Effect of microstructure on mechanical, electrical and thermal properties of B4C-HfB2 composites prepared by arc melting

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Effect of microstructure on mechanical, electrical and thermal properties of B4 C-HfB2 composites prepared by arc melting Rong Tu a , Nian Li a , Qizhong Li b,c , Song Zhang a,∗ , Lianmeng Zhang a , Takashi Goto d a

State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, China Hubei Key Laboratory of Advanced Technology for Automotive Components, Wuhan University of Technology, Wuhan 430070, China Hubei Collaborative Innovation Center for Automotive Components Technology, Wuhan University of Technology, Wuhan 430070, China d Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan b c

a r t i c l e

i n f o

Article history: Received 8 May 2016 Received in revised form 27 June 2016 Accepted 29 June 2016 Available online xxx Keywords: Arc-melting B4 C-HfB2 composites Vickers hardness Electrical conductivity Thermal conductivity

a b s t r a c t B4 C-HfB2 composites were prepared by arc-melting using B4 C and HfB2 as raw materials. The eutectic composition of B4 C-HfB2 system was 70B4 C-30HfB2 (mol%) with a lamellar eutectic microstructure. HfB2 about 1 ␮m in thickness was dispersed in B4 C matrix uniformly of the eutectic composite, much smaller than raw powders. At the eutectic composition, the B4 C-HfB2 composites showed the maximum Vickers hardness (31.2 GPa) and fracture toughness (5.3 MPa m1/2 ) at room temperature, and maximum thermal expansion coefficient (7.1 × 10−6 K−1 ) from 293 to 1273 K. The electrical and thermal conductivity of B4 C-HfB2 composites increased with increasing HfB2 content. The electrical conductivity of B4 C-HfB2 eutectic composites decreased from 8.94 × 104 to 7.43 × 104 Sm−1 with increasing temperature from 298 to 800 K, showing a metallic electrical behavior. The thermal conductivity of B4 C-HfB2 eutectic composite was 16–18 WK−1 m−1 from 298 to 973 K. © 2016 Elsevier Ltd. All rights reserved.

1. Introduction Boron carbide (B4 C) and hafnium diboride (HfB2 ) are excellent ultra-high temperature structural (UHTS) materials due to their extraordinary mechanical, electrical and thermal properties as shown in Table 1 [1–7]. The utilization of UHTS materials are greatly limited by their poor machinability due to high hardness. However, they may be machined precisely to be many kinds of complicated shape by electric spark cutting. Therefore, high electrical conductivity is a desirable property. Moreover, high thermal conductivity and low coefficient of thermal expansion are also beneficial to the improvement of thermal shock resistance by reducing temperature gradients and thermal stresses within the materials [8]. Previous studies revealed that the thermal conductivity of HfB2 based materials involves the contribution of electronic mobility because of its high electrical conductivity, besides that of phonons [6,8]. In order to overcome the poor sinterability of HfB2 and achieve the excellent combination properties of each component, B4 C-HfB2 composites have been primarily prepared by conventional solid state sintering at high temperatures (2173–2473 K), such as hot-

pressing (HP) [9], reactive hot-pressing (reactive-HP) [3,10] and pressureless sintering [4]. As shown in Table 1, their mechanical properties are usually reported whereas the electrical and thermal properties have been rarely concerned so far. Ordan’yan et al. [11] have reported that the B4 C-HfB2 was a eutectic system with the eutectic composition of B4 C-(20–25 mol%) HfB2 and the eutectic temperature of 2653 ± 30 K. However, no details of the experimental procedure were presented, nor were the microstructure and properties of the eutectic composites studied. Our research group has previously fabricated several carbide-boride eutectic composites using arc melting and floating zone melting, and investigated the effect of microstructure on some characters of B4 C-SiC [12], B4 C-TiB2 [2], TiB2 -SiC [13] and ZrB2 -SiC [14]. These composites showed unique performance at the eutectic compositions, which may be resulted from their self-assembled microstructures by eutectic reaction [15]. The melting behavior and properties of B4 C-HfB2 composites are expected to be similar to that of B4 C-TiB2 composites since Hf belongs to the same family of Ti and Zr. Therefore, in the present study, the B4 C-HfB2 binary composites were prepared by arc melting. The effects of the microstructure and composition on the mechanical, electrical and thermal properties were investigated.

∗ Corresponding author. E-mail address: [email protected] (S. Zhang). http://dx.doi.org/10.1016/j.jeurceramsoc.2016.06.049 0955-2219/© 2016 Elsevier Ltd. All rights reserved.

Please cite this article in press as: R. Tu, et al., Effect of microstructure on mechanical, electrical and thermal properties of B4 C-HfB2 composites prepared by arc melting, J Eur Ceram Soc (2016), http://dx.doi.org/10.1016/j.jeurceramsoc.2016.06.049

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Table 1 Mechanical, electrical and thermal properties of B4 C, HfB2 and B4 C-HfB2 composites. Material

Method

B4 C HfB2 B4 C-11HfB2 (mol%) B4 C-33HfB2 −7C (mol%) B4 C-90HfB2 (mol%) B4 C-93HfB2 (mol%) a

Reactive hot pressing Reactive hot pressing Hot pressing Pressureless sintering

Hardness (GPa) Sintering temperature (K)

Fracture toughness (MPa m1/2 )

Electrical conductivity (Sm−1 )

Thermal conductivity (WK−1 m−1 )

Coefficient of thermal expansion (×10−6 K−1 )

Reference

2813a

36.8

2.4 ± 0.2

10–28

5.5

[1–4]

3653a 2173

28 28.3

3.8 7.07

8.79 × 103 8.04 × 102 9.1 × 106

104

7.15

[5–7] [3]

2423

27

6

[10]

2173–2273 2473

114–131 (at RT) 87–93 (at 1273 K) 19.5

4.1

[9] [4]

Melting temperature.

 E 1/2  P 

2. Experimental

KIC = 0.016

HfB2 powder (48–75 ␮m, purity 99.0%; Alfa Aesar, Shanghai, China) and B4 C powder (1–10 ␮m, purity 98%; Aladdin, Shanghai, China) were used as starting materials. The powders were weighed and mixed in a high-energy planetary ball mill (PM100, Retsch, German) at a speed of 300 rpm for 45 min under the atmosphere of argon. A WC–10 wt% Co jar was employed as a milling container and zirconia balls together with a small amount of ethanol as grinding media. The ball to powder ratio (BPR) was around 3 in weight, i.e., 10 g powder using a mixture of 4, 30 and 50 zirconia balls 10, 5 and 3 mm in diameter, respectively. The homogenized slurry was dried under a vacuum condition at 333 K for 7 h. The powder mixture was isostatically pressed into disks with 15 mm in diameter and 5 mm in thickness at 30 MPa. The powder disks were melted twice by an arc-melting method and solidified on a water-cooled copper hearth in Ar atmosphere at 60 kPa. The melting temperature of B4 C-HfB2 composites was determined by monitoring the shrinkage curve of the powder compacts with a plasma activated sintering apparatus (PAS, ED-PAS III, Elenix, Japan). The temperature in the PAS equipment was measured using a pyrometer (IR-CA, CHINO, Japan) focused on a hole of ␾2 × 5 mm in the graphite mold wall of 10 mm in thickness. Due to the measured temperature (T) is different to the actual temperature (real melting point, Tm ) in the mold, it was calibrated by the melting point of several standard materials, i.e., Cu, Ti and Al2 O3 powders under the same conditions, as reported in the previous study [16]. The crystal structure was characterized using X-ray diffraction (XRD, Rigaku Ultima III, Japan) with Cu-K˛ radiation. The content of W and Zr impurity caused by milling container and balls in the B4 C-HfB2 mixing powder was measured by inductively coupled plasma (ICP, Optima4300DV, PerkinElmer, USA) and that in the melted composite was examined by electron probe microanalysis (EPMA, JXA-8230, JEOL, Japan). The crystal orientation was determined by transmission electron microscopy (TEM, JEM-2100UHR, JEOL, Japan, at 200 kV). The microstructures were investigated by field-emission scanning electron microscopy (FESEM, FEI Quanta FEG250, USA). The hardness of B4 C-HfB2 composites was measured by a Vickers micro-hardness tester (430SVD, Wolpert, USA) using a diamond indenter with a load of 9.8 N for 10 s on a polished surface perpendicular and parallel to the growth direction. The fracture toughness (KIC ) was evaluated by an indentation method and calculated by the following equations [3,17,18]. KIC = 0.16HV a1/2



 c −3/2 a

KIC = 0.0719 P/C 3/2



(1) (2)

HV

C 3/2

(3)

where P is the indentation load (9.8 N), ␣ is half of the average diagonal length of indentation (m), c is the indentation radial crack length (m), C is the average crack length from the center of the indent to the crack tip (m), E is the elastic modulus of composites calculated assuming a mixture rule (EB4 C = 460 [19] and EHfB2 = 480 [5] GPa) and HV is Vickers micro-hardness (GPa). The reported hardness and fracture toughness values were an average of 10 points. Electrical conductivity () was measured by a commercial equipment (ZEM-3, Ulvac Riko, Japan) using a DC four-probed method for rectangular specimens (3 × 3 × 10 mm). Thermal conductivity () was calculated from the thermal diffusivity (), specific heat (Cp ), and density (d) using the relationship of  = Cp d. The thermal diffusivity was tested by the laser flash method using the Netzsch LFA457 system for square specimens (8 × 8 × 3 mm). The specific heat (Cp ) of each investigated composite was calculated according to the specific heat values from the HSC chemistry database [20] for each constituent phase, and its corresponding weight fraction by using the rule of mixtures. The densities of the bulk specimens were measured using the Archimedes’ principle. The coefficient of thermal expansion (CTE) was determined by a thermo-mechanical analyzer (DIL402C, Germany) in the temperature range of 293–1273 K using rectangular specimens (3 × 3 × 10 mm). The change in dimensions of the specimens with increasing temperature was continuously recorded and the value of CTE (␣) was calculated using the relation: ˛=

L L0 T

(4)

where L0 is the length of the specimens at ambient temperature, T0 is about 293 K, L and T are the changes in the length and the temperature, with respect to their initial values, respectively. 3. Results and discussion 3.1. Crystalline phase of B4 C-HfB2 composites Fig. 1 shows the XRD patterns of composites on the cross section perpendicular to the growth direction at the composition of (a) 78B4 C-22HfB2 , (b) 70B4 C-30HfB2 , and (c) 65B4 C-35HfB2 (mol%). Only B4 C and HfB2 , without other phase, was identified, implying no chemical reactions between B4 C and HfB2 . In addition, the relative intensity of HfB2 (100) in the B4 C-HfB2 composite was significantly higher than that in raw powders, indicating HfB2 (100) preferred orientation along growth direction. On the other hand, the impurity caused by the WC–10 wt% Co (jar) was almost zero and that by zirconia (balls) was less than 2 wt% although their hardness is

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Fig. 1. XRD patterns on the cross section perpendicular to the growth direction of B4 C-HfB2 composites at (a) 78B4 C-22HfB2 , (b) 70B4 C-30HfB2 , and (c) 65B4 C-35HfB2 (mol%).

lower than that of B4 C and HfB2 powder, which was too small to be appeared in XRD patterns. 3.2. Microstructure of B4 C-HfB2 composites Fig. 2 depicts several typical backscattering electron microstructures of B4 C-HfB2 composites for the cross section perpendicular to the growth direction, where the black phase was B4 C and the white phase was HfB2 . In Fig. 2(a), the microstructure at the composition of 78B4 C-22HfB2 (mol%) consisted of B4 C primary phase and B4 CHfB2 binary eutectic phase (BE), suggesting the content of B4 C was higher than that of the eutectic composition. With reducing B4 C

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content, BE increased and B4 C phase decreased at 75B4 C-25HfB2 (mol%) as shown in Fig. 2(b). The rod-like HfB2 grains were observed with further decrease of B4 C in 65B4 C-35HfB2 (mol%) composite, implying a B4 C-poor composition comparing to BE (Fig. 2(d)). Fig. 2(e) shows 50B4 C-50HfB2 (mol%) composite was a mixture of first crystallized HfB2 and BE. A uniform eutectic microstructure was observed at the composition of 70B4 C-30HfB2 (mol%) as shown in Fig. 2(c). A uniformly lamellar eutectic texture is observed on the cross section of 70B4 C-30HfB2 (mol%) composite perpendicular (Fig. 3(a)) and parallel (Fig. 3(b)) to the growth direction, indicating the eutectic composition. The eutectic lamellar microstructure was composed of black B4 C matrix with the white HfB2 phase about 1 ␮m in thickness, which was much smaller than the grain size of raw material. Moreover, the HfB2 phase preferred a specific orientation along the growing direction. The normal binary eutectic structure is either lamellar or fibrous depending on the volume fraction of the two phases, i.e., a lamellar or rod structure is generally expected if the volume fraction of the minor phase is more than or less than 28 vol% [21,22]. In the present study, the dispersed phase (HfB2 ) is about 28 vol% and the microstructure was mainly lamellarlike accompanying with some rod-like (Fig. 3(b)), which is basically consistent with the above-mentioned rule. Besides, the higher degree of supercooling is required for rod-like structure [23], which may also result in preferring the formation of lamellar B4 C-HfB2 eutectic composites. Hunt & Jackson proposed that the eutectic microstructure can be predicted from the type of growth of the two individual phases, which was related to the interface-roughness parameter (␣) [24]. The liquid/solid interface will be atomically rough, and a non-faceted interface occured when ␣ <2. While ␣ >2, a smooth surface and a faceted growth will result since the growth will be limited by the rate of nucleation [24]. The interfaceroughness parameter was defined as ˛ ≈ Sf /R , where Sf is the entropy of fusion and R the gas constant [22,24]. The Sf of the B4 C matrix and HfB2 phase is 38 and 3 J/mol K [20,25], and thus the ␣ is higher than 2 for B4 C and less than 2 for HfB2 , respectively. Therefore, the microstructure appear to have faceted/non-faceted growth types, and complex regular or broken lamellar structures

Fig. 2. Microstructures of composites for cross section perpendicular to the growth direction at (a) 78B4 C-22HfB2 , (b) 75B4 C-25HfB2 , (c) 70B4 C-30HfB2 , (d) 65B4 C-35HfB2 , and (e) 50B4 C-50HfB2 (mol%).

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Fig. 3. Microstructures of the 70B4 C-30HfB2 (mol%) eutectic composite for the cross section (a) perpendicular and (b) parallel to the growth direction.

Fig. 5. Temperature dependence of upper punch position of B4 C-HfB2 eutectic composite powder compacts. Fig. 4. High-resolution TEM image of the interface region of B4 C-HfB2 eutectic composite perpendicular to growth direction.

might form [26]. Since the major phase (B4 C) has a high entropy of fusion, the complex regular structure is favored over broken lamellar, which is consistent with that proposed by Hunt & Jackson [24,26]. Fig. 4 depicts the high resolution TEM image of the phase boundary of B4 C-HfB2 eutectic composite. The interface between B4 C and HfB2 reveals the tight joint ability and the conformability of HfB2 (101) plane paralleling to B4 C (104) plane. Some Moire fringes that caused by the stocking grains were observed, as shown in the circled area, which is similar to that in the high-resolution TEM image of Cu nanowires reported by Wang et al. [27]. 3.3. Melting point of B4 C-HfB2 eutectic composite Fig. 5 shows the temperature dependence of upper punch position (L) for compacting 70B4 C-30HfB2 (mol%) eutectic composite powder by PAS system. L increased firstly because of the expansion of graphite punch rods with increasing temperature, and then almost kept constant because of compensation of the increase in graphite punch rods and the decrease in specimen by sintering. Then, L decreased slowly since sintering played a dominant role during this period. Finally, L abruptly dropped at 2231 K because the melted specimen was extruded from the mold. Moreover, the solidified ball-like specimen composed of B4 C and HfB2 only, implying no interactions with the graphite die and/or sheet similar to the

previous report about B4 C-HfB2 -SiC system [16]. On the other hand, according to the formula that reported in B4 C-HfB2 -SiC system, i.e., Tm = 1.008T + 178 [16], the eutectic temperature of B4 C-HfB2 was calibrated to be 2425 K, which is lower than that reported as 2653 ± 30 K of B4 C-(20–25 mol%) HfB2 by Ordan’yan et al. [11]. The eutectic temperature in the present study may be more close to the real eutectic point than that in Ref. [11] because the eutectic microstructure was much fine and homogeneous in the present study. 3.4. Mechanical properties of B4 C-HfB2 composites Fig. 6 presents the effect of B4 C content on the Vickers hardness (Hv ) on the cross section perpendicular to the growth direction of B4 C-HfB2 composites at a load of 9.8 N. Almost no difference was obtained between perpendicular and parallel to the growth direction. The Hv increased fast with increasing B4 C content because B4 C (36.8 GPa [3]) is much harder than HfB2 (28 GPa [5]). The Hv at the eutectic composition showed the maximum value of 31.2 GPa, which might have been attributed to the dense and uniform microstructure with submicron grain size. The Hv of B4 C-HfB2 composite prepared by reactive-HP was 28.3 GPa (at 1.96 and 9.8 N) for B4 C-11HfB2 (mol%) [3] and 27 GPa (at 1N) for 60B4 C-33HfB2 7C (mol%) [10], while that prepared by pressureless sintering was 19.5 GPa (at 9.8 N) for B4 C-93HfB2 (mol%) composite [4], which were lower than that of eutectic composite in the present study. Ordan’yan et al. [11] reported 80B4 C-20HfB2 (mol%) eutectic composite with the Hv of 32 GPa at 0.49–1.47 N, lower load than ours,

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Fig. 6. Composition dependence of Vickers micro hardness of B4 C-HfB2 composites at a load of 9.8 N.

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tendency, although the KIC calculated by Eq. (1) was the highest, which showed 5.8–6.5 MPa m1/2 at 50–80 mol% B4 C. In the previous literatures, only Eq. (3) was applied to estimate the KIC of the B4 C-HfB2 sintered composites [3,4]. Therefore, the KIC of B4 C-HfB2 eutectic composite was evaluated as 4.2–4.8 MPa m1/2 by Eq. (3) in the present study, which is lower than that of B4 C-11 mol% HfB2 by reactive-HP using B4 C and HfO2 (7.0 MPa m1/2 ) [3], but higher than that of B4 C-93 mol% HfB2 by pressureless sintering (4.1 MPa m1/2 ) [4]. The existence of compressive stress in the B4 C matrix contributes to the reduction in stress intensity factor at the crack tip and thereby enhances the fracture toughness of B4 C-11 mol% HfB2 composites. The Chornobuk et al. [10] prepared a 60B4 C-33HfB2 -7C (mol%) composite by reactive-HP whose KIC was 6 MPa m1/2 (measured by indentation on a modernized PMT–3M device but without stating the equation), which is comparable to the KIC by arc melting. Therefore, B4 C-HfB2 eutectic composites may be applied for high-temperature structural ceramics with the highest Hv and a relatively high KIC . The indentation and cracks of B4 C-HfB2 composites are shown in Fig. 8. The propagation of the indentation crack at the eutectic composition (70B4 C-30HfB2 (mol%)) was predominantly transgranular mode in a zig-zag route (Fig. 8(a), (b)), implying a strong interfacial bonding among B4 C and HfB2 phases. The crack at the hypereutectic composition (50B4 C-50HfB2 (mol%)) distinctly extended in mixed transgranular and intergranular modes (Fig. 8(c), (d)). Moreover, many crack deflections at the interface were observed, mainly around the HfB2 grains (white arrows in Fig. 8(b), (d)), which might result from the generation of residual strain due to the difference in elastic modulus and/or thermal expansion mismatches between matrix (B4 C) and second phase (HfB2 ) [3]. Crack deflection, as a toughening mechanism, could consume more energy during crack propagation and result in reducing the driving force for further propagation, as well as the smaller grain size in the 70B4 C-30HfB2 (mol%) eutectic composite. Besides, the higher fracture toughness at the eutectic composition might also result from the good interfacial match as shown in Fig. 4. The primary propagation mode in the B4 C-HfB2 eutectic composite with the highest fracture toughness was the transgranular fracture in the present study, which was the same as the dominating fracture mode in the B4 C-HfB2 composites with the highest fracture toughness of 7.0 MPa m1/2 prepared by reactive-HP [3].

Fig. 7. Composition dependence of fracture toughness of B4 C-HfB2 composites.

3.5. Electrical property of B4 C-HfB2 composites which was close to the Hv value at the eutectic composition in the present study. Fig. 7 depicts the composition dependence of fracture toughness (KIC ) on the cross section perpendicular to the growth direction of B4 C-HfB2 composites. Almost no difference was observed between perpendicular and parallel to the growth direction. The KIC first increased with increasing content of B4 C and had the maximum value around the eutectic composition, which may result from the regular texture with the smaller grain size at the eutectic composition, as shown in Fig. 8(a). Three experiential equations were applied to evaluate the KIC in the present study. Eq. (1) is usually applied for polycrystal with properties of hardness and toughness that range 1–70 GPa and 0.9–16 MPa m1/2 , respectively [28], Eq. (2) for brittle solids with well-developed cracks that are basically penny-like in form [29], and Eq. (3) for a working range of

cal(particle) =

 1 4

Fig. 9 shows the temperature dependence of electrical conductivity () for the B4 C-HfB2 composites, and the reference values of B4 C [2] and HfB2 [8]. The ␴ of B4 C-HfB2 composites slightly decreased with increasing temperature showing a metallic conducting behavior, and increased with the increase of the content of HfB2 because the  of HfB2 was much higher than that of B4 C. The  of 70B4 C-30HfB2 (mol%) eutectic composite decreased from 8.94 × 104 to 7.43 × 104 Sm−1 with increasing temperature from 298 to 800 K. The  of B4 C-HfB2 eutectic composite was compared with those estimated by parallel ( cal(parallel) ), series ( cal(series) ) and dispersion particle models ( cal(particle) ) as shown in Eq. (7)–(9) [14,31]. cal(parallel) = VA A + VB B cal(series)

−1

= VA A

−1

+ VB B

(7) −1

((3VA − 1)A + (3VB − 1)A ) + (((3VA − 1)A + (3VB − 1)A )2 + 8A B )

indentation loads which satisfies the requirement that the crack pattern be well developed (C ≥2a) and no chipping occurs [30]. The KIC calculated by three equations showed almost the same

 1/2

(8) (9)

where V and  are volume fraction and electrical conductivity, respectively, and subscripts A and B indicate the matrix and the dispersed phase. The temperature dependence of  cal(parallel) was similar to that of HfB2 because the HfB2 phases in the plate shape

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Fig. 8. Crack morphology of B4 C-HfB2 eutectic composites at the load of 9.8 N at the composition of 70B4 C-30HfB2 (a, b) and 50B4 C-50HfB2 (c, d) (mol%).

flat layers were perpendicular to the direction of current flow, and the current cannot avoid the regions of high resistance [31]. The  cal(particle) was the closest to the experimental values, suggesting that the HfB2 phase dispersed in the B4 C matrix. In Fig. 3, the components of B4 C phase connected with each other whereas the HfB2 was separated by the B4 C phase, which coincided with the model of HfB2 dispersed in the B4 C matrix. 3.6. Thermal property of B4 C-HfB2 composites Fig. 10 shows the temperature dependence of thermal conductivity () for the B4 C-HfB2 composites, and the reference values of B4 C [2] and HfB2 [32]. The  of B4 C-HfB2 composites increased with the increase of the HfB2 content because of the higher  of HfB2 . The  of B4 C-HfB2 eutectic composite was 16–18 WK−1 m−1 in the temperature range of 298–973 K. The total thermal conductivity  can be written as:  = L + C

(10)

where L and C are the lattice and carrier thermal conductivity contributions, respectively. The carrier component (C ) can be calculated using the Wiedemann-Franz law as [33]: Fig. 9. Temperature dependence of electrical conductivity of B4 C-HfB2 composites.

was almost continuously aligned to the growth direction as shown in Fig. 3, and parallel to the direction of current flow. Therefore, the current mainly flows straight through the regions of low resistance preferentially [31], which was consistent with the manner of TiB2 observed in B4 C-TiB2 eutectic composite [2]. The temperature dependence of  cal(series) was close to that of B4 C since the alternate

C = LT

(11)

where L is the Lorenz number whose value has been generally taken as 2.45 × 10−8 WK−2 [6] and  is the measured electrical conductivity. Although this may be a good estimation for the carrier thermal conductivity (C ) at room temperature, it does not hold true for metallic materials or for heavily doped semiconductors where a strong change with temperature is observed in the chemical potential [34]. For most these materials, the true Lorenz numbers are in fact lower than 2.45 × 10−8 WK−2 especially at

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Fig. 10. Temperature dependence of thermal conductivity of B4 C-HfB2 composites. Fig. 12. Experimentally obtained CTE and theoretical prediction values of B4 C-HfB2 composites in the temperature range of 293–1273 K.

The  of B4 C-HfB2 eutectic composite was compared with those estimated by parallel (cal(parallel) ), series (cal(series) ) and dispersion particle models (cal(particle) ) as shown in Eq. (12)–(14) [12]. cal(parallel) = VA A + VB B cal(series)

−1

= VA A

−1

+ VB B

(12) −1

cal(particle) = A + 3(B − A )A VB /(2A + B )

Fig. 11. Composition dependence of electrical conductivity, thermal conductivity and C / of B4 C-HfB2 composites at room temperature (298 K).

high temperature, which may range from nondegenerate limit (1.5 × 10−8 WK−2 ) to the degenerate limit (2.45 × 10−8 WK−2 ) [34]. The ratio of electrical component (C ) to total thermal conductivity () for the investigated composites at room tem perature (298 K) was calculated from the relation C = 298L  (L = 1.5 × 10−8 –2.45 × 10−8 WK−2 ), and the estimated values are shown in Fig. 11. The ratios of C ⁄ were small (lower than 0.1) for all materials, particularly in 70B4 C-30HfB2 (mol%) eutectic composite, inferring the contribution of phonon is far more significant than that of free electron movement to the thermal conductivity in the present study. In Fig. 10, the  of B4 C-HfB2 decreased slightly with increasing temperature from 373 to 973 K, which may be attributed by the lower mean free path for phonon scattering with increasing temperature [6]. Moreover, the presence of phase interface is expected to have strong influence on phonon scattering, and further on the resultant thermal conductivity of the composites [6]. Therefore, the  around the eutectic composition had lower values, which could have contributed to the eutectic microstructure consisted of submicron grain size with more interfaces.

(13) (14)

where V and  are volume fraction and thermal conductivity, respectively, and subscripts A and B indicate the matrix and the dispersed phase. Since the cal(series) was the closest to the measurements, the phonon should be transported across the B4 C and HfB2 phases perpendicular to the heat flow. Therefore, the thermal conduction could be close to the series model whereas the electrical conductivity could be close to the dispersion particle model, which was the same with that illustrated in ZrB2 -SiC eutectic composite [14]. Fig. 12 shows the experimentally obtained CTE (␣) values of the investigated composites calculated by using Eq. (4) in the temperature range of 293–1273 K, as well as the values obtained through theoretical predictions for two phase materials. The ␣ for monolithic B4 C and HfB2 in the literatures was 5.5 × 10−6 [4] and 7.15 × 10−6 K−1 [6], respectively, indicating that the increase of B4 C may result in a slight decrease change in CTE. Several theoretical equations in literature are applied to evaluate CTE of the B4 C-HfB2 composites. The linear rule-of-mixtures (ROM) formulation [35], known as the Voigt approximation, assumes that the physical behaviors of each phase are not influenced by their presence in the mixture and therefore the effects of microstructure, plasticity and thermal softening are not accounted for. The linear ROM for calculating CTE can be written in the following form as: ˛c = Vm ˛m + Vp ˛p

(15)

where ␣ and V are the CTE (K−1 ), volume fraction, and the subscripts c, m and p refer to the composite, matrix and particles, respectively. On the assumption of the uniform hydrostatic stresses only existing in the interface, thermal expansion model for composites proposed by Turner could be expressed as follows [36]. ˛c =

˛m Vm Km + ˛p VP KP Vm K m + Vp Kp

(16)

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where K is bulk modulus (KHfB2 = 212 GPa [5] and KB4 C = 235 GPa [37]). The Kerner’s model [6,36] assumes that the reinforcement is spherical, and is wetted by a uniform layer of matrix. Besides, the stress and shear stress both exist in the interface. According to this model, the CTE is given by ˛c = ˛ +

Vp (1 − Vp )(˛p − ˛m )(Kp − Km ) (1 − Vp )Km + Vp Kp + (3Kp Km )/4Gm

˛ = (1 − Vp )˛m + Vp ˛p

(17) (18)

where G is the shear modulus (GB4 C = 193 GPa [38]). The Schapery’s model [39] believed that the effect of CTE of twophase composites depends strongly on the overall bulk modulus of the composite. The expression for the effect of the CTE of composite was derived as ˛c = ˛p + (˛m − ˛p )

[(1/Kc ) − (1/Kp )] [(1/Km ) − (1/Kp )]

(19)

The CTE calculated by the four theoretical models showed no remarkable difference and a decreasing tendency as B4 C content increases. The CTE of 50B4 C–50HfB2 (mol%) composite predicted by theoretical calculation was nearly in agreement with the experimental value of 6.2 × 10−6 K−1 . However, the experimental first increased and then decreased with increasing B4 C content, showing the maximum value of 7.1 × 10−6 K−1 at 70B4 C–30HfB2 (mol%) eutectic composite. Moreover, the experimental CTE of B4 C-(65–78 mol%) HfB2 was higher than the corresponding theoretical prediction in the temperature range of 293–1273 K, in which the phenomenon was also observed in the ZrB2 -20 vol% SiC and HfB2 20 vol% SiC composites reported by Mallik et al. [6] 4. Conclusion B4 C-HfB2 was a binary eutectic system with the eutectic composition of 70B4 C-30HfB2 (mol%) and the eutectic point of 2425 K. The lamellar eutectic structure consisted of HfB2 about 1 ␮m in thickness uniformly dispersing in B4 C matrix. The B4 C-HfB2 eutectic composite showed the highest Vickers micro-hardness of 31.2 GPa in the present study, and also higher than those prepared by solid state sintering. The fracture toughness of the B4 C-HfB2 eutectic composite showed the highest value of 5.9 MPa m1/2 . Both the electrical conductivity and the thermal conductivity of B4 CHfB2 composites increased with the increase of HfB2 content and decreased nearly concomitantly with increasing the temperature. The electrical conductivity and the thermal conductivity of B4 CHfB2 eutectic composite were 7.43 × 104 –8.94 × 104 Sm−1 in the range of 298–800 K and 16–18 WK−1 m−1 in the range of 298–973 K, respectively. The thermal expansion coefficient of B4 C-HfB2 composites was 6.2 × 10−6 –7.1 × 10−6 K−1 from 293 to 1273 K and showed the highest value at the eutectic composition. Acknowledgements This work was supported by National Natural Science Foundation of China, No.51272196, No.51372188, No.51521001 and the 111 Project (B13035). This research was also supported by the International Science & Technology Cooperation Program of China (2014DFA53090) and the Fundamental Research Funds for the Central Universities, China (WUT:2015III023). We also acknowledge Ibiden Co. Ltd. for their partially financial support. References [1] M. Shahedi Asl, M. Ghassemi Kakroudi, B. Nayebi, A fractographical approach to the sintering process in porous ZrB2 –B4 C binary composites, Ceram. Int. 41 (2015) 379–387.

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