CONTENTS

1. Cover
2. Title page
3. Copyright page
4. Dedication page
5. Acknowledgments
6. Contributors List
7. 1 Introduction
   1. 1.1 Background
   2. 1.2 Ultra-High Temperature Ceramics
   3. 1.3 Description of Contents
   4. References
8. 2 A Historical Perspective on Research Related to Ultra-High Temperature Ceramics
   1. 2.1 Ultra-High Temperature Ceramics
   2. 2.2 Historic Research
   3. 2.3 Initial NASA Studies
   4. 2.4 Research Funded by the Air Force Materials Laboratory
   5. 2.5 Summary
   6. Acknowledgments
   7. References
9. 3 Reactive Processes for Diboride-Based Ultra-High Temperature Ceramics
   1. 3.1 Introduction
   2. 3.2 Reactive Processes for the Synthesis of Diboride Powders
   3. 3.3 Reactive Processes for Oxygen Removing during Sintering
   4. 3.4 Reactive Sintering Processes
   5. 3.5 Summary
   6. References
10. 4 First-Principles Investigation on the Chemical Bonding and Intrinsic Elastic Properties of Transition Metal Diborides TMB2 (TM=Zr, Hf, Nb, Ta, and Y)
    1. 4.1 Introduction
    2. 4.2 Calculation Methods
    3. 4.3 Results and Discussion
    4. 4.4 Conclusion Remarks
    5. Acknowledgment
    6. References
11. 5 Near-Net-Shaping of Ultra-High Temperature Ceramics
    1. 5.1 Introduction
    2. 5.2 Understanding Colloidal Systems: Interparticle Forces
    3. 5.3 Near-Net-Shape Colloidal Processing Techniques
    4. 5.4 Summary, Recommendations, and Path Forward
    5. Acknowledgments
    6. References
12. 6 Sintering and Densification Mechanisms of Ultra-High Temperature Ceramics
    1. 6.1 Introduction
    2. 6.2 MB₂ with Metals
    3. 6.3 MB₂ with Nitrides
    4. 6.4 MB₂ with Metal Disilicides
    5. 6.5 MB₂ with Carbon or Carbides
    6. 6.6 MB₂ with SiC
    7. 6.7 MB₂–SiC Composites with Third Phases
    8. 6.8 Effects of Sintering Aids on High-Temperature Stability
    9. 6.9 Transition Metal Carbides
    10. 6.10 Conclusions
    11. Acknowledgments
    12. References
13. 7 UHTC Composites for Hypersonic Applications
    1. 7.1 Introduction
    2. 7.2 Preparation of Continuous-Fiber-Reinforced UHTC Composites
    3. 7.3 UHTC Coatings
    4. 7.4 Short-Fiber-Reinforced UHTC Composites
    5. 7.5 Hybrid UHTC Composites
    6. 7.6 Summary and Future Prospects
    7. References
14. 8 Mechanical Properties of Zirconium-Diboride Based UHTCs
    1. 8.1 Introduction
    2. 8.2 Room Temperature Mechanical Properties
    3. 8.3 Elevated-Temperature Mechanical Properties
    4. 8.4 Concluding Remarks
    5. References
15. 9 Thermal Conductivity of ZrB₂ and HfB₂
    1. 9.1 Introduction
    2. 9.2 Conductivity of ZrB₂ and HfB₂
    3. 9.3 ZrB₂ and HfB₂ Composites
    4. 9.4 Electron and Phonon Contributions to Thermal Conductivity
    5. 9.5 Concluding Remarks
    6. References
16. 10 Deformation and Hardness of UHTCs as a Function of Temperature
    1. 10.1 Introduction
    2. 10.2 Elastic Properties
    3. 10.3 Hardness
    4. 10.4 Hardness and Yield Strength
    5. 10.5 Deformation Mechanism Maps
    6. 10.6 Lattice Resistance to Dislocation Glide
    7. 10.7 Dislocation Glide Controlled by Other Obstacles
    8. 10.8 Deformation by Creep
    9. 10.9 Deformation of Carbides versus Borides
    10. 10.10 Conclusions
    11. References
17. 11 Modeling and Evaluating the Environmental Degradation of UHTCs under Hypersonic Flow
    1. 11.1 Introduction
    2. 11.2 Oxidation Modeling
    3. 11.3 UHTC Behavior under Simulated Hypersonic Conditions
    4. 11.4 Comparing Model Predictions to Leading-Edge Behavior
    5. 11.5 Behavior of UHTCs under Other Test Methods
    6. 11.6 Summary
    7. References
18. 12 Tantalum Carbides: Their Microstructures and Deformation Behavior
    1. 12.1 Crystallography of Tantalum Carbides
    2. 12.2 Microstructures of Tantalum Carbides
    3. 12.3 Mechanical Properties of Tantalum Carbides
    4. 12.4 Summary
    5. Acknowledgments
    6. References
19. 13 Titanium Diboride
    1. 13.1 Introduction
    2. 13.2 Phase Diagram, Crystal Structure, and Bonding
    3. 13.3 Synthesis of Titanium Diboride Powders
    4. 13.4 Densification of Transition Metal Borides
    5. 13.5 Mechanical Properties at Ambient and Elevated Temperatures
    6. 13.6 Physical Properties and Oxidation Resistance
    7. 13.7 Oxidation Resistance
    8. 13.8 Tribological Properties
    9. 13.9 Applications of TiB₂
    10. 13.10 Conclusions
    11. References
20. 14 The Group IV Carbides and Nitrides
    1. 14.1 Background
    2. 14.2 Group IV Carbides
    3. 14.3 Preparation and Processing
    4. 14.4 Mechanical and Physical Properties
    5. 14.5 Oxidation of the UHTC Carbides and Nitrides
    6. 14.6 Oxidation of the UHTC Carbides
    7. 14.7 UHTC Nitrides
    8. 14.8 Preparation, Diffusion, and Phase Formation
    9. 14.9 Mechanical and Physical Properties
    10. 14.10 Oxidation of Nitrides
    11. 14.11 Conclusions and Future Research
    12. Acknowledgments
    13. References
21. 15 Nuclear Applications for Ultra-High Temperature Ceramics and MAX Phases
    1. 15.1 Future Nuclear Reactors
    2. 15.2 Current Nuclear Ceramics
    3. 15.3 Future Nuclear Ceramics
    4. 15.4 Non-Oxide Nuclear Fuels
    5. 15.5 Other Possible Future Fission and Fusion Applications
    6. 15.6 Thermodynamics of Nuclear Systems
    7. 15.7 Conclusions
    8. References
22. 16 UHTC-Based Hot Structures
    1. 16.1 Introduction
    2. 16.2 TPS: Test Articles and Prototypes
    3. 16.3 Plasma Tests of Nose Test Articles
    4. 16.4 Expert Project: Computational Fluid Dynamics Computations and Plasma Tests
    5. 16.5 In-Fling Testing of the Capsule “SHARK”
    6. 16.6 Future Work
    7. References
23. Index
24. End User License Agreement

List of Tables

1. Chapter 02
   1. Table 2.1. Selected recommendations for future research and development activities related to UHTCs from Reference [10]
   2. Table 2.2. Compositions examined in the second series of studies by ManLabs [54]
   3. Table 2.3. Summary of compositions studied for the third series of ManLabs projects
2. Chapter 03
   1. Table 3.1.  Thermodynamics of the main reactions including the temperatures at which the reactions become favorable at standard state and under mild vacuum
3. Chapter 04
   1. Table 4.1. Lattice constants and bond lengths of TMB₂
   2. Table 4.2. Second-order elastic constants (c_ij) and bulk modulus B, Young's modulus E, shear modulus G of TMB₂ (TM = Y, Zr, Hf, Nb, and Ta)
4. Chapter 05
   1. Table 5.1 Influence of surface forces on suspension behavior
   2. Table 5.2 Isoelectric point (IEP) of most commonly used UHTCs and other relevant powders
5. Chapter 06
   1. Table 6.1. Sintering agents and corresponding hot pressing temperature ranges (T_MAX) for ZrB₂ and HfB₂
   2. Table 6.2. MB₂–MeSi₂ composites reached specific final relative density (rd) using different amounts of MeSi₂, sintering techniques (Tech), and peak temperatures (T_MAX)
   3. Table 6.3. ZrB₂–SiC_W and ZrB₂–SiC_F composites (W: whisker, F: fiber) sintered by hot pressing (HP) using different sintering aids (s.a): peak temperature (T_MAX), and final relative density (rd)
   4. Table 6.4. ZrB₂–xSiC_P composites (P: particulates) densified by HP, SPS, or PS using different sintering aids (s.a): peak temperature (T_MAX), and final relative density (rd)
   5. Table 6.5. Literature overview of sintering techniques (Tech), parameters, and additives adopted for sintering of MC-composites
6. Chapter 08
   1. Table 8.1. Elastic modulus, Vickers hardness, fracture toughness by direct crack method, and four-point flexure strength of ZrB₂ ceramics with and without sintering additives
   2. Table 8.2. Summary of various fitted models of elastic modulus as a function of porosity for ZrB₂
   3. Table 8.3. Elastic modulus, Vickers hardness, fracture toughness by direct crack method, and four-point flexure strength of ZrB₂–SiC ceramics
   4. Table 8.4. Elastic modulus, Vickers hardness, fracture toughness by direct crack method, and four-point flexure strength of ZrB₂–SiC ceramics with various additives
   5. Table 8.5. Elastic modulus, Vickers hardness, fracture toughness by direct crack method, and four-point flexure strength of ZrB₂–(Zr, Mo, Ta)Si₂ ceramics
7. Chapter 09
   1. Table 9.1. Thermal conductivity of pure ZrB₂ with information on starting/final materials, processing, and density.
   2. Table 9.2. Summary of solid solution effects on thermal conductivity of ZrB₂
   3. Table 9.3. Thermal conductivity of pure HfB₂ with information on starting/final materials, processing, and density
   4. Table 9.4. Thermal conductivity of ZrB₂-SiC with information on starting/final materials, processing, and density
   5. Table 9.5. Thermal conductivity of two-phase ZrB₂-based composites with information on starting/final materials, processing, and density
   6. Table 9.6. Thermal conductivity of three- and 4-phase ZrB₂-based composites with information on starting/final materials, processing, and density
   7. Table 9.7. Thermal conductivity of HfB₂–SiC with information on starting/final materials, processing, and density
   8. Table 9.8. Thermal conductivity of HfB₂-based composites with information on starting/final materials, processing, and density
8. Chapter 10
   1. Table 10.1. Elastic constants (C₁₁, C₁₂, and C₄₄) and elastic properties of UHTC carbides with the cubic rock salt structure (NaCl, Fm-3 m), with K as the bulk modulus and E_avg the average Young's modulus over all orientations
   2. Table 10.2. Elastic constants (C₁₁, C₁₂, and C₄₄) and elastic properties of UHTC nitrides with the cubic rock salt structure (NaCl, Fm-3 m), with K as the bulk modulus and E_avg the average Young's modulus over all orientations
   3. Table 10.3. Elastic constants and elastic properties of UHTC borides with the hexagonal structure (P6/mmm), with K as the bulk modulus and E_avg the average Young's modulus over all orientations
   4. Table 10.4. Rate of decay of the elastic modulus with temperature
   5. Table 10.5. Average shear modulus (G), Peierls stress (τ_p), activation energy (Q), slip planes, and Burgers vector (b) for UHTCs
   6. Table 10.6.  Parameters used to construct the deformation mechanism maps. Parameters for ZrB₂ from Ref. [63] and for ZrC from Ref. [62]. Where the treatment deviates from Ashby and Frost, parameters were adapted to get coincidence of the maps.
9. Chapter 12
   1. Table 12.1. Experimentally determined elastic constants of polycrystalline TaC
   2. Table 12.2. Cubic elastic constants and lattice constants of TaC single crystals obtained from experiments and simulation
10. Chapter 13
    1. Table 13.1. Basic physical, mechanical, and oxidation properties of TiB₂, as well as the other popular Ultra-High-temperature transition metal borides [1–4]
    2. Table 13.2. Summary of densification, microstructure, and mechanical properties of TiB₂ and other transition metal borides
    3. Table 13.3. Summary of variation of hardness with respect to temperature for TiB₂-based ceramics with different compositions and processing conditions
    4. Table 13.4. The effects of temperature on strength of TiB₂ and other transition metal diborides [4-point (4-P) and 3-point (3-P) flexural strength]
    5. Table 13.5. Summary of thermal conductivity as a function of temperature for TiB₂ ceramics
11. Chapter 14
    1. Table 14.1. Materials with melting temperatures above 3000°C
    2. Table 14.2. Selected eutectic temperatures (°C)
12. Chapter 15
    1. Table 15.1. The GIF reactor designs
    2. Table 15.2. Typical properties of some current nuclear ceramics
    3. Table 15.3. Typical properties of UHTCs
    4. Table 15.4. Typical properties of MAX phases
    5. Table 15.5. Properties of carbide and nitride fuels
13. Chapter 16
    1. Table 16.1. Thermomechanical and physical properties of ZrB₂ + 15 vol% SiC + 2 vol% MoSi₂ (ZS) and ZrB₂ + 10 vol% HfB₂ + 15 vol% SiC + 2 vol% MoSi₂ (ZHS) formulations [45]
    2. Table 16.2. Ceramic formulations and related densification processes: hot-pressing (HP) and pressureless sintering (PLS)
    3. Table 16.3. Thermomechanical properties of massive Si₃N₄ + 35 vol% MoSi₂ + 2.5 Y₂O₃ + 1 Al₂O₃ (RAY2535)
    4. Table 16.4. Thermomechanical properties of massive ZrB₂ + 15 vol% SiC + 10 vol% LaB₆ [59]
    5. Table 16.5. Experimental flow conditions during plasma test on the qualification model EXPERT PL15

List of Illustrations

1. Chapter 01
   1. Figure 1.1. Materials with the highest reported melting temperature grouped by material family.
2. Chapter 02
   1. Figure 2.1. Summary of types of thermal protection systems as a function of heat flux and exposure time from Reference [10].
   2. Figure 2.2. Strength as a function of temperature for several engineering materials along with a clearly defined Ultra-High temperature regime from Reference [20].
   3. Figure 2.3. Notional temperature requirements for orbital reentry vehicles based on projected wing loading and hypersonic lift-to-drag (L/D) ratio from Reference [41].
   4. Figure 2.4. Trajectories and methods for dealing with heat loads from Reference [41].
   5. Figure 2.5. Comparison of kinetic rate constants for the oxidation of ZrB₂ and HfB₂ as a function of temperature [45].
   6. Figure 2.6. Relative density as a function of sintering time for ZrB₂ with different B/Me ratios [53].
   7. Figure 2.7. Analysis of densification behavior of ZrB₂ (B/Me ratio = 1.89) as a function of densification temperature where t is sintering time and GS is grain size [53].
   8. Figure 2.8. Oxide-scale thickness as a function of oxidation temperature for HfB₂, SiC, and HfB₂ containing 20 vol% SiC based on data from Reference [55].
   9. Figure 2.9. Strength as a function of temperature for nominally pure ZrB₂ (Material I) [56].
   10. Figure 2.10. Strength as a function of SiC content in composition IV (HfB₂–SiC) [56].
   11. Figure 2.11. Thermal conductivity of composition I (nominally pure ZrB₂) as a function of temperature using two methods, cut bar for temperatures below 1000°C and thermal flash for temperature above 1000°C. The materials were nominally fully dense with a grain size of ~20 µm [57].
   12. Figure 2.12. Schematic of the system built for cold gas/hot wall testing at high gas velocities. The system consisted of an induction heater and high-velocity gas-handling unit [58].
   13. Figure 2.13. Schematic of the 10 MW Arc Splash Facility at AVCO [59].
   14. Figure 2.14. Summary of the results of furnace kinetic studies based on the recession of the parent material after 2 h. HfB₂ is always marginally better than the corresponding ZrB₂ composition. Carbides are not good at “moderate temperature, but extend temperature to higher values. JTA = graphite grade with ZrB₂ and Si additions. KT-SiC = Si-rich SiC (9 vol% free Si). SiO₂ + W = SiO₂ + 60 wt% W. JTO992 is C–HfC–SiC and JTO981 is C–ZrC–SiC [60].
   15. Figure 2.15. Schematic description of the temperature gradients observed across the oxide scales for specimens tested in (left) an arc plasma facility that uses hot gas, cold way, and high velocity; (center) conventional tube furnace with low velocity flow; and (right) inductively heated specimen in cold gas/hot wall/high velocity [61].
   16. Figure 2.16. Schematic with information about a model trajectory for a lifting body reentry vehicle showing stagnation pressure and enthalpy along with other information for a vehicle with a 3-in. leading-edge radius [61].
   17. Figure 2.17. Comparison of measured recession rates (points) as a function of heat flux and total enthalpy. Lines are shown for a calculated surface temperature of 6100°F (3300°C) under two different conditions. The plot also includes a line (– - –) showing the speed and altitude of a potential reentry trajectory [62].
   18. Figure 2.18. Schematic of the Pirani furnace used for melting point determinations [64].
   19. Figure 2.19. Comparison of melting temperature as a function of composition in the HfC–TaC system for data from Rudy [64] and Agte [65].
   20. Figure 2.20. Lattice parameter as a function of Ta to Ti ratio and carbon content for the TiC–TaC system [66].
   21. Figure 2.21. Liquidus project for the Zr–B–C ternary phase diagram [66].
3. Chapter 03
   1. Figure 3.1.  The life cycle of diboride-based ceramics.
   2. Figure 3.2.  Roadmap of the fabrication process of MeB₂ discussed in this chapter.
   3. Figure 3.3.  Standard free energy of reactions as a function of temperature [4].
   4. Figure 3.4.  TEM image of the submicrometer ZrB₂ powder by RWR [10].
   5. Figure 3.5.  Calculated vapor pressure of B₂O₃ as a function of temperature in the pressure range maintained in the sintering furnace [15].
   6. Figure 3.6.  Molar content of the products calculated by reactions between 3 mole MeC and 1 mole ZrO₂ as a function of the temperature at a vacuum level of 5 Pa: (a) WC, (b) VC, (c) NbC, (d) TiC,(e) TaC, and (f) HfC [28].
   7. Figure 3.7.  SEM images of indentation crack propagation in ZrB₂–SiC–WC ceramics by Zou et al. [29]
   8. Figure 3.8.  (a) The flexural strength of ZrB₂–SiC (ZS), ZrB₂–SiC–WC (ZSW), and ZrB₂–SiC–ZrC (ZSZ) as a function of testing temperature, (b) the load–displacement curves for ZS, ZSW, and ZSZ at 1600°C [35].
   9. Figure 3.9.  Microstructure formation mechanism of the ZrB₂–SiC composite in the reaction-synthesis process, depicting the transformation from (a) the powder compact to (b) the final microstructure of the composite [36].
   10. Figure 3.10.  Microstructure formation mechanism of ZrB₂–ZrC–SiC composites in the reaction-synthesis process, depicting conversion from (a) the powder compact to (b) the intermediate state, and (c) the final microstructure [37].
   11. Figure 3.11.  Backscattered electron images of the cross section of a typical ZrB₂-platelet-reinforced ZrC product taken approximately 2 mm from the top (a) and bottom (b) of a 12.7-mm-thick part. The darkest phase is ZrB₂, the gray phase is ZrC, and the lightest phase is zirconium metal [54].
   12. Figure 3.12.  ZrB₂ JCPDS 35-0741 reference (a) and XRD patterns of cross section (b) and sintered surface (c) surface of the PECS samples [43].
   13. Figure 3.13.  (a and b) TEM image of ZrB₂ platelet grains at different magnifications; (c) selected-area electron diffraction pattern of platelet grains of (b); (d and e) SEM images of polished surfaces before and after hot forging; (f and g) SEM images of fractured surface before and after hot forging [62].
4. Chapter 04
   1. Figure 4.1. Crystal structure of TMB_2.
   2. Figure 4.2. Pressure dependence of lattice constants a and c of TMB_2.
   3. Figure 4.3. Pressure dependence of TM–B and B–B bond lengths.
   4. Figure 4.4. Electron density difference maps on planes parallel to (0001) that are across Zr (a) and B (b) atoms, and on (1120) that is across both Zr and B atoms (c).
   5. Figure 4.5. Band structure of TMB₂: (a) YB₂, (b) ZrB₂, (c) HfB₂, (d) NbB₂, and (e) TaB₂.
   6. Figure 4.6. (a) Total and projected electronic density of states of YB₂, and decomposed charge density on (11 20) plane in the energy range from −10.6 to −7.1 eV (b), from −6.6 to −2.0 eV (c), from −4.3 to 0.45 eV (d), from −2.3 to 0.45 eV (e), and from −0.99 to 2.0 eV (f).
   7. Figure 4.7. (a) Total and projected electronic density of states of ZrB₂, and decomposed charge density on (11 20) plane in the energy range from −12.7 to −7.8 eV (b), from −8.7 to −3.1 eV (c), from −6.8 to −1.1 eV (d), from −4.1 to −1.1 eV (e), and from −2.7 to 0.6 eV (f), and from −0.03 to 4.0 eV (g).
   8. Figure 4.8. (a) Total and projected electronic density of states of HfB₂, and decomposed charge density on (11 20) plane in the energy range from −13.7 to −9.5 eV (b), from −9.4 to −4.1 eV (c), from −7.7 to −1.4 eV (d), from −4.8 to −1.4 eV (e), from −3.4 to 1.7 eV (f), and from −0.07 to 4.2 eV (g).
   9. Figure 4.9. (a) Total and projected electronic density of states of NbB₂, and decomposed charge density on (11 20) plane in the energy range from −14.1 to −10.0 eV (b), from −9.8 to −4.7 eV (c), from −7.7 to −2.4 eV (d), from −5.5 to −2.4 eV (e), from −4.4 to −1.2 eV (f), from −1.6 to 1.9 eV (g), from −0.7 to 3.5 eV (h), and from −0.6 to 3.8 eV (i).
   10. Figure 4.10. (a) Total and projected electronic density of states of TaB₂, and decomposed charge density on (11 20) plane in the energy range from −14.9 to −10.7 eV (b), from −10.5 to −5.3 eV (c), from −8.3 to −2.5 eV (d), from −6.1 to −2.5 eV (e), from −4.8 to −1.3 eV (f), from −1.7 to 2.1 eV (g), from −0.8 to 3.7 eV (h), and from −0.6 to 4.0 eV (i).
5. Chapter 05
   1. Figure 5.1. Representation of the repulsion and attraction forces as a function of interparticle distance. (a) When ceramic particles are suspended in a polar solvent, particle surfaces become charged depending on the chemistry and pH of the solution. M–OH groups represent surface hydroxyl group that reacts with acid or base. (b) The surface charge is balanced with a counterion cloud around the particle to provide electrical neutrality. Surface charge and the counterion cloud form the electrical double layer. (c) In addition to using the EDL to create repulsive forces between particles, steric and electrosteric mechanisms could be used by adding polymers or polyelectrolytes, respectively, which will adsorb on particle surfaces.
   2. Figure 5.2. Schematic representation of the influence of volume fraction on the viscosity of suspensions as a function of shear rate. At low shear rate, Brownian motion dominates producing high-viscosity randomized structures. At high shear rates, particles line up in preferred flow structures and viscosity decreases.
   3. Figure 5.3. Volume fraction of consolidated green body as a function of applied pressure for a well-dispersed suspension and attractive particle networks.
   4. Figure 5.4. Classification of green near-net-shaping ceramic processing techniques.
   5. Figure 5.5. Dry processing route to prepare UHTC components. The main challenge associated with current technology for preparing UHTCs is the need for high temperature and pressure to densify the materials. This leads to the use of sintering aids, which reduces the service performance and limits shapes to very simple geometries.
   6. Figure 5.6. Colloidal processing route to prepare UHTC components. In addition to removing flaws related to powder aggregates and improvement in the homogeneity of the sample, the control of the interparticle forces leads to higher particle packing that reduces the temperature for sintering and the need of pressure. In addition, near-net-shaping allows the manufacturing of UHTC complex shapes.
   7. Figure 5.7. Examples of colloidal shaping techniques. (a) Slip casting: the control of suspension rheology determines particle packing; the green body is formed by the removal of solvent by filtration; (b) Gelcasting: the green body strength is determined by the amount of monomer, crosslinker, initiator (and catalyst), and the solid content of the suspension; (c) Freeze casting: the green body microstructure is designed through control of ice growth, which is controlled by solid content, freezing temperature, freezing device, and cyoprotector addition.
   8. Figure 5.8. Viscosity versus shear rate curves for ZrB₂ suspensions prepared with different amounts of dispersant. The dispersant is Hypermer A70 and the solvent is cyclohexane. The volume fraction of solids is 50%.
   9. Figure 5.9. Sintered density of ZrB₂ specimens as a function of processing route and sintering temperature. Densities of the green bodies for colloidal and dry processing routes were included as dashed horizontal lines for comparison.
   10. Figure 5.10. Microstructure of ZrB₂ after sintering at 2100°C/1 h at different magnifications. (a and b) Colloidal processing and PS; (c and d) dry processing and PS; (e and f) colloidal processing and HP; (g and h) dry pressing and HP.
   11. Figure 5.11. Shrinkage for ZrB₂ samples as a function of the processing route and type and temperature of sintering. (The linear shrinkage for PS samples showed in the graph represents the average of height and diameter of the samples tested; in the case of the HP samples, the linear shrinkage represents the average of their height only, since the diameter is constrained by die dimension.)
   12. Figure 5.12. ZrB₂ Leading edge. (a) Green body produced by slip casting as-unmolded; (b) after pressureless sintering at 2100°C/1 h; (c) after oxytorch testing.
6. Chapter 06
   1. Figure 6.1. Relative density (rd) versus temperature (T) of ZrB₂-based compositions using 5 vol% Si₃N₄/ or AlN, as sintering aid; onset temperatures and final relative densities are also reported on each curve.
   2. Figure 6.2. ZrB₂ ceramic sintered using 5 vol% Si₃N₄ as sintering aid: (a) SEM micrograph showing ZrB₂ (1), ZrO₂ (2), and BN (3), (b) high-resolution TEM micrograph of a grain-boundary phase.
   3. Figure 6.3.  Relative density (rd) versus temperature (T) of ZrB₂ sintered with 15 vol% of ZrSi₂, MoSi₂, or WSi₂; onset temperatures and final relative densities are also reported on each curve.
   4. Figure 6.4.  Examples of microstructures of MB₂–MeSi₂ composites: SEM micrographs showing (a) ZrB₂–MoSi₂, (b) ZrB₂–WSi₂, and (c) HfB₂–ZrSi₂ (d) high-resolution TEM image of the interface between core and rim in ZrB₂–TaSi₂ [41] and (e) the same interface showing low angle grain boundaries [41].
   5. Figure 6.5.  Isobaric multiphase equilibrium amount (kmol) versus temperature (T) calculated using HSC Chemistry v.6.1, 1 bar (a and b) or 1 mbar (c and d) of total equilibrium pressure; starting compositions (in kmol): 0.9 ZrO₂ + 0.8 B₂O₃ (a and c), 0.9 ZrO₂ + 0.8 B₂O₃ + 1.2 SiC + 0.05 SiO₂ (b and d).
   6. Figure 6.6.  Hot pressing of ZrB₂-based compositions (ZSx) with varying SiC particulate content (x, vol%), compared to an only milled ZrB₂ powder (Z0): relative density (rd) versus temperature (T). Onset temperatures are indicated for each system.
   7. Figure 6.7.  Polished section of a hot-pressed ZrB₂–20% SiC: ZrB₂- (1), SiC- (2), ZrO₂- (3) and SiO₂-based glassy pockets (4).
   8. Figure 6.8. Polished sections from hot-pressed ZrB₂-based ceramics with 5 vol% (a) and 20 vol% SiC particulates (b).
   9. Figure 6.9.  (a) Relative density (rd) versus temperature (T) of ZrB₂ + 15 vol% SiC with (ZS15M), or without MoSi₂ (ZS15): onset temperatures are indicated. Polished sections by SEM from hot-pressed ZS15 (b) and ZS15M (c) are shown.
   10. Figure 6.10.  Isobaric multiphase equilibrium amount (kmol) versus temperature (T) calculated using HSC Chemistry v.6.1, 1 mbar (a) or 1 bar (b) of total equilibrium pressure, and 0.9 ZrO₂ + 0.8 B₂O₃ + 1.2 SiC + 0.4 B₄C + 0.05 SiO₂ of starting composition (in kmol).
   11. Figure 6.11.  Relative density (rd) of ZrB₂–15SiC–xWC composition (vol%) using high-energy milled (x = 2 for ZSWC–HM up to T_{1 MAX} = 1900°C) or only mixed ZrB₂ (x = 5 for ZSWC up to T_{2 MAX} = 1930°C): (a) rd versus temperature (T), (b) rd versus time (t) at T_{1 MAX} and T_{2 MAX}. For ZSWC, uniaxial pressure was applied at the constant value of 30 MPa from RT, while in three steps for ZSWC–HM.
   12. Figure 6.12.  Polished regions by SEM of hot-pressed ZrB₂–15SiC–2WC composite (see ZSWC–HM in Fig. 6.11): (a) overall microstructure with ZrB₂ (1), SiC (2), (W,Zr)B (3) and (b) magnification of ZrB₂ cores (C) and (Zr,W)B₂ rim (R).
   13. Figure 6.13.  Strength (σ) versus displacement (x) curves recorded during 4-pt flexure test at 1500°C in air using different ceramics sintered by hot pressing (HP) or pressureless sintering (PS): (a) HfB₂–15 vol% TaSi₂ (HF15Ta–HP), HfB₂–15 vol% MoSi₂ (HF15Mo–HP), ZrB₂–20 vol% MoSi₂ (Z20Mo–PS); (b) ZrB₂–15 vol% SiC (ZS15) with B₄C, WC, or MoSi₂ as sinter additive.
   14. Figure 6.14.  ZrB₂-based composites hot-pressed with different MeSi₂ (Me = Mo, Ta, W, Zr): average flexural strength data (σ) measured at different temperatures (T). (a) MeSi₂ < 5 vol% [13, 15, 33, 57, 80], (b) MeSi₂ > 10 vol% [17, 19, 32]. For the sake of comparison, the composite containing SiC and B₄C is also reported, as one of the most refractory compositions.
   15. Figure 6.15.  Relative density (rd) versus temperature (T) of pure HfC and HfC–15 vol%TaSi₂; onset temperatures and final relative densities are also reported on each curve.
   16. Figure 6.16.  Examples of microstructures of MC sintered with MeSi₂: SEM micrographs showing (a) HfC–MoSi₂ showing the cleaning effect of the silicide trapping HfO₂ and reduced to SiOC, (b) HfC–ZrSi₂ showing multiple core–shell grains, (c) TEM image showing dislocation between core and shell in TaC–TaSi₂, (d) TEM image of a complex triple point in HfC–TaSi₂, (e) HR–TEM showing clean interfaces in ZrC–TaSi₂.
7. Chapter 07
   1. Figure 7.1. Schematic of the matrix microstructure formation mechanism of an RMI Cf–ZrC composite. (a) Heterogeneous nucleation sites of ZrC at 1950°C; (b) growth and grouping of ZrC grains at 1950°C; (c) coalescence of ZrC grains and trapping of liquid Zr at 1950°C; (d) growth of ZrC particles with liquid Zr inclusions and precipitation of β-Zr at 1950°C; (e) coalescence, growth of ZrC, and trapping of β-Zr as temperature decreases (above 1835°C); (f) transformation of liquid Zr into the eutectic phase at 1835°C; (g) phase transformation of β-Zr into α-Zr at 1159°C and (h) final microstructure at room temperature, showing ZrC particles with α-Zr + ZrC and α-Zr inclusions. The eutectic phase composed of α-Zr + ZrC and α-Zr serves as the grain boundaries in areas of densely distributed ZrC particles.
   2. Figure 7.2. Comparison of C/C–UHTC composites ablated for a 30 s period under a 3920 kW m⁻² heat flux: (a) C/C–ZrB₂, (b) C/C–4ZrB₂–1SiC, (c) C/C–1ZrB₂–2SiC, (d) C/C–2SiC–1ZrB₂–2HfC, (e) C/C–2SiC–1ZrB₂–2TaC, and (f) C/C.
   3. Figure 7.3. Cross section of a 30 mm diameter × 20 mm thick UHTC composite showing the distribution of UHTC powder.
   4. Figure 7.4. UHTC composites after 60 s oxyacetylene torch testing.
   5. Figure 7.5. The 30 mm diameter × 20 mm thick, Cf–HfB₂ composites after 60 s oxyacetylene torch testing at >2500°C showing negligible surface erosion.
   6. Figure 7.6. Electron image and EDS mapping on the cross section of a Cf–HfB₂ composite subjected to 60 s oxyacetylene torch testing. (a) Back scattered electron image, (b) carbon, (c) hafnium, and (d) oxygen. The bright top layer in (a) indicates HfO₂.
   7. Figure 7.7. Microstructure of polished sections of ZrB₂ plus 20 vol% SiC plus SCS-9a fibers composite showing (a) representative fiber distribution and (b) matrix porosity.
   8. Figure 7.8. Microstructures of the ablated HfC coating on a C/C composite in different regions: (a) central; (b) transitional; and (c) outer ablation region.
   9. Figure 7.9. Cross-sectional microstructure of a hybrid UHTC composite. The bonding between the composite and monolith layers are fundamentally good as seen in the higher magnification image.
8. Chapter 08
   1. Figure 8.1. Room-temperature elastic modulus as a function of porosity for ZrB₂ (left) with and without sintering aids [11–14, 16, 17, 20–23, 25–29, 31–35, 37–39]. Line represents fitted relationship of elastic modulus to porosity according to Nielsen's relationship [40, 41].
   2. Figure 8.2. Room-temperature flexure strength as a function of grain size for ZrB₂ (left) with and without sintering additives [11–14, 16–29, 31, 33, 34, 36, 37, 48]. Line is not fitted to data, and is meant to guide the eye.
   3. Figure 8.3. Room-temperature flexure strength as a function of SiC cluster size (equivalent area diameter) for ZrB₂–30 vol% SiC ceramics produced by hot pressing [7–9].
   4. Figure 8.4. Room-temperature flexure strength, elastic modulus, and Vickers hardness as a function of maximum SiC cluster size (major axis of ellipse) for ZrB₂–30 vol% SiC ceramics prepared by hot pressing. The dashed line indicates the microcracking threshold that occurs at an SiC cluster size of approximately 11.5 μm [8].
   5. Figure 8.5. Room-temperature flexure strength [16, 22, 26, 37, 50, 57] and fracture toughness [16, 22, 26, 37, 50, 57] as a function of SiC concentration for ZrB₂–SiC ceramics produced by hot pressing and pressureless sintering.
   6. Figure 8.6. Thermally etched cross section of ZrB₂–30 vol% SiC. The image shows the crack path from a Vickers indent with arrows indicating predominantly transgranular fracture for the ZrB₂ grains and crack deflection near the ZrB₂–SiC interfaces.
   7. Figure 8.7. Elastic modulus as a function of additive content for selected hot-pressed ZrB₂-based composites with SiC [16, 18, 26, 28, 52, 54, 63] , MoSi₂ [14, 64–67] , and ZrSi₂ [17] additives. Values have been corrected for porosity using a linear relationship and b = 2.0.
   8. Figure 8.8. Room-temperature flexure strength and fracture toughness as a function of disilicide concentration for ZrB₂–MeSi₂ ceramics produced by hot pressing [17, 27, 64].
   9. Figure 8.9. Room-temperature flexure strength and fracture toughness as a function of SiC content for ZrB₂–MoSi₂–SiC and ZrB₂–TaSi₂–SiC ceramics [64, 88, 89].
   10. Figure 8.10. Elevated-temperature elastic modulus of hot-pressed ZrB₂ with and without additives [20, 25,29].
   11. Figure 8.11. Elevated-temperature elastic modulus of hot- pressed ZrB₂–SiC with and without additives [25, 69].
   12. Figure 8.12. Elevated-temperature flexure strength of selected hot-pressed ZrB₂ ceramics with and without additives in air and argon [11–13, 20, 25, 29, 30].
   13. Figure 8.13. Elevated-temperature flexure strength of selected hot-pressed ZrB₂–SiC ceramics with and without additives in argon [25, 69, 90, 91].
   14. Figure 8.14. Elevated-temperature flexure strength of selected hot-pressed ZrB₂–SiC ceramics with various additives in argon [11, 15, 25, 67].
   15. Figure 8.15. Elevated-temperature four-point flexure strength of selected ZrB₂–MeSi₂ ceramics in air [25, 65–67, 79, 82, 83].
   16. Figure 8.16. Elevated-temperature fracture toughness (CNB) of hot-pressed ZrB₂ and ZrB₂–SiC ceramics [30, 69].
9. Chapter 09
   1. Figure 9.1. Thermochemical and experimental heat capacity (C_p) values for ZrB₂ [8, 14–17, 24, 26, 27].
   2. Figure 9.2. Historic thermal conductivity as a function of temperature for ZrB₂. Data for Clougherty changed testing method at 1000°C [6–12].
   3. Figure 9.3. Current thermal conductivity as a function of temperature values for ZrB₂. ^aData corrected for ρ. ^bData corrected for C_p [13–18, 20–23] (Jason Lonergan, Missouri University of Science and Technology, personal communication).
   4. Figure 9.4. Thermal conductivity as a function of temperature for ZrB₂ with solid solution additions. ^aData corrected for ρ [18, 21–23].
   5. Figure 9.5. Heat capacity as a function of temperature for HfB₂ [24, 27, 35].
   6. Figure 9.6. Thermal conductivity as a function of temperature for historic and current HfB₂. ^aData corrected for ρ [9, 10, 14, 18, 37, 39, 40].
   7. Figure 9.7. Thermal conductivity as a function temperature for ZrB₂ with SiC additions ranging from 5 to 50 vol%. (Note: Clougherty changed testing methods at 1000°C.) ^aData corrected for ρ [8, 14, 15, 18, 36, 41–45].
   8. Figure 9.8. Thermal conductivity as a function of temperature for ZrB₂ with additions of carbon, MoSi₂, or ZrC. Clougherty changed testing methods at 1000°C. [8, 11, 12, 20, 21, 48].
   9. Figure 9.9. Thermal conductivity as a function of temperature for ZrB₂-SiC-based composites with additions of, B₄C, C (elemental, nanotubes (CNT) and graphite (Cg)), MoSi₂, Si₃N₄, SiCw (whiskers), or ZrC. Clougherty changed testing methods at 1000°C. ^aData corrected for ρ [8, 18, 36, 41, 43, 48, 60, 72].
   10. Figure 9.10. Thermal conductivity as a function of temperature for HfB₂–SiC with SiC contents ranging from 2 vol% to 30 vol%. Clougherty changed testing methods at 1000°C. ^aData corrected for ρ [8, 14, 18, 28, 36, 39, 78].
   11. Figure 9.11. Thermal conductivity as a function of temperature for HfB₂ with additions of B_xC (x = 3 or 12), C, or SiC with C or B₄C. Clougherty changed testing methods at 1000°C. ^aData corrected for ρ [8, 18, 54, 75].
   12. Figure 9.12. Total, electron, and phonon thermal conductivities as a function of temperature for ZrB₂ and HfB₂. ^aData corrected forρ [15–17, 20, 79].
   13. Figure 9.13. Thermal conductivities as a function of temperature for ZrB₂–SiC and HfB₂–SiC, including separation of the electron and phonon contributions to total conductivity.^aData corrected for ρ [16, 20, 50, 84].
10. Chapter 10
    1. Figure 10.1. (a) Elastic constants for ZrB₂ as a function of temperature as measured by Okamoto et al. [12] and (b) the average Young's modulus, E_avg (filled squares); shear modulus, G_avg (filled triangles); and bulk modulus, K (filled circles), as a function of temperature using the same data. Also shown are the variation of Young's modulus as measured in flexure by Neuman et al. (half-filled diamonds) [16] and Rhodes et al. (open diamonds) [17] and the variation of Young's modulus of ZrB₂ as measured from the natural resonance frequency (open squares) [18].
    2. Figure 10.2. Young's modulus versus temperature for a range of UHTCs. Closed symbols are measurements based on vibration, whereas open symbols were obtained from flexural tests. Data from Refs. [18, 20–23].
    3. Figure 10.3. Hardness of two types of zirconium diboride (100% dense with addition of 20 vol% SiC and 90% dense with no additions) as a function of the size of the applied load. Data from Ref. [32].
    4. Figure 10.4. Hardness as a function of load in a ZrB₂ containing SiC and B₄C. Data taken from Ref. [32]. Where indents were apparently made in a single phase, they have been grouped accordingly.
    5. Figure 10.5. TEM bright-field micrograph of a cross section through a Berkovich indent in ZrB₂ containing SiC. It appears that the SiC has resisted deformation more and has been pushed into the ZrB₂ grain above it. Reproduced with permission from Ref. 37. © The American Ceramic Society.
    6. Figure 10.6. Scanning electron micrograph of a 50 mN indent in ZrB₂ showing multiple slip lines in three orientations formed by dislocations surfacing close to the indent.
    7. Figure 10.7. Hardness variation with temperature of UHTCs: (a) diborides, (b) carbides, and (c) nitrides. Data from Refs. [37, 41–47].
    8. Figure 10.8. Hardness, H, over elastic modulus, E, as a function of the ratio of the yield strength, Y, to the elastic modulus according to the models of Tabor [24], Johnson [52], and Vandeperre, Giuliani, and Clegg [53]. For the latter, the effect of Poisson's ratio is shown with the lower curve for ν = 0 and the upper curve for ν = 0.5. Also shown is the finite element calculation of the relationship taken from Ref. [54–56].
    9. Figure 10.9. Hardness of ZrB₂ as a function of plastic strain rate. Data taken from Bhakhri et al. [41].
    10. Figure 10.10. Deformation mechanism map for ZrB₂ recalculated based on the assessment of Wang [63]. Experimental data taken from the following sources: hardness [41, 44, 73, 74] and creep and flow stress measurements [65, 75].
    11. Figure 10.11. Deformation mechanism map for ZrC recalculated using the assessment of Ashby and Frost [62]_. Experimental data taken from the following sources: hardness [45] and creep and flow stress measurements [66, 84, 85].
11. Chapter 11
    1. Figure 11.1. Overview of the approach used to model and evaluate UHTC leading-edge materials under simulated hypersonic flow conditions by Parthasarathy et al. [39, 40, 51–53, 57].
    2. Figure 11.2. (a) Thermodynamic model for the oxidation of ZrB₂ by Fahrenholtz [49] plotted in terms of phase stability regions for various stoichiometric compounds. (b) Observation by Talmy et al. of the decrease in retained boria in the scale with temperature shown replotted using data [50] and (c) microstructural cross section of ZrB₂ after oxidation at 1500°C in air for 30 min, presented by Fahrenholtz [49].
    3. Figure 11.3. (a) A schematic of the microstructure interpreted from experimental data and used to build the oxidation model for ZrB₂. The loss of boria was taken to be limited by diffusion through porous channels in the intermediate temperature regime. (b) At lower temperatures, an external liquid boria forms and remains stable. (c) At very high temperatures, the boria evaporates as fast as it can form leading to rapid oxidation. (d) The transition between the three regimes as a function of temperature as predicted by the model of Parthasarathy et al. [52].
    4. Figure 11.4. The oxidation model of Parthasarathy et al. [53] was able to rationalize the sudden jumps in oxidation kinetics with temperature in the ZrB₂ and HfB₂ systems, by proposing that the volume change associated with phase transformation from monoclinic to tetragonal oxide (ZrO₂ or HfO₂) opens the porous channels in the scale. At the highest temperatures, the possible effect of unintentional dopant on the electronic conductivity of the oxide and thus the oxidation kinetics was estimated and was found to correlate with experimental data.
    5. Figure 11.5. The proposed oxidation model [52] appears to capture the effect of oxygen partial pressure, but data in the literature are rather limited.
    6. Figure 11.6. Microstructure and EDS mapping of the oxidation product of a 20 vol% SiC-containing ZrB₂ sample showing the phases present along with morphology and a depleted zone lacking SiC in a matrix of ZrB₂ after exposure in air at 1627°C for 100 min [20, 31].
    7. Figure 11.7. Thermodynamic model for the oxidation of ZrB₂–SiC calculated by Fahrenholtz [48] along with a schematic sketch showing a rationale for the formation of a depleted zone as observed by Opila et al. (Fig. 11.6).
    8. Figure 11.8. (a) Experimental observation of microstructural morphology (e.g., Fig. 11.6), (b, c) Schematics of the microstructural morphology and phase content of the oxidation product used in the model of Parthasarathy et al. [57].
    9. Figure 11.9. Predicted variation in oxidation kinetics of SiC-containing ZrB₂ as a function of SiC content compared with (a) experimental data of Talmy [66] and (b, c) Wang et al. [67]. Figure reproduced from the work of Parthasarathy et al. [57].
    10. Figure 11.10. Thermal model of a leading-edge sample of UHTC was compared for two cases, one for the sample used in the scramjet tests and another simulating free flight. The results showed that the thermal profiles are nearly the same for the two cases near the leading-edge tip, which were of experimental interest [40].
    11. Figure 11.11. The oxidation scale formed on the UHTC sample tested in the scramjet under conditions representing free flight Mach numbers of 6.2–7. No external glassy layer or depleted zone was observed; however, hafnon (HfSiO₄) was present in the oxide scale as evidenced by both X-ray diffraction and EPMA analysis shown here [40].
    12. Figure 11.12. The thermal model for the leading edge (made of HfB₂–20 vol% SiC) under hypersonic flight conditions when combined with oxidation models can predict parameters of interest for design. The temperature at the tip of the leading edge is lower than the total temperature often assumed. Similarly, the steady-state heat flux is lower than the cold wall heat flux. The thermal profiles show a steep drop in temperature away from the tip, and the oxidation rates appear to be tolerable for UHTCs at Mach 6.5 [40].
12. Chapter 12
    1. Figure 12.1. Ta–C phase diagram. From Ref. [5].
    2. Figure 12.2. Crystal structures of (a) TaC, (b) ζ-Ta₄C₃, and (c) α-Ta₂C.
    3. Figure 12.3. The total and partial density of states (DOS) for TaC computed from electronic structure density function theory using full-potential linearized augmented plane wave plus local orbitals and the local density approximation. The continuity of the DOS through the Fermi level (0 eV) demonstrates that TaC has no band gap and is an electrical conductor. The partial density of states (pDOS) shows that the DOS at the Fermi level is mainly due to tantalum d-electrons, which suggests that the metallic nature is associated with the bonding between neighboring tantalum atoms through overlap of the d-orbitals. Taken from Ref. [11].
    4. Figure 12.4. Left image is a series of {111} planes in TaC viewed along <110>. The right image is the removal of a {111} plane of carbon atoms and the subsequent shear along the now formed metallic Ta–Ta bonds. Stacking of three sequential highlighted boxes, one on top of another (or, alternatively, the loss of every fourth carbon plane with a shear), results in a unit cell of Ta₄C₃.
    5. Figure 12.5. SEM backscattered micrographs of HIP processed tantalum carbides in at%: (a) 56Ta44C, (b) 58Ta42C, (c) 60Ta40C, (d) 64Ta36C, and (e) 68Ta32C. Images taken from Ref. [31].
    6. Figure 12.6. VPS processed tantalum carbide microstructure: (a) schematic of the as-sprayed microstructure taken from Ref. [2]. (b) SEM micrograph of an as-sprayed tantalum carbide microstructure.
    7. Figure 12.7. (a) TEM bright-field micrograph showing the Ta₄C₃ crisscross lath pattern in TaC. (b) Scanning TEM high-angle annular dark-field (HAADF) micrograph revealing a series of parallel Ta₄C₃ laths (gray contrast) parallel to Ta₂C (bright contrast).
    8. Figure 12.8. The potential mechanisms of dislocation glide on {111} planes in TaC. In this figure, the slip occurs between two tantalum layers, A and B, whose stacking is shown as white open circles and gray circles. The carbon atoms are shown as solid black circles and sit in the octahedral interstices between the tantalum layers. In this simple example, it is assumed that layer B will slip relative to layer A by a perfect dislocation, a/2<110>. (a) The large black arrow represents the slip of layer B relative to A along the <110> direction, that is, a perfect dislocation. If it is assumed the dislocations split into Shockley partials, the atoms at B will move first from its original position over the atom at site A and then back to a position at B, which is illustrated by the shorter dashed black arrows. (b) Under the assumption that the motion of the B tantalum atom over the A tantalum atom is unfavorable, then it is possible for the B atom to move to the C position, which is occupied by the carbon atoms. This motion is certainly less favorable than even the motion to the A position. This can be favorable if the carbon atom moves in a coordinated fashion with the A atom. The black dashed arrows show the slip associated with these new partial dislocations, and the dashed gray arrows represent the coordinated motion of the carbon atoms. If the material is substoichiometric, then the carbon atoms in B may not be present, making slip even easier and explaining the loss of hardness with decreasing carbon content for single-phase TaC_1−x materials.
    9. Figure 12.9. Stress–strain curve for TaC at 2433 K. Taken from Ref. [59].
    10. Figure 12.10. Hardness variation as a function of C/Ta composition and temperature. (a) The hardness at room temperature from various groups plotted as a function of carbon content. All hardness measurements are presumed to be made on polycrystals [5, 46, 59, 85]. (b) The hardness of TaC plotted as a function of temperature. The data of Kumashiro [58] is for indentation on a {001} surface, while the data of Koester and Moak [84] represent the hardness of a polycrystalline surface.
13. Chapter 13
    1. Figure 13.1. (a) Ti–B binary equilibrium phase diagram [17]. (b) Schematic representation of AlB₂ crystal structure of TiB₂ [76]. (c) Illustration of the hexagonal network of boron atoms, with metal atoms situated above and below the boron network [1].
    2. Figure 13.2. Varying sizes and morphological features of TiB₂ powder, synthesized via different routes. (a) Nanocrystalline TiB₂ powder prepared by the reaction of TiCl₄ with NaBH₄ [55]. (b) TiB₂ powders synthesized via benzene–thermal reaction of metallic sodium with amorphous boron powder and TiCl₄ at 400°C [57]. (c) High-energy ball-milled and mechanical alloyed Ti–67B nanocrystalline TiB₂ powder [52]. (d and e) Sol–gel-synthesized nanocrystalline TiB₂ powder [115].
    3. Figure 13.3. SEM images of pressureless sintered TiB₂–TiC composites sintered at (a) 1700°C without HEBM, (b) 1750°C without HEBM, (c) 1700°C with HEBM for 48 h, and (d) 1750°C with HEBM for 48 h [134].
    4. Figure 13.4. STEM bright-field images of hot-pressed TiB₂–MoSi₂, showing the phase assemblage (Ti₅Si₃, Mo₅Si₃) and grain structure [26].
    5. Figure 13.5. Variation of Gibbs free energy change (ΔG) of sintering reactions taking place during hot pressing of TiB₂ with TiSi₂ [37].
    6. Figure 13.6. TEM micrographs of 4.8Ti–B₄C hot pressed at 1800°C, showing (a) well-distributed TiB₂ and TiC grains, (b) platelike TiC_x grain, (c) triangular TiC_x, and (d) irregular TiC_x [62].
    7. Figure 13.7. Variations of sinter densities of (a) TiB₂–6 wt% Cu and (b) ZrB₂–6 wt% Cu, processed using SPS [34].
    8. Figure 13.8. (a, b) SEM micrographs of TiB₂–6 wt%Cu, processed using SPS (c) fracture surface showing a small amount of porosity for the same. By contrast, for ZrB₂–6 wt% Cu composite, prepared under identical conditions, (d) irregular morphology and (e) (fractured surface) greater porosity can be observed [34].
    9. Figure 13.9. (a) Lower and (b) higher magnification TEM micrographs of multi-stage spark plasma sintered TiB₂–5%TiSi₂ (at 1450°C) [70].
    10. Figure 13.10. Temperature variations of (a) hardness of different borides with different additives, (b) elastic modulus, (c) room temperature hardness of TiB₂-based ceramics [24], and (d) flexural strength of monolithic TiB₂ and TiB₂–TiSi₂ [75].
    11. Figure 13.11. ΔG as a function of temperature for two possible reactions leading to the formation of TiB during SPS of TiB₂. The dotted line shows ΔG = 0 [133].
    12. Figure 13.12. (a) The variation of CTE as a function of temperature for TiB₂–TiSi₂ [158]. (b) Schematic representation of sharp wing leading-edge component [110]. (c) Finite element modeling results showing the generation of stress gradient across the cross section in rocket motor nozzles during the early stages of firing [107]. Red (or darker shade) signifies position of the peak tensile stress.
    13. Figure 13.13. (a) Schematic representation of the heat flux of sharp leading edges of hypersonic vehicles [121]. (b) Plot showing dependence of thermal conductivity with temperature for different diboride-based composites [109].
    14. Figure 13.14. Thermal conductivities of hot-pressed TiB₂–MoSi₂, containing varying amounts of MoSi₂ [113].
    15. Figure 13.15. SEM images of the surfaces of monolithic TiB₂ after oxidation at 850°C for (a) 1 h and (b) 4 h [4].
    16. Figure 13.16. Internal cracking in oxide layer and highly textured rutile phase on the surface of monolithic TiB₂ oxidized at 800°C for (a) 10 h and 1000°C for (b) 30 h [4].
    17. Figure 13.17. Cross-sectional SEM images showing the surface and subsurface layers after oxidation at (a) 800°C for 10 h and (b) 1000°C for 2 h. Note the absence of B₂O₃ at high temperature [128].
    18. Figure 13.18. Specific weight gain with respect to time during isothermal oxidation at 850°C for TiB₂–WSi₂ composites with different WSi₂ loadings [131].
    19. Figure 13.19. SEM images of ZrB₂–SiC showing (a) 2 µm thick layer of B₂O₃ and 6 µm thick ZrO₂-rich layer formed on the surface of ZrB₂–SiC after exposure to air at 1000°C for 30 min and (b) SiO₂ outer layer and second layer composed of ZrO₂ above of ZrB₂–SiC layer after exposure to air at 1200°C for 30 min [128].
    20. Figure 13.20. (a) Variations in wear rate with COF for TiB₂ and TiB₂-based cermet against different counter bodies. (b)The TiB₂-cermet has a composition of TiB₂-16 vol% Ni₃(Al,Ti); while that of monolithic TiB₂ has TiB₂-5 vol% SiC. Fretting parameters include: load of 8N for 100,000 cycles with a frequency of 10 Hz and a displacement of 200 µm [139, 147, 148]. Wear of different ceramics after sliding against each other. The sliding wear test conditions : (plate-on-plate configuration) at rotation speed of 220 revolutions/min with sliding speed of 0.2 m/s and a load of 214N under unlubricated conditions.
    21. Figure 13.21. (a) Three dimensional topographical view of the worn surface of TiB₂-5 wt% TiSi₂/steel at 10 N load, (b) the maximum wear peak profiles obtained at various loading conditions of the TiB₂ composite after fretting against steel counterbody, (c) three dimensional topographical view of worn surface of the TiB₂-5 wt% TiSi₂/ WC-6 wt% Co at 10 N load and (d) the maximum wear depth profiles obtained at various loading conditions of the TiB₂ composite after fretting against WC-6 wt% Co counterbody. Fretting conditions: 4 Hz frequency, 100,000 cycles and 100 µm stroke length.
    22. Figure 13.22. (a) Worn surfaces of TiB₂-5 wt% TiSi₂ after fretting against bearing steel ball, (b) the magnified image of the worn surface along with the EDS reveals the tribochemical layer. (c) The worn surfaces of TiB₂-5 wt% TiSi₂ after fretting against WC-6 wt% Co ball and (d) the magnified image of the worn surface along with the EDS. Fretting conditions: 10 N load, 4 Hz frequency, 100 µm stroke length and 100,000 cycles. (Arrow marks indicate the fretting direction.)
14. Chapter 14
    1. Figure 14.1. Hf–C phase diagram [41].
    2. Figure 14.2. Optical micrograph of HfC_0.5 oxidized at 1865°C for 600 s. Showing the bilayer carbide–oxide scale with sharp interface boundary [74].
    3. Figure 14.3. Partial pressures across a porous HfO₂ scale at 1400°C calculated using the Courtright–Holcomb gas shuttle model [76, 77].
    4. Figure 14.4. Weight gain for HfC_x oxidized at 1500°C for 15 min.
    5. Figure 14.5. Optical micrographs of HfC_0.67 (left) and HfC_0.98 (right) samples oxidized at 1500°C for 15 min showing oxide scale thickness [78].
    6. Figure 14.6. (a) Calculated CO pressure at the HfC_x–HfO₂ interface for x = 1.0 and 0.5 [78]. (b) Free energies of formation for CO and HfO₂ as a function of temperature (Opeka M. Unpublished data).
    7. Figure 14.7. Hf–N phase diagram [85].
    8. Figure 14.8. Optical photograph of HfN_0.95 after 3 min arcjet exposure at 2000°C showing an adherent oxide scale [78].
    9. Figure 14.9. (a) Posttest micrograph of Hf(33N) showing wavy oxide scale (Wuchina E, Opeka M. Unpublished data). (b) SEM micrograph of Hf(33N) showing a cavity within the oxide scale (Wuchina E, Opeka M. Unpublished data).
    10. Figure 14.10. Posttest micrograph of HfN_0.75 showing oxide scale disruption (Wuchina E, Opeka M. Unpublished data).
    11. Figure 14.11. Oxide scale thicknesses of HfC_0.98, HfN_0.92, and HfB₂ after 2000°C rocket motor firings at 3.43 and 10.3 MPa total pressure for 5, 10, and 20 s.
15. Chapter 15
    1. Figure 15.1. Phase diagram of the uranium–oxygen system.
    2. Figure 15.2. Schematic of a 17 × 17 PWR Fuel assembly with inserted control cluster, fuel pin, and dished pellet.
    3. Figure 15.3. Schematic representations of (a) composite fuel and (b) composite fuel using a multilayer-coated fuel particle in which the coating acts as a buffer layer between the fuel particle and the matrix material.
    4. Figure 15.4. Evolution of the coated fuel particle from uncoated to the standard TRISO and proposed QUADRISO as well as common fuel element compacts.
    5. Figure 15.5. C-Pu-U isothermal section at 1973 K.
    6. Figure 15.6. C-Si-U isothermal section at 1673 K.
16. Chapter 16
    1. Figure 16.1. CIRA activities on UHTCs for thermal protection systems.
    2. Figure 16.2. Configuration of test articles. Nose_1: breaking of nose tip during the plasma test.
    3. Figure 16.3. (a) Monolithic ceramic winglet flight models mounted on the EXPERT TPS and the (b) EXPERT capsule.
    4. Figure 16.4. CFD analysis: (a) surface heat flux (W/m²), (b) pressure (Pa), (c) temperature (K) distributions in fully catalytic conditions, (d) heat fluxes (W/m²), and Figure 16.4. (e) pressure (Pa) disturbances around the winglet.
    5. Figure 16.5. IR thermography images recorded during the test and before the holder fracture (t = 32 s) (a) test article in centerline and (b) predicted CFD wall temperature in test conditions.
    6. Figure 16.6. 3D model and image of SHARK wherein the gray UHTC tip is visible.
    7. Figure 16.7. Fracture surface of SHARK Nose tip wherein the three separated fragments are also indicated.

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