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Effect of low-melting-point sintering aid on densification mechanisms of boron carbide during spark plasma sintering
Scripta Materialia 163 (2019) 34–39
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Scripta Materialia journal homepage: www.elsevier.com/locate/scriptamat
Effect of low-melting-point sintering aid on densification mechanisms of boron carbide during spark plasma sintering Mei Zhang a, Ruidi Li a,⁎, Tiechui Yuan a, Xiao Feng b, Siyao Xie a a b
Science and Technology on High Strength Structural Materials Laboratory, State Key Laboratory of Powder Metallurgy, Central South University, Changsha 410083, PR China Hunan Zoomwe Zheng Yuan Advanced Material trade Co., Ltd, Changsha 410000, PR China
a r t i c l e
i n f o
Article history: Received 5 November 2018 Received in revised form 30 December 2018 Accepted 31 December 2018 Available online xxxx Keywords: Boron carbide High entropy alloy Densification Spark plasma sintering
a b s t r a c t A densification creep model was proposed to analyze the densification mechanism involved in spark plasma sintering (SPS) of boron carbide containing low-melting-point sintering aid. This model incorporated the effect of the sintering aid on relative density as well as the actual internal stress during SPS of boron carbide ceramics. The internal stress bias caused by sintering aid was considered and a more accurate effective stress was used to investigate the kinetics during SPS. The proposed model explains why an increase of sintering aid amount decreases the sintering activation energy and promotes densification. © 2019 Published by Elsevier Ltd on behalf of Acta Materialia Inc.
Spark plasma sintering (SPS) is an advanced consolidation technique which can simultaneously achieve high temperature, high pressure and rapid densification [1–4]. This technique has been successfully applied to sinter refractory materials such as W [5], TiCN [6], and B4C [7–10]. The densification mechanisms of SPS pure ceramics are considered to be very important and [6,11,12] have been thoroughly investigated using the creep deformation model proposed by Bernard-Granger [13]. The densification models considering addition of sintering aid for SPS were rarely studied, although adding sintering aid has been widely used for promotion of sintering densification in covalent ceramics, such as B4C [14–17]. During the sintering process, low melting point sintering aid becomes liquid phase at an elevated temperature, resulting in the variation of actual pressure of the compact [14]. However, such internal biases caused by the formation of liquid phase during SPS were hardly reported. Studies to date using conventional analyzing methods failed to consider the fact that the consequently varied pressure can significantly affect the densification process [13,18–20]. Therefore, it is required to study the effect of low melting point sintering aid [21] on the densification mechanisms involved in the sintering of high-temperature ceramics. Recent progress in the high entropy alloys (HEAs) showed the feasibility of HEAs as efficient low melting point sintering aids for high temperature ceramics due to their excellent stabilities and mechanical properties [22–24]. In the present work, nonequiatomic
⁎ Corresponding author. E-mail address: [email protected] (R. Li).
https://doi.org/10.1016/j.scriptamat.2018.12.036 1359-6462/© 2019 Published by Elsevier Ltd on behalf of Acta Materialia Inc.
HEA Fe50Mn30Co10Cr10 as a low melting point sintering aid which is inert to B4C was applied to study the densification mechanisms of B4C during the SPS process. B4C powders with an average diameter of 2.11 μm and lab-made nonequiatomic Fe50Mn30Co10Cr10 HEA powders (gas atomization) were used for experiment, as described in our previous work [21]. At first, B4C and 1–4 vol% HEA powders were mixed by ball milling with WC balls and alcohol medium at 100 r/min for 2 h. After that, the slurry was dried in a vacuum oven. The mixed powders were sintered in a SPS apparatus (HP D25, FCT Systeme GmbH, Rauenstein, Germany) with a vacuum chamber and a 40-mm-inner diameter graphite die. A fixed heating rate of 100/min, a fixed applied stress of 40 MPa and a soaking time of 20 min were used. The soaking temperatures were 1900 °C, 1950 °C, 2000 °C. The samples with 1%, 2%, 3% and 4% of HEA in volume fraction were named Specimen A, B, C and D, respectively. The instantaneous height L of each sample was calculated via displacement of piston during the SPS process. The thermal expansion deviation can be eliminated from the recorded data using the blank test performed by submitting a fully dense pellet into the die. Thus, the instantaneous relative density D can be calculated via the following expression [7]: D¼
Lf Df L
ð1Þ
where Df is the final relative density of the samples measured by Archimedes method which was repeated for at least 5 times; Lf is the final height of the samples.
M. Zhang et al. / Scripta Materialia 163 (2019) 34–39
The as-prepared samples were coated with Au and characterized by scanning electron microscopy (SEM, NOVATM NanoSEM230, Holland). The average grain sizes of the samples were obtained from images of the polished and etched surfaces by measuring a hundred grains. High resolution microstructures of samples were characterized by transmission electron microscopy (TEM, Tecnai G2 F20 S-TWIN, FEI, USA). At first, effects of different temperature and varied HEA volume fractions- on the properties of B4 C powders were investigated. Fig. 1a shows the dependences of instantaneous relative density and the densification rate (1/D(dD/dt)) on the sintering temperature for sample C3. It can be found that densification started at around 1600 °C and densification rate exhibited a clear peak at around 1900 °C. Also, a weaker peak appeared at around 1200 °C, which was consistent with the HEA melting point. Grain sizes of samples with different HEA volume fraction sintered at different temperature are shown in Fig. 1b. Alarmingly, adding 2 vol% of HEA can significantly promote the grain growth compared with 1 vol% HEA. The grain growth becomes, however, less profound when further increases either the HEA aid fraction (B to D) or sintering temperature (1900 to 2000 °C). It can be postulated that HEA melted and adhered to the B 4 C particles joints by capillarity, which consequently increased the contact area and facilitate the diffusion between HEA and B 4C, resulting in promoted densification and grain growth. Fig. 1c shows the relative density variation versus sintering temperature with different HEA aid fraction. Fig. 1d shows the relative
35
density variation versus sintering time at different temperature (1900–2000 °C) for specimen A to D. With the increase of HEA aid content, the difference between the densification curves at different sintering temperatures became smaller, which indicates that appropriate HEA addition can promote the densification and lower the sintering temperature. Matter transport during SPS is similar to that of hot-pressing, which has been successfully elaborated by high-temperature creep models [13]. The steady-state creep strain, also referred to as densification rate, έ, which occurs at the high temperature stage of SPS, can be described by Bernard-Granger model as [19]: ε_ ¼
dε 1 dD p ¼ ¼ Aϕμ eff b=kT ðb=GÞ ðσ eff =μ eff Þn dt D dt
ð2Þ
where t is the time, A a constant, Φ the diffusion coefficient, μeff the instantaneous shear modulus of the powder bed, b the Burgers vector, k the Boltzmann constant, T the thermodynamic temperature, G the grain size, σeff the instantaneous effective macroscopic applied stress acting on the powder bed, p the grain size exponent and n the stress exponent. The instantaneous shear modulus can be described by an empirical equation with the elastic modulus E and Poisson ratio ʋ [7]: μ eff ¼
Eth D−D0 2ð1 þ ν eff Þ 1−D0
ð3Þ
Fig. 1. The effects of temperature and HEA sintering aid volume fraction on densification of B4C powders. (a) Densification rate and relative density vs. sintering temperature for specimen C3; (b) Grain size evolution and SEM images of B4C for different temperature and volume of HEA sintering aid; (c) The relative density of the samples for different temperature and volume of HEA volume; (d) The sintering curves with different HEA volume fraction and temperature.
36
M. Zhang et al. / Scripta Materialia 163 (2019) 34–39
where Eth is the theoretical elastic modulus of dense material, which is 470 GPa for most pure dense B4C ceramics [25]; ʋeff is the effective Poisson ratio which is 0.18 [25]; D 0 is the starting green density which is around 60% [7]. According to Fig. 1a, densification started at around 1600 °C, which is obviously higher than the melting point of sintering aid HEA. The proposed formation process of liquid phase is shown in Fig. 2a. When the sintering aid melted, the axial pressure applied to the graphite die forced the B 4 C powders to fill up the vacancies and improved their contacts with the other B 4 C powders, and the formed liquid phase filled the connected pores within the matrix. Therefore, the effect of the effective macroscopic applied stress caused by the amount of liquid phase must be considered. Assuming that the B 4C particles are identical spheres, in the temperature range of 1300–1600 °C, where the sintering aid was melted and the B4C powder were compacted, the effective density of B4C ceramic, Dreal, can be described as: mC ρth πr 2 ¼ Df mC L− ρth πr 2
The average area, S, of a contact between two adjacent particles, has a geometric relationship as: S¼
π ðDreal −D0 Þ 2 R 3 ð1−D0 Þ
where R is the initial particle radius. The macroscopic applied pressure σ is applied to the compact, then the average contact force, f, is easily shown to be as follow: f ¼
4πR2 σ ZDreal
ð4Þ
ð6Þ
where Z = 12Dreal is the contact neighbors per particle [26]. In order to simplify the calculation, it is assumed that the pressure transfer mainly relies on B4 C contact particles at lower relative density stage, without considering the negligible contribution of the liquid phase matter. The contact force produces a contact pressure, which corresponds to the effective applied pressure, σeff, on each particle contact, shown as follow:
Lf −
Dreal
ð5Þ
σ eff ¼
f 4πR2 ¼ σ S SZDreal
ð7Þ
Combining Eqs. (4–7), the effective applied pressure can be given as: where m is the mass of the powder, C is the volume of the sintering aid, r is the radius of the die. ρth is the theoretical density of B 4CHEA ceramics. Compared to Eq. (1), the influence of formed liquid phase on relative density was considered in this case.
σ eff ¼
σ ð1−D0 Þ Dreal 2 ðDreal −D0 Þ
ð8Þ
In most of the previous studies, effective applied pressure was calculated by apparent relative density according to BernardGranger's original model. By contrast, using the modified relative density and effective applied pressure can minimize the deviation caused by the different volume sintering aid. This is proven by Fig. 2b which shows the comparison of σeff obtained by the original model and the modified model. In general, the deviation of effective apparent pressure calculated by two models (compare dash line to solid line of each sample) obviously decreased with the increase of the relative density. More importantly, higher fraction of sintering aid resulted in a more distinguished difference of σeff between the two models, bettering agreeing with the fact that more sintering aid means more liquid phase produced. As a result, at the same apparent relative density, the more amount of sintering aid led to the decrease of B 4 C matrix, and the apparent pressure generated a higher pressure on the smaller contact area inside the matrix compact. The transmission electron microscopy (TEM) analyses of sample D3 are shown in Fig. 3. Fig. 3a shows the bright-field image where the HEA (darker area) is located on the grain boundary and fills up an interior vacancy. The HRTEM images of the selected HEA and B4C areas are shown in Fig. 3b and c, respectively, where their insets depict the corresponding Fractional Fourier transform. The interplanar distance of B4C (011) and HEA (111) were measured to be around 0.43 nm and 0.22 nm, respectively, which is well matched to the value obtained from the HEA PDF card. The EDX spectrum of a representative point in the darker area in Fig. 3a is shown in Fig. 3d, confirming that the HEA is mainly composed of Fe, Mn, Co and Cr, without detection of B and C elements. It is known that HEA does not completely react with B4C and still exists in the form of liquid phase. Incidentally, the element W was introduced by high-energy milling. Using the modified σeff, to merge Eqs. (3) and (8) with Eq. (2), and giving the fact that the grains did not grow in this temperature range, it can be simplified as: Qd
Fig. 2. (a) Assumptive formation process of liquid phase; (b) σeff bias between original model and modified model.
1 1 dD e− RT ¼B ðσ eff =μ eff Þn μ eff D dt T
ð9Þ
M. Zhang et al. / Scripta Materialia 163 (2019) 34–39
37
Fig. 3. TEM analyses of specimen D3: (a) bright field image; (b) HRTEM image of sintering aid; (c) HRTEM image of matrix; (d) EDX pattern of sintering aid.
where Qd is the apparent activation energy, which is related to the densification process and also called densification activation energy, B is a constant. Assuming only one Qd was obtained at a fixed fraction of HEA, stress exponent n values at different soaking temperatures were fitted and shown in Fig. 4a, which exhibiting different values at different regime. For the four samples with different HEA fractions, n kept at around 0.85 in the relatively low-stress regime (the upper right part of the curves). The densification rate D1 dD was set as 0.0004, dt which was in low-stress regime. The effect of HEA fractions on the Qd values were shown in Fig. 4b. It can be seen that increasing the fractions of HEA from 1% to 4% can effectively reduce the apparent activation energy Qd from 234.4 kJ/mol to 75 kJ/mol. At a highstress regime (the left side of the curve), n was around 2 at soaking temperatures of 1900 and 1950 °C; n was higher than 3 at soaking temperature 2000 °C (Fig. 4a). Therefore, the identified two distinguishable stress regimes clearly indicated two distinct densification mechanisms of B4C-HEA ceramics during soaking: first, in the low-stress (intermediate) stage where n was around 0.85, the densification was controlled by atoms diffusion or viscous flow. This n value also accorded with the results reported by Tadaaki and Joseph [27]; second, in the high-stress (final) stage where n value was higher than 3, the densification process followed the known dislocation model proposed by Weertman [28], in which the dislocation-climbcontrolled mechanism was dominant, which has also been confirmed by Bernard-Granger [13] and Deng [5,29]. Antou's model [18] applied different pressures to calculated Qd in order to eliminate the deviation caused by its strong dependence of the stress exponent n. But it is well known that the stress exponent n
and the apparent activation energy Qd are dependent on the pressure. For example, the sintering activation energy was calculated to be 717 kJ/mol [25] during the pressureless sintering of B4C and a relatively low value of 660 kJ/mol [30] was obtained under the pressure of 30 MPa during the hot pressing. In our previous work, pure B4C was sintered using SPS with a fixed pressure of 40 MPa, where apparent activation energy of 459.6 kJ/mol was obtained [7]. In the present work, to avoid the effect of variation of pressure, a fixed pressure of 40 MPa was applied to study the densification and the effect of liquid phase volume from HEA quantitatively. The HEA promote the densification of B4C ceramics during SPS by reducing the apparent activation energy from 234.4 kJ/mol for 4% addition of HEA to 75 kJ/mol for 1% addition of HEA. In summary, a modified densification model was proposed by considering different fractions of HEA sintering aid to study their effects on effective applied pressure and densification mechanisms. Results showed that HEA as an inert sintering aid did not react with B4C matrix and contributed the densification and grain growth. Further, it is proven that adjusting the sintering aid amount can effectively reduce the activation energy from 234.4 ± 6.8 kJ/mol to 75 kJ/mol and promote densification during SPS process. Acknowledgements This work was supported by the National Key R&D Program of China (grant Nos. 2017YFB0305401), National Natural Science Foundation of China (grant Nos. 51874369, 51474245, 51871249), Natural Science Foundation of Hunan Province (2018JJ3659) and Huxiang Young Talents Plan (grant No.2018RS3007).
38 M. Zhang et al. / Scripta Materialia 163 (2019) 34–39
Fig. 4. (a) Stress exponent n obtained with different sintering aid additions; (b) Apparent activation energy Qd of specimens with different sintering aid additions.
M. Zhang et al. / Scripta Materialia 163 (2019) 34–39
References [1] S. Xie, R. Li, T. Yuan, M. Zhang, M. Wang, H. Wu, F. Zeng, Scr. Mater. 149 (2018) 125. [2] J. Zou, S. Grasso, L. Liu, H. Ma, M. Reece, J. Binner, Scr. Mater. 156 (2018) 115. [3] M.A. Auger, Y. Huang, H. Zhang, C.A. Jones, Z. Hong, M.P. Moody, S.G. Roberts, P.S. Grant, J. Alloys Compd. 762 (2018) 678. [4] T.N. Maity, K. Biswas, B. Basu, Acta Mater. 152 (2018) 215. [5] S. Deng, R. Li, T. Yuan, S. Xie, M. Zhang, K. Zhou, P. Cao, Scr. Mater. 143 (2018) 25. [6] G. Liu, R. Li, T. Yuan, M. Zhang, F. Zeng, Int. J. Refract. Met. Hard Mater. 66 (2017) 68. [7] M. Zhang, T. Yuan, R. Li, S. Xie, M. Wang, Q. Weng, Ceram. Int. 44 (2018) 3571. [8] X. Zhang, Z. Zhang, R. Wen, G. Wang, X. Zhang, J. Mu, H. Che, W. Wang, Ceram. Int. 44 (2018) 2615. [9] M. Zhang, T. Yuan, R. Li, J. Micromech. Mol. Phys. (2017) 1750014. [10] Q. Song, Z. Zhang, Z. Hu, S. Yin, H. Wang, H. Wang, X. Cheng, Mater. Res. Express 5 (2018). [11] J.G. Santanach, A. Weibel, C. Estournès, Q. Yang, C. Laurent, A. Peigney, Acta Mater. 59 (2011) 1400. [12] M. Gendre, A. Maître, G. Trolliard, Acta Mater. 58 (2010) 2598. [13] G. Bernard-Granger, C. Guizard, Acta Mater. 55 (2007) 3493. [14] W. Ji, J. Zhang, W. Wang, H. Wang, F. Zhang, Y. Wang, Z. Fu, J. Eur. Ceram. Soc. 35 (2015) 879. [15] R. Seetharam, S.K. Subbu, M.J. Davidson, J. Eng. Mater. Technol. ASME 140 (2018).
39
[16] S. Eqtesadi, A. Motealleh, F.H. Perera, P. Miranda, A. Pajares, R. Wendelbo, F. Guiberteau, A.L. Ortiz, Scr. Mater. 145 (2018) 14. [17] T.G. Abzianidze, A.M. Eristavi, S.O. Shalamberidze, J. Solid State Chem. 154 (2000) 191. [18] G. Antou, N. Pradeilles, M. Gendre, A. Maître, Scr. Mater. 101 (2015) 103. [19] S. Deng, T. Yuan, R. Li, F. Zeng, G. Liu, X. Zhou, Powder Technol. 310 (2017) 264. [20] P. Guyot, G. Antou, N. Pradeilles, A. Weibel, M. Vandenhende, G. Chevallier, A. Peigney, C. Estournès, A. Maître, Scr. Mater. 84–85 (2014) 35. [21] M. Zhang, X. Feng, T. Yuan, R. Li, Int. J. Appl. Ceram. Technol. (2019) 389. [22] R. Li, M. Wang, T. Yuan, B. Song, Y. Shi, Metall. Mater. Trans. A 48A (2017) 841. [23] Z. Li, K.G. Pradeep, Y. Deng, D. Raabe, C.C. Tasan, Nature 534 (2016) 227. [24] Z. Zhang, M.M. Mao, J. Wang, B. Gludovatz, Z. Zhang, S.X. Mao, E.P. George, Q. Yu, R.O. Ritchie, Nat. Commun. 6 (2015), 10143. [25] S. Ebrahimi, M.S. Heydari, H.R. Baharvandi, N. Ehsani, Int. J. Refract. Met. Hard Mater. 57 (2016) 78. [26] A.S. Helle, K.E. Easterling, M.F. Ashby, Acta Metall. (12) (1985) 2163. [27] J.A.P. Tadaaki Sugita, J. Am. Ceram. Soc. 11 (1970) 609. [28] J. Weertman, Trans. ASM 61 (1968) 681. [29] S. Deng, R. Li, T. Yuan, P. Cao, Mater. Lett. 229 (2018) 126. [30] I. Mizrahi, A. Raviv, H. Dilman, M. Aizenshtein, M.P. Dariel, N. Frage, J. Mater. Sci. 42 (2007) 6923.
Contents lists available at ScienceDirect
Scripta Materialia journal homepage: www.elsevier.com/locate/scriptamat
Effect of low-melting-point sintering aid on densification mechanisms of boron carbide during spark plasma sintering Mei Zhang a, Ruidi Li a,⁎, Tiechui Yuan a, Xiao Feng b, Siyao Xie a a b
Science and Technology on High Strength Structural Materials Laboratory, State Key Laboratory of Powder Metallurgy, Central South University, Changsha 410083, PR China Hunan Zoomwe Zheng Yuan Advanced Material trade Co., Ltd, Changsha 410000, PR China
a r t i c l e
i n f o
Article history: Received 5 November 2018 Received in revised form 30 December 2018 Accepted 31 December 2018 Available online xxxx Keywords: Boron carbide High entropy alloy Densification Spark plasma sintering
a b s t r a c t A densification creep model was proposed to analyze the densification mechanism involved in spark plasma sintering (SPS) of boron carbide containing low-melting-point sintering aid. This model incorporated the effect of the sintering aid on relative density as well as the actual internal stress during SPS of boron carbide ceramics. The internal stress bias caused by sintering aid was considered and a more accurate effective stress was used to investigate the kinetics during SPS. The proposed model explains why an increase of sintering aid amount decreases the sintering activation energy and promotes densification. © 2019 Published by Elsevier Ltd on behalf of Acta Materialia Inc.
Spark plasma sintering (SPS) is an advanced consolidation technique which can simultaneously achieve high temperature, high pressure and rapid densification [1–4]. This technique has been successfully applied to sinter refractory materials such as W [5], TiCN [6], and B4C [7–10]. The densification mechanisms of SPS pure ceramics are considered to be very important and [6,11,12] have been thoroughly investigated using the creep deformation model proposed by Bernard-Granger [13]. The densification models considering addition of sintering aid for SPS were rarely studied, although adding sintering aid has been widely used for promotion of sintering densification in covalent ceramics, such as B4C [14–17]. During the sintering process, low melting point sintering aid becomes liquid phase at an elevated temperature, resulting in the variation of actual pressure of the compact [14]. However, such internal biases caused by the formation of liquid phase during SPS were hardly reported. Studies to date using conventional analyzing methods failed to consider the fact that the consequently varied pressure can significantly affect the densification process [13,18–20]. Therefore, it is required to study the effect of low melting point sintering aid [21] on the densification mechanisms involved in the sintering of high-temperature ceramics. Recent progress in the high entropy alloys (HEAs) showed the feasibility of HEAs as efficient low melting point sintering aids for high temperature ceramics due to their excellent stabilities and mechanical properties [22–24]. In the present work, nonequiatomic
⁎ Corresponding author. E-mail address: [email protected] (R. Li).
https://doi.org/10.1016/j.scriptamat.2018.12.036 1359-6462/© 2019 Published by Elsevier Ltd on behalf of Acta Materialia Inc.
HEA Fe50Mn30Co10Cr10 as a low melting point sintering aid which is inert to B4C was applied to study the densification mechanisms of B4C during the SPS process. B4C powders with an average diameter of 2.11 μm and lab-made nonequiatomic Fe50Mn30Co10Cr10 HEA powders (gas atomization) were used for experiment, as described in our previous work [21]. At first, B4C and 1–4 vol% HEA powders were mixed by ball milling with WC balls and alcohol medium at 100 r/min for 2 h. After that, the slurry was dried in a vacuum oven. The mixed powders were sintered in a SPS apparatus (HP D25, FCT Systeme GmbH, Rauenstein, Germany) with a vacuum chamber and a 40-mm-inner diameter graphite die. A fixed heating rate of 100/min, a fixed applied stress of 40 MPa and a soaking time of 20 min were used. The soaking temperatures were 1900 °C, 1950 °C, 2000 °C. The samples with 1%, 2%, 3% and 4% of HEA in volume fraction were named Specimen A, B, C and D, respectively. The instantaneous height L of each sample was calculated via displacement of piston during the SPS process. The thermal expansion deviation can be eliminated from the recorded data using the blank test performed by submitting a fully dense pellet into the die. Thus, the instantaneous relative density D can be calculated via the following expression [7]: D¼
Lf Df L
ð1Þ
where Df is the final relative density of the samples measured by Archimedes method which was repeated for at least 5 times; Lf is the final height of the samples.
M. Zhang et al. / Scripta Materialia 163 (2019) 34–39
The as-prepared samples were coated with Au and characterized by scanning electron microscopy (SEM, NOVATM NanoSEM230, Holland). The average grain sizes of the samples were obtained from images of the polished and etched surfaces by measuring a hundred grains. High resolution microstructures of samples were characterized by transmission electron microscopy (TEM, Tecnai G2 F20 S-TWIN, FEI, USA). At first, effects of different temperature and varied HEA volume fractions- on the properties of B4 C powders were investigated. Fig. 1a shows the dependences of instantaneous relative density and the densification rate (1/D(dD/dt)) on the sintering temperature for sample C3. It can be found that densification started at around 1600 °C and densification rate exhibited a clear peak at around 1900 °C. Also, a weaker peak appeared at around 1200 °C, which was consistent with the HEA melting point. Grain sizes of samples with different HEA volume fraction sintered at different temperature are shown in Fig. 1b. Alarmingly, adding 2 vol% of HEA can significantly promote the grain growth compared with 1 vol% HEA. The grain growth becomes, however, less profound when further increases either the HEA aid fraction (B to D) or sintering temperature (1900 to 2000 °C). It can be postulated that HEA melted and adhered to the B 4 C particles joints by capillarity, which consequently increased the contact area and facilitate the diffusion between HEA and B 4C, resulting in promoted densification and grain growth. Fig. 1c shows the relative density variation versus sintering temperature with different HEA aid fraction. Fig. 1d shows the relative
35
density variation versus sintering time at different temperature (1900–2000 °C) for specimen A to D. With the increase of HEA aid content, the difference between the densification curves at different sintering temperatures became smaller, which indicates that appropriate HEA addition can promote the densification and lower the sintering temperature. Matter transport during SPS is similar to that of hot-pressing, which has been successfully elaborated by high-temperature creep models [13]. The steady-state creep strain, also referred to as densification rate, έ, which occurs at the high temperature stage of SPS, can be described by Bernard-Granger model as [19]: ε_ ¼
dε 1 dD p ¼ ¼ Aϕμ eff b=kT ðb=GÞ ðσ eff =μ eff Þn dt D dt
ð2Þ
where t is the time, A a constant, Φ the diffusion coefficient, μeff the instantaneous shear modulus of the powder bed, b the Burgers vector, k the Boltzmann constant, T the thermodynamic temperature, G the grain size, σeff the instantaneous effective macroscopic applied stress acting on the powder bed, p the grain size exponent and n the stress exponent. The instantaneous shear modulus can be described by an empirical equation with the elastic modulus E and Poisson ratio ʋ [7]: μ eff ¼
Eth D−D0 2ð1 þ ν eff Þ 1−D0
ð3Þ
Fig. 1. The effects of temperature and HEA sintering aid volume fraction on densification of B4C powders. (a) Densification rate and relative density vs. sintering temperature for specimen C3; (b) Grain size evolution and SEM images of B4C for different temperature and volume of HEA sintering aid; (c) The relative density of the samples for different temperature and volume of HEA volume; (d) The sintering curves with different HEA volume fraction and temperature.
36
M. Zhang et al. / Scripta Materialia 163 (2019) 34–39
where Eth is the theoretical elastic modulus of dense material, which is 470 GPa for most pure dense B4C ceramics [25]; ʋeff is the effective Poisson ratio which is 0.18 [25]; D 0 is the starting green density which is around 60% [7]. According to Fig. 1a, densification started at around 1600 °C, which is obviously higher than the melting point of sintering aid HEA. The proposed formation process of liquid phase is shown in Fig. 2a. When the sintering aid melted, the axial pressure applied to the graphite die forced the B 4 C powders to fill up the vacancies and improved their contacts with the other B 4 C powders, and the formed liquid phase filled the connected pores within the matrix. Therefore, the effect of the effective macroscopic applied stress caused by the amount of liquid phase must be considered. Assuming that the B 4C particles are identical spheres, in the temperature range of 1300–1600 °C, where the sintering aid was melted and the B4C powder were compacted, the effective density of B4C ceramic, Dreal, can be described as: mC ρth πr 2 ¼ Df mC L− ρth πr 2
The average area, S, of a contact between two adjacent particles, has a geometric relationship as: S¼
π ðDreal −D0 Þ 2 R 3 ð1−D0 Þ
where R is the initial particle radius. The macroscopic applied pressure σ is applied to the compact, then the average contact force, f, is easily shown to be as follow: f ¼
4πR2 σ ZDreal
ð4Þ
ð6Þ
where Z = 12Dreal is the contact neighbors per particle [26]. In order to simplify the calculation, it is assumed that the pressure transfer mainly relies on B4 C contact particles at lower relative density stage, without considering the negligible contribution of the liquid phase matter. The contact force produces a contact pressure, which corresponds to the effective applied pressure, σeff, on each particle contact, shown as follow:
Lf −
Dreal
ð5Þ
σ eff ¼
f 4πR2 ¼ σ S SZDreal
ð7Þ
Combining Eqs. (4–7), the effective applied pressure can be given as: where m is the mass of the powder, C is the volume of the sintering aid, r is the radius of the die. ρth is the theoretical density of B 4CHEA ceramics. Compared to Eq. (1), the influence of formed liquid phase on relative density was considered in this case.
σ eff ¼
σ ð1−D0 Þ Dreal 2 ðDreal −D0 Þ
ð8Þ
In most of the previous studies, effective applied pressure was calculated by apparent relative density according to BernardGranger's original model. By contrast, using the modified relative density and effective applied pressure can minimize the deviation caused by the different volume sintering aid. This is proven by Fig. 2b which shows the comparison of σeff obtained by the original model and the modified model. In general, the deviation of effective apparent pressure calculated by two models (compare dash line to solid line of each sample) obviously decreased with the increase of the relative density. More importantly, higher fraction of sintering aid resulted in a more distinguished difference of σeff between the two models, bettering agreeing with the fact that more sintering aid means more liquid phase produced. As a result, at the same apparent relative density, the more amount of sintering aid led to the decrease of B 4 C matrix, and the apparent pressure generated a higher pressure on the smaller contact area inside the matrix compact. The transmission electron microscopy (TEM) analyses of sample D3 are shown in Fig. 3. Fig. 3a shows the bright-field image where the HEA (darker area) is located on the grain boundary and fills up an interior vacancy. The HRTEM images of the selected HEA and B4C areas are shown in Fig. 3b and c, respectively, where their insets depict the corresponding Fractional Fourier transform. The interplanar distance of B4C (011) and HEA (111) were measured to be around 0.43 nm and 0.22 nm, respectively, which is well matched to the value obtained from the HEA PDF card. The EDX spectrum of a representative point in the darker area in Fig. 3a is shown in Fig. 3d, confirming that the HEA is mainly composed of Fe, Mn, Co and Cr, without detection of B and C elements. It is known that HEA does not completely react with B4C and still exists in the form of liquid phase. Incidentally, the element W was introduced by high-energy milling. Using the modified σeff, to merge Eqs. (3) and (8) with Eq. (2), and giving the fact that the grains did not grow in this temperature range, it can be simplified as: Qd
Fig. 2. (a) Assumptive formation process of liquid phase; (b) σeff bias between original model and modified model.
1 1 dD e− RT ¼B ðσ eff =μ eff Þn μ eff D dt T
ð9Þ
M. Zhang et al. / Scripta Materialia 163 (2019) 34–39
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Fig. 3. TEM analyses of specimen D3: (a) bright field image; (b) HRTEM image of sintering aid; (c) HRTEM image of matrix; (d) EDX pattern of sintering aid.
where Qd is the apparent activation energy, which is related to the densification process and also called densification activation energy, B is a constant. Assuming only one Qd was obtained at a fixed fraction of HEA, stress exponent n values at different soaking temperatures were fitted and shown in Fig. 4a, which exhibiting different values at different regime. For the four samples with different HEA fractions, n kept at around 0.85 in the relatively low-stress regime (the upper right part of the curves). The densification rate D1 dD was set as 0.0004, dt which was in low-stress regime. The effect of HEA fractions on the Qd values were shown in Fig. 4b. It can be seen that increasing the fractions of HEA from 1% to 4% can effectively reduce the apparent activation energy Qd from 234.4 kJ/mol to 75 kJ/mol. At a highstress regime (the left side of the curve), n was around 2 at soaking temperatures of 1900 and 1950 °C; n was higher than 3 at soaking temperature 2000 °C (Fig. 4a). Therefore, the identified two distinguishable stress regimes clearly indicated two distinct densification mechanisms of B4C-HEA ceramics during soaking: first, in the low-stress (intermediate) stage where n was around 0.85, the densification was controlled by atoms diffusion or viscous flow. This n value also accorded with the results reported by Tadaaki and Joseph [27]; second, in the high-stress (final) stage where n value was higher than 3, the densification process followed the known dislocation model proposed by Weertman [28], in which the dislocation-climbcontrolled mechanism was dominant, which has also been confirmed by Bernard-Granger [13] and Deng [5,29]. Antou's model [18] applied different pressures to calculated Qd in order to eliminate the deviation caused by its strong dependence of the stress exponent n. But it is well known that the stress exponent n
and the apparent activation energy Qd are dependent on the pressure. For example, the sintering activation energy was calculated to be 717 kJ/mol [25] during the pressureless sintering of B4C and a relatively low value of 660 kJ/mol [30] was obtained under the pressure of 30 MPa during the hot pressing. In our previous work, pure B4C was sintered using SPS with a fixed pressure of 40 MPa, where apparent activation energy of 459.6 kJ/mol was obtained [7]. In the present work, to avoid the effect of variation of pressure, a fixed pressure of 40 MPa was applied to study the densification and the effect of liquid phase volume from HEA quantitatively. The HEA promote the densification of B4C ceramics during SPS by reducing the apparent activation energy from 234.4 kJ/mol for 4% addition of HEA to 75 kJ/mol for 1% addition of HEA. In summary, a modified densification model was proposed by considering different fractions of HEA sintering aid to study their effects on effective applied pressure and densification mechanisms. Results showed that HEA as an inert sintering aid did not react with B4C matrix and contributed the densification and grain growth. Further, it is proven that adjusting the sintering aid amount can effectively reduce the activation energy from 234.4 ± 6.8 kJ/mol to 75 kJ/mol and promote densification during SPS process. Acknowledgements This work was supported by the National Key R&D Program of China (grant Nos. 2017YFB0305401), National Natural Science Foundation of China (grant Nos. 51874369, 51474245, 51871249), Natural Science Foundation of Hunan Province (2018JJ3659) and Huxiang Young Talents Plan (grant No.2018RS3007).
38 M. Zhang et al. / Scripta Materialia 163 (2019) 34–39
Fig. 4. (a) Stress exponent n obtained with different sintering aid additions; (b) Apparent activation energy Qd of specimens with different sintering aid additions.
M. Zhang et al. / Scripta Materialia 163 (2019) 34–39
References [1] S. Xie, R. Li, T. Yuan, M. Zhang, M. Wang, H. Wu, F. Zeng, Scr. Mater. 149 (2018) 125. [2] J. Zou, S. Grasso, L. Liu, H. Ma, M. Reece, J. Binner, Scr. Mater. 156 (2018) 115. [3] M.A. Auger, Y. Huang, H. Zhang, C.A. Jones, Z. Hong, M.P. Moody, S.G. Roberts, P.S. Grant, J. Alloys Compd. 762 (2018) 678. [4] T.N. Maity, K. Biswas, B. Basu, Acta Mater. 152 (2018) 215. [5] S. Deng, R. Li, T. Yuan, S. Xie, M. Zhang, K. Zhou, P. Cao, Scr. Mater. 143 (2018) 25. [6] G. Liu, R. Li, T. Yuan, M. Zhang, F. Zeng, Int. J. Refract. Met. Hard Mater. 66 (2017) 68. [7] M. Zhang, T. Yuan, R. Li, S. Xie, M. Wang, Q. Weng, Ceram. Int. 44 (2018) 3571. [8] X. Zhang, Z. Zhang, R. Wen, G. Wang, X. Zhang, J. Mu, H. Che, W. Wang, Ceram. Int. 44 (2018) 2615. [9] M. Zhang, T. Yuan, R. Li, J. Micromech. Mol. Phys. (2017) 1750014. [10] Q. Song, Z. Zhang, Z. Hu, S. Yin, H. Wang, H. Wang, X. Cheng, Mater. Res. Express 5 (2018). [11] J.G. Santanach, A. Weibel, C. Estournès, Q. Yang, C. Laurent, A. Peigney, Acta Mater. 59 (2011) 1400. [12] M. Gendre, A. Maître, G. Trolliard, Acta Mater. 58 (2010) 2598. [13] G. Bernard-Granger, C. Guizard, Acta Mater. 55 (2007) 3493. [14] W. Ji, J. Zhang, W. Wang, H. Wang, F. Zhang, Y. Wang, Z. Fu, J. Eur. Ceram. Soc. 35 (2015) 879. [15] R. Seetharam, S.K. Subbu, M.J. Davidson, J. Eng. Mater. Technol. ASME 140 (2018).
39
[16] S. Eqtesadi, A. Motealleh, F.H. Perera, P. Miranda, A. Pajares, R. Wendelbo, F. Guiberteau, A.L. Ortiz, Scr. Mater. 145 (2018) 14. [17] T.G. Abzianidze, A.M. Eristavi, S.O. Shalamberidze, J. Solid State Chem. 154 (2000) 191. [18] G. Antou, N. Pradeilles, M. Gendre, A. Maître, Scr. Mater. 101 (2015) 103. [19] S. Deng, T. Yuan, R. Li, F. Zeng, G. Liu, X. Zhou, Powder Technol. 310 (2017) 264. [20] P. Guyot, G. Antou, N. Pradeilles, A. Weibel, M. Vandenhende, G. Chevallier, A. Peigney, C. Estournès, A. Maître, Scr. Mater. 84–85 (2014) 35. [21] M. Zhang, X. Feng, T. Yuan, R. Li, Int. J. Appl. Ceram. Technol. (2019) 389. [22] R. Li, M. Wang, T. Yuan, B. Song, Y. Shi, Metall. Mater. Trans. A 48A (2017) 841. [23] Z. Li, K.G. Pradeep, Y. Deng, D. Raabe, C.C. Tasan, Nature 534 (2016) 227. [24] Z. Zhang, M.M. Mao, J. Wang, B. Gludovatz, Z. Zhang, S.X. Mao, E.P. George, Q. Yu, R.O. Ritchie, Nat. Commun. 6 (2015), 10143. [25] S. Ebrahimi, M.S. Heydari, H.R. Baharvandi, N. Ehsani, Int. J. Refract. Met. Hard Mater. 57 (2016) 78. [26] A.S. Helle, K.E. Easterling, M.F. Ashby, Acta Metall. (12) (1985) 2163. [27] J.A.P. Tadaaki Sugita, J. Am. Ceram. Soc. 11 (1970) 609. [28] J. Weertman, Trans. ASM 61 (1968) 681. [29] S. Deng, R. Li, T. Yuan, P. Cao, Mater. Lett. 229 (2018) 126. [30] I. Mizrahi, A. Raviv, H. Dilman, M. Aizenshtein, M.P. Dariel, N. Frage, J. Mater. Sci. 42 (2007) 6923.