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Implementing continuous freeze-casting by separated control of thermal gradient and solidification rate
International Journal of Heat and Mass Transfer 133 (2019) 986–993
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Implementing continuous freeze-casting by separated control of thermal gradient and solidification rate Tao Zheng, Jun-jie Li, Li-lin Wang ⇑, Zhi-jun Wang ⇑, Jin-cheng Wang State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, PR China
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Article history: Received 10 October 2018 Received in revised form 2 January 2019 Accepted 3 January 2019
Keywords: Freeze-casting Porous materials Directional freezing Heat conduction
a b s t r a c t Ice-templated porous materials from freeze-casting have attracted widespread attentions in many research fields. Several apparatuses based on the freeze-casting have been proposed to fabricate aligned porous materials, where the unidirectional growth of ice is mainly controlled by changing temperatures at the sample ends. The thermal conduction cross the whole sample restricts the freezing process in traditional freeze-casting methods. In this paper, a new approach of freeze-casting is proposed, where the thermal gradient and the solidification rate can be controlled independently for continuous directional freezing. The lateral thermal conduction provides an effective way to produce axially homogeneous porous structural materials with unrestricted length and controllable microstructures. Moreover, the axial homogeneity can also be further improved by adding a small amount of sucrose. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Freeze-casting is a versatile technique to fabricate porous materials with attractive properties via ice-templating [1,2]. It can produce porous materials with highly controllable porosities. Freeze-casting is a kind of freeze-dried physical process [3], where the ice morphology determines microstructures of porous materials and hence their properties [4–6]. During the freezing process, particles in the slurry are ejected from the solidification front and trapped within the growing lamellar ice crystals. The porous morphology and microstructure can be controlled by adjusting processing parameters, such as solid content, particle size, additives, and freezing rate. Since the porous structures are the replica of ice crystals, it is quite important to control the growth of ice crystals. Traditionally, the crystallization process in the freeze-casting method is mainly controlled by adjusting temperatures at the sample ends to obtain the unidirectional solidification. According to the method of temperature-control, the single-side and doubleside cooling approaches have been proposed successively. In the single-side cooling method, the bottom of the mold is made of a copper plate with high thermal conductivity, while the side of the mold is made of resin with pretty low thermal conductivity. After chilled by a freezing bath, the slurries are frozen from bottom
⇑ Corresponding authors. E-mail addresses: [email protected] (L.-l. Wang), [email protected] (Z.-j. Wang). https://doi.org/10.1016/j.ijheatmasstransfer.2019.01.014 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
to top in the vertical direction. This method has been widely used to prepare porous materials with aligned pores [7–9]. In this single-side cooling method, the interface propagation rate V decreases along with the freezing process with V / t 1=2 when Stefan number (ratio of sensible heat to latent heat) is small [10,11]. The retarded growth of ice results in the significant change of microstructures along the growth direction, leading to the nonuniform microstructures across the whole sample. In order to overcome this disadvantage, Deville et al. [3] proposed a double-side cooling approach, where two copper cold fingers are set at both ends of the sample. The bottom and upper plates are cooled simultaneously to obtain a thermal gradient and unidirectional solidification. The porous structures can be tailored by controlling the thermal gradient and cooling rate. The side of the mold in double-side cooling approach is made of polytetrafluorethylene with poor thermal conductivity (about 0.3 W/(mK) [12]), which is expected to be thermal insulation wall. Thus, most of the heat flows along the axial direction to the bottom. This improved approach has been widely used to prepare porous materials [13–15]. However, in this approach, the thermal gradient and cooling rate in the sample is greatly affected by the sample length due to the restriction of thermal conduction in the ice and the slurry. Usually, the sample length is in the centimeter range about 3 cm [16,17]. Moreover, if the cooling rates are the same at both ends, the cooling rate cannot be directly used to describe the growth rate due to 4 times discrepancies in the thermal conductivity between ice (2.22 W/(mK) [18]) and water (0.54 W/(mK) [19]).
T. Zheng et al. / International Journal of Heat and Mass Transfer 133 (2019) 986–993
Therefore, it is difficult to regulate the ice growth only through controlling the temperatures at the ends of a long sample. To solve this problem, Waschkies et al. [20] improved the double-side cooling system by thermal calculation and setting different cooling rates to the upper and bottom plates. Through this improved setup, the constant thermal gradient and interface velocity are maintained successfully, but the length of sample is still limited. In this work, we proposed a new method with continuous directional solidification in freeze-casting. To solve the axial thermal conduction problem, we introduced a linear motion setup and a mold with copper side. The method independently regulates the thermal gradient and the growth rate to produce a uniform temperature field and a continuous growth rate. Moreover, this approach can prepare samples with large, unlimited length dimensions and can improve the axial homogeneity of microstructures and properties. 2. Experimental 2.1. Apparatus The apparatus built for directional freeze-casting is shown in Fig. 1. The experiment platform can be referred as a Bridgman directional freezing stage [21,22]. There are three parts of heating zone, gradient zone and cooling zone in the system. The temperature in the gradient zone gradually decreases from the heating zone to the cooling zone. During the solidification process, a suitable thermal gradient in the raw materials can be maintained by adjusting the temperatures of the thermal baths. Ice crystals can continuously grow as the sample moves downwards in a constant pulling rate with the rotation of the motor. In this experimental setup, the thermal gradient is produced by a gap between the separated heating and cooling zones. The temperature of the heating end is controlled by a thermostatic bath, in which temperature can vary from 0 °C to 80 °C. And the temperature of the cooling end is provided by a low-temperature cycle machine that can change from 40 °C to 0 °C. The mold filled with
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ceramic slurries is moved across the thermal gradient controlled by a servo-drives motor with a linear ball-screw driven stage. Moreover, we use the copper mold with high capacity of heattransmission as an alternative to polytetrafluoroethylene. The heat conductivity of copper is 401 W/(mK) [24], much larger than aforementioned 0.3 W/(mK) for polytetrafluoroethylene. Thus, heat can mainly flow along the radial direction, which is totally different from single-side and double-side cooling approach. The main technological parameters, the thermal gradient and solidification rate, can be controlled independently. The former is mainly determined by the heating and cooling environments, while the latter depends on the pulling rate. In a stable state, the pulling rate can be regarded as equal to the axial solidification rate. Hence, we can achieve a solidification rate from 1 to 300 mm/s, which is limited by the capacity of the mechanical pulling system. By adjusting both the thermal gradient and the solidification rate, a wide range of freezing conditions can be investigated. The variation of primary dendrite spacing with growth rate and thermal gradient has been extensively investigated, and there is an applicable Hunt-model. The primary dendrite spacing is proportional to thermal gradient and solidification rate: k1 / G1=2 V 1=4 [25]. In ice lamellae, it is supposed that the case is also similar with diffusion-controlled growth. The solidification rate has a stronger effect to the ice lamellar spacing than thermal gradient. Accordingly, we mainly discuss the effect of solidification rate on the microstructure under a constant thermal gradient of 10 K/cm. The solidification rate in traditional freeze-casting system is mainly in the range of 5–100 mm/s [17,26], according to which we chose the range of 10–150 mm/s in this study. 2.2. Materials and methods The alumina powder with an average particle size of 300 nm was used to test this new setup. Slurries were prepared by mixing distilled water with a small amount dispersant (ammonium polyacrylate, 0.5 wt.% of the powder), an organic binder (polyvinyl alcohol, 2 wt.% of the powder), and the alumina powder (50 wt.% of water). To further improve the axial homogeneity by suppressing
Fig. 1. Schematic illustration of the directional freezing approach [23]. The temperature of the copper mold full of ceramic slurries is controlled by a thermostatic bath and a low-temperature bath, respectively. The mold moves with a linear ball-screw driven stage driven by a servo-drives motor.
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the settlement, an additive (sucrose, 1 wt.% of the powder) was added to the solution of dispersant and organic binder, after which alumina powder was added. Slurries were ball-stirred for 24 h and de-aired in a vacuum desiccator until complete removal of air bubbles. The freeze-casting experiment was carried out by pouring slurries into a cylindrical copper mold (14 mm diameter, 100 mm length) at room temperature. The solidification rate in the axial direction of the cylindrical sample was set by 10 mm/s, 50 mm/s, 100 mm/s, 150 mm/s, respectively. Frozen samples were freezedried for 24 h to sublimate the ice. Sintering was carried out in air by heating to 600 °C and holding for 2 h to burn out the organics at a constant heating rate of 5 °C/min, and then heated with the same rate to 1550 °C for a further 2 h of holding. Microstructures of porous alumina samples were observed by scanning electron microscopy (SEM). Compression tests were carried out on cylindrical samples with heights of 12 mm and diameters of 12 mm using a universal testing machine, with a compressive loading rate of 0.5 mm/min at room temperature. Five compressive samples for each data were represented to obtain an average with a standard deviation. The ceramic wall thickness and the spacing between adjacent walls are measured by ImageJ software through the SEM images. The average values obtained in each were averaged from at least 20 data points. The 20 measured data gives the standard deviation. Since all the additives were eliminated during sintering, the porous ceramics in this study is made up of pure Al2O3 particles. The porosity P can be approximately calculated by the density ratio between the bulk materials and porous materials:
P¼
q 100% 1
q0
ð1Þ
where q0 ¼ 3:90 g=cm3 (provided by manufacturers) is the bulk density of Al2O3 particles and q is the density of the current porous ceramics. 3. Results and discussion 3.1. Heat conduction pattern The heat conduction pattern in this approach is totally different from that in single-side and double-side cooling approach. In this method, heat flows along both the axial and the radial direction. Fig. 2a and c show the typical temperature distribution along the alumina ceramic specimen during the freezing process under the solidification rates of 10 lm/s and 150 lm/s, respectively. The temperature curves were obtained by immobilizing three thermoelectric couples in the slurry on the same horizontal plane of the mold, moving synchronously with slurry. Two thermoelectric couples were set in marginal region and the other in the center region of the mold. When the temperatures were near the freezing point, the temperatures of slurry around the in wall of the copper mold (marginal region 1 and 2) were lower than that of the center region due to the horizontal heat conduction. Owing to the release of latent heat, the temperatures remain unchanged near the melting point of ice, resulting in temperature platforms around freezing point in Fig. 2a. Heat conduction in the marginal regions is apparently faster, making a longer platform of the center region, especially for solidification rate of 150 lm/s in Fig. 2c. With a much slower rate of 10 lm/s, there is sufficient time for heat conducting in the center region, resulting in the almost coincident temperature curves in Fig. 2a. Fig. 2b and d show the isothermal surfaces in the sample under the solidification rate of 10 lm/s and 150 lm/s reconstructed from the temperature record of marginal and center regions. It reveals that the freezing front at the isother-
mal interface greatly depends on the solidification rate. The difference in interface height between the marginal and the center regions can be obtained to be 0.9 mm and 6 mm under solidification rate of 10 lm/s and 150 lm/s, respectively. In the horizontal plane, heat flows from center to margin in the mold. Thus, ice lamellae may grow slantwise from the periphery to the center as shown in Fig. 2b and d. Accordingly, there is a radial structure in the cross section of the whole sample, as shown in Fig. 3a. Overall, the finer structure appears near the copper mold and in the very center, as shown in Fig. 3. The ice simultaneously grows from bottom to up while it grows from the side to the center. Near the copper mold, the ice grows much faster and generates new fine structures. In the center region, several ice lamellas with different orientation converges to form fine structure. 3.2. Microstructures of porous Al2O3 ceramics Fig. 4 presents the cross section microstructures of Al2O3 ceramics at the middle of samples prepared by the freeze-casting method with different solidification rates. It is obvious that all samples exhibit porous lamellar structures but with a large amount of ceramic bridges between the ceramic lamellas, which may be related to the crystallization process of ice crystals [2,27]. The influence of solidification rates on pore structures can also be observed from Fig. 4. Through Fig. 4, the average wall thickness of porous Al2O3 ceramics under increasing solidification rates was measured to be 31 ± 4 mm, 24 ± 5, 15 ± 3 mm and 11 ± 3 mm, respectively, becoming thinner with the increase of solidification rate, which is correlated with the growth mechanism of ice crystals. The growth process of crystals is also a process of solid-liquid interface moving forward. At low solidification rate, the solid-liquid interface propagates slowly, and the thickness of ice lamellae is bigger, leading to an increase in the spacing between adjacent walls, which represents the pore size. With the increase of solidification rate, the growth rate is faster, so the thickness of ice lamellae becomes smaller. With a constant solid fraction, the ceramic wall thickness has the similar variation to the ice lamellar, resulting in a scaled-down microstructure. Fig. 5 shows SEM images of Al2O3 ceramics in details at a constant solidification rate of 150 mm/s. The images a, b and c are from the cross sections for top, middle and bottom regions along the length of samples, respectively. The images exhibit oriented porous lamellar structures with the spacing between adjacent wall of 11 ± 2 mm, 10 ± 2 mm, 13 ± 3 mm, from top to bottom portion, respectively. As shown, there is no significant difference in the pore size from the bottom to the top of the samples. Hence, the porous Al2O3 ceramics frozen at a constant solidification rate present a homogeneous microstructures along the length direction of samples. Moreover, microstructures at longitudinal sections also show well-aligned pore structures along the freezing direction in Fig. 5d. 3.3. Mechanical properties of porous Al2O3 ceramics Mechanical properties are the basic comprehensive evaluation for the application of this kind of porous ceramics [28–31]. Hence, a compression test was carried out to assess the mechanical response of porous Al2O3 ceramics. Fig. 6 shows the compression stress-strain curves with different solidification rates from 10 to 150 mm/s. All the curves exhibit four distinct stages during the compression process: linear region, yield region, non-linear region and final fracture region. The linear region can be characterized as an elastic deformation, exhibiting a linear increase in stress. With the increase of load, the porous ceramics produced an obvious yield platform, which suggested that the pore structure had been locally destroyed. Beyond the yield platform, the stress-strain
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Fig. 2. (a) and (c) are the temperature distributions along the sample during freezing under the solidification rates of 10 lm/s and 150 lm/s, respectively. (b) and (d) are and the isothermal surfaces under the solidification rate of 10 lm/s and 150 lm/s, respectively.
Fig. 3. SEM images of porous ceramics’ typical structure. (a) On the whole near the center. (b) At the edge.
curves gradually became flexural. Finally, the macro-cracks formed in the ceramics, leading to the failure. Fig. 7a shows the influence of solidification rate on the average compressive strength. At a low solidification rate of 10 mm/s, the compressive strength is about 24.0 MPa. As the solidification rate is increased to 50 mm/s and 100 mm/s, the compressive strength slowly decreases to 21.9 MPa and 20.8 MPa, respectively. With
further increasing the solidification rate to 150 mm/s, the compressive strength is around 22.6 MPa. Based on the porosity results, porous ceramics samples fabricated by different solidification rates appear no significant difference in porosity, which is all around 66% measured with Eq. (1). Although the solidification rate has a significant effect on microstructures, it has little impact on the mechanical properties.
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Fig. 4. SEM images of Al2O3 ceramics cross sections from the samples middle with different solidification rates. (a) 10 mm/s, (b) 50 mm/s, (c) 100 mm/s, (d) 150 mm/s.
Fig. 5. SEM images of Al2O3 ceramics with cross sections of different parts and longitudinal sections under a constant solidification rate of 150 mm/s. (a) top portions, (b) middle portions, (c) bottom portions, (d) longitudinal sections.
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Fig. 6. The compression stress-strain curves of Al2O3 samples with different solidification rates. (a) 10 mm/s, (b) 50 mm/s, (c) 100 mm/s, (d) 150 mm/s.
Fig. 7. (a) Effect of solidification rates on the average compressive strength. (b) Compressive strength Influence at the different parts of the selected position of samples on the compressive strength.
A possible reason may be from the high content of ceramic bridge. There are a large amount of ceramic bridges between the ceramics walls under all solidification rates in this experiment. Although the formation mechanism of ceramic bridge is still not well understood, the bridges have been proved to have great influence on
the strength [16,32]. The combined action of wall thickness and ceramic bridge might lead to the independence of strength to the solidification rate. Fig. 7b shows the compressive strength in different parts of porous ceramics. Obviously, there are significant differences in com-
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pressive strength from the bottom to the top along the sample. The bottom strength of all samples is the highest, which can be explained by the gravity effect. Due to the gravity effect, sedimentation in the ceramic slurries usually occurs during the preparation and freezing processes with a long sample, particularly for the dilute suspensions. The porosities from the bottom to the top along the length of the samples are measured to be 65.6%, 66.2% and 67.6%, respectively, which confirms the existence of sedimentation. In the setup of single-side cooling or the double-side cooling, the phenomenon of sedimentation still exists. Moreover, the transient state of ice growth in the single-side and double-side cooling setup greatly induce the non-uniformity across the length of the sample. 3.4. Additives for the axially homogenous mechanical properties In order to decrease the sedimentation and improve the axial homogeneity in the long samples, the additive of sucrose was incorporated to fabricate Al2O3 ceramics. Fig. 8a–c show the effect of sucrose on the microstructures of porous Al2O3 ceramics. The images are shown for the top, middle, bottom with cross sections and longitudinal sections of samples frozen under a constant solidification rate of 150 mm/s. As shown, the porous Al2O3 ceramics with 1 wt.% sucrose addition still exhibit aligned lamellar structures, which is similar to that observed in Fig. 4. It can be seen that the pore structures distribute homogeneously from the bottom to the top along the length of samples. SEM images of longitudinal sections in Fig. 8d also show oriented and uniform pore structures. In comparison, the porous Al2O3 ceramics with 1 wt.% sucrose addition presented a thicker ceramics wall. The average wall thickness of porous Al2O3 ceramics increases from 11 to 16 mm with the
addition of sucrose. The reason for the variation of pore morphology should be attributed to the effect of sucrose on the freezing behavior and the crystal morphology of ice [16]. Fig. 9 shows the effect of sucrose on the compressive strength. It is observed that the incorporation of sucrose has an improvement on the compressive strength of porous Al2O3 ceramics, which is increased from 22.6 to 24.7 MPa. More importantly, the results indicate that the homogeneity of mechanical properties at different parts along the axial direction are enhanced owing to the addition of sucrose. The increasing strength and strength homogeneity could be attributed to the additives sucrose that can change the viscosity of solvent and the forces between ceramics particles in the solution. Such interactions can prevent the settlement of particles to a certain extent, thereby improve the homogeneity at different parts along the length of samples. 4. Conclusions In this study, a continuous directional solidification approach for fabricating porous materials with a large length is proposed, where the solidification rate and the thermal gradient can be well regulated independently. During solidification, heat can mainly flow along the radial direction across the copper mold filled with slurries. The porous Al2O3 ceramics with a large length were successfully prepared by this approach. Results show that the porous Al2O3 ceramics had aligned lamellar structures, and reliable mechanical properties. The addition of sucrose can improve the mechanical strength and the axial homogeneity in properties. The proposed approach of freeze-casting can be used to fabricate porous materials with promising applications, including filters, catalyst supports and water purification.
Fig. 8. SEM images of Al2O3 ceramics with 1 wt.% sucrose addition at different parts with cross sections and longitudinal sections under a constant solidification rate of 150 mm/s. (a) top portions, (b) middle portions, (c) bottom portions, (d) longitudinal sections.
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Fig. 9. (a) Effect of sucrose on the average compressive strength. (b) Effect of sucrose on the compressive strength for the different regions of samples.
Conflict of interest We declare: No conflict of interest exists in the submission of this manuscript. Acknowledgement This research is supported by the Research Fund of the State Key Laboratory of Solidification Processing (Grant No. 158-QP-2016), National Natural Science Foundation of China (Grant No. 51701155), and Natural Science Basic Research Plan in Shanxi Province of China (Program No. 2017JM5112). We acknowledge the help of Associate Professor. Jie Xu from Northwestern Polytechnical University for Al2O3 ceramic sintering experiment, and the assistance from Jienan Shen, Lin Jia and Xiaobing Hu. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.ijheatmasstransfer. 2019.01.014. References [1] W.L. Li, K. Lu, J.Y. Walz, Freeze casting of porous materials: review of critical factors in microstructure evolution, Int. Mater. Rev. 57 (1) (2013) 37–60. [2] S. Deville, Freeze-casting of porous ceramics: a review of current achievements and issues, Adv. Eng. Mater. 10 (3) (2008) 155–169. [3] S. Deville, E. Saiz, R.K. Nalla, A.P. Tomsia, Freezing as a path to build complex composites, Science 311 (5760) (2006) 515–518. [4] H. Zhang, A.I. Cooper, Aligned porous structures by directional freezing, Adv. Mater. 19 (11) (2007) 1529–1533. [5] J. Lee, Y. Deng, The morphology and mechanical properties of layer structured cellulose microfibril foams from ice-templating methods, Soft Matter 7 (13) (2011) 6034. [6] S.-H. Park, K.-H. Kim, K.C. Roh, K.-B. Kim, Morphology control of threedimensional carbon nanotube macrostructures fabricated using ice-templating method, J. Porous Mater. 20 (5) (2013) 1289–1297. [7] F. Takayuki, A. Motohide, O. Tatsuki, K. Shuzo, Synthesis of porous ceramics with complex pore structure by freeze-dry processing, J. Am. Ceram. Soc. 84 (1) (2001) 230–232. [8] L. Ren, Y.-P. Zeng, D. Jiang, Preparation of porous TiO2 by a novel freeze casting, Ceram. Int. 35 (3) (2009) 1267–1270. [9] L. Jing, K. Zuo, Z. Fuqiang, X. Chun, F. Yuanfei, D. Jiang, Y.-P. Zeng, The controllable microstructure of porous Al2O3 ceramics prepared via a novel freeze casting route, Ceram. Int. 36 (8) (2010) 2499–2503. [10] J.-J. Xu, Interfacial wave theory of pattern formation in solidification, second ed., Springer Series in Synergetics (Complexity), Springer, Cham, Switzerland, 2017, pp. 52–73. [11] C. Bénard, A. Afshari, Inverse stefan problem: tracking of the interface position from measurements on the solid phase, Int. J. Numer. Meth. Eng. 35 (4) (1992) 835–851.
[12] J. Blumm, A. Lindemann, M. Meyer, C. Strasser, Characterization of PTFE using advanced thermal analysis techniques, Int. J. Thermophys. 31 (10) (2010) 1919–1927. [13] H. Zhang, I. Hussain, M. Brust, M.F. Butler, S.P. Rannard, A.I. Cooper, Aligned two- and three-dimensional structures by directional freezing of polymers and nanoparticles, Nat. Mater. 4 (10) (2005) 787–793. [14] A. Preiss, B. Su, S. Collins, D. Simpson, Tailored graded pore structure in zirconia toughened alumina ceramics using double-side cooling freeze casting, J. Eur. Ceram. Soc. 32 (8) (2012) 1575–1583. [15] B. Delattre, H. Bai, R.O. Ritchie, J. De Coninck, A.P. Tomsia, Unidirectional freezing of ceramic suspensions: in situ X-ray investigation of the effects of additives, ACS Appl. Mater. Interfaces 6 (1) (2014) 159–166. [16] E. Munch, E. Saiz, A.P. Tomsia, S. Deville, Architectural control of freeze-cast ceramics through additives and templating, J. Am. Ceram. Soc. 92 (7) (2009) 1534–1539. [17] S. Deville, E. Saiz, A.P. Tomsia, Ice-templated porous alumina structures, Acta Mater. 55 (6) (2007) 1965–1974. [18] Y.-C. Yen, Review of Thermal Properties of Snow, Ice and Sea Ice, Cold Regions Research and Engineering Lab, Hanover NH, 1981. [19] M.L.V. Ramires, C.A.N.d. Castro, Y. Nagasaka, A. Nagashima, M.J. Assael, W.A. Wakeham, Standard reference data for the thermal conductivity of water, J. Phys. Chem. Ref. Data 24 (3) (1995) 1377–1381. [20] T. Waschkies, R. Oberacker, M.J. Hoffmann, Control of lamellae spacing during freeze casting of ceramics using double-side cooling as a novel processing route, J. Am. Ceram. Soc. 92 (s1) (2009) S79–S84. [21] P.W. Bridgman, Certain physical properties of single crystals of tungsten, antimony, bismuth, tellurium, cadmium, zinc, and tin, in: Proceedings of the American Academy of Arts and Sciences, JSTOR, 1925, pp. 305–383. [22] D.C. Stockbarger, The production of large single crystals of lithium fluoride, Rev. Sci. Instrum. 7 (3) (1936) 133–136. [23] T. Zheng, X. Hu, J. Shen, J. You, L. Wang, Z. Wang, J. Li, J. Wang, Microstructure and mechanical property of porous ceramics prepared by freeze-casting method under regulation of sucrose, J. Chinese Ceramic Soc. 46 (06) (2018) 785–791. [24] C. Hammond, The Elements, CRC Handbook of Chemistry and Physics, Taylor and Francis Group, LLC, 2010, pp. 4–25. [25] J.D. Hunt, Cellular and primary dendrite spacings, Solidificat. Cast. Metals 1977 (1979) 35–39. [26] S. Deville, The lure of ice-templating: recent trends and opportunities for porous materials, Scripta Mater. 147 (2018) 119–124. [27] J.S. Wettlaufer, Dynamics of ice surfaces, Interface Sci. 9 (1) (2001) 117–129. [28] R.Z. Legeros, S. Lin, R. Rohanizadeh, D. Mijares, J.P. Legeros, Biphasic calcium phosphate bioceramics: preparation, properties and applications, J. Mater. Sci. - Mater. Med. 14 (3) (2003) 201. [29] J.F. Yang, T. Ohji, S. Kanzaki, A. Díaz, S. Hampshire, Microstructure and mechanical properties of silicon nitride ceramics with controlled porosity, 2002. [30] I. Sopyan, M. Mel, S. Ramesh, K.A. Khalid, Porous hydroxyapatite for artificial bone applications, Sci. Technol. Adv. Mater. 8 (1–2) (2007) 116–123. [31] J.R. Woodard, A.J. Hilldore, S.K. Lan, C.J. Park, A.W. Morgan, J.A.C. Eurell, S.G. Clark, M.B. Wheeler, R.D. Jamison, A.J.W. Johnson, The mechanical properties and osteoconductivity of hydroxyapatite bone scaffolds with multi-scale porosity, Biomaterials 28 (1) (2007) 45–54. [32] H. Zhao, Y. Yue, L. Guo, J. Wu, Y. Zhang, X. Li, S. Mao, X. Han, Cloning nacre’s 3D interlocking skeleton in engineering composites to achieve exceptional mechanical properties, Adv. Mater. 28 (25) (2016) 5099–5105.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Implementing continuous freeze-casting by separated control of thermal gradient and solidification rate Tao Zheng, Jun-jie Li, Li-lin Wang ⇑, Zhi-jun Wang ⇑, Jin-cheng Wang State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, PR China
a r t i c l e
i n f o
Article history: Received 10 October 2018 Received in revised form 2 January 2019 Accepted 3 January 2019
Keywords: Freeze-casting Porous materials Directional freezing Heat conduction
a b s t r a c t Ice-templated porous materials from freeze-casting have attracted widespread attentions in many research fields. Several apparatuses based on the freeze-casting have been proposed to fabricate aligned porous materials, where the unidirectional growth of ice is mainly controlled by changing temperatures at the sample ends. The thermal conduction cross the whole sample restricts the freezing process in traditional freeze-casting methods. In this paper, a new approach of freeze-casting is proposed, where the thermal gradient and the solidification rate can be controlled independently for continuous directional freezing. The lateral thermal conduction provides an effective way to produce axially homogeneous porous structural materials with unrestricted length and controllable microstructures. Moreover, the axial homogeneity can also be further improved by adding a small amount of sucrose. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Freeze-casting is a versatile technique to fabricate porous materials with attractive properties via ice-templating [1,2]. It can produce porous materials with highly controllable porosities. Freeze-casting is a kind of freeze-dried physical process [3], where the ice morphology determines microstructures of porous materials and hence their properties [4–6]. During the freezing process, particles in the slurry are ejected from the solidification front and trapped within the growing lamellar ice crystals. The porous morphology and microstructure can be controlled by adjusting processing parameters, such as solid content, particle size, additives, and freezing rate. Since the porous structures are the replica of ice crystals, it is quite important to control the growth of ice crystals. Traditionally, the crystallization process in the freeze-casting method is mainly controlled by adjusting temperatures at the sample ends to obtain the unidirectional solidification. According to the method of temperature-control, the single-side and doubleside cooling approaches have been proposed successively. In the single-side cooling method, the bottom of the mold is made of a copper plate with high thermal conductivity, while the side of the mold is made of resin with pretty low thermal conductivity. After chilled by a freezing bath, the slurries are frozen from bottom
⇑ Corresponding authors. E-mail addresses: [email protected] (L.-l. Wang), [email protected] (Z.-j. Wang). https://doi.org/10.1016/j.ijheatmasstransfer.2019.01.014 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
to top in the vertical direction. This method has been widely used to prepare porous materials with aligned pores [7–9]. In this single-side cooling method, the interface propagation rate V decreases along with the freezing process with V / t 1=2 when Stefan number (ratio of sensible heat to latent heat) is small [10,11]. The retarded growth of ice results in the significant change of microstructures along the growth direction, leading to the nonuniform microstructures across the whole sample. In order to overcome this disadvantage, Deville et al. [3] proposed a double-side cooling approach, where two copper cold fingers are set at both ends of the sample. The bottom and upper plates are cooled simultaneously to obtain a thermal gradient and unidirectional solidification. The porous structures can be tailored by controlling the thermal gradient and cooling rate. The side of the mold in double-side cooling approach is made of polytetrafluorethylene with poor thermal conductivity (about 0.3 W/(mK) [12]), which is expected to be thermal insulation wall. Thus, most of the heat flows along the axial direction to the bottom. This improved approach has been widely used to prepare porous materials [13–15]. However, in this approach, the thermal gradient and cooling rate in the sample is greatly affected by the sample length due to the restriction of thermal conduction in the ice and the slurry. Usually, the sample length is in the centimeter range about 3 cm [16,17]. Moreover, if the cooling rates are the same at both ends, the cooling rate cannot be directly used to describe the growth rate due to 4 times discrepancies in the thermal conductivity between ice (2.22 W/(mK) [18]) and water (0.54 W/(mK) [19]).
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Therefore, it is difficult to regulate the ice growth only through controlling the temperatures at the ends of a long sample. To solve this problem, Waschkies et al. [20] improved the double-side cooling system by thermal calculation and setting different cooling rates to the upper and bottom plates. Through this improved setup, the constant thermal gradient and interface velocity are maintained successfully, but the length of sample is still limited. In this work, we proposed a new method with continuous directional solidification in freeze-casting. To solve the axial thermal conduction problem, we introduced a linear motion setup and a mold with copper side. The method independently regulates the thermal gradient and the growth rate to produce a uniform temperature field and a continuous growth rate. Moreover, this approach can prepare samples with large, unlimited length dimensions and can improve the axial homogeneity of microstructures and properties. 2. Experimental 2.1. Apparatus The apparatus built for directional freeze-casting is shown in Fig. 1. The experiment platform can be referred as a Bridgman directional freezing stage [21,22]. There are three parts of heating zone, gradient zone and cooling zone in the system. The temperature in the gradient zone gradually decreases from the heating zone to the cooling zone. During the solidification process, a suitable thermal gradient in the raw materials can be maintained by adjusting the temperatures of the thermal baths. Ice crystals can continuously grow as the sample moves downwards in a constant pulling rate with the rotation of the motor. In this experimental setup, the thermal gradient is produced by a gap between the separated heating and cooling zones. The temperature of the heating end is controlled by a thermostatic bath, in which temperature can vary from 0 °C to 80 °C. And the temperature of the cooling end is provided by a low-temperature cycle machine that can change from 40 °C to 0 °C. The mold filled with
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ceramic slurries is moved across the thermal gradient controlled by a servo-drives motor with a linear ball-screw driven stage. Moreover, we use the copper mold with high capacity of heattransmission as an alternative to polytetrafluoroethylene. The heat conductivity of copper is 401 W/(mK) [24], much larger than aforementioned 0.3 W/(mK) for polytetrafluoroethylene. Thus, heat can mainly flow along the radial direction, which is totally different from single-side and double-side cooling approach. The main technological parameters, the thermal gradient and solidification rate, can be controlled independently. The former is mainly determined by the heating and cooling environments, while the latter depends on the pulling rate. In a stable state, the pulling rate can be regarded as equal to the axial solidification rate. Hence, we can achieve a solidification rate from 1 to 300 mm/s, which is limited by the capacity of the mechanical pulling system. By adjusting both the thermal gradient and the solidification rate, a wide range of freezing conditions can be investigated. The variation of primary dendrite spacing with growth rate and thermal gradient has been extensively investigated, and there is an applicable Hunt-model. The primary dendrite spacing is proportional to thermal gradient and solidification rate: k1 / G1=2 V 1=4 [25]. In ice lamellae, it is supposed that the case is also similar with diffusion-controlled growth. The solidification rate has a stronger effect to the ice lamellar spacing than thermal gradient. Accordingly, we mainly discuss the effect of solidification rate on the microstructure under a constant thermal gradient of 10 K/cm. The solidification rate in traditional freeze-casting system is mainly in the range of 5–100 mm/s [17,26], according to which we chose the range of 10–150 mm/s in this study. 2.2. Materials and methods The alumina powder with an average particle size of 300 nm was used to test this new setup. Slurries were prepared by mixing distilled water with a small amount dispersant (ammonium polyacrylate, 0.5 wt.% of the powder), an organic binder (polyvinyl alcohol, 2 wt.% of the powder), and the alumina powder (50 wt.% of water). To further improve the axial homogeneity by suppressing
Fig. 1. Schematic illustration of the directional freezing approach [23]. The temperature of the copper mold full of ceramic slurries is controlled by a thermostatic bath and a low-temperature bath, respectively. The mold moves with a linear ball-screw driven stage driven by a servo-drives motor.
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the settlement, an additive (sucrose, 1 wt.% of the powder) was added to the solution of dispersant and organic binder, after which alumina powder was added. Slurries were ball-stirred for 24 h and de-aired in a vacuum desiccator until complete removal of air bubbles. The freeze-casting experiment was carried out by pouring slurries into a cylindrical copper mold (14 mm diameter, 100 mm length) at room temperature. The solidification rate in the axial direction of the cylindrical sample was set by 10 mm/s, 50 mm/s, 100 mm/s, 150 mm/s, respectively. Frozen samples were freezedried for 24 h to sublimate the ice. Sintering was carried out in air by heating to 600 °C and holding for 2 h to burn out the organics at a constant heating rate of 5 °C/min, and then heated with the same rate to 1550 °C for a further 2 h of holding. Microstructures of porous alumina samples were observed by scanning electron microscopy (SEM). Compression tests were carried out on cylindrical samples with heights of 12 mm and diameters of 12 mm using a universal testing machine, with a compressive loading rate of 0.5 mm/min at room temperature. Five compressive samples for each data were represented to obtain an average with a standard deviation. The ceramic wall thickness and the spacing between adjacent walls are measured by ImageJ software through the SEM images. The average values obtained in each were averaged from at least 20 data points. The 20 measured data gives the standard deviation. Since all the additives were eliminated during sintering, the porous ceramics in this study is made up of pure Al2O3 particles. The porosity P can be approximately calculated by the density ratio between the bulk materials and porous materials:
P¼
q 100% 1
q0
ð1Þ
where q0 ¼ 3:90 g=cm3 (provided by manufacturers) is the bulk density of Al2O3 particles and q is the density of the current porous ceramics. 3. Results and discussion 3.1. Heat conduction pattern The heat conduction pattern in this approach is totally different from that in single-side and double-side cooling approach. In this method, heat flows along both the axial and the radial direction. Fig. 2a and c show the typical temperature distribution along the alumina ceramic specimen during the freezing process under the solidification rates of 10 lm/s and 150 lm/s, respectively. The temperature curves were obtained by immobilizing three thermoelectric couples in the slurry on the same horizontal plane of the mold, moving synchronously with slurry. Two thermoelectric couples were set in marginal region and the other in the center region of the mold. When the temperatures were near the freezing point, the temperatures of slurry around the in wall of the copper mold (marginal region 1 and 2) were lower than that of the center region due to the horizontal heat conduction. Owing to the release of latent heat, the temperatures remain unchanged near the melting point of ice, resulting in temperature platforms around freezing point in Fig. 2a. Heat conduction in the marginal regions is apparently faster, making a longer platform of the center region, especially for solidification rate of 150 lm/s in Fig. 2c. With a much slower rate of 10 lm/s, there is sufficient time for heat conducting in the center region, resulting in the almost coincident temperature curves in Fig. 2a. Fig. 2b and d show the isothermal surfaces in the sample under the solidification rate of 10 lm/s and 150 lm/s reconstructed from the temperature record of marginal and center regions. It reveals that the freezing front at the isother-
mal interface greatly depends on the solidification rate. The difference in interface height between the marginal and the center regions can be obtained to be 0.9 mm and 6 mm under solidification rate of 10 lm/s and 150 lm/s, respectively. In the horizontal plane, heat flows from center to margin in the mold. Thus, ice lamellae may grow slantwise from the periphery to the center as shown in Fig. 2b and d. Accordingly, there is a radial structure in the cross section of the whole sample, as shown in Fig. 3a. Overall, the finer structure appears near the copper mold and in the very center, as shown in Fig. 3. The ice simultaneously grows from bottom to up while it grows from the side to the center. Near the copper mold, the ice grows much faster and generates new fine structures. In the center region, several ice lamellas with different orientation converges to form fine structure. 3.2. Microstructures of porous Al2O3 ceramics Fig. 4 presents the cross section microstructures of Al2O3 ceramics at the middle of samples prepared by the freeze-casting method with different solidification rates. It is obvious that all samples exhibit porous lamellar structures but with a large amount of ceramic bridges between the ceramic lamellas, which may be related to the crystallization process of ice crystals [2,27]. The influence of solidification rates on pore structures can also be observed from Fig. 4. Through Fig. 4, the average wall thickness of porous Al2O3 ceramics under increasing solidification rates was measured to be 31 ± 4 mm, 24 ± 5, 15 ± 3 mm and 11 ± 3 mm, respectively, becoming thinner with the increase of solidification rate, which is correlated with the growth mechanism of ice crystals. The growth process of crystals is also a process of solid-liquid interface moving forward. At low solidification rate, the solid-liquid interface propagates slowly, and the thickness of ice lamellae is bigger, leading to an increase in the spacing between adjacent walls, which represents the pore size. With the increase of solidification rate, the growth rate is faster, so the thickness of ice lamellae becomes smaller. With a constant solid fraction, the ceramic wall thickness has the similar variation to the ice lamellar, resulting in a scaled-down microstructure. Fig. 5 shows SEM images of Al2O3 ceramics in details at a constant solidification rate of 150 mm/s. The images a, b and c are from the cross sections for top, middle and bottom regions along the length of samples, respectively. The images exhibit oriented porous lamellar structures with the spacing between adjacent wall of 11 ± 2 mm, 10 ± 2 mm, 13 ± 3 mm, from top to bottom portion, respectively. As shown, there is no significant difference in the pore size from the bottom to the top of the samples. Hence, the porous Al2O3 ceramics frozen at a constant solidification rate present a homogeneous microstructures along the length direction of samples. Moreover, microstructures at longitudinal sections also show well-aligned pore structures along the freezing direction in Fig. 5d. 3.3. Mechanical properties of porous Al2O3 ceramics Mechanical properties are the basic comprehensive evaluation for the application of this kind of porous ceramics [28–31]. Hence, a compression test was carried out to assess the mechanical response of porous Al2O3 ceramics. Fig. 6 shows the compression stress-strain curves with different solidification rates from 10 to 150 mm/s. All the curves exhibit four distinct stages during the compression process: linear region, yield region, non-linear region and final fracture region. The linear region can be characterized as an elastic deformation, exhibiting a linear increase in stress. With the increase of load, the porous ceramics produced an obvious yield platform, which suggested that the pore structure had been locally destroyed. Beyond the yield platform, the stress-strain
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Fig. 2. (a) and (c) are the temperature distributions along the sample during freezing under the solidification rates of 10 lm/s and 150 lm/s, respectively. (b) and (d) are and the isothermal surfaces under the solidification rate of 10 lm/s and 150 lm/s, respectively.
Fig. 3. SEM images of porous ceramics’ typical structure. (a) On the whole near the center. (b) At the edge.
curves gradually became flexural. Finally, the macro-cracks formed in the ceramics, leading to the failure. Fig. 7a shows the influence of solidification rate on the average compressive strength. At a low solidification rate of 10 mm/s, the compressive strength is about 24.0 MPa. As the solidification rate is increased to 50 mm/s and 100 mm/s, the compressive strength slowly decreases to 21.9 MPa and 20.8 MPa, respectively. With
further increasing the solidification rate to 150 mm/s, the compressive strength is around 22.6 MPa. Based on the porosity results, porous ceramics samples fabricated by different solidification rates appear no significant difference in porosity, which is all around 66% measured with Eq. (1). Although the solidification rate has a significant effect on microstructures, it has little impact on the mechanical properties.
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Fig. 4. SEM images of Al2O3 ceramics cross sections from the samples middle with different solidification rates. (a) 10 mm/s, (b) 50 mm/s, (c) 100 mm/s, (d) 150 mm/s.
Fig. 5. SEM images of Al2O3 ceramics with cross sections of different parts and longitudinal sections under a constant solidification rate of 150 mm/s. (a) top portions, (b) middle portions, (c) bottom portions, (d) longitudinal sections.
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Fig. 6. The compression stress-strain curves of Al2O3 samples with different solidification rates. (a) 10 mm/s, (b) 50 mm/s, (c) 100 mm/s, (d) 150 mm/s.
Fig. 7. (a) Effect of solidification rates on the average compressive strength. (b) Compressive strength Influence at the different parts of the selected position of samples on the compressive strength.
A possible reason may be from the high content of ceramic bridge. There are a large amount of ceramic bridges between the ceramics walls under all solidification rates in this experiment. Although the formation mechanism of ceramic bridge is still not well understood, the bridges have been proved to have great influence on
the strength [16,32]. The combined action of wall thickness and ceramic bridge might lead to the independence of strength to the solidification rate. Fig. 7b shows the compressive strength in different parts of porous ceramics. Obviously, there are significant differences in com-
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pressive strength from the bottom to the top along the sample. The bottom strength of all samples is the highest, which can be explained by the gravity effect. Due to the gravity effect, sedimentation in the ceramic slurries usually occurs during the preparation and freezing processes with a long sample, particularly for the dilute suspensions. The porosities from the bottom to the top along the length of the samples are measured to be 65.6%, 66.2% and 67.6%, respectively, which confirms the existence of sedimentation. In the setup of single-side cooling or the double-side cooling, the phenomenon of sedimentation still exists. Moreover, the transient state of ice growth in the single-side and double-side cooling setup greatly induce the non-uniformity across the length of the sample. 3.4. Additives for the axially homogenous mechanical properties In order to decrease the sedimentation and improve the axial homogeneity in the long samples, the additive of sucrose was incorporated to fabricate Al2O3 ceramics. Fig. 8a–c show the effect of sucrose on the microstructures of porous Al2O3 ceramics. The images are shown for the top, middle, bottom with cross sections and longitudinal sections of samples frozen under a constant solidification rate of 150 mm/s. As shown, the porous Al2O3 ceramics with 1 wt.% sucrose addition still exhibit aligned lamellar structures, which is similar to that observed in Fig. 4. It can be seen that the pore structures distribute homogeneously from the bottom to the top along the length of samples. SEM images of longitudinal sections in Fig. 8d also show oriented and uniform pore structures. In comparison, the porous Al2O3 ceramics with 1 wt.% sucrose addition presented a thicker ceramics wall. The average wall thickness of porous Al2O3 ceramics increases from 11 to 16 mm with the
addition of sucrose. The reason for the variation of pore morphology should be attributed to the effect of sucrose on the freezing behavior and the crystal morphology of ice [16]. Fig. 9 shows the effect of sucrose on the compressive strength. It is observed that the incorporation of sucrose has an improvement on the compressive strength of porous Al2O3 ceramics, which is increased from 22.6 to 24.7 MPa. More importantly, the results indicate that the homogeneity of mechanical properties at different parts along the axial direction are enhanced owing to the addition of sucrose. The increasing strength and strength homogeneity could be attributed to the additives sucrose that can change the viscosity of solvent and the forces between ceramics particles in the solution. Such interactions can prevent the settlement of particles to a certain extent, thereby improve the homogeneity at different parts along the length of samples. 4. Conclusions In this study, a continuous directional solidification approach for fabricating porous materials with a large length is proposed, where the solidification rate and the thermal gradient can be well regulated independently. During solidification, heat can mainly flow along the radial direction across the copper mold filled with slurries. The porous Al2O3 ceramics with a large length were successfully prepared by this approach. Results show that the porous Al2O3 ceramics had aligned lamellar structures, and reliable mechanical properties. The addition of sucrose can improve the mechanical strength and the axial homogeneity in properties. The proposed approach of freeze-casting can be used to fabricate porous materials with promising applications, including filters, catalyst supports and water purification.
Fig. 8. SEM images of Al2O3 ceramics with 1 wt.% sucrose addition at different parts with cross sections and longitudinal sections under a constant solidification rate of 150 mm/s. (a) top portions, (b) middle portions, (c) bottom portions, (d) longitudinal sections.
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Fig. 9. (a) Effect of sucrose on the average compressive strength. (b) Effect of sucrose on the compressive strength for the different regions of samples.
Conflict of interest We declare: No conflict of interest exists in the submission of this manuscript. Acknowledgement This research is supported by the Research Fund of the State Key Laboratory of Solidification Processing (Grant No. 158-QP-2016), National Natural Science Foundation of China (Grant No. 51701155), and Natural Science Basic Research Plan in Shanxi Province of China (Program No. 2017JM5112). We acknowledge the help of Associate Professor. Jie Xu from Northwestern Polytechnical University for Al2O3 ceramic sintering experiment, and the assistance from Jienan Shen, Lin Jia and Xiaobing Hu. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.ijheatmasstransfer. 2019.01.014. References [1] W.L. Li, K. Lu, J.Y. Walz, Freeze casting of porous materials: review of critical factors in microstructure evolution, Int. Mater. Rev. 57 (1) (2013) 37–60. [2] S. Deville, Freeze-casting of porous ceramics: a review of current achievements and issues, Adv. Eng. Mater. 10 (3) (2008) 155–169. [3] S. Deville, E. Saiz, R.K. Nalla, A.P. Tomsia, Freezing as a path to build complex composites, Science 311 (5760) (2006) 515–518. [4] H. Zhang, A.I. Cooper, Aligned porous structures by directional freezing, Adv. Mater. 19 (11) (2007) 1529–1533. [5] J. Lee, Y. Deng, The morphology and mechanical properties of layer structured cellulose microfibril foams from ice-templating methods, Soft Matter 7 (13) (2011) 6034. [6] S.-H. Park, K.-H. Kim, K.C. Roh, K.-B. Kim, Morphology control of threedimensional carbon nanotube macrostructures fabricated using ice-templating method, J. Porous Mater. 20 (5) (2013) 1289–1297. [7] F. Takayuki, A. Motohide, O. Tatsuki, K. Shuzo, Synthesis of porous ceramics with complex pore structure by freeze-dry processing, J. Am. Ceram. Soc. 84 (1) (2001) 230–232. [8] L. Ren, Y.-P. Zeng, D. Jiang, Preparation of porous TiO2 by a novel freeze casting, Ceram. Int. 35 (3) (2009) 1267–1270. [9] L. Jing, K. Zuo, Z. Fuqiang, X. Chun, F. Yuanfei, D. Jiang, Y.-P. Zeng, The controllable microstructure of porous Al2O3 ceramics prepared via a novel freeze casting route, Ceram. Int. 36 (8) (2010) 2499–2503. [10] J.-J. Xu, Interfacial wave theory of pattern formation in solidification, second ed., Springer Series in Synergetics (Complexity), Springer, Cham, Switzerland, 2017, pp. 52–73. [11] C. Bénard, A. Afshari, Inverse stefan problem: tracking of the interface position from measurements on the solid phase, Int. J. Numer. Meth. Eng. 35 (4) (1992) 835–851.
[12] J. Blumm, A. Lindemann, M. Meyer, C. Strasser, Characterization of PTFE using advanced thermal analysis techniques, Int. J. Thermophys. 31 (10) (2010) 1919–1927. [13] H. Zhang, I. Hussain, M. Brust, M.F. Butler, S.P. Rannard, A.I. Cooper, Aligned two- and three-dimensional structures by directional freezing of polymers and nanoparticles, Nat. Mater. 4 (10) (2005) 787–793. [14] A. Preiss, B. Su, S. Collins, D. Simpson, Tailored graded pore structure in zirconia toughened alumina ceramics using double-side cooling freeze casting, J. Eur. Ceram. Soc. 32 (8) (2012) 1575–1583. [15] B. Delattre, H. Bai, R.O. Ritchie, J. De Coninck, A.P. Tomsia, Unidirectional freezing of ceramic suspensions: in situ X-ray investigation of the effects of additives, ACS Appl. Mater. Interfaces 6 (1) (2014) 159–166. [16] E. Munch, E. Saiz, A.P. Tomsia, S. Deville, Architectural control of freeze-cast ceramics through additives and templating, J. Am. Ceram. Soc. 92 (7) (2009) 1534–1539. [17] S. Deville, E. Saiz, A.P. Tomsia, Ice-templated porous alumina structures, Acta Mater. 55 (6) (2007) 1965–1974. [18] Y.-C. Yen, Review of Thermal Properties of Snow, Ice and Sea Ice, Cold Regions Research and Engineering Lab, Hanover NH, 1981. [19] M.L.V. Ramires, C.A.N.d. Castro, Y. Nagasaka, A. Nagashima, M.J. Assael, W.A. Wakeham, Standard reference data for the thermal conductivity of water, J. Phys. Chem. Ref. Data 24 (3) (1995) 1377–1381. [20] T. Waschkies, R. Oberacker, M.J. Hoffmann, Control of lamellae spacing during freeze casting of ceramics using double-side cooling as a novel processing route, J. Am. Ceram. Soc. 92 (s1) (2009) S79–S84. [21] P.W. Bridgman, Certain physical properties of single crystals of tungsten, antimony, bismuth, tellurium, cadmium, zinc, and tin, in: Proceedings of the American Academy of Arts and Sciences, JSTOR, 1925, pp. 305–383. [22] D.C. Stockbarger, The production of large single crystals of lithium fluoride, Rev. Sci. Instrum. 7 (3) (1936) 133–136. [23] T. Zheng, X. Hu, J. Shen, J. You, L. Wang, Z. Wang, J. Li, J. Wang, Microstructure and mechanical property of porous ceramics prepared by freeze-casting method under regulation of sucrose, J. Chinese Ceramic Soc. 46 (06) (2018) 785–791. [24] C. Hammond, The Elements, CRC Handbook of Chemistry and Physics, Taylor and Francis Group, LLC, 2010, pp. 4–25. [25] J.D. Hunt, Cellular and primary dendrite spacings, Solidificat. Cast. Metals 1977 (1979) 35–39. [26] S. Deville, The lure of ice-templating: recent trends and opportunities for porous materials, Scripta Mater. 147 (2018) 119–124. [27] J.S. Wettlaufer, Dynamics of ice surfaces, Interface Sci. 9 (1) (2001) 117–129. [28] R.Z. Legeros, S. Lin, R. Rohanizadeh, D. Mijares, J.P. Legeros, Biphasic calcium phosphate bioceramics: preparation, properties and applications, J. Mater. Sci. - Mater. Med. 14 (3) (2003) 201. [29] J.F. Yang, T. Ohji, S. Kanzaki, A. Díaz, S. Hampshire, Microstructure and mechanical properties of silicon nitride ceramics with controlled porosity, 2002. [30] I. Sopyan, M. Mel, S. Ramesh, K.A. Khalid, Porous hydroxyapatite for artificial bone applications, Sci. Technol. Adv. Mater. 8 (1–2) (2007) 116–123. [31] J.R. Woodard, A.J. Hilldore, S.K. Lan, C.J. Park, A.W. Morgan, J.A.C. Eurell, S.G. Clark, M.B. Wheeler, R.D. Jamison, A.J.W. Johnson, The mechanical properties and osteoconductivity of hydroxyapatite bone scaffolds with multi-scale porosity, Biomaterials 28 (1) (2007) 45–54. [32] H. Zhao, Y. Yue, L. Guo, J. Wu, Y. Zhang, X. Li, S. Mao, X. Han, Cloning nacre’s 3D interlocking skeleton in engineering composites to achieve exceptional mechanical properties, Adv. Mater. 28 (25) (2016) 5099–5105.