electrons15; there is one free

16 electron per each trivalent metal. Thus, divalent europium in ferromagnetic EuB6 is the exception. Admittedly, the ordering in europium hexaboride is more complicated than a simple valence electron count, as it possesses two magnetic transitions17. Ferromagnetism has been induced in calcium doped lanthanum hexaboride through electron-hole pairs18.

3. HARD AND SUPERHARD MATERIALS

The propensity for boron to catenate usually results in extended 3-D networks of covalent bonds.

This results in a high shear modulus as dislocations do not traverse across strong directional bonds. Preparing a boride with an ultraincompressible metal will result in a compound that approaches the incompressibility and hardness found in diamond. This has inspired the development of superhard metal borides, of which we have discovered several. As the focus of this review is towards the applications of boride materials, we direct the reader to more detailed reviews on the nature of superhard materials2.

The current uses of hard borides have been largely limited to machining19, but the high wear resistance afforded by borides may lead to other applications, such as prosthetics20. Applying a hard coating to mating surfaces will extend the lifetime of a prosthetic joint, reducing the need

45 for further surgery, thus avoiding additional complications. Fortunately, the majority of borides are known to be hard and protective films of borides can be prepared via straight forward methods. Borodizing is a process by which boron is diffused into the surface of metal workpiece.

As this is a diffusion limited process, a metal rich boride is created on the surface of the metal, typically of composition M2B. As these lower borides generally crystallize in the CuAl2 structure, isolated borons sit in what can be considered as a true interstitial site. The strong metal-boron bond prevents the metal planes from sliding past each other, thus strengthening the surface with increased hardness which imparts increased wear resistance.

4. HIGH TEMPERATURE MATERIALS

As boron is the second highest melting main group element after carbon, it is not surprising that the majority of metal borides are refractory. Among the refractory borides is zirconium diboride

o 21 (Tmp = 3230 C) , which crystallizes in an AlB2-type structure with 2-D honeycomb boron.

Combining the high melting point with a high elastic modulus (from the pliable boron sheets) results in a robust structural material resistant to extreme thermal events. Zirconium diboride also exhibits excellent oxidation resistance, surviving thermal cycling up to 2700°C in air22. As the byproducts of oxidation are ZrO2 and B2O3, significant oxidation only occurs above 1000°C

23 resulting from the sublimation of B2O3, which exposes fresh surfaces for degradation . The addition of silicon to form a composite results in a formation of a protective SiO2 layer that

o prevents further oxidation up to the vaporization temperature of SiO2 (Tbp = 2950 C).

Zirconium diboride has been investigated by the United States Air Force for use in rocket engines and United States Navy for hypersonic flight vehicles24.

5. SUPERCONDUCTIVITY

The promise of high power transmission with limited resistance and levitated trains has spurred the development of superconductors. The ability to carry large currents without Ohmic heating enables the generation of strong magnetic fields25, and as such, they are often used as the windings for NMR. Combining a superconductor with a topological insulator (see the section on topological insulators) results in what can be a crucial component for a solid state quantum computer. It is not surprising that with the plethora of bonding geometries found in borides, that there are several strong superconducting candidates.

Magnesium diboride has been used as an effective reagent to yield transition metal borides through solid state metathesis reactions26, but perhaps its most interesting property is the loss of resistivity at 39 K.27–29 This temperature exceeds all type-I superconductors, even exceeding

30 La2-xBaxCuO4, the first type-II superconductor discovered . Unlike traditional type-I superconductors, which rely on S-orbital overlap, MgB2 also posses significant P-orbital overlap,

31 resulting in a higher heat capacity and higher Tc . Noting that MgB2 possesses one of the longest c-axis among the diborides (3.52 Å) and the deleterious role of pressure on Tc, Wan et al. theoretically modeled various MgB2 lattice parameters and found that stretching the c-axis and compressing the a-axis should raise the Tc. Indeed, parallel experiments with NbB2+x (Tc = 9.4

32 33 K) and MoB2+x (Tc = 7.5 K) have shown that the addition of excess boron can help separate the boron layers and induce superconductivity in non-superconducting diborides. We envision further enhancements in the superconducting properties of borides through increased lattice expansion by doping or structural modifications.

Not surprisingly, there are many other borides34 with superconducting properties, although none surpass the Tc of MgB2. Metal-rich borides that possess isolated boron atoms, such as Mo2B (Tc

= 5.07 K) and W2B (Tc = 3.22 K), superconduct because the valence electron count places the

Fermi surface in contact with the reciprocal lattice35. Of the monoborides that crystallize with 1-

D linear boron chains, TaB (Tc = 4 K) and NbB (Tc = 8.25 K), are known to superconduct.

Virtually all higher borides9 that do not possess antiferromagnetism superconduct, as can be seen with ScB12 (Tc = 0.39 K), YB6 (Tc = 7.1 K), YB12 (Tc = 4.7 K), ZrB12 (Tc = 5.82 K), LaB6 (Tc =

5.7 K), LuB12 (Tc = 0.48 K), and ThB6 (Tc = 0.74 K).

6. KONDO INSULATORS

While many rare earth borides are known to superconduct at low temperatures, there are a select few that lose their conductivity, and they are known as Kondo insulators. This phenomenon occurs in rare earth borides where the rare earth possesses mixed valency i.e. Yb can be Yb+2 or

Yb+3. This mixed valency results in the opening of a band gap at low temperatures. As seen in

YbB12, the valence band is comprised of 36 electrons from the boron cage and 2 electrons from the metal. The extra electron transferred from a trivalent rare earth solely occupies the conduction band. It is not too surprising then, that some borides were found to be ideal Kondo insulators as a result of the strong coupling36 and the possession of mixed valency in the f- orbitals37. Samarium hexaboride became one of the first experimentally confirmed Kondo insulators, as indicated using resistivity and magnetic measurements37.

7. TOPOLOGICAL INSULATORS

At first glance, topological insulators seem to be merely small band gap topological insulators.

However, due to intricacies in the spin-orbit coupling, topological insulators exhibit bulk insulating behavior like could traditional insulators, but also possess metallic conductivity on their surfaces. Thus, these materials could find applications where a topologically protected metallic surface state is needed. It has been postulated that Majorana fermions can be found at

48 the interface between a topological insulator and a superconductor, where the superconductor induces a superconducting surface state. As the vortex state is confined to the surface, this creates the aforementioned quasiparticle. These Majorana fermions can then be paired to form a quantum bit. Therefore, the search for new topological insulators has drawn considerable interest given the possibility of quantum computing.

Because topological insulators require strong spin-orbit coupling, the search for new ones has been largely restricted to the heavy elements of the P-block38. In 2010, Coleman et al.39 noted that potential topological insulators can be found in cubic Kondo insulators. In addition to these materials becoming insulating at low temperatures due to a mixing of f-electrons and the conduction band, the cubic symmetry in hexaborides ensures that transport is limited to a few directions resulting in a strong topological insulator40. Shortly thereafter, the classical Kondo insulator SmB6 confirmed theoretical predictions and demonstrated a topologically protected conductivity41–43. Beyond samarium, Several ytterbium borides were hypothesized to be topological Kondo insulators44.

8. OPTICAL PROPERTIES OF BORIDES

As most metal borides are metallic conductors, it may be somewhat surprising to see a section on optical properties. While borides generally do not possess any interesting optical properties in the visible spectrum (save for color), borides do interact with photons of other wavelengths45, and these properties have led to some niche applications of borides. For example, thin films of borides have been used as filters for ultraviolet light46, which has potential applications for deep space telescopes.

For more terrestrial applications, lanthanum hexaboride is often used by crystallographers as an

11 X-ray standard, SRM 660a. Isotopically enriching to yield La B6 allows for the hexaboride to be used as a standard for neutron diffraction, SRM 660c. As lanthanum hexaboride possess a cubic structure, it exhibits a periodic arrangement of diffraction peaks, making it a reliable diffraction standard. Hexaborides also find uses as hot cathodes as low work function, refractory compounds. As such, a significant body of work has focused on the use of lanthanum hexaboride as cathodes for electron microscopes, where the improved oxidation resistance and enhanced electron emissivity has allowed it to supplant tungsten electrodes. Recently, lanthanum hexaboride nanoparticles have found uses as near infrared absorbers47 for windows, selectively absorbing infrared light while transmitting visible photons due to free electron plasmon resonance48.

Since YB66 possesses one of the largest unit cells known (a = 23.44 Å = 2.344 nm) from the presence of over 1600 atoms per unit cell, it can be used as an X-ray monochromator. More importantly, YB66 is comprised mainly of light boron atoms, allowing improved transmission of soft X-rays. YB66 is particularly useful for synchrotron radiation as it encompasses the entire 1-2

KeV range, replacing three crystals that had previously been needed49. Note that the high energy of the photons will heat the crystal upwards of 637 K, but fortunately, borides are refractory50.

Conclusions

For the past 60 years, the boride family has only been studied primarily for their rich crystal chemistry this leads to a host of properties that provide many possibilities for applications. Here we present a non-exhaustive compilation of crystal structure data, materials properties, and

50 synthetic routes towards metal borides. Given the chemical tunability of those properties, we encourage the materials community to revisit metal borides.

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Chapter 4

Superhard metals possess many benefits over traditional superhard materials such as diamond and cubic boron nitride. Most notably, they are easy to synthesize. They can be made at ambient pressure and thus can be cast from the melt like common metals. Furthermore, their metallic character allows them to be easily cut and shaped post-synthesis by electric discharge machining. The scientific factors involved in designing mechanically superhard compounds

(Vickers Hardness, Hv ≥ 40 GPa) are complex: both elastic deformations (reflected in bulk modulus and shear resistance) and plastic deformations (reflected in elastic limits) must be optimized. Due to limitation in our ability to control material strength, the design of superhard materials is quite difficult. As such, there are only a handful of material compositions in existence known to be intrinsically superhard: diamond, cubic boron nitride, rhenium diboride, tungsten tetraboride, and chromium tetraboride. 1-6

In 2005, it was suggested that superhard compounds can be designed rather than discovered by following two simple rules. 7 The first step is to start with a high valence electron density, which leads to a large bulk modulus and high incompressibility. 1 The second step is to add short, strong covalent bonds to prevent shear and slipping of planes. For example, diamond is both the hardest and stiffest single-phase material known with a hardness of 70 – 110 GPa, a bulk modulus of 442 GPa, and a valence electron density of 0.71 e-Å-3. 8 These design rules can be applied to yield superhard metals by introducing short, highly covalent bonds using electron deficient atoms such as boron into metals with a large number of valence electrons, such as rhenium and tungsten. 4, 9, 10 Based on these ideas, it is not surprising that the five aforementioned superhard compositions are either fully covalent compounds, or they are the

58 highest boride in a metal boride system. 11 In the case of the heavy metal tungsten, the simplest method to obtain a superhard phase is by introducing at least four molar equivalents of boron to yield WB4. This increases the covalent bonding, and resulted in the first superhard composition in the tungsten-boron system. 10

With the lower borides of tungsten, the significantly reduced level of covalent bonding should result in a softer material. Pristine tungsten tetraboride, the highest boride in the W-B system, is superhard with a Vickers Hardness of ~43 GPa under a load of 0.5 N. As such, tungsten monoboride (WB) should be significantly softer. 10 Experimental hardness measurements confirm that pristine WB is not naturally superhard, exhibiting a Vickers hardness of 36 GPa under a load of 0.49 N. 12 More rigorous computational studies have shown that WB should have a high shear modulus, but not nearly as high as those found in superhard materials.

13, 14 Furthermore, in tungsten monoboride, the tungsten-tungsten bond distance (2.8 angstroms) approaches that of pure tungsten metal (2.7 angstroms), which suggests significantly stronger metallic bonding character. This brings with it some of the malleability and toughness found in conventional metals. Indeed, WB is suggested to have a good balance between hardness and ductility, which can lead to higher wear resistance. 15

Because of the higher metallic character, metallic bonding should play a greater role in the mechanical properties of tungsten monoboride. Unfortunately, metallic bonding is generally weak. Metals, while possessing high electron density and incompressibility, have non-directional metallic bonds, 11 which allows for transient bond breaking and dislocation formation. This is why most metals are ductile and malleable. 11 Based on our design rules, the best way to increase the hardness of metallic tungsten monoboride would be to add more equivalents of boron to yield

59 the more covalent tungsten tetraboride. For the lower borides, however, a different method must be employed.

Here, we demonstrate an alternative approach, where we identify the crystallographic planes that slip at the lowest loads, and from there, we can find ways to increase the mechanical strength of these planes to make tungsten monoboride superhard. This is accomplished by 1) identifying the weak slip plane and 2) selectively strengthening this plane through solid solution hardening. We have followed the aforementioned approach to create a completely new superhard material (W0.5Ta0.5B). This approach suggests that along with the previously discussed design rules of incompressibility and shear, bonding motifs can also play an important role in materials strength.

Tungsten (Strem, 99.95%), tantalum (Roc/Ric, 99.9%), and boron (Materion, 99%) powders were stoichiometrically ground in an agate mortar and pestle (typical total loadings were 1 gram). Some samples had a slight excess of boron due to boron sublimation from the high temperatures of arcing. The homogeneous powders were pressed into a pellet, arced, turned over, and re-arced to ensure homogeneity. Samples were arced under high-purity argon under ambient pressure. The ingots were then bisected, with one half crushed for powder X-ray diffraction, high pressure radial diffraction, and thermal gravimetric analysis. The other half was mounted in epoxy and polished, for hardness and scanning electron microscopy (SEM), and for phase analysis. Mounted samples were polished with a SouthBay Technologies Polishing Station using polishing papers from 120 to 1200 grit (Allied High Tech Products Inc.).

Samples were analyzed by powder X-ray diffraction on a Panalytical X’Pert diffractometer using a Cu Kα1 source (λ = 1.5418 Å). The as-collected spectra were compared against JCPDS Card #00-006-0541 using X’Pert HighScore Plus as the processing software.

Powder samples were then refined by size using a solvent suspension method, and imaged under a TF-20 transmission electron microscope (TEM) for size analysis. Size-refined powders were then used for high pressure radial diffraction.

Polished samples were imaged under backscatter SEM using a Nova 230 electron microscope with electron dispersive spectroscopy (EDS) used to determine homogeneity.

Polished samples were measured for hardness on a Micromet 2103 equipped with a pyramid diamond indenter tip. With a dwell time of 15 s, the samples were indented under loads of 0.49,

0.98, 1.96, 2.9, and 4.9 N. Indent diagonals were measured using a Zeiss Axiotech 100HD optical microscope (Carl Zeiss Vision GmbH, Germany). Vickers hardness is determined from

Equation 1 using the arithmetic mean of 14 randomly chosen indents:

[1]

where P is the applied load and d is the average of the diagonals.

Radial diffraction was performed at the Advanced Light Source at Lawrence Berkeley

National Labs using a diamond anvil cell (DAC). Incompressibility was determined using the third-order finite strain Birch-Murnaghan equation of state (Equation 2):

[2]

where P is the applied load, K0 is the bulk modulus, V is the deformed unit cell volume, V0 is the un-deformed unit cell volume, and K0’ is the derivative of the K0 with respect to P. Here, K0’ is fixed to 4.

Differential strain was interpreted using lattice strain theory from the high-pressure radial diffraction using Equation 3 16, 17:

[3]

61 where Ψ is the angle between the diffracting plane normal and the maximum stress axis, dhydro(hkl) is the hydrostatic d-spacing (measured when Ψ = 54.7°), and dmeas(hkl) is the measured d-spacing under pressure. Q(hkl), the orientation dependent differential strain, can be written as:

[4]

where G is the aggregate shear strain, and t is the differential stress 18. The differential stress, t, can be rewritten using the Tresca yield criterion,

[5] where σaxial, max is the maximum stress along the axial direction, σradial, min is the minimum stress

19 along the radial direction, and σy is the yield strength . The elastically-supported differential stress, t, enables one to estimate the lower-bound of the material’s yield strength, y.

Thermal stability in air of each of the materials was determined using a Pyris Diamond thermogravimetric/differential thermal analyzer. Powder samples were heated in air up to 200°C at a rate of 20°C/min, held for 20 min to remove residual moisture, and then heated up to 1000°C at a rate of 2°C/min.

Tungsten monoboride crystallizes in either a low temperature tetragonal or a high temperature orthorhombic unit cell. The primary difference between these two phases is found in the layer of boron chains, where in the tetragonal (low temperature) form, the boron chains alternate orthogonally, while in the orthorhombic (high temperature) form the boron chains are all aligned along the a-axis. Both structures possess a bilayer of tungsten atoms; the high temperature orthorhombic phase is shown in Figure 9a.

The bilayers of tungsten atoms separated by boron chains in WB are likely to dominate the mechanical properties of the material. Because tungsten monoboride (unlike tungsten tetraboride, WB4) is a lower boride, the number of covalent bonds that can prevent the formation

A B

Figure 9: (A) Crystal structure of high-temperature, orthorhombic tungsten monoboride, WB.

Tungsten atoms are gray The purple plane marks the location of a metallic bilayer. (B) The a, b, c lattice parameters of TaxW(1-x)B (x = 0.01, 0.05, 0.10, 0.25, and 0.50). Note the linear progression of the lattice parameters with respect to tantalum content, consistent with Vegard’s law. (C) Powder X-ray diffraction patterns of TaxW(1-x)B (x = 0.01, 0.05, 0.10, 0.25, and 0.50) with peaks indexed to orthorhombic WB (JCPDS Card #00-006-0541).

63 or movement of dislocations is limited. This fact, combined with the W-W bond lengths approaching that of tungsten metal, suggests that the hardness of WB is likely to be limited by slip in the tungsten bilayers. Indeed, computational studies of isostructural chromium monoboride have shown that the metal bilayer is indeed a slip plane 20. As a result, if we can prevent dislocations in this metallic plane, we should be able to increase the overall hardness of tungsten monoboride.

Therefore, solid-solution strengthening has the potential to dramatically alter the mechanical properties of the WB system. Specifically, by substituting tungsten with larger atoms, slipping of the metallic planes can be reduced through dislocation pinning. With higher resistance to dislocations, the overall hardness should increase. As such, we chose to substitute tantalum onto the tungsten sites because tantalum has a similar valence, electronegativity, and only a modestly larger atomic radius when compared to tungsten. Furthermore, tantalum monoboride crystallizes into the same phase as the high temperature form of tungsten monoboride, which satisfies the Hume-Rothery rules for solid solutions. It should be noted that the end members of W1-xTaxB are not known to be superhard, and as such this is an excellent system to study. 21, 22

Tantalum monoboride crystallizes in an orthogonal unit cell, and when combined with the fast cooling rate of the copper hearth of the arc melter, it is expected that all W1-xTaxB compositions (where x = 0.01 to 0.5) will crystallize in the orthorhombic phase. Indeed, powder

X-ray diffraction suggests that even at 1% Ta concentration, as seen in W0.99Ta0.01B, the favored phase is the high temperature orthorhombic modification. Moreover, TaB is miscible in WB at high concentrations with no secondary phases as observed by powder X-ray diffraction (Figure

9C). There is a noticeable shift towards larger lattice parameters with increased tantalum

64 concentration, which is expected because tantalum (1.343 Å) has a slightly larger atomic radius when compared to tungsten (1.299 Å). 23 As seen in Figure 9B, these lattice parameters increase linearly, as expected from Vegard’s Law. This suggests a well-behaved alloy system with tantalum randomly distributed across the tungsten sites. Backscattered scanning electron microscopy confirms that there are no secondary phases, and elemental mapping with electron dispersive spectroscopy (EDS) suggests that both tantalum and tungsten are well dispersed

(Figure 10A). Transmission electron microscopy of freshly fractured and crushed powder suggests that the samples are highly crystalline and not nanostructured, as seen in Figure 10B.

The lack of a secondary phase observed by XRD, EDS, and electron microscopy indicates that extrinsic hardening mechanisms such as precipitation hardening or dispersion hardening are not responsible for the observed mechanical properties.

Vickers hardness was then measured under loads of 0.49, 0.98, 1.96, 2.9, and 4.9 N

(Figure 11). Under a low load of 0.49 N, the tungsten monoboride sample containing 1% tantalum has a Vickers hardness of ~35.1 GPa, in good agreement with a previously reported value of 36 GPa for pristine, polycrystalline WB. 12 As the tantalum concentration is increased, there is an increase in hardness. This trend is linear with Ta concentration, reaching 42.8 GPa at the 50% composition. This breaks the threshold for superhard materials (Hv ≥ 40 GPa); therefore,

W0.5Ta0.5B can be considered as a new superhard metal. Aside from WB4, this is the only other superhard composition in the tungsten-boron system. And unlike WB4, which is understood to derive its hardness purely from the covalent boron network, it appears that hardness in tungsten monoboride is achieved through a combination of covalent bonding and solution effects.

This linear hardness trend that maximizes at a 50% concentration is quite unusual amongst the borides. For example, WB4 forms solid solutions with tantalum, chromium, and

Figure 10: (A) Energy-dispersive spectroscopy (EDS) plots demonstrate that tantalum

(bottom) and tungsten (top) are evenly distributed throughout the alloy. Scale bar = 10 μm (B)

Transmission electron microscopy of freshly fractured powder indicate that the majority of the grains are not nanostructured, ruling out extrinsic hardening mechanisms. Scale bar = 1 µm

Figure 11: The Vickers indentation hardness of TaxW(1-x)B as a function of different loads (0.49 N/50 gram-force [r2 = 0.85], 0.98 N/100 gram-force [r2 = 0.70], 1.96 N/200 gram- force [r2 = 0.92], 2.9 N/300 gram-force [r2 = 0.91], and 4.9 N/500 gram-force [r2 = 0.71]) follows a linear trend. The hardness value of the 50% Ta composition under a load of 0.49 N is 42.8 ±

2.6 GPa indicating that W0.5Ta0.5B is a superhard material.

2 manganese, but the hardness trend for WB4 solid solutions is not linear. For the WB4 system, the highest hardness values are achieved at very low substitution levels (~5 at%) and are believed

10 to arise mostly from electronic structure effects. Likewise, the hardness of Os1-xRuxB2 solid solutions is linear with composition, but it does not show any hardness maxima near 50% concentration. Instead, the data exhibit simple Vegard’s law behavior connecting the two end

24 members. The unique behavior in W1-xTaxB, combined with inspection of the orthorhombic crystal structure, suggests that modification of the metallic bilayer may be responsible for the increase in the material’s strength. By substituting tungsten with larger tantalum atoms, plane slipping will be diminished through dislocation pinning. At 50% concentration, pinning should be maximized, and this is reflected in the hardness measurements. Indeed, W0.5Ta0.5B is much harder than its parent structures: WB (36 Gpa 12 at 0.49 N) and TaB (30.7 Gpa 25 at 0.49 N). This chemical tuning of the structure shows that the hardness of tungsten monoboride can be increased through solid solution hardening.

To confirm the hardening effects of substituting tantalum into the metallic bilayer, high- pressure diffraction studies are used to correlate macroscopic hardness with microscopic deformations. By compressing samples under non-hydrostatic stress in a high-pressure diamond anvil cell, conditions similar to those found under the indenter tip can be controllably produced in a geometry that can be readily probed using X-ray diffraction. Such experiments can provide a lattice specific measure of yield strength and the predominant slip systems available in the material. 26 High-pressure radial diffraction is a well-known technique that has been satisfactorily used previously to determine the amount of load each plane supports in nanocrystalline WB. 27

Here, high-pressure radial diffraction is used to determine which planes in tungsten monoboride limit the hardness. Specifically, we can specifically learn about the slip system in the material by differential strain, which is given by the ratio of differential stress to shear modulus (t/G). Linearly increasing t/G values corespond to elastically supported differential strain, but when the curve plateaus, it corresponds to the onset of plastic deformation. Planes that have a low t/G plateau pressure tend to dislocate and slip easily, while planes that have a

4 high t/G plateau pressure can support more deformation . For W0.50Ta0.50B, the planes (200),

(020), and (002) were chosen for study because they represent the anisotropy of the unit cell.

Dislocations in the (200) set of planes cut between the boron-boron chains, while the (020) set of planes cut through the tungsten bilayer, and the (002) planes cut through the boron-boron bonds

(Figure 9a). In other words, the (200) and (002) represents more covalent/boron bonding, while the (020) possesses more metallic/tungsten bonding.

As can be seen in Figure 12, the elastically-supported differential strain for the (200) and

(002) planes is lower than that of the (020) planes at lower pressures , suggesting that the bonds in the (200) and (002) directions are stiffer. As pressure is increased, the (020) planes are also the first to plateau at 36 GPa. The plateau is an indication of transition from elastic to plastic deformation, and so these data indicate that the (020) planes constitute the primary slip system for this material, in agreement with calculations on isostructural CrB20. While these factors all suggest that the metal bilayers are the weakest directions in the material, the actual plateau value of 5.1% differential strain is quite high. We note that unlike differential stress, differential strain cannot be directly related to hardness becasue elastic anistropy can produce high strains in elastically soft directions. Unfortunately, the elastic constants for W0.50Ta0.50B are not known, so the plateau value of the differential stress cannot be directly calculated from the plateau

Figure 12: The differential strain plot of W0.5Ta0.5B with respect to the (200), (020), and

(002) set of planes. The (020) planes support the highest differential strain (t/G) and indicate that they are the load-bearing planes.

70 differential strain. Despite these issues, the (020) plateau strain value is high, and the fact that the

(200) curve only meets the (020) curve near 50 GPa further indicates that substituting Ta into

WB appears to be an effective way to strengthen the weakest lattice direction in W0.50Ta0.50B.

Intriguingly, the detailed behavior of the (020) set of planes further reveals insights into the nature of the bonding. As can be seen in Figure 12, the differential strain supported by the

(020) planes increases up to a maxima of 5.5% differential strain at 35 GPa, and then the strain decreases. This non-monotonic behavior is reminiscent of pure niobium metal. 18 These results thus further suggest that the tungsten bilayer, represented by the (020) planes, behaves like a pure metal. Thus, because this system combines metal-metal bonding and metal-boron bonding, hardness needs to be optimized using two methods. Where present, metal-boron bonds can prevent slip much like they do in WB4. For the metal-metal bilayers, however, which are the first planes to slip, solid-solution effects are needed to reduce slip.

From the high-pressure studies, the bulk modulus of W0.5Ta0.5B was determined to be 337

± 3 GPa using a second order Birch-Murnaghan equation-of-state (Figure 13). This demonstrates that W0.5Ta0.5B is not only superhard, but also ultra-incompressible. This value is slightly lower than the theoretically predicted bulk modulus of 350 GPa for WB, which is expected because tantalum contains fewer electrons than tungsten. 13, 27 This tungsten monoboride solid solution is therefore even more incompressible than tungsten tetraboride (326

± 3 GPa), the other superhard boride in the tungsten-boron system. 28 This was expected, since incompressibility is related to high electron density that comes from the tungsten. With a high tungsten content and tungsten-tungsten bonds that approach those found in tungsten metal, tungsten monoboride should have a high bulk modulus.

Figure 13: The deformation in the unit cell volume is fit to a third-order Birch-

Murnaghan equation of state, and shows that W0.5Ta0.5B is ultra-incompressible.

Oxidation resistance was measured using thermal gravimetric analysis. In practical applications, high oxidation resistance is needed because the act of machining generates high temperatures from friction. Oxidation of W0.5Ta0.5B begins at 550 °C in air (Figure 14). This suggests that W0.5Ta0.5B has a higher resistance to oxygen than tungsten carbide, which begins oxidizing at 500 °C. 29 Tungsten carbide is one of the most useful materials for cutting tools. 30, 31

The added oxidation resistance provided by adding tantalum, is likely due to the formation of a protective oxide coating, which prevents further oxidation until 550 °C. 32 Furthermore, tungsten monoboride behaves as a metallic conductor as seen with a temperature vs. resistance plot

(Figure 15), which suggests that tungsten monoboride can easily be shaped post-synthesis via electric discharge machining.

The greatly increased role of metallic bonding in the hardness of WB offers an intriguing line of inquiry into superhard materials. Typically, non-directional metallic bonds are prone to slip and thus, conventional wisdom would suggest that the best way to make a superhard metal would be to add more boron until covalent bonding dominates and prevents the movement of dislocations. As such, superhardness should generally be found in strongly covalent materials such as diamond or tungsten tetraboride, which are both brittle materials. Here, we demonstrate that metallic bilayers can be present in a superhard material if they are properly engineered to reduce slip. Solid solution strengthening can be used to increase the hardness of tungsten monoboride because it is effective at strengthening these metal bilayers. Furthermore, high- pressure radial diffraction experiments confirm that the metallic bilayer of tungsten monoboride is the easy slip system of the material and should be the focus of solid-solution optimization. In conclusion, strengthening of the weakest planes is an alternate and viable approach to creating new superhard materials in more metallic materials.

Figure 14: Thermogravimetric analysis (TGA) of W0.5Ta0.5B suggests that the onset of oxidation does not begin until 550 °C.

Figure 15: The electrical resistance of the ingot increases with temperature, which indicates that W0.5Ta0.5B is metallic.

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25. Ivankov, A., Handbook of Hardness Data. Naukova Dumka: Kiev, 1968.

26. Hemley, R. J.; Mao, H.-k.; Shen, G.; Badro, J.; Gillet, P.; Hanfland, M.; Häusermann, D.

Science 1997, 276, (5316), 1242-1245.

27. Dong, H.; Dorfman, S. M.; Chen, Y.; Wang, H.; Wang, J.; Qin, J.; He, D.; Duffy, T. S.

Journal of Applied Physics 2012, 111, (12), -.

28. Xie, M.; Mohammadi, R.; Mao, Z.; Armentrout, M. M.; Kavner, A.; Kaner, R. B.;

Tolbert, S. H. Physical Review B 2012, 85, (6), 064118.

29. Voitovich, R. F.; Pugach, É. A. Powder Metall Met Ceram 1973, 12, (4), 314-318.

30. Brookes, K. A. Metal Powder Report 1995, 50, (12), 22-28.

31. Exner, H. E. International Metals Reviews 1979, 24, (1), 149-173.

32. Zhang, X.; Hilmas, G. E.; Fahrenholtz, W. G. Journal of the American Ceramic Society

2008, 91, (12), 4129-4132.

Chapter 5

The search for new superhard materials has predominately focused on intrinsically hard materials. Nature has only provided the covalent crystal diamond, and since then, the superhard materials field has blossomed with the development of new compounds (such as cubic boron nitride) that mimic diamond’s crystal structure.1 More recently, by adding short covalent bonds into electron-dense metals, a new class of superhard metals, that can be synthesized at ambient

2 3 4 pressure, has been developed including ReB2 , WB4 , and CrB4 . Crystal structure engineering has led to a deeper understanding of the bonding motifs responsible for this new class of superhard metals with exciting potential for practical applications. Recently, tungsten monoboride was induced to be superhard through the amelioration of a slip plane. By selectively substituting tungsten atoms with tantalum, the (020) plane is solid-solution hardened, thus removing the weakest link and promoting the W1-xTaxB (x = 0.0 - 0.5) system into the superhard regime5.

To date, however, little emphasis has been placed on examining extrinsic hardening effects in this new class of materials. As superhard materials are at the limit of material strength, it is completely unknown how conventional extrinsic mechanisms such as the Hall-Petch effect, morphological control, and nanostructuring will affect the high hardness possessed by these materials. Preliminary work on diamond6, cubic boron nitride7, and tungsten tetraboride8 have shown that nanostructuring can indeed increase hardness, but morphological control of crystallite and grain shape have yet to be demonstrated.

Here, we demonstrate that W0.5Ta0.5B can be synthesized in an aluminum flux at ambient pressures to yield nanowires. By controlling the flux ratio, the aspect ratio of the nanowires can

79 be controlled. This material in bulk has been previously shown to be superhard (Hv = 42.3 ± 2.6

GPa at a load of 0.49 N) and ultraincompressible (Ko = 337 ± 3.0 GPa), and to date, this is the only reported synthesis of a superhard nanostructure under ambient pressure.

Experimental

Tungsten (Strem, 99.95%), tantalum (Roc/Ric, 99.9%), and boron (Materion, 99%) powders were stochiometrically ground in a ratio of W0.5Ta0.5B in an agate mortar and pestle.

The mixed elemental powders were then loaded into an alumina boat with aluminum shavings

(Strem Chemicals 99+%), and heated in a tube furnace under flowing argon. The heating profile was as follows: ramp up to 1050°C at 1.71°C/min, dwell for 12 hours, cool down to 700°C at

3.92°C/min, cool down to 25°C at 11.25°C/min. The molar ratio of aluminum to W0.5Ta0.5B varied from (250:1) to (50:1) to (10:1). The aluminum was then etched away with 6.0 M NaOH.

The resulting powders were characterized by powder X-ray diffraction (PXRD), scanning electron microscopy (SEM), and transmission electron microscopy (TEM). PXRD was carried out using a Bruker D8 Discover Powder X-ray Diffractometer (Bruker Corporation, Germany) with CuKα X-ray radiation (λ = 1.5418 Å). The collected patterns were cross-referenced against the patterns found in the database of the Joint Committee on Powder Diffraction Standards

(JCPDS) to identify the phases present. SEM images were acquired using a JEOL JSM-67 Field

Emission Scanning Electron Microscope, and TEM images were acquired using an FEI TF20.

Results and Discussion

To prepare highly crystalline nanowires with few defects, we modified the experimental conditions used for single crystal growth. Aluminum was chosen as it is the solvent of choice for borides9. The heating profile closely mirrors the method used in the synthesis of single crystal

10 ReB2 . This method had previously been used to synthesize highly crystalline metal borides, and thus the ramp rates were used with minor modifications. According to nucleation theory, there are two factors that dominate final crystallite size: cooling rate and nucleation site density. As the heating rates were preserved to maximize crystallinity, the chief mechanism for controlling crystallite size becomes flux to monoboride loading ratio. A low flux to monoboride ratio should lead to a higher density of nucleation sites as upon cooling, the monoboride will quickly precipitate en masse out of the molten flux due to saturation. This high density of nucleation sites will result in smaller nanocrystals. On the other hand, a high flux to monoboride ratio should lead to a lower density of nucleation sites and larger crystallites. Thus, the following various loading ratios of Al to W0.5Ta0.5B were tested: 250:1, 50:1 and 10:1.

As can be seen from the PXRD (Figure 16), the resulting black powders are highly crystalline and index nicely to the anticipated W0.5Ta0.5B pattern, with some minor impurities peaks present from trapped oxidized flux (Al2O3). Noticeably, the PXRD peaks broaden as the flux to monoboride ratio drops, confirming that by varying this ratio, the resulting crystallite size can be controlled. Indeed, the 10:1 sample shows far more broadening than the 250:1 or the 50:1 samples. According to Scherrer equation analysis of the (021) peak, the crystallite size of the nanocrystals prepared from the 10:1 flux is approximately 37.8 nm, confirming that the prepared samples are indeed nanostructured. Analysis of samples prepared from flux ratios of 250:1 and

50:1 showed negligible broadening.

Figure 16: Powder X-ray diffraction patterns of superhard metal nanowires prepared using monoboride (W0.5Ta0.5B) to flux ratio of 250:1, 50:1 and 10:1.

Not only can the crystallite size of the nanowires be controlled by varying the flux ratio, but the morphology of the superhard nanocrystallites can be controlled by altering the flux to monoboride loading ratio as observed through SEM analysis. At a high flux to monoboride ratio of 250:1, the low nucleation density results in large crystallites (Figure 17A). As the loading ratio is lowered to 50:1, the resulting product grows into nanowires (Figure 17B), with the width of the nanowires as low as 500 nm. Finally, as the loading ratio is further lowered to 10:1, the resulting product grows into nanorods (Figure 17C), with the width of the nanorods roughly 100 nm. This morphology results from the low loading ratio and is consistent with classical nucleation theory and nucleation site density.

To elucidate the growth direction of these nanowires, we performed high resolution

3 3 TEM. Unfortunately, W0.5Ta0.5B (14.97 g/cm ) is even denser than lead (11.34 g/cm ), and we were only able to obtain a few selected area electron diffraction images on the thinnest nanowires. To account for the low transmission of electrons, we performed convergent beam electron diffraction (CBED). The CBED patterns allowed us to gauge the orientation of the nanowires similar in thickness to the ones observed in SEM. From the TEM images (Figure 18), we were able to determine that the nanowires grow along the (002) direction, which is parallel to the boron-boron chains (Figure 19). It is fortuitous that these nanowires grow along the boron- boron chains, as the directionality of the covalent bonds in turn prevents shear11.

It is interesting to speculate on the growth mechanism of these superhard nanowires.

W0.5Ta0.5B crystallizes in the same crystal structure as high temperature orthorhombic WB. High temperature tungsten monoboride can be best described as tungsten metal bilayers separated by parallel boron chains. As this is a highly anisotropic structure, one would expect to find a defined crystal habit. One can draw an analogy to the crystal habits found in silicates. Sheet silicates

2n- (such as mica) possess a crystal structure comprised of [Si2nO5n] layers, while silicates that grow as fibers (such as asbestos) possess a crystal structure comprised of linear chains of

2n- [SinO3n] . This is a result of periodic bond chain theory, where growth is favored along directions where bonding is the strongest. With tungsten-tantalum monoborides, the crystal habit will prefer an elongated fibrous structure along the strong covalent boron-boron chains (Figure

19).

Figure 17: Scanning electron microscopy images of samples prepared using an aluminum flux to metal boride (W0.5Ta0.5B) ratio of

(A) 250:1, (B) 50:1, and (C) 10: 1. Note the drastic reduction in size and change in morphology resulting from altering the flux to monoboride ratio.

Indeed, flux growth by Okada et al.12 of low temperature tetragonal tungsten monoboride, where the boron chains alternate layers in a perpendicular fashion, yielded a crystal habit of flattened squares which confirms that the growth of the boron chains is crucial to the resulting crystal shape. Interestingly, there seems to be some self-assembly of the nanowires

(Figure 20) found in the 50:1 sample. We note that several of the nanowires begin to fuse to form 2-D plates which is indicative of hierarchical assembly. Indeed, the assembly of these nanowires resemble that of polymer self-assembly13. From the SEM images, there is clear evidence for 1-D nanowires, oriented 1-D nanowires, and 2-D sheets. We anticipate that if the growth were allowed to continue, we would expect to see morphologies similar to that found in of the 250:1 flux to monoboride sample.

Conclusions

Superhard metal nanowires have been grown for the first time in bulk. Careful control of the flux to monoboride ratio yields highly crystalline W0.5Ta0.5B nanostructures. The aspect ratio and size of these nanowires can be controlled by modifying the flux to metal boride ratio. This falls in line with classical nucleation theory, where more concentrated solutions lead to more nucleation sites (and thus, smaller nanowires approaching nanorods). From the CBED pattern, the nanowires are found to grow along the c-axis (along the boron chains), as expected from periodic bond chain theory. Interestingly, these nanowires exhibit hierarchical assembly, where some nanowires are observed to fuse into 2-D plates. These superhard nanowires may find exciting applications in composites where both electrical conductivity and mechanical robustness are required.

Figure 18: TEM images of superhard nanowires prepared from a 10:1 ratio. The convergent beam electron diffraction indicates that the nanowires are highly crystalline and grow along the boron-boron chains, i.e. the (002) direction.

Figure 19: The crystal structure of W0.5Ta0.5B is isostructural with TaB and comprised of parallel linear boron chains (blue) separated by tungsten bilayers (gray). The lattice is orthorhombic, Cmcm5. The bonding of boron appears to be responsible for the growth mechanism of the W0.5Ta0.5B nanowires.

Figure 20: A Scanning electron microscopy image of superhard metal nanowires shows evidence for hierarchical assembly.

89 References

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9262.

91 Chapter 6

The surface area of a material can dramatically affect its chemical reactivity. A classic example is the noble metal platinum: in bulk, platinum has superior oxidation resistance, but when ground to a very fine powder, it will actually combust in air.1 Furthermore, through greater exposure of platinum’s active sites, the melting point, and catalytic rate can also be optimized.2–4

Typically, such high surface area is achieved through changing morphology by controlling the size and shape of the material. Templating is another common bottom-up method to increase surface area by creating mesopores.5,6 Likewise, top-down procedures such as synthesizing nanostructures have also demonstrated increased surface area.7–9

Unfortunately, morphological control often creates a high density of grain boundaries.

The resulting loss of crystallinity is detrimental to electronic properties as grain boundary scattering soon becomes the limiting step.10,11 This has led to the development of new crystalline materials where the surface area comes not from the morphology, but rather from the arrangement of the unit cells and polyhedra. This approach has led to many materials with record-breaking surface areas.12 However, these materials are relatively fragile, as they are either electrically insulating, water- and air-sensitive, and/or difficult to synthesize.13,14 Therefore, there is a need for novel materials that can provide internal surface area along with durability and electrical conductivity.

Tungsten trioxide (WO3) is an ideal model material because it crystallizes into several distinct structures, most notably the monoclinic WO3 (m-WO3) and hexagonal WO3 (h-WO3)

Figure 21 The crystal structures of WO3. (a) h-WO3 and (b) m-WO3 projected along the (001) direction.

93 polymorphs. Both h-WO3 and m-WO3 consist of WO6 octahedra, but differ in the arrangement of their octahedra. In h-WO3, WO6 octahedra are arranged in a six-membered ring by sharing corner oxygens along the (001) plane. This forms rigid tunnels along the c-axis throughout the entire unit cell. The diameter can be estimated by measuring the distance between two oxygen atoms as shown in Figure 21a. After subtracting the covalent radius of oxygen, the theoretical intracrystalline tunnel size is 3.9 Å. In contrast, the WO6 octahedra in m-WO3 arrange themselves into corner sharing octahedra, similar to a distorted ReO3 structure. While h-WO3 has great potential, aside from its synthesis, a full characterization demonstrating the accessibility of the internal surface area has not yet been reported. Furthermore, because h-WO3 is chemically similar to m-WO3, but differs by possessing a periodic microporous structure, a direct comparison can be made leading to an understanding of the role of intracrystalline tunnels in reactivity.

Here, we have rigorously studied the porosity in h-WO3 using transmission electron microscopy (TEM) to image pores, CO2 adsorption to measure surface area, and inductively coupled plasma-optical emission spectroscopy (ICP-OES) to probe ion selectivity. Additionally, we demonstrate a useful application of the internal surface area of h-WO3 as a pseudocapacitive electrode. In essence, we show that high surface area can be achieved in highly crystalline hexagonal WO3 from exposing the internal structure.

15 The h-WO3 was synthesized by a hydrothermal reaction following Gerand et al. and m-

WO3 was used as received from Sigma-Aldrich. The h-WO3 was then washed with HNO3 to remove the sodium ions from within its tunnels. This result is supported by ICP-OES, where no

Na in the h-WO3 is detected after acid washing, while before acid washing the h-WO3 holds

94 0.449 w.t.% of Na. Powder X-ray diffraction (PXRD) confirmed the synthesis of highly crystalline, phase pure h-WO3 (Figure 22a).

Figure 22 Characterization of h-WO3. (a) Powder X-ray diffraction pattern of h-WO3 before (black line) and after (red line) ion exchange. (b) TEM images of h-WO3 with SEAD pattern inset, and (c) zoomed in part enclosed by red dash line. (d) Low pressure CO2 adsorption isotherms at 273 K and (e) calculated pore size distributions.

96 In order to characterize the intracrystalline tunnels in h-WO3, we performed TEM with selected area electron diffraction (SAED). As shown in the TEM image in Figure 22b, the reflection indexes to the projection along the (001) axis, corresponding to the SAED pattern shown in the inset of Figure 22b. The SAED pattern depicts a highly crystalline hexagonal pattern without Debye rings. Furthermore, the zoomed-in atomic structure is clarified in Figure

22c, and the periodic unit cell corresponds to the lattice-like molecular structure in Figure 21a.

This suggests that the tunnel structure of h-WO3 is indeed periodic. Further characterizations of h-WO3 and m-WO3 are presented in the supporting information.

To further elucidate the size of the intracrystalline tunnels in h-WO3, low-pressure CO2 adsorption isotherms have been conducted at 273 K for both h-WO3 and m-WO3. The micropore analysis is based on a non-local density functional theory (NLDFT) model. As shown in Figure

22d, the CO2 adsorption isotherm of h-WO3 shows a large uptake at low relative pressure, indicating the presence of ultramicro-sized tunnels. The pore size distribution calculated from

2 NLDFT is shown in Figure 22e. The total surface area for h-WO3 is 46.585 m /g, where only

22.560 m2/g comes from pores bigger than 10.48 Å. Clearly, the majority of the surface area comes from the intracrystalline tunnels. The h-WO3 shows a maxima pore peak at 3.67 Å, which agrees reasonably well with the approximation of the tunnel diameter of 3.9 Å determined from the crystal structure. In contrast, m-WO3 shows a linear isotherm curve (Figure 22d), which suggests the lack of micropores. Moreover, there is no distinguishable porosity under 1 nm

2 (Figure 22e). NLDFT calculations suggest that m-WO3 has only 18.045 m /g of surface area.

Interestingly, no intracrystalline tunnels were detected for h-WO3 by N2 adsorption isotherms

(Figure 23).

Figure 23 (a) N2 adsorption isotherm of h-WO3 and m-WO3 at 77 K. (b) Pore size distributions of h-WO3 and m-WO3 were calculated based on the Barret-Joyner-Halenda (BJH) equation. The smallest pore sizes for h-WO3 and m-WO3 are 13.0 Å and 11.4 Å, respectively. The Brunauer-

2 -1 2 -1 Emmett-Teller (BET) surface area for h-WO3 and m-WO3 are 8.1187 m g and 5.7336 m g , respectively. BET surface areas were calculated from the isotherm data P/P0 between 0.05~0.3, using the BET equation.

98 In regard to a potential application as a pseudocapacitor, the accessibility of different electrolytes into the intracrystalline tunnels has been tested by thermal gravimetric analysis

(TGA) and ICP-OES in Figure 24 and Table 1, respectively. The h-WO3 was soaked in 1.0 M

H2SO4, then dried at 80 °C in an oven. TGA was then carried out on the dried sample. There is a continual weight loss up to 200 °C as shown in Figure 24, resulting in a drop of 1.7 w.t.%. In contrast, m-WO3 (which has no tunnels) was subjected to the same conditions, and it lost around

0.6 w.t.%. The ratio of water loss between h-WO3 and m-WO3 is 2.8:1, which agrees with the surface area ratio (from CO2 adsorption isotherm and NLDFT calculations). This difference in water loss supports the assumption that intracrystalline tunnels in h-WO3 are accessible to the aqueous electrolyte. The ICP-OES results will be discussed later.

The surface area indicated by the CO2 adsorption, while highly suggestive of an internal intracrystalline tunnel structure, is low. Indeed, oxides known for their high surface area – the

12 zeolites – possess surface areas of roughly 20 times higher than h-WO3. However, unlike the electrically insulating zeolites, h-WO3 is sufficiently conductive to perform favorably in electrical energy storage devices,16,17 known as pseudocapacitors.

A pseudocapacitor can be simply described as a hybrid between a redox battery and an electrochemcial double layer capacitor.18 Because of this synergy, pseudocapacitors possess unique advantages over their parent devices. When compared to conventional batteries, they exhibit both higher power from shorter ion diffusion lengths and longer cycle life.5,19 By functioning through fast Faradaic reactions, pseudocapacitors can possess up to ten times higher energy density when compared to electrochemical double layer capacitors.20 These capacitors rely on a high surface area for faster ion kinetics, and this is often achieved by nanostructuring to greatly increase the number of redox active sites. However, high surface area does not always

Figure 24 Thermogravimetric analysis (TGA) of h-WO3 (red line) and m-WO3 (black line) taken in argon at a heating rate of 1 °C /min. Before the TGA run, h-WO3 and m-WO3 were each soaked in 1.0 M H2SO4 for 1 hour, washed by DI water, then dried at 80 °C in an oven for 12 hours.

100 lead to high capacitance because the resulting reduction in crystallinity leads to low electrical

21-26 conductivity. Thus, h-WO3 is an excellent candidate for pseudocapacitive studies.

A series of electrochemical experiments were carried out which demonstrate that the structure defined surface area facilitates h-WO3 in reaching a high specific capacitance. In order to test the intrinsic electrochemical properties in h-WO3 without blocking the tunnels, h-WO3 was homogeneously mixed with functionalized single-wall carbon nanotubes (SWCNTs). The mixture of h-WO3/SWCNTs shows a conductivity as high as 26,490 S/m, comparable to the

35,000 S/m reported for a pure CNT film.27

Cyclic voltammetry (CV) was performed in a three-electrode configuration with various aqueous electrolytes. In 1.0 M H2SO4, the readily distinguishable pair (labeled e and e’) and the broad pair (labeled f and f’) of oxidation and reduction peaks of h-WO3/SWCNTs suggest the following reactions [1] and [2]:

[1]

[2]

The electrochemical reactions occurring for h-WO3 can be rationalized as the insertion and removal of hydrated protons. As a comparison, m-WO3/SWCNTs shows two pairs of oxidation peaks and two reduction peaks with relatively poor pseudocapacitive behavior. Similar to a previous report,21 these peaks can be defined as two states of the intercalation reaction [3]:

[3]

101 The presence of the open and rigid intracrystalline tunnels in h-WO3 facilitates electrolyte infiltration and allows protons to transport through the tunnels, which is vital for the effective utilization of every unit cell of WO3 for electron storage. The insertion/removal reaction does not lead to any change in crystallographic phase as confirmed by powder X-ray diffraction patterns of h-WO3/SWCNTs in both charged and discharged states (Figure 25). Since there is no discernable difference in phase between charged and discharged electrodes, this suggests that the crystal structure is maintained throughout the electrochemical reaction. Therefore, the hexagonal structure is extremely robust. The hexagonal WO3 that we have developed reaches a specific capacitance as high as 510 F/g, while the specific capacitance of m-WO3 is only 232 F/g, which

23 matches previously published results on m-WO3. As can be seen in Figure 26, the volumetric

3 capacitance of h-WO3/SWCNTs reaches 490.2 F/cm at 2 mV/s, which is superior to most

26 carbon-based supercapacitors . This suggests that h-WO3 possesses significantly more active sites from the intracrystalline tunnels. Meanwhile, the h-WO3/SWCNTs before acid washing shows a similar CV curve at lower current density (Figure 27), which suggests after removing

Na+ ions in the tunnels, more active sites are getting involved in the electrochemical reactions.

More accessible active sites results in higher energy storage.

Since h-WO3 shows higher specific capacitance than m-WO3 in 1.0 M H2SO4, we explored other electrolytes with larger alkali ions. Figure 28b and 28c present the CV curves of h-WO3/SWCNTs and m-WO3/SWCNTs in 1.0 M Li2SO4 and 1.0 M Na2SO4 aqueous solutions at 2 mV/s, respectively. Considering the rectangular shape and absence of a phase change according to powder X-ray diffraction (Figure 25) for h-WO3/SWCNTs in both charged and discharged states, the electrochemical reaction for h-WO3 can be defined as electroadsorption

[4]; [4]

102

Figure 25 Ex situ powder X-ray diffraction of h-WO3/SWCNTs electrode fully discharged (red line) and charged (black line) in a 1.0 M Li2SO4 aqueous solution. No change in crystal structure is observed.

103

Figure 26 Volumetric capacitance of h-WO3/SWCNTs and m-WO3/SWCNTs calculated at different scan rates.

104

Figure 27 Cyclic voltammograms (CV) of h-WO3/SWCNTs before and after acid washing in 1.0 M

H2SO4 aqueous electrolyte at 2 mV/s.

105

Figure 28 Electrochemistry characterizations. Cyclic voltammograms (CV) of h-WO3/SWCNTs and m-WO3/SWCNTs at 2 mV/s in (a) H2SO4, (b) Li2SO4 and (c) Na2SO4.

106 As for m-WO3, the electrochemical reaction in an Li2SO4 aqueous electrolyte is intercalation [5]:

[5]

Surprisingly, by simply switching the electrolyte from Li2SO4 to Na2SO4, h-

WO3/SWCNTs shows two peaks similar to m-WO3/SWCNTs. The electrochemical behavior of

+ h-WO3/SWCNTs with sodium ions implies that due to their large size, Na cannot traverse through the intracrystalline tunnels (Table 1). By comparison, m-WO3/SWCNT in Li2SO4 shows two pronounced peaks for oxidation and reduction, respectively, similar to its curves in H2SO4 and Na2SO4. To confirm that size constrains different electrolytes, h-WO3 and m-WO3 were soaked in different aqueous alkali solutions, then analyzed with ICP-OES. As shown in Table 1, h-WO3 holds over 1000 times more Li than m-WO3. However, h-WO3 only has about 10 times the content of Na compared to m-WO3. The ICP-OES data suggest that the intracrystalline

+ + tunnels in h-WO3 are freely accessible to Li , but not to Na . According to previous molecular dynamic simulations for ion transfer through narrow pores, the energy barriers for ion transfer are mainly determined by the partial dehydration, pore size, ion type, and pore surface charge.29

+ All these suggest that h-WO3 with intracrystalline tunnels shows free transport for H , high adsorption for Li+, and no distinguishable adsorption for Na+ in aqueous electrolytes.

Due to the limitations of reduced ion penetrability, it is not possible for most microporous supercapacitors to maintain high capacitance at high scan rates, especially for ill-defined,

30 randomly distributed porous structures. The h-WO3 was therefore cycled under various scan speeds to see if the structure-defined surface area is still accessible at faster scan rates. Figure 29 shows h-WO3/SWCNTs in 1.0 M H2SO4 run at different scan rates, resulting in highly

107

Figure 29 Cyclic voltammograms (CV) of h-WO3/SWCNTs in 1.0 M H2SO4 aqueous electrolyte at different scan rates.

108 Table 1 Alkali Concentrations in WO3 via ICP-OES

Samples w.t. % Li w.t. % Na

h-WO3* 0.104

m-WO3* 0.001

h-WO3§ 0.870

m-WO3§ 0.082

*Before running ICP-OES, h-WO3 and m-WO3 were soaked into 1.0 M Li2SO4 electrolyte for 3 hours, and then washed with DI water 6 times.

§Before running ICP-OES, h-WO3 and m-WO3 were soaked into 1.0 M Na2SO4 electrolyte for 3 hours, then washed with DI water 6 times.

109 symmetric curves, suggesting a completely reversible redox reaction, and the sharply polarized curves at the offsets indicate high conductivity.

In order to test the durability of the intracrystalline tunnels of h-WO3 during charge/discharge, cycling stability was tested in a 1.0 M H2SO4 aqueous solution at 10 mV/s. As can be seen in Figure 30a, h-WO3/SWCNTs maintains 87 percent of capacitance after 5,000 cycles, which is superior to the 79 percent for m-WO3/SWCNTs. The powder X-ray diffraction pattern in Figure 30b shows that h-WO3/SWCNTs after 5,000 cycles does not undergo a phase change. Since no phase change occurs either before or after charging (Figure 25), h-WO3 is able to maintain its structure. As can be seen in Figure 31, h-WO3/SWCNTs shows a higher specific capacitance than m-WO3/SWCNTs across all scan rates, with reasonable capacitance (216 F/g) even at a high scan rate (50 mV/s). According to the electrochemical impedance spectrum (EIS)

(Figure 32), h-WO3/SWCNTs possesses a lower resistance to electrochemical reactions compared to m-WO3/SWCNTs, consistent with more active sites in h-WO3 being exposed to electrolyte.

In conclusion, we have rigorously studied the 3.67 Å intracrystalline tunnels of h-WO3 by

CO2 low pressure isotherms and non-local density functional theory. This internal surface area is accessible to both CO2 and electrolytes, the latter demonstrated by constructing a device with the

24 highest known capacitance (510 F/g) reported for WO3 to date . Moreover, ultra-microsized tunnels could find interesting applications, such as in the selective adsorption of Li+ vs. Na+ in aqueous solution and more accessible electrochemical active sites for electron storage. This work demonstrates that through exposing intracrystalline active sites, high surface areas can be achieved with potential implications for scalable applications for pseudocapacitors, selective ion transfer and selective gas adsorption.

110

Figure 30 (a) Cycle performance of h-WO3/SWCNTs and m-WO3/SWCNTs at 10 mV/s in H2SO4.

(b) Powder X-ray diffraction of h-WO3/SWCNTs electrode after 5,000 cycles in 1.0 M H2SO4 aqueous electrolyte at 10 mV/s in a three-electrode configuration.

111

Figure 31 (a) Specific capacitance of h-WO3/SWCNTs and m-WO3/SWCNTs at different scan rates. (b) Specific capacitance of h-WO3, m-WO3 and SWCNTs at different scan rates.

112

Figure 32 Nyquist plot of h-WO3/SWCNTs and m-WO3/SWCNTs at -0.12 V vs. Ag/AgCl from

10 mHz to 20 kHz in a three-electrode configuration, respectively.

113 METHODS

Synthesis of h-WO3. In an ice bath, 30 mL of 0.1 M Na2WO4 was cooled to <4 °C for 10 minutes. Then, 4 mL of 3.0 M hydrochloric acid was added dropwise into the Na2WO4 solution with constant magnetic stirring for 1 hour to form a white gel. The precipitates were washed with distilled (DI) water until the supernatant reached a pH of 4. The washed precipitates were dispersed in 20 mL of water, and the mixture was transferred into a 22 mL Teflon-lined stainless steel autoclave. The autoclave was heated to 100-150 °C for 20-24 hours. After cooling to room temperature, the mixture was centrifuged to recover the precipitates. After drying at 80 °C for 6 hours, the product was annealed at 330 °C in air for 3 hours. The annealed precipitates were immersed into 20 mL in 3.0 M HNO3 and refluxed at 80 °C for 3 days. Finally, the h-WO3 was collected by filtration, washed several times with DI water and dried.

Functionalization of Single Wall Carbon Nanotubes (SWCNT). Pristine single walled carbon nanotubes (P2 from Carbon Solution Inc.) were refluxed in 6.0 M HNO3 at 120 °C for 3 h to remove the metal catalyst impurities and anchored oxygenated functional groups. The oxidized SWCNTs were thoroughly washed with distilled water and dried in an oven at 60 °C.

Reparation of WO3/SWCNTs Films. Functionalized carbon nanotubes as prepared were sonicated in a bath sonicator (B2500A-DTH, VMR) with WO3 at a 1:1 weight ratio in ethanol for 2 hours to create a homogeneous dispersion. The as-prepared suspension was filtered through an alumina filtration membrane (200 nm pore size from Whatman). After filtration, a film formed that could be readily peeled off from the filtration membrane. The filtrated membrane was cut into 1×1 cm2 pieces, and the mass of each film was determined using a microbalance. A typical mass loading of a 1×1 cm2 film with thickness around 10 m was 2 mg.

114 Characterization. The X-ray diffraction patterns were collected on a powder X-ray diffractometer (PANalytical, X’Pertpro) with Cu Kα radiation (λ = 1.54184 Å). The morphology was investigated using a field-emission electron microscope (JEOL 7001) and a transmission electron microscope (Gatan Tecnai TF20 TEM). Element contents were measured using an

Inductively Coupled Plasma Optical Emission Spectrometer (Optima 4300DV). X-ray photoelectron spectroscopy data were collected with a Kratos AXIS Ultra DLD spectrometer using a monochromatic Al Kα X-ray source (hυ = 1486.6 eV). CO2 adsorption isotherms were measured at 273 K, while N2 adsorption isotherms were taken at 77 K on a TriStar volumetric adsorption analyzer (Micromeritics). The isotherm fitting and pore size distributions were calculated using NLDFT provided by Micromeritics. Thermogravimetric analysis (TGA) was recorded on a thermogravimetric/differential thermal analyzer (Perkin Elmer TGA Pyris 1) by heating the samples from room temperature to 500 °C at a rate of 1 °C/min in an argon atmosphere. Raman spectra were acquired with a Microscope Raman Spectrometer (Renishaw

1000), using a 633 nm laser as the excitation source in backscattering mode. Cyclic voltammetry and charge-discharge measurements were carried out using a potentiostat (Versa STAT3 from

Princeton Applied Resarch) and electrochemical impedance spectra were recorded using a potentiostat (Bio-Logic VMP3) by applying an ac signal of 10 mV amplitude over the frequency range 10 mHz to 20 kHz at 0.12 V vs. Ag/AgCl. The resistances of the WO3/SWCNTs films were measured using a two-point probe setup by painting two silver lines of 1 cm in length and 1 cm in distance onto the surface. The specific capacitance of the electrode can be calculated

according to the following equation: , where I is corresponding current density (A*cm-

2), V is the potential (V), ν is the potential scan rate (mV*s-1) and m is the mass of the

WO3/SWCNTs composite (g). The specific capacitance can be calculated according to the

115 following equation: , where m is mass of WO3/SWCNTs composite

(g), C is the specific capacitance of WO3/SWCNTs composite (F/g), CSWCNTs is the specific capacitance of SWCNTs (F/g).

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118 Conclusions/Future Work

The search for new superhard metals can thus take one of two routes. The first method is the development of new crystal structures following the design rules I discussed earlier. While it would be extremely gratifying to discover a new crystal structure, it is difficult coming up with something that Nature has not already thought of. The second method is to build upon what

Nature has provided. This requires a thorough understanding of what has made previous structures mechanically strong. In the end, it is more fruitful to modify known materials than to discover new structures simply because it is easier to design materials for applications rather than searching for applications for newly discovered materials.

Thus, the field of superhard metals should venture towards already known structures.

While this may seem restrictive, there are several untrodden paths. First is the development of dodecaborides. As the parent structure of many of the higher borides, they should possess high covalency despite their higher boron content. Furthermore, they maximize metal-boron bonds, and thus can support high strain. Beyond crystal structures, extrinsic hardening routes are yet to be explored. These superhard materials are metals and thus may be susceptible to the hardening mechanisms found in steels: i.e. grain refining, precipitation hardening, strain hardening, and diffusionless transformations.

119