SiC composites prepared in situ by spark-plasma sintering

Available online at www.sciencedirect.com

ScienceDirect Journal of the European Ceramic Society 34 (2014) 1433–1438

Short Communication

Contact-mechanical properties at pre-creep temperatures of fine-grained graphene/SiC composites prepared in situ by spark-plasma sintering Benito Román-Manso a , Estíbaliz Sánchez-González b , Angel L. Ortiz b,∗ , Manuel Belmonte a , M. Isabel Osendi a , Pilar Miranzo a,∗∗ b

a Instituto de Cerámica y Vidrio, Consejo Superior de Investigaciones Científicas (CSIC), 28049 Madrid, Spain Departamento de Ingeniería Mecánica, Energética y de los Materiales, Universidad de Extremadura, 06006 Badajoz, Spain

Received 25 July 2013; received in revised form 7 October 2013; accepted 1 November 2013 Available online 9 December 2013

Abstract Hertzian indentation was used to investigate for the first time the elastic–plastic behavior and contact damage evolution with temperature (in the 25–850 ◦ C range) in air of different in situ grown graphene/SiC composites. Three SiC starting powders differing in polytypes and particle sizes were liquid-phase densified by spark-plasma sintering, thus producing ceramic composites that contain about 4 vol.% of epitaxial grown graphene flakes at the grain boundaries and have interesting differences in their microstructure. The general trend in the contact mechanical behavior is qualitatively similar among the different composites, with the elastic modulus, yield stress, and critical loads for the onset of quasi-plasticity and ring/cone cracking all decreasing with increasing temperature, with the differences at the quantitative level being explained in terms of the particular microstructure of each graphene/SiC composite. © 2013 Elsevier Ltd. All rights reserved. Keywords: SiC; Graphene; Composites; Contact-mechanical properties; Spark-plasma sintering; Hertzian indentation tests

1. Introduction Silicon carbide (SiC) is one of those strong, hard, stiff, lightweight, and chemically inert non-oxide structural ceramics, and therefore is especially well-suited for the manufacture of engineering components subjected to large mechanical stresses even under extreme conditions (i.e., high temperatures and hostile environments).1,2 Currently, the vast majority of the advanced SiC ceramics are processed by liquid-phase sintering (LPS) with oxide additives,3,4 which not only enables their complete densification at lower sintering temperatures and times than solid-state sintering, but also results in enhanced fracture toughness.5,6 Not surprisingly, the mechanical characterization of the LPS SiC ceramics processed by both conventional pressureless sintering and hot-pressing has been the subject of extensive research both at room and high temperatures.7–10

∗

Corresponding author. Tel.: +34 924289600x86726; fax: +34 924289601. Corresponding author. Tel.: +34 917355872; fax: +34 917355843. E-mail addresses: [email protected], [email protected] (A.L. Ortiz), [email protected] (P. Miranzo). ∗∗

0955-2219/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jeurceramsoc.2013.11.003

With the information accumulated so far, nowadays there is a comprehensible understanding of the correlation between microstructure (grain size and morphology, as well as nature and concentration of the secondary intergranular phase) and mechanical properties (hardness, toughness, strength, contact, fatigue, wear, plastic deformation, creep, etc.). However, little is known on the mechanical properties of the LPS SiC ceramics with more refined microstructures obtained by the new rapid sintering techniques, among which spark plasma sintering (SPS) is one of the most extended. This is particularly true for the novel graphene/SiC composites, a new type of electrically conductive LPS SiC ceramics today obtained only by SPS and in which the epitaxial graphene multilayers grow in situ directly from the SiC particles at the grain boundaries.11 Evidently, these new liquidphase, spark-plasma sintered (LPSPS) SiC ceramics cannot be put in service without detailed mechanical information, which underscores the importance of the corresponding evaluation of properties. With these premises in mind, the present study seeks to contribute at addressing this deficiency, and is thus aimed at evaluating for the first time the pre-creep contact mechanical properties of three LPSPS graphene/SiC composites with

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different microstructural features. The study has been carried out by high-temperature Hertzian indentation, which is a type of testing that provides a full description of the temperature dependence of the contact response, including the damage modes (quasi-plasticity and fracture).12 2. Experimental procedure 2.1. Processing The starting materials were three commercially-available powders of SiC with different particle sizes identified as fine (F; ␣-SiC, S-2022, Cerac, USA, d50 = 0.8 ␮m), ultra-fine (UF; ␤-SiC, BF-17A, H.C. Starck, Germany, d50 = 0.5 ␮m), and nano (N; ␤-SiC, NanoAmor, USA, d50 = 45–55 nm), together with Y2 O3 (Grade C, H.C. Starck, Germany) and Al2 O3 (SM8, Baikowski Chimie, France) powders that will act as liquid-phase sintering additives. The selected composition was 93 wt.% SiC, 5 wt.% Y2 O3 and 2 wt.% Al2 O3. The respective powder batches were prepared by attrition milling in isopropanol with alumina grinding media for 2 h, followed by evaporation of the solvent in a rotary-evaporator at 93 ◦ C, drying of the mixture at 120 ◦ C, and sieving through a 63 ␮m mesh. Subsequently, powders of each batch were put in the SPS furnace (SPS510CE, SPS Syntex Inc., Japan) and densified under the same sintering conditions, specifically, in vacuum atmosphere (∼4 Pa) at a peak temperature of 1800 ◦ C, achieved with a heating ramp of 133 ◦ C min−1 , a holding time of 5 min, and uniaxial pressure of 50 MPa, which are appropriate conditions for the complete densification of SiC ceramics with that type and content of sintering additives.11 The resulting ceramics (20 mm diameter discs, denoted hereafter simply as SiC-X, where the letter X represents the type of SiC starting powder used) contained ∼4 vol.% of graphene-like nanostructures (i.e., few layer and multilayered epitaxial graphene).11 The specimens were then ground down to ensure plane parallel surfaces, and afterwards polished to a 3 ␮m finish. 2.2. Microstructural characterization The relative density of the sintered ceramics was measured by the Archimedes method using distilled water as the immersion media. To estimate the theoretical densities, the oxygen content in the starting SiC powders (1.2, 1.9 and 4.1 wt.% for SiC-F, SiC-UF and SiC-N, respectively11 ) was converted to silica and the amount of in situ grown graphene (∼4 vol.%) was also considered. In this way, the calculated theoretical densities are 3.25, 3.24 and 3.19 g cm−3 for SiC-F, SiC-UF, and SiC-N composites, respectively.11 The microstructural characterization was carried out by field-emission scanning electron microscopy (FESEM; S-4700, Hitachi, Japan), X-ray diffractometry (XRD; Bruker D5000, Siemens, Germany), and confocal micro-Raman spectroscopy (CmRS; model Alpha300 WITec GmbH, Germany). The FESEM observations were done on polished surfaces after plasma-etching with CF4 + 5% O2 gas for 27 min, and metal sputter coating processes; the median size and aspect ratio of

the SiC grains were estimated by image analysis using the Jimage software from various FESEM micrographs measuring at least 400 grains. The XRD patterns were collected in the step-scanning mode using conventional Cu-K␣ radiation, and were indexed with the help of the PDF2 database to identify the crystalline phases. The Raman spectra were recorded at room temperature on the surfaces subjected to Hertzian contact with an acquisition range up to 3000 cm−1 using a laser wavelength excitation of 532 nm, and used to evaluate the evolution with temperature of the graphene phase by analyzing the intensity ratio between the D band, very sensitive to the presence of structural defects in the sample, and the G band of graphene. 2.3. Mechanical characterization The elastic modulus (E) and hardness (HV ) at roomtemperature were measured by depth sensing indentation (Zwick/Roell, Zhu 2.5, Germany) using a Vickers diamond indentation force of 49 N; at least five well-defined indentations were considered on each ceramic, and the mean and deviation of the measured values are reported here. The load and the penetration depth were continuously and simultaneously recorded during each test. E was obtained from the unloading branch using the Oliver–Pharr method,13 and corrected from the frame compliance of the instrumented indenter. HV was calculated from the peak load and the indentation area measured on the optical microscope. The Hertzian contact tests were performed in air in the temperature range 25–850 ◦ C using a universal testing machine (AG-IS 100 kN, Shimadzu Corp., Japan) equipped with a split furnace and Al2 O3 pistons to deliver the load. The indentation sequences were carried out at a constant crosshead speed of 0.05 mm min−1 over the peak load (P) range of 50–3500 N, using a Si3 N4 half-sphere of 3 mm radius (r) as the indenter; note that at these testing temperatures there are no creep effects on the size of the residual impressions (i.e., loading rate does not play a role on the stress–strain curves), as confirmed by performing selective 1000 N indentations at two different crosshead speeds (0.05 mm min−1 and 0.005 mm min−1 ). Before testing, the specimens were first conveniently metalized to facilitate observation of the contact zone even in the elastic regime and then stuck to the lower piston by using Al2 O3 paste (Ceramabond 569, Aremco Products Inc., USA). Temperature was raised at 6 ◦ C min−1 and soaked at the given set point for 1 h to ensure thermal equilibrium. Several indentations were done at increasing loads and the contact radius (a) for each peak load was measured at room-temperature using an optical microscope with Nomarski interference contrast. Indentation stress–strain curves were constructed by plotting p0 = P/πa2 vs. a/r. The elastic moduli (E) were then measured from the linear stretch of each indentation curve using the Hertzian relation for elastic contacts14,15 : p0 =

a (1 − ν2 )/E + (1 − ν )/E r 4/3π

2

(p0 < 1.1 Y )

where ν is Poisson’s ratio, and the primes indicate indenter properties16 ; the error in E was calculated by the error propagation in the expression. Furthermore, the critical loads for

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Fig. 1. Representative FESEM micrographs of the polished and plasma etched surface of (A) SiC-F, (B) SiC-UF, and (C) SiC-N, as well as of the fracture surface of (D) SiC-F. Black arrows in (A)–(C) point out to what is thought to be graphene flakes after etching, and red ones in (D) to confirmed graphene flakes at the fracture surface. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

the initiation of quasi-plasticity (PY ) were calculated from the yield stresses (Y) determined experimentally, using the relation derived for the Hertzian mechanical contact14,15 : 2   9 1 − ν2 1−ν2 (π1.1 Y )3 r 2 PY = + 16 E E where Y is in turn calculated from the contact pressure at which the experimental indentation curve deviates from linearity (pY ) using the expression pY ≈ 1.1 Y; again, the error in PY was calculated by error propagation in the expression. Finally, the critical loads for the onset of fracture in the form of ring/cone cracking (PC ) were taken as the lowest applied load at which such damage was observed during the post-test observation of the specimens; the error in PC was considered to be the difference between that load and the preceding one in the test sequence (i.e., error bars plotted only in the minus direction).

oxygen is forming silica) and, furthermore, shifts its composition toward the difficult-to-crystallize field of the corresponding Al2 O3 -Y2 O3 -SiO2 phase equilibrium diagram17 · Additionally, SiC-F has larger grain size (i.e., 1.11 ␮m with aspect ratio of 1.4) than SiC-UF (i.e., 0.54 ␮m with aspect ratio of 1.3) and SiC-N (i.e., 0.44 ␮m with aspect ratio of 1.7), both having similar grain sizes but differing slightly in aspect ratio. The relatively faster grain growth in SiC-N is then due to a higher content of liquid phase at the sintering temperature as well as the higher reactivity of the SiC starting nanoparticles. On the other hand, SiC-F exhibits a larger number of flatter grain-to-grain contacts whereas the secondary phase is mainly located at multigrain junctions because the grain size is more than twice as large as in SiC-UF and SiC-N. It is also inferred from Fig. 1A–C that the three ceramics are completely dense because there is no residual

3. Results and discussion Fig. 1A–C shows representative FESEM micrographs of SiC-F, SiC-UF, and SiC-N, respectively. It is seen that in the three cases the microstructure essentially consists of fine, equiaxed SiC grains together with a homogeneously-distributed secondary phase. According to the XRD patterns shown in Fig. 2, the secondary phase in SiC-F and SiC-UF crystallized as Y3 Al5 O12 (i.e., YAG), but remained amorphous in SiC-N. This is explained because of the higher oxygen content associated to the passivating layer covering the raw SiC-N powder particles (i.e., 4.1 wt.% oxygen vs. 1.2 and 1.9 wt.% oxygen in SiC-F and SiC-UF, respectively11 ), which leads to a higher content of secondary phase (i.e., 14.2 wt.% vs. 9.1 and 10.2 wt.% in SiC-F and SiC-UF, respectively, calculated assuming that the

Fig. 2. XRD patterns of SiC-F, SiC-UF, and SiC-N. The phase identification is included. The arrows in the diffractogram of SiC-UF denote to ␣-SiC peaks.

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porosity. The direct measurements by the Archimedes method lead to a density of 3.24 g cm−3 for both SiC-F and SiC-UF and of 3.17 g cm−3 for SiC-N, values that are >99% of the corresponding theoretical densities. The composites also contain graphene flakes, which are hardly discernible in the FESEM images of Fig. 1A–C most likely because of the damage caused by the plasma etching but that are nevertheless clearly observed in the FESEM images of the fracture surfaces, as shown by way of example in Fig. 1D for SiC-F (see the arrows in Fig. 1D). In a previous work11 it has been shown that the graphene flake size scales with the starting SiC particle size. SiC-F, SiC-UF, and SiC-N have a hardness of 21.0 ± 0.7, 22.6 ± 0.7, and 19.0 ± 0.1 GPa, respectively. Thus, SiC-N is slightly softer than the other two ceramics, attributable to the higher content of secondary phase, which is mainly amorphous and then of lower hardness (∼7 GPa17 ) than YAG (15 GPa18 ), as the grain sizes in the three materials are too large (i.e., in the range 0.44–1.11 ␮m) to exhibit a size effect hardening. Fig. 3 shows the Hertz indentation stress–strain curves for SiC-F, SiC-UF, and SiC-N at various temperatures, from 25 to 850 ◦ C. The shape of the curves is the typical of a polycrystalline ceramic,12,16,19–22 that is, an initial linear stretch attributable to the elastic deformation regime, followed by a nonlinear stretch associated to the quasi-plastic deformation regime. It is also observed that the slope of the linear stretch and the contact pressure for the deviation of the linearity decrease with increasing temperature. The particular details are however different for the three ceramics, as discussed next. Fig. 4A shows the evolution of the elastic moduli on the temperature, slowly decaying in the tested temperature range. This is indeed the type of trend previously observed in other polycrystalline ceramics.23–25 For the SiC-F and SiC-UF materials, E values at room temperature (390–425 GPa) and their decay with temperature are both similar to those observed for pressureless LPS SiC with comparable amount of additives.22 However, in the case of the SiC-N, the elastic modulus remains practically constant up to 700 ◦ C. At 850 ◦ C the elastic moduli of the three materials fall more notably and become similar, which suggests the activation and relevance of the reversible grain-boundary sliding.23,24 This general behavior indicates that the 4 vol.% of in situ grown graphene at the SiC grain boundaries does not seem to interfere with the grain-boundary sliding process. It is also seen in Fig. 4A that SiC-UF with ␤-SiC grains is slightly stiffer than SiC-F with ␣-SiC grains26 ; SiC-N only has ␤-SiC grains, but it is nevertheless less stiff than SiC-F due to its higher content of compliant secondary phase. Note that the elastic moduli measured by instrumented Vickers indentation at room temperature were 392 ± 16, 430 ± 25, and 350 ± 7 GPa for SiC-F, SiC-UF, and SiC-N, respectively, which lends strong credence to those determined by Hertzian indentation. It is observed in Fig. 4B that for the three materials the yield stress decreases progressively with increasing temperature. This is a reasonable tendency because quasi-plasticity in LPS SiC occurs by shear-faulting along the weak interfaces facilitated by the increased thermal energy.22 SiC-F systematically exhibits much lower yield stresses than the other two finer-grained ceramics, SiC-UF and SiC-N, of similar grain sizes, 0.54 and 0.44 ␮m,

Fig. 3. Indentation stress–strain curves of (A) SiC-F, (B) SiC-UF, and (C) SiC-N at temperatures in the range 25–850 ◦ C. The points are the experimental data, and the solid curves are guides to the eye. The error bars are lower than the point size.

respectively, which is then attributable to a higher tendency to undergo shear faulting because of its coarser microstructure (d50 = 1.1 ␮m).8,9 In addition, SiC-F shows a yield stress temperature decay similar to coarse pressureless LPS SiC.22 On the other hand, the finer-grained SiC-UF and SiC-N show a faster decay in the yield stress with temperature due to the

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Fig. 5. Dependence of the critical load for the initiation of (A) quasi-plasticity and (B) ring/cone cracking in SiC-F, SiC-UF, and SiC-N with the temperature in the range 25–850 ◦ C. The points are the experimental data, and the solid curves are guides to the eye. Included in (B) is also the toughness calculated from the critical loads for ring/cone cracking. Fig. 4. Dependence of the (A) elastic modulus and (B) yield stress of SiC-F, SiC-UF, and SiC-N with the temperature in the range 25–850 ◦ C. The points are the experimental data, and the solid curves are guides to the eye.

grain-boundary weakening, apart from similar yield stress values themselves despite the latter having a 5 wt.% higher amount of secondary phase. Therefore, the grain size seems to play the dominant role in the yield stress of the present LPSPS SiC ceramics, with differences in secondary phase content of 5 wt.% just playing a minor role. Nevertheless, larger differences (15 wt.%) in the secondary phase content are the dominant effect in the yield stress of pressureless LPS SiC.22 In regards to the damage modes, Fig. 5 shows the critical loads for the initiation of quasi-plasticity and fracture (specifically ring/cone cracking) in SiC-F, SiC-UF, and SiC-N as a function of temperature. Logically, the former decrease with increasing temperature because they are computed analytically from the experimentally-measured E and Y values according to the functional dependence Y3 /E2 ,14 thus resembling the temperature dependence of Y. On the other hand, as it is seen in Fig. 5B, SiC-N is the least prone of the three ceramics to ring/cone cracking. Indeed, apart from these higher critical loads, SiC-N always exhibited less ring/cone cracks than SiCF and SiC-UF under the same applied load, and, in addition, they were normally incomplete. As PC satisfies the expression 2 rE−1 ,14 this behavior can be explained by PC = 8.63 × 103 KIC the higher compliance of SiC-N as well as its higher toughness

probably associated to the slightly greater aspect ratio of the SiC grains and the higher number of graphene flakes at grain boundaries (the three ceramics contain approximately the same volume fraction of graphene flakes, ∼4 vol.%, but their sizes scale with the starting SiC grain size11 ) that would increase the effectiveness of the crack-bridging mechanism. In fact, as also shown in Fig. 5B, the toughness values calculated from PC increase as the particle size of starting SiC particles decreases, i.e., with the number of flakes. For the three ceramics, the critical loads for ring/cone cracking decrease appreciably with increasing temperature above 400 ◦ C, a trend that indeed reflects the evolution of the toughness. This fall in toughness above 400 ◦ C may be related with a slight increase of defects in the multilayered graphene flakes located at grain boundaries, inferred from the observed increase in the intensity ratio of the D to G Raman bands of graphene. This ratio is 0.55 up to 400 ◦ C, but increased up to 0.65 at temperatures ≥700 ◦ C. Accordingly, toughness of SiC-F decays slower with temperature compared to the other two finer-grained ceramics because of the larger size of the graphene flakes that leads to a lesser abundance of interfaces (so an attribute that makes it less tough at room-temperature could contribute to toughen it at high-temperatures). Interestingly, SiC-N exhibits a brittle-to-ductile transition at ∼400 ◦ C, with fracture no longer being the first damage mode. SiC-UF and SiC-F are however brittle in the entire temperature range investigated in the present study, with cone/ring cracking occurring always at lower critical loads than quasi-plasticity. This

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is different from what has been reported for pressureless LPS SiC ceramics, which have been found to be “ductile” under hightemperature Hertzian indentation, a fact that is attributed to their more heterogeneous microstructure. 4. Concluding remarks The pre-creep contact mechanical properties (elasto-plastic behavior and damage modes) of LPSPS graphene/SiC composites prepared in situ from different commercially-available SiC powders have been investigated by Hertzian indentation, considering different microstructures regarding matrix grain and graphene flake sizes, matrix aspect ratio, and secondary phase. In general, the elastic modulus, yield stress, and critical loads for the onset of quasi-plasticity and ring/cone cracking all decrease with increasing temperature. It emerges that the two factors more largely affecting the resistance to quasi-plastic damage in these ceramics are the grain refinement and the in situ grown multilayered graphene, with the content of secondary phase being a second-order effect. In this way, the yield stress and the resistance to quasi-plasticity increase with the microstructure refinement, whereas the presence of multilayered graphene at grain boundaries significantly increases the resistance to cone/ring cracking and the toughness. Conversely to the behavior observed for the more heterogeneous pressureless LPS SiC ceramics, the fine-grained microstructures of the LPSPS SiC materials lead to a cone-crack damage dominating over the quasiplastic damage in the studied temperature range, excepting the case of the ceramic prepared from nanopowders which shows a brittle-to-ductile transition at ∼400 ◦ C. Conflict of interest statement There is no conflict of interest. Acknowledgments This work was funded by the Spanish Government under projects MAT2009-09600, MAT2012-32944 and MAT201016848. B. Román-Manso acknowledges the financial support of the FPI fellowship program. References 1. Schwetz KA. Silicon carbide based hard materials – handbook of ceramic hard materials. Wiley Online Library; 2008. 2. Roewer G, Herzog U, Trommer K, Müller E, Frühauf S. Silicon carbide – a survey of synthetic approaches, properties and applications. High performance non-oxide ceramics: I. Structure and bonding, Vol. 101. Springer; 2002. p. 59–135. 3. Rodríguez-Rojas F, Ortiz AL, Guiberteau F, Nygren M. Oxidation behaviour of pressureless liquid-phase-sintered ␣-SiC with additions of 5Al2 O3 + 3RE2 O3 (RE = La, Nd, Y, Er, Tm, or Yb). J Eur Ceram Soc 2010;30(15):3209–17.

4. Rodríguez-Rojas F, Ortiz AL, Guiberteau F, Nygren M. Anomalous oxidation behaviour of pressureless liquid-phase-sintered SiC. J Eur Ceram Soc 2011;31(13):2393–400. 5. Padture NP. In situ-toughened silicon carbide. J Am Ceram Soc 1994;77(2):519–23. 6. Borrero-López O, Ortiz AL, Guiberteau F, Padture NP. Effect of the liquid phase content on the contact mechanical properties of liquid-phase-sintered ␣-SiC. J Eur Ceram Soc 2007;27(6):2521–7. 7. Roebben G, Duan RG, Sciti D, Van der Biest O. Assessment of the high temperature elastic and damping properties of silicon nitrides and carbides with the impulse excitation technique. J Eur Ceram Soc 2002;22(14-15): 2501–9. 8. Padture NP, Lawn BR. Toughness properties of a silicon carbide with in situ-induced heterogeneous grain structure. J Am Ceram Soc 1994;77(10):2518–22. 9. Padture NP, Lawn BR. Contact fatigue of a silicon carbide with a heterogeneous grain structure. J Am Ceram Soc 1995;78(6):1431–8. 10. Jensen RP, Luecke WE, Padture NP, Wiederhorn SM. High-temperature properties of liquid-phase-sintered alpha-SiC. Mater Sci Eng A: Struct Mater Prop Microstruct Process 2000;282(1–2):109–14. 11. Miranzo P, Ramírez C, Román-Manso B, Garzón L, Gutiérrez HL, Terrones M, et al. In situ processing of electrically conducting graphene/SiC nanocomposites. J Eur Ceram Soc 2013;33(10):1665–74. 12. Sánchez-González E, Meléndez-Martínez JJ, Pajares A, Miranda P, Guiberteau F, Lawn BR. Application of hertzian tests to measure stress–strain characteristics of ceramics at elevated temperatures. J Am Ceram Soc 2007;90(1):149–53. 13. Oliver WC, Pharr GM. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res 1992;7(6):1564–83. 14. Lawn BR. Indentation of ceramics with spheres: a century after Hertz. J Am Ceram Soc 1998;81(8):1977–94. 15. Johnson KL. Contact mechanics. Cambridge: Cambridge University Press; 1985. 16. Sánchez-González E, Miranda P, Guiberteau F, Pajares A. Effect of temperature on the pre-creep mechanical properties of silicon nitride. J Eur Ceram Soc 2009;29(12):2635–41. 17. Sainz MA, Osendi MI, Miranzo P. Sintering behaviour and properties of YAlSiO and YAlSiON glass-ceramics. Ceram Int 2011;37(5): 1485–92. 18. deWith G, Parren JED. Translucent Y3 Al5 O12 ceramics: mechanical properties. Solid State Ionics 1985;16(1–4):87–93. 19. Sánchez-González E, Miranda P, Meléndez-Martínez JJ, Guiberteau F, Pajares A. Temperature dependence of mechanical properties of alumina up to the onset of creep. J Eur Ceram Soc 2007;27(11):3345–9. 20. Sánchez-González Miranda P, Meléndez-Martínez JJ, Guiberteau F, Pajares A. Contact properties of yttria partially stabilized zirconia up to 1000 ◦ C. Am Ceram Soc 2007;90(11):3572–7. 21. Zamora V, Sánchez-González E, Ortiz AL, Miranda P, Guiberteau F. Hertzian indentation of a ZrB2 -30% SiC ultra-high-temperature ceramic up to 800 ◦ C in Air. J Am Ceram Soc 2010;93(7):1848–51. 22. Sánchez-González E, Miranda P, Guiberteau F, Pajares A. Effect of microstructure on the mechanical properties of liquid-phase-sintered silicon carbide at pre-creep temperatures. J Eur Ceram Soc 2011;31(6):1131–9. 23. Wachtman Jr JB, Lam Jr DG. Young’s modulus of various refractory materials as a function of temperature. J Eur Ceram Soc 1959;42(5):254–60. 24. Bruls RJ, Hintzen HT, deWith G, Metselaar R. The temperature dependence of the Young’s modulus of MgSiN2 , AlN and Si3 N4 . J Eur Ceram Soc 2001;21(3):263–8. 25. Osendi MI, Baudin C. Mechanical properties of mullite materials. J Eur Ceram Soc 1996;16(2):217–24. 26. Paquin RA. Metal mirror. In: Ahmad A, editor. Handbook of optomechanical engineering. New York: CRC Press LLC; 1997. p. 89–110.