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Synthesis in molten salts and formation reaction kinetics of tantalum carbide coatings on various carbon fibers
Surface & Coatings Technology 212 (2012) 169–179
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Synthesis in molten salts and formation reaction kinetics of tantalum carbide coatings on various carbon fibers Z.J. Dong a, b, X.K. Li a, b,⁎, G.M. Yuan a, Z.W. Cui a, Y. Cong a, A. Westwood c a b c
The Hubei Province Key Laboratory of Coal Conversion & New Carbon Materials, Wuhan University of Science and Technology, Wuhan 430081, China The Hubei Province Key Laboratory of Ceramics & Refractories, Wuhan University of Science and Technology, Wuhan 430081, China Institute for Materials Research, University of Leeds, Leeds LS2 9JT, United Kingdom
a r t i c l e
i n f o
Article history: Received 30 March 2012 Accepted in revised form 24 September 2012 Available online 2 October 2012 Keywords: TaC coatings Carbon fibers Molten salts Diffusion XRD SEM
a b s t r a c t Tantalum carbide (TaC) coatings were prepared on polyacrylonitrile (PAN)-based, graphitized PAN-based and pitch-based carbon fibers by synthesis in molten salts. The characteristics of the TaC coating were studied in relation to the structure of the carbon fiber, the molten salt composition, reaction temperature and reaction time. Thicker TaC coatings with larger grain sizes tended to form on carbon fibers with a lower degree of crystallinity. Molten salt mixtures with a relatively low melting point are appropriate for use as the reaction medium for synthesis of TaC coatings on carbon fibers. However, with increasing reaction temperature and reaction time, the thickness and grain size of the TaC coating increase obviously. Internal diffusion control and external diffusion control models of TaC coating growth were established on the basis of mass transfer and reaction dynamics theory. The result indicates that the TaC coating growth is controlled by the internal diffusion of tantalum in the TaC coating. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Carbon fibers and ceramic fibers (e.g., silicon carbide, alumina) are promising reinforcements for metal matrix and ceramic matrix composites because of their excellent properties, such as high tensile strength, high modulus and light weight [1–3]. However, the poor wettability and chemical reactions between these reinforcement fibers and most metal matrices limit the fabrication and high temperature application of the fiber-reinforced metal matrix composites [4–9]. In addition, the low oxidation resistance of the carbon fibers also hinders their application as reinforcements in metal or ceramic composites. Once the temperature is above 400 °C, the carbon fibers react with oxygen and rapidly burn away with an oxidation rate increasing quickly above 500 °C [10]. To overcome these shortcomings and promote the application of carbon fibers and ceramic fibers, many methods for the modification of these fibers have been reported. It is believed that coating of these fiber reinforcements is helpful for improving the wettability and compatibility between fiber and matrix [8]. Moreover, coatings such as carbon, carbides, oxides and nitrides could act as an interface barrier to slow down the inter-diffusion and possible chemical reactions between fiber and matrix [7–12]. As one of the most important transition metal carbides, tantalum carbide (TaC) is characterized by high hardness, high melting point ⁎ Corresponding author at: The Hubei Province Key Laboratory of Coal Conversion & New Carbon Materials, Wuhan University of Science and Technology, Wuhan 430081, China. Tel./fax: +86 27 86556906. E-mail address: [email protected] (X.K. Li). 0257-8972/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.surfcoat.2012.09.040
(3950 °C), high resistance to chemical attack and oxidation, together with good thermal conductivity and excellent electrical conductivity [13]. Stoichiometric TaC is also inert towards carbon up to its melting temperature. These properties make TaC very attractive as a functional coating for the modification of carbon fibers [14]. TaC coatings are usually synthesized by chemical vapor deposition (CVD) or carbothermal reduction [15–17]. However, crystals of TaC coatings prepared by CVD often have textured structures (or preferential orientations), which significantly limit the ablation-resistant properties of the coatings [15,16]. In addition, uneven coating thickness, crack formation and poor compatibility with carbon fibers are often associated with the CVD process [18]. The carbothermal reduction synthesis is also difficult since this requires high temperature (1500–2500 °C) and rigorous handling of gaseous (TaCl5) or solid (Ta2O5) precursors [19,20]. The control of quality and thickness of coatings on carbon fibers with varying degrees of graphitization cannot be achieved easily by these methods. In our previous work [21–23], we reported the synthesis of TaCand TiC-coated carbon fiber by reaction of transition metal (Ta and Ti) or titanium hydride powders with PAN-based carbon fibers in a molten salt medium composed of LiCl–KCl–KF at a relatively low temperature. This synthesis route in molten salts offers the possibility to control the thickness and quality of carbide coatings by adjusting the reaction parameters (such as molten salt composition, reaction temperature, reaction time as well as the molar ratio of metal and carbon fibers) and by varying the choice of fiber to be used as the carbon source in terms of its degree of graphitization. This work reports the synthesis and characterization of TaC coatings prepared by reaction between carbon fibers with various crystal
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structures and Ta powder in various molten salt reaction media. The formation reaction kinetics of TaC coatings on carbon fibers prepared by synthesis in molten salts are also discussed. The objective of this work is to show the influence of the molten salt composition, reaction temperature, reaction time and crystal structure of the carbon fiber precursors on the morphology and microstructure of the TaC coating formed on these carbon fibers and to further elucidate the growth mechanism of TaC coatings in molten salt media. 2. Experimental 2.1. Synthesis of TaC coating on carbon fibers Three types of carbon fiber were used as carbon sources: polyacrylonitrile (PAN)-based carbon fibers (Jilin Carbon Plant in China), graphitized PAN-based carbon fibers (Jilin Carbon Plant in China) and pitch-based carbon fibers (P55-S by Amoco Performance Products, Inc.). The average diameter of PAN-based, graphitized PAN-based and pitch-based carbon fibers was around 7 μm, 6 μm and 13 μm, respectively, and the mean length of these carbon fibers was about 5 mm in each case. Before coating, carbon fibers were immersed in acetone to remove the organic binders and then dried for use. The TaC-coated carbon fibers were synthesized by allowing tantalum powder (200 mesh, 99.95% purity, Beijing Mountain Technical Development Center for Non-ferrous Metals in China) to react with carbon fibers at 1:4 (Ta/C) molar ratio in various molten salt media. Salts used as reaction media in this study include pure NaCl, pure KCl, NaCl–LiCl in a molar ratio of 50:50 (eutectic composition), and KCl–LiCl in a molar ratio of 41.2:58.8 (eutectic composition). The weight ratio of salts to reactants (tantalum and carbon fibers) was 14:1. The carbon fibers, covered by a mixture of tantalum powder and the salts, were placed in an alumina crucible and reacted in the temperature range of 850–1200 °C for 1–5 h under a flowing argon atmosphere. After cooling, the crucible was repeatedly boiled in distilled water to remove the salts. The TaC-coated short carbon fiber products were then separated and dried at 80 °C for 2 h. 2.2. Characterization of TaC coated carbon fibers The phases present in the coated short carbon fibers were identified by use of an X-ray diffraction (XRD) instrument (Philips X'Pert Pro MPD) using Cu-Kα radiation (λ = 1.54056 Å). The working voltage and current of the Cu target were 40 kV and 40 mA, respectively. A field emission gun scanning electron microscope (FESEM, NOVA400 NANOSEM) was used to examine surface morphology and to measure the coating thickness on the coated fibers. Fiber samples were cut with scissors to expose a transverse cross-section for SEM observation. The elemental composition of the coating was determined by energy dispersive X-ray spectroscopy (EDS, attachment to the SEM) and by X-ray photoelectron spectroscopy (XPS, VG MultiLab 2000) with a monochromic Al Kα X-ray source operating at 300 W. The photoelectric peak of C 1s located at 284.6 eV was used as the standard for correction of XPS binding energies. 3. Results and discussion 3.1. Influence of the carbon fiber sources on the formation of TaC coatings Fig. 1 shows the XRD patterns of the PAN-based, graphitized PAN-based and pitch-based carbon fiber sources. It can be seen that the intensity and the full width at half maximum (FWHM) of the diffraction peak at around 2θ = 25.5°, corresponding to the (002) reflections of the pseudo-graphite structure, show significant differences between these carbon fibers. The PAN based carbon fibers (curve a) show a broad and weak (002) peak, which is related to their low degree of graphitization and crystallinity [24]. The intensity of the (002) peak for the graphitized PAN-based carbon fibers (curve b) is higher
Fig. 1. XRD patterns of the (a) PAN-based, (b) graphitized PAN-based and (c) pitch-based carbon fibers.
than that of the PAN-based carbon fibers, confirming its higher degree of graphitization and crystallinity. In contrast to the two PAN-based carbon fibers, the pitch-based carbon fibers (curve c) present a strong and sharp (002) peak. This indicates that the pitch based carbon fibers have the highest degree of graphitization and crystallinity among the three types of carbon fibers. For graphitized PAN-based carbon fibers and particularly for pitch-based carbon fibers, two weak bands at around 2θ = 44° and 2θ =53° are evident. The former is usually assigned to the (100) turbostratic band of disordered carbon materials, and the latter corresponds to the (004) reflections of the pseudo-graphite structure [25]. The SEM images of the three types of carbon fiber are presented in Fig. 2. As can be seen from Fig. 2a, PAN-based carbon fibers exhibit groove-like features along the fiber axis and a rough surface. Graphitized PAN-based carbon fibers show a morphology similar to that of PAN-based carbon fibers, but its surfaces appear slightly smoother (shown in Fig. 2c). Both types of carbon fiber exhibit isotropic and featureless transverse texture as shown in Fig. 2b and d. The pitch-based carbon fibers with a diameter of approximately 13 μm display a relatively smoother surface texture (shown in Fig. 2e) and the transverse texture of the cross-sectional area of this carbon fiber under a slightly lower magnification is shown in Fig. 2f, exhibiting a typical radial folded structure. Fig. 3 shows the XRD patterns of the products prepared at 950 °C for 1 h in KCl–LiCl molten salt medium using the various carbon fibers as carbon sources. Only carbon and TaC diffraction peaks can be observed in these XRD patterns. The peaks at about 2θ = 34.9°, 40.5°, 58.7°, 70.1°, 73.8° and 87.8° correspond to the (111), (200), (220), (311), (222) and (400) crystal planes of cubic TaC (JCPDS card no. 0077–0205). The broad peak at about 2θ = 25.5° can be attributed to the carbon fibers. There was no evidence of residual unreacted Ta. The occurrence of carbon and cubic phase TaC indicated that tantalum had reacted with carbon in the molten salt medium and formed TaC on the surface of the carbon fibers. However, the relative intensity and FWHM of the characteristic peaks of TaC derived from the three types of carbon fibers show obvious differences that may result from the differences in thickness and grain size between the TaC coatings. This implies that the degree of graphitization and crystallinity in the carbon fibers may be closely related to the rate of reaction between carbon and tantalum in the molten salt medium. Fig. 4 shows the typical morphologies of the TaC coatings on the various carbon fibers prepared at 950 °C for 1 h in KCl–LiCl molten salts. The SEM images shown in Fig. 4b, d, and f are representative of the cross-sectional morphologies of the TaC-coated PAN-based carbon fibers, graphitized PAN-based carbon fibers and pitch-based carbon
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Fig. 2. Typical SEM images of (a–b) PAN-based, (c–d) graphitized PAN-based and (e–f) pitch-based carbon fibers.
Fig. 3. XRD patterns of the products prepared by reaction of Ta in KCl–LiCl molten salts at 950 °C for 1 h with (a) PAN-based carbon fibers, (b) graphitized PAN-based carbon fibers and (c) pitch-based carbon fibers as carbon sources.
fibers, respectively. Continuous and fairly uniform TaC coatings are formed on the surfaces of all three types of carbon fiber, with the most uniform coating being observed on the PAN-based carbon fiber. To obtain information about the elemental composition of the fiber surface, XPS measurements were carried out. As expected, the survey XPS spectrum recorded from the PAN-based carbon fibers reveals the presence of carbon, oxygen and traces of nitrogen (Fig. 5a). For the TaC-coated PAN-based carbon fibers, the survey XPS spectrum shows that carbon, oxygen, tantalum and traces of nitrogen are present in the coatings, and no residual contaminants such as lithium, potassium and chlorine are detected on the surface of the TaC coating (Fig. 5b). The average thickness (measured by SEM scale bar) of the TaC coating formed on PAN-based carbon fibers, graphitized PAN-based carbon fibers and pitch-based carbon fibers is around 180 nm, 100 nm and 40 nm, respectively. It appears that the coating thickness decreases with the increasing degree of graphitization and crystallinity in the carbon fibers, consistent with the XRD results from carbon fibers and carbide-coated carbon fibers shown in Figs. 1 and 3, respectively. The differences in coating thickness between the three types of carbon fiber might be attributed to the different surface reactivities of these
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(a)
(b)
(c)
(d)
(e)
(f)
Fig. 4. Typical SEM images of the surface and cross-section of TaC-coated (a–b) PAN-based carbon fibers, (c–d) graphitized PAN-based carbon fibers and (e–f) pitch based-carbon fibers prepared at 950 °C for 1 h in KCl–LiCl molten salts.
Fig. 5. Survey XPS spectra of the PAN-based carbon fiber (a) and TaC-coated PAN-based carbon fiber (b).
carbon materials, which correlate with their structural ordering or graphitization degree [26]. PAN-based carbon fibers consist mainly of polyaromatic, structurally disordered carbon [27]. In contrast, pitchbased fibers consist mainly of medium or highly textured carbon, where there exist large in-plane crystallites with a high degree of order in three dimensional structures [28]. The structurally disordered PAN-based carbon fibers, especially when ungraphitized, therefore offer many more active carbon sites for reaction with tantalum atoms than the structurally ordered pitch-based carbon fibers and this results in the thicker TaC coating formed on the PAN-based carbon fibers. Images in Fig. 4a, c, and e show the surface morphologies of TaC coatings on PAN-based carbon fibers, graphitized PAN-based carbon fibers and pitch-based carbon fibers, respectively. The SEM observation indicates that the TaC coating formed on PAN-based carbon fibers has a denser, rather more uniform structure and larger grain size than that formed on graphitized PAN-based carbon fibers and pitch-based carbon fibers. This suggests that the grain size and thickness of the TaC coating are distinctively affected by the degree of graphitization and crystallinity of the carbon source.
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3.2. Influence of the molten salt composition on the formation of TaC coatings In order to understand the influence of the molten salt composition on the formation of TaC coatings, TaC-coated carbon fiber products were synthesized in various molten salts. Fig. 6 shows the XRD patterns of the products prepared by reaction of Ta powder at 850 °C for 1 h in four molten salt systems using PAN-based carbon fibers as the carbon source. It can be seen that the products synthesized in LiCl–KCl, NaCl– KCl and pure KCl molten salts show obvious diffraction peaks due to carbon and cubic TaC phase (shown in Fig. 6b, c and d). The intensity of the TaC diffraction peaks for the product prepared in LiCl–KCl molten salts is evidently higher compared to that of the products obtained in other molten salt media. This high intensity of the TaC diffraction peaks can be related to the higher thickness of this TaC coating (shown in Fig. 7). In contrast, no crystalline TaC phase is observed for the product synthesized in pure NaCl medium (shown in Fig. 6a). The further SEM/EDS analysis for the carbon fibers treated in pure NaCl medium indicates that there is no coating formed on the carbon fibers. This suggests that the molten salt composition has a significant influence on the crystal formation and growth of TaC. Fig. 7 shows typical SEM micrographs of the surface and cross-section of each of the products prepared from reaction of PAN-based carbon fibers and Ta at 850 °C for 1 h in LiCl–KCl, NaCl–KCl and KCl molten salt media. As shown in Fig. 7a, c and e, continuous and quite homogeneous coatings on the carbon fibers, with similar surface morphologies, can be observed in each case. The average thickness of the TaC coatings synthesized in LiCl–KCl, NaCl–KCl and pure KCl molten salt media (shown in Fig. 7b, d and f) is about 80 nm, 50 nm and 30 nm, respectively. The SEM observations in terms of coating thickness are consistent with the XRD results in terms of TaC peak intensity. The effect of molten salt composition on TaC coating thickness can be attributed to the different solubilities of tantalum in LiCl–KCl, NaCl–KCl and pure KCl molten salt media and the different melting points and viscosities of these molten salts. The eutectic point of LiCl–KCl is 352 °C, much lower than that of NaCl–KCl (650 °C) and the melting point of KCl (771 °C). In contrast, the melting point of NaCl is 801 °C and this may be so high that it does not facilitate sufficient tantalum solubility or mobility to allow formation of TaC. However, in the low-melting point salts, the reactants could achieve effective dissolution, transport and distribution in the flux [29], thereby enabling formation of TaC coatings. The higher mass transfer rate of tantalum and the consequent faster rate of reaction between tantalum and carbon in the LiCl–KCl molten salt medium result in the formation of a thicker TaC coating. This suggests that LiCl–KCl is a more effective molten salt
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medium for forming a TaC coating on carbon fibers in comparison to NaCl–KCl, KCl and NaCl molten salt media. 3.3. Influence of reaction temperature on the formation of TaC coatings In order to explore the effect of the reaction temperature on the microstructure of TaC coating, TaC-coated PAN-based carbon fibers were prepared by treatment at 1000 °C, 1100 °C and 1200 °C for 1 h in LiCl– KCl molten salt. Fig. 8 shows the XRD patterns of the products obtained. It can be seen that the intensity of the diffraction peaks from the cubic TaC phase increases and the intensity of the carbon diffraction peaks diminishes to almost nothing with the increase of reaction temperature from 1000 °C to 1200 °C. In addition, the diffraction peaks of TaC are broad at low temperatures (1000 °C) and become narrow at high temperatures (1200 °C), which can be attributed to the growth of the crystal size in the TaC coating with increasing reaction temperature. The SEM images of the TaC-coated carbon fibers prepared by treatment at 1000 °C, 1100 °C and 1200 °C for 1 h in LiCl–KCl molten salts are represented in Fig. 9. The coating thickness estimated from the cross-section of the TaC-coated carbon fibers synthesized at 1000 °C, 1100 °C and 1200 °C (shown in Fig. 9b, e and h) is about 230 nm, 400 nm and 480 nm, respectively, indicating that the coating thickness increases with increasing reaction temperature. Furthermore, it can be seen from Fig. 9a and d that the TaC coatings synthesized at 1000 °C and 1100 °C are uniform along their length and circumferential directions and no rough defects can be found on the surface of these TaC-coated carbon fibers. No cracking or peeling of the coating is observed on the surface of these carbon fibers. However, for the TaC-coated carbon fibers synthesized at 1200 °C, significant cracking of the TaC coating (shown in Fig. 9g) and separation of the TaC coating from the carbon fiber substrate (shown in Fig. 9h) can be seen. This demonstrates that reaction temperature is a very important factor for the controllable fabrication of the adherent, crack-free and continuous TaC coating on carbon fibers. The fibers do not appear to become connected by coating “bridges” in any of the above cases. The grain size of the TaC coatings prepared at the relatively low temperature of 1000 °C and 1100 °C is small and uniform, especially in the former case, as can be seen from Fig. 9c and f. Fine grain size in the nano-range is expected to be beneficial in terms of increasing the strength of the coating and in relaxing residual stresses by grain boundary sliding [30]. Upon increasing the reaction temperature to 1200 °C, the mean grain size of TaC coating increases remarkably, and a great number of large TaC grains with polyhedral shape are visible on the coating surfaces (shown in Fig. 9i). The dependence of grain size in the TaC coating on reaction temperature is attributed to the varying mobility of atoms at different temperatures. High reaction temperatures lead to high atom mobility, which encourages growth and annealing of the TaC resulting in the formation of large grains [14]. The formation of large grains significantly decreases resistance to crack initiation and growth in coating materials [31] and, as a result, cracks and peeling are observed in the surface of TaC-coated carbon fibers prepared at 1200 °C. 3.4. Influence of reaction time on the formation of TaC coatings
Fig. 6. XRD patterns of the products prepared by reaction of Ta with PAN-based carbon fibers, as carbon source, at 850 °C for 1 h in (a) NaCl, (b) KCl, (c) NaCl–KCl and (d) LiCl–KCl molten salt media.
In order to evaluate further the effect of reaction time on the morphology and structure of TaC coatings, TaC-coated PAN-based carbon fibers were synthesized at 900 °C for 1–5 h in LiCl–KCl molten salt mixture. The XRD patterns of the products are presented in Fig. 10a. The relative intensity of the characteristic peaks of TaC increases with the increase of the holding time as it would be expected in the case of increasing coating thickness with the extension of the reaction time. The SEM images shown in Fig. 10b–e show the representative cross-sectional morphology of the TaC coating formed on the PAN-based carbon fibers. The thicknesses of these TaC coatings synthesized at 900 °C for 1, 2, 4 and 5 h in LiCl–KCl molten salts are 130 nm, 180 nm, 380 nm and 560 nm, respectively. This indicates that the TaC coating thickness increases with the
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(a)
(b)
(c)
(d)
(e)
(f)
Fig. 7. Typical SEM images of the surface and cross-section of the products prepared by reaction of tantalum with PAN-based carbon fibers at 850 °C for 1 h in (a–b) LiCl–KCl, (c–d) NaCl–KCl and (e–f) KCl molten salt media.
reaction time, which is in accordance with the XRD patterns shown in Fig. 10a. It is worth noting that, although the coating thickness in Fig. 10e is greater than that in Fig. 9h, almost no cracking or peeling of the former coating can be observed, as shown in Fig. 10f. A careful comparison of Fig. 10f with Fig. 9g reveals that the cracking and breakaway of coating in the latter appear mainly to be caused by the larger grain size rather than excessive thickness of the coating. Thus, reduction of grain size by limiting the reaction temperature is a critical factor for the synthesis of crack-free, adherent and continuous TaC coatings on carbon fibers. From Fig. 10b–e, it can be also observed that the diameter of the TaC-coated carbon fibers increases slightly with increasing coating thickness, which may be caused by volume expansion due to the conversion of hexagonal phase carbon into cubic phase TaC. Furthermore, the diameter of the unreacted carbon fiber core decreases with increasing reaction time as the interface between the TaC coating and carbon moves towards the center of the fiber as carbon is consumed by reaction with tantalum. 3.5. Reaction kinetics of TaC coating formation on carbon fibers Fig. 8. XRD patterns of the TaC-coated carbon fibers prepared by treatment at (a) 1000 °C, (b) 1100 °C and (c) 1200 °C for 1 h in LiCl–KCl molten salt.
In the molten salt medium, carbon fiber and tantalum exist in different states. Tantalum has a slight solubility in molten salts and the
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Fig. 9. Typical SEM images of the TaC-coated carbon fibers prepared by treatment at (a–c) 1000 °C, (d–f) 1100 °C and (g–i) 1200 °C for 1 h in LiCl–KCl molten salt.
dissolved tantalum exists as atoms or atomic clusters [32–34]. Carbon does not dissolve in molten salts and remains in a solid state [35]. In the initial stage of the reaction, carbon fibers are immersed in the molten salt solvent containing tantalum atoms formed by the dissolution of metallic tantalum and the reaction between tantalum and carbon occurs at the liquid–solid interface between the molten salts and carbon fibers. After a continuous TaC coating has formed on the carbon fibers, the reaction between tantalum and carbon may involve the following steps:
(1) The diffusion of tantalum atoms through a liquid boundary layer to the outer surface of the TaC coating, i.e. external diffusion; (2) The diffusion of tantalum atoms through the TaC coating to the interface between the TaC coating and unreacted carbon fiber [19], i.e. internal diffusion; (3) The formation of TaC by the interfacial reaction between tantalum and carbon, which leads to the continuous increase of the coating thickness.
(b)
(c)
(e)
(f)
(a)
(d)
Fig. 10. (a) XRD patterns and typical cross-section SEM images of TaC-coated carbon fibers synthesized at 900 °C for (b) 1 h, (c) 2 h, (d) 4 h and (e–f) 5 h in LiCl–KCl molten salts.
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For the abovementioned multi-step process, the slowest step is the rate-determining step that determines the rate of the whole process. Thermodynamic calculations indicate that tantalum metal will react directly with carbon to form TaC even at room temperature but, in practice, this solid-state reaction requires high temperatures up to 1800 °C in order to proceed at an appreciable rate, due to the kinetic limitation [36]. In the molten salt medium, however, tantalum and carbon can react at a relatively low temperature of 850 °C because the molten salt mixture facilitates the dissolution and transport of the tantalum. Therefore, it is reasonable to assume that the interfacial reaction between tantalum and carbon is relatively fast and that the growth of the TaC coating on carbon fibers is governed by the diffusion of tantalum atoms. Fig. 11 shows a geometrical model of the TaC-coated carbon fibers and the concentration distribution of tantalum atoms in the coating and liquid boundary layer, where R0 is the initial radius of the cylindrical carbon fiber (μm), Ri is the radius of the unreacted carbon fiber core (μm), and Rm is the radius of the TaC-coated carbon fiber (μm). CTb denotes the concentration of tantalum atoms in the bulk liquid (mol/m3). Because the amount of tantalum powder present in the molten salts is in great excess cf. what is consumed by reaction and because the dissolution of tantalum powder in the molten salts would reach saturation very quickly owing to its low solubility, CTb can be considered to be a constant. CTm and CTi represent the concentration of tantalum atoms (mol/m 3) at the coating surface and at the reaction interface, respectively. For each mole of TaC generated, one mole of carbon is consumed. The relationship of Ri and Rm can be described as follows: 2 2 π R0 −Ri LρC MC
¼
2 2 π Rm −Ri LρMC
ð1Þ
M MC
where the length of the carbon fiber is L (cm), density of carbon fiber ρC = 1.68 g/cm3, atomic weight of carbon MC = 12 g/mol, density of
formed TaC coating ρMC = 14.5 g/cm3 and atomic weight of formed TaC coating MMC = 193 g/mol. Equation Eq. (1) can be simplified as follows: ffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a R20 −R2i þ R2i M ρ where a ¼ MC C ¼ 1:86: MC ρMC
Rm ¼
ð2Þ
3.5.1. External diffusion control model When the internal diffusion rate of tantalum atoms is far greater than the external diffusion rate of tantalum atoms, the growth of TaC coating is controlled by the external diffusion of tantalum atoms. There is no concentration gradient of tantalum atoms from the coating surface to the reaction interface between the TaC coating and unreacted carbon fiber core, i.e. CTm =CTi, as shown in Fig. 11a. According to mass transfer theory, the mass transfer rate of tantalum atoms, NT (mol/s), through the liquid boundary layer surrounding an individual carbon fiber can be expressed as: NT ¼ 2πRm Lkl ðC Tb −C Tm Þ
ð3Þ
where kl is the mass transfer coefficient of tantalum atoms in the liquid boundary layer, which is influenced by the liquid flow pattern, liquid viscosity and diffusion coefficient of tantalum atoms in molten salt solvent. Considering the irreversibility of the reaction between tantalum and carbon, there is no concentration build-up of tantalum atoms in the coating, namely
C Tm ¼ C Ti ≈0:
ð4Þ
Surface of the coating on an individual carbon fibre
Liquid boundary layer
Unreacted carbon fibre core Reaction interface
Surface of an individual carbon fibre before the coating formed
CT
CTb
CTm
CTb (Bulk liquid concentration)
CTi
(a)
Rm R0 Ri
0
Ri R0 Rm
R
CT CTm
CTi
CTb
CTb
0
(b)
RmR0 Ri
0
Ri R0 Rm
R (Radial position)
Fig. 11. Geometrical model of a TaC-coated carbon fiber and concentration distribution of tantalum atoms in the coating and liquid boundary layer corresponding to (a) external diffusion control and (b) internal diffusion control.
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Substituting Eq. (4) into Eq. (3) yields: NT ¼ 2πRm Lkl C Tb :
ð5Þ
The rate of interfacial reaction between carbon and tantalum can be expressed in terms of the consumption of carbon in a period of time, which can be written as: vC ¼ −
2πRi LρC dRi MC dt
ð6Þ
where vc is the rate of interfacial reaction (mol/s) and t represents the reaction time. When steady-state conditions have been reached, the mass transfer rate of tantalum atoms through the liquid boundary layer is equal to the rate of interfacial reaction between carbon and tantalum: N T ¼ vC :
ð7Þ
Substituting Eqs. (5) and (6) into Eq. (7) yields, −
2πRi Lρc dRi ¼ 2πRm Lkl C Tb : Mc dt
ð8Þ
Substituting Eq. (2) into Eq. (8) yields, −
ρC Ri dRi ¼ kl C Tb MC dt
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi a R20 −R2i þ R2i :
ð9Þ
Ri R t k C Mc ffidRi ¼ −∫0 l Tb dt ∫Ri0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ρC 2 2 a R0 −Ri þ Ri
ð10Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k ða−1ÞC Tb MC t: aR20 −ða−1ÞR2i −R0 ¼ l ρC
ð11Þ
kl ða−1ÞC Tb M C : ρC
J T ¼ 2πRLD
R
∫Rim
ð15Þ
JT C dR ¼ ∫C TiTm dC T 2πRLD
JT ¼
ð16Þ
2πLD ðC −C Ti Þ: lnðRm =Ri Þ Tm
ð17Þ
Taking into account the irreversibility of the reaction between tantalum and carbon, the tantalum atom concentration at the reaction interface is close to zero, i.e. CTi ≈ 0. Eq. (17) can be simplified as: JT ¼
2πLD 2πLD C ¼ C : lnðRm =Ri Þ Tm lnðRm =Ri Þ Tb
ð19Þ
Substituting Eqs. (6) and (18) into Eq. (19) yields, 2πRi LρC dRi 2πLD ¼ C : lnðRm =Ri Þ Tb MC dt
R
ð12Þ
ð14Þ
From Eq. (14), it can be seen that the reaction coordinate Y is proportional to the reaction time t when the external diffusion of tantalum atom becomes the rate-determining step for the growth of TaC coating. 3.5.2. Internal diffusion control model When the external diffusion rate of tantalum atoms is far greater than the internal diffusion rate of tantalum atoms, the growth of the TaC coating is controlled by the internal diffusion of tantalum atoms. Fig. 11b shows the concentration gradient distribution of tantalum atoms in the TaC coating and liquid boundary layer. The concentration distribution of tantalum atoms is uniform throughout the bulk liquid to the TaC coating surface (CTb = CTm), but for the region from coating surface to the reaction interface, there is a concentration gradient and the tantalum atom concentration at the reaction interface is much less than that at the TaC coating surface, that is CTi b b CTm =
ð20Þ
Separating variable and then integrating Eq. (20) yield, t
−∫Ri0 Ri lnðRm =Ri ÞdRi ¼ ∫0
ð13Þ
ð18Þ
When steady-state conditions have been reached, the internal diffusion rate of tantalum atoms in the TaC coating is equal to the rate of interfacial reaction between carbon and tantalum. Accordingly, the following equation can be obtained.
DMC C Tb dt: ρC
ð21Þ
Substituting Rm according to Eq. (2) yields, a R20 −R2i þ R2i 4ða−1Þ DMC C Tb t: ¼ ρC
Eq. (11) can be simplified as: Y ¼ Kt:
dC T dR
where D is the efficient diffusion coefficient of the tantalum atoms in the TaC coating and R is the radial distance over which diffusion is occurring, resulting in a gradual decrease in the tantalum concentration CT. Separating the variables and then integrating Eq. (15) yield,
−
Denote
K¼
CTb. According to Fick's laws of diffusion, the internal diffusion rate of tantalum atoms, JT (mol/s), in the TaC coating can be described as:
vC ¼ J T
Separating the variables and then integrating Eq. (9) yield,
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Y ¼ aR20 −ða−1ÞR2i −R0
177
h i R2 lnR R2 lnRi −R20 lnR0 2 2 2 0 ln a R0 −Ri þ Ri − 0 þ i 2ða−1Þ 2 ð22Þ
Eq. (22) describes the relationship between the reaction time t and the radius Ri of the unreacted carbon fiber core. Denote ′
Y ¼
′
K ¼
a R20 −R2i þ R2i
h i R2 lnR 2 2 2 0 ln a R0 −Ri þ Ri − 0 4ða−1Þ 2ða−1Þ 2 2 R lnRi −R0 lnR0 þ i 2 DMC C Tb : ρC
ð23Þ ð24Þ
Eq. (22) can be simplified as: ′
′
Y ¼ K t:
ð25Þ
From Eq. (25), it can be seen that the reaction coordinate Y′ is proportional to the reaction time t when the internal diffusion of tantalum
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atoms becomes the rate-determining step for the growth of the TaC coating. To validate further the abovementioned diffusion control model, the diameter of the TaC-coated carbon fibers Dm (=2Rm), the diameter of the unreacted carbon fiber core Di (=2Ri) and the thickness of the TaC coatings δ were measured from Fig. 10. The two variables Y and Y′, which correspond to the external diffusion control model and internal diffusion control model, respectively, are related with Ri and R0 and the latter can be obtained from Rm and Ri according the Eq. (2). Y and Y′ can be calculated from Eqs. (12) and (23). The relationships between Y and Y′ and reaction time t are presented in the scatter point plots in Fig. 12. The linear fitting of these data points has been performed by using the Origin 8 software and the coefficient of determination R 2 has been calculated automatically. The coefficient of determination is the square of the correlation coefficient R, and it is an important tool in determining the degree of linear correlation of variables and the goodness of fit of a model in regression analysis. The value of coefficient of determination R 2 varies from 0 to 1. A higher value means a better fit. In this work, the coefficient of determination R 2 for the linear fitting of Y − t (Fig. 12a) is 0.890, i.e. less than 0.985 for the linear fitting of Y′ − t (Fig. 12b). This indicates that the latter fit is more better and that the internal diffusion control model is therefore more appropriate than the external diffusion control model. Thus, the growth of the TaC coating is controlled by the internal diffusion of tantalum atoms through the TaC coating.
4. Conclusion TaC coatings have been prepared on the surfaces of PAN-based, graphitized PAN-based and pitch-based carbon fibers by synthesis in molten salts. The degree of carbon fiber graphitization, molten salt composition, reaction temperature and reaction time have important influence on the thickness, grain size, adhesion and surface morphology of the TaC coatings on the carbon fibers. In comparison with graphitized PAN-based and pitch-based carbon fibers, PAN-based carbon fibers with a lower degree of graphitization are more reactive towards TaC coating formation, leading to the formation of thicker tantalum carbide coatings. The LiCl–KCl salt mixture has a relatively low melting point compared with NaCl–KCl, KCl and NaCl and is therefore more suitable as a molten salt medium in which to synthesize TaC coatings on carbon fibers. With increasing reaction temperature and reaction time, the thickness and the grain size of the TaC coatings increase noticeably. The formation of excessively large TaC grains on the surfaces of carbon fibers appears to induce the cracking and peeling of the carbide coatings. However, a homogeneous, continuous and crack-free TaC coating can be prepared by limiting the reaction temperature and controlling the reaction time. The experimental results for PAN-based
0.55 0.50
The authors acknowledge the financial support of the National Natural Science Foundation of China (project 50972110) and the Hubei Provincial Natural Science Foundation of China (project 2009CDA036). References [1] T. Piquero, H. Vincent, C. Vincent, J. Bouix, Carbon 33 (1995) 455. [2] N.I. Baklanova, T.M. Zima, A.I. Boronin, S.V. Kosheev, A.T. Titov, N.V. Isaeva, D.V. Graschenkov, S.S. Solntsev, Surf. Coat. Technol. 201 (2006) 2313. [3] Y. Sasaki, Y. Nishina, J. Mater. Sci. 22 (1987) 443. [4] K. Landry, S. Kalogeropoulou, E. Eustathopoulos, Mater. Sci. Eng., A 254 (1998) 99. [5] N. Popovska, H. Gerhard, D. Wurm, S. Poscher, G. Emig, R.F. Singer, Mater. Des. 18 (1997) 239. [6] G. Hackl, H. Gerhard, N. Popovska, Thin Solid Films 513 (2006) 217. [7] Y.C. Fu, N.L. Shi, D.Z. Zhang, R. Yang, Mater. Sci. Eng., A 426 (2006) 278. [8] T.P.D. Rajan, R.M. Pillai, B.C. Pai, J. Mater. Sci. 33 (1998) 3491. [9] P. Deodati, R. Donnini, S. Kaciulis, M. Kazemian-Abyaneh, A. Mezzi, R. Montanari, C. Testani, N. Ucciardello, Mater. Sci. Forum 678 (2011) 23. [10] R. Gadiou, S. Serverin, P. Gibot, C. Vix-Guterl, J. Eur. Ceram. Soc. 28 (2008) 2265. [11] R. Donnini, S. Kaciulis, A. Mezzi, R. Montanari, C. Testani, Surf. Interface Anal. 40 (2008) 277. [12] S. Kaciulis, A. Mezzi, R. Donnini, P. Deodati, R. Montanari, N. Ucciardello, M. Amati, M. Kazemian-Abyaneh, C. Testanid, Surf. Interface Anal. 42 (2010) 707. [13] H. Pierson, Handbook of Refractory Carbides and Nitrides: Properties, Characteristics, Processing and Applications, 1st ed. Noyes Publications, New Jersey, 1996. [14] Z.K. Chen, X. Xiong, B.Y. Huang, Thin Solid Films 516 (2008) 8248. [15] Z.K. Chen, X. Xiong, G.D. Li, Appl. Surf. Sci. 257 (2010) 656. [16] X. Xiong, Z.K. Chen, B.Y. Huang, G.D. Li, F. Zheng, P. Xiao, H.B. Zhang, Thin Solid Films 517 (2009) 3222. [17] N.I. Baklanova, T.M. Zima, A.V. Utkin, A.T. Titov, Inorg. Mater. 47 (2011) 728. [18] Y.J. Lee, Diam. Relat. Mater. 13 (2004) 383. [19] L. Massot, P. Chamelot, P. Winterton, P. Taxil, J. Alloys Compd. 471 (2009) 561. [20] H.W. He, K.C. Zhou, X. Xiong, J. Mater. Sci. Technol. 21 (2005) 381. [21] Z.J. Dong, X.K. Li, G.M. Yuan, Y. Cong, N. Li, Z.J. Hu, Z.Y. Jiang, A. Westwood, Appl. Surf. Sci. 254 (2008) 5936. [22] Z.J. Dong, X.K. Li, G.M. Yuan, Y. Cong, N. Li, Z.Y. Jiang, Z.J. Hu, Thin Solid Films 517 (2009) 3248. [23] X.K. Li, Z.J. Dong, A. Westwood, A. Brown, S.W. Zhang, R. Brydson, N. Li, B. Rand, Carbon 46 (2008) 305. [24] F.Y. Zhang, D.M. He, S.T. Ge, Q.Y. Cai, Surf. Coat. Technol. 203 (2008) 99. [25] Z.W. Xu, L.S. Liu, Y.D. Huang, Y. Sun, X.Q. Wu, J.L. Li, Mater. Lett. 63 (2009) 1814. [26] J.B. Donnet, Carbon 6 (1968) 161. [27] P. Morgan, in: Carbon Fibres and their Composites, Taylor & Francis Group, CRC Press, Boca Raton, 2005, p. 185. [28] A.A. Bright, L.S. Singer, Carbon 17 (1979) 59. [29] B.R. Li, N.Q. Zhang, H.B. Chang, Y. Cheng, B. Cao, J. Alloys Compd. 505 (2010) 542. [30] G.M. Chow, I.A. Ovid'ko, T. Tsakalakos, in: Nanostructured Films and Coatings, Kluwer Academic Publishers, Netherlands, 1999, p. 283. [31] F. Yuan, K. Hayashi, Wear 225–229 (1999) 83.
0.50 0.45
(b)
0.40
R2=0.890
Y'(10-12m2)
0.40
Y(10-6m)
Acknowledgments
(a)
0.45
0.35 0.30 0.25
R2=0.985
0.35 0.30 0.25 0.20
0.20
0.15
0.15 0.10
fibers agree well with the internal diffusion control model, which suggests that the growth of the TaC coating is limited by the internal diffusion of tantalum atoms through the TaC coating.
1.0
1.5
2.0
2.5
t (h)
3.0
3.5
4.0
0.10
1.0
1.5
2.0
2.5
3.0
3.5
4.0
t (h)
Fig. 12. Linear fitting of (a) Y − t and (b) Y′ − t, which corresponds to the external diffusion control model and internal diffusion control model, respectively.
Z.J. Dong et al. / Surface & Coatings Technology 212 (2012) 169–179 [32] M.A. Bredig, Mixtures of Metals with Molten Salts, University of Michigan Library, USA, 1963. [33] Z.X. Qiu, L.M. Fan, K. Grjotheim, H. Kvande, J. Mater. Sci. Technol. 6 (1990) 157. [34] C.W. Forsberg, in: CD-ROM, Proc. of the 2006 International Congress on Advances in Nuclear Power Plants (ICAPP '06), American Nuclear Society, Reno, USA, 2006, p. 699.
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Contents lists available at SciVerse ScienceDirect
Surface & Coatings Technology journal homepage: www.elsevier.com/locate/surfcoat
Synthesis in molten salts and formation reaction kinetics of tantalum carbide coatings on various carbon fibers Z.J. Dong a, b, X.K. Li a, b,⁎, G.M. Yuan a, Z.W. Cui a, Y. Cong a, A. Westwood c a b c
The Hubei Province Key Laboratory of Coal Conversion & New Carbon Materials, Wuhan University of Science and Technology, Wuhan 430081, China The Hubei Province Key Laboratory of Ceramics & Refractories, Wuhan University of Science and Technology, Wuhan 430081, China Institute for Materials Research, University of Leeds, Leeds LS2 9JT, United Kingdom
a r t i c l e
i n f o
Article history: Received 30 March 2012 Accepted in revised form 24 September 2012 Available online 2 October 2012 Keywords: TaC coatings Carbon fibers Molten salts Diffusion XRD SEM
a b s t r a c t Tantalum carbide (TaC) coatings were prepared on polyacrylonitrile (PAN)-based, graphitized PAN-based and pitch-based carbon fibers by synthesis in molten salts. The characteristics of the TaC coating were studied in relation to the structure of the carbon fiber, the molten salt composition, reaction temperature and reaction time. Thicker TaC coatings with larger grain sizes tended to form on carbon fibers with a lower degree of crystallinity. Molten salt mixtures with a relatively low melting point are appropriate for use as the reaction medium for synthesis of TaC coatings on carbon fibers. However, with increasing reaction temperature and reaction time, the thickness and grain size of the TaC coating increase obviously. Internal diffusion control and external diffusion control models of TaC coating growth were established on the basis of mass transfer and reaction dynamics theory. The result indicates that the TaC coating growth is controlled by the internal diffusion of tantalum in the TaC coating. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Carbon fibers and ceramic fibers (e.g., silicon carbide, alumina) are promising reinforcements for metal matrix and ceramic matrix composites because of their excellent properties, such as high tensile strength, high modulus and light weight [1–3]. However, the poor wettability and chemical reactions between these reinforcement fibers and most metal matrices limit the fabrication and high temperature application of the fiber-reinforced metal matrix composites [4–9]. In addition, the low oxidation resistance of the carbon fibers also hinders their application as reinforcements in metal or ceramic composites. Once the temperature is above 400 °C, the carbon fibers react with oxygen and rapidly burn away with an oxidation rate increasing quickly above 500 °C [10]. To overcome these shortcomings and promote the application of carbon fibers and ceramic fibers, many methods for the modification of these fibers have been reported. It is believed that coating of these fiber reinforcements is helpful for improving the wettability and compatibility between fiber and matrix [8]. Moreover, coatings such as carbon, carbides, oxides and nitrides could act as an interface barrier to slow down the inter-diffusion and possible chemical reactions between fiber and matrix [7–12]. As one of the most important transition metal carbides, tantalum carbide (TaC) is characterized by high hardness, high melting point ⁎ Corresponding author at: The Hubei Province Key Laboratory of Coal Conversion & New Carbon Materials, Wuhan University of Science and Technology, Wuhan 430081, China. Tel./fax: +86 27 86556906. E-mail address: [email protected] (X.K. Li). 0257-8972/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.surfcoat.2012.09.040
(3950 °C), high resistance to chemical attack and oxidation, together with good thermal conductivity and excellent electrical conductivity [13]. Stoichiometric TaC is also inert towards carbon up to its melting temperature. These properties make TaC very attractive as a functional coating for the modification of carbon fibers [14]. TaC coatings are usually synthesized by chemical vapor deposition (CVD) or carbothermal reduction [15–17]. However, crystals of TaC coatings prepared by CVD often have textured structures (or preferential orientations), which significantly limit the ablation-resistant properties of the coatings [15,16]. In addition, uneven coating thickness, crack formation and poor compatibility with carbon fibers are often associated with the CVD process [18]. The carbothermal reduction synthesis is also difficult since this requires high temperature (1500–2500 °C) and rigorous handling of gaseous (TaCl5) or solid (Ta2O5) precursors [19,20]. The control of quality and thickness of coatings on carbon fibers with varying degrees of graphitization cannot be achieved easily by these methods. In our previous work [21–23], we reported the synthesis of TaCand TiC-coated carbon fiber by reaction of transition metal (Ta and Ti) or titanium hydride powders with PAN-based carbon fibers in a molten salt medium composed of LiCl–KCl–KF at a relatively low temperature. This synthesis route in molten salts offers the possibility to control the thickness and quality of carbide coatings by adjusting the reaction parameters (such as molten salt composition, reaction temperature, reaction time as well as the molar ratio of metal and carbon fibers) and by varying the choice of fiber to be used as the carbon source in terms of its degree of graphitization. This work reports the synthesis and characterization of TaC coatings prepared by reaction between carbon fibers with various crystal
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structures and Ta powder in various molten salt reaction media. The formation reaction kinetics of TaC coatings on carbon fibers prepared by synthesis in molten salts are also discussed. The objective of this work is to show the influence of the molten salt composition, reaction temperature, reaction time and crystal structure of the carbon fiber precursors on the morphology and microstructure of the TaC coating formed on these carbon fibers and to further elucidate the growth mechanism of TaC coatings in molten salt media. 2. Experimental 2.1. Synthesis of TaC coating on carbon fibers Three types of carbon fiber were used as carbon sources: polyacrylonitrile (PAN)-based carbon fibers (Jilin Carbon Plant in China), graphitized PAN-based carbon fibers (Jilin Carbon Plant in China) and pitch-based carbon fibers (P55-S by Amoco Performance Products, Inc.). The average diameter of PAN-based, graphitized PAN-based and pitch-based carbon fibers was around 7 μm, 6 μm and 13 μm, respectively, and the mean length of these carbon fibers was about 5 mm in each case. Before coating, carbon fibers were immersed in acetone to remove the organic binders and then dried for use. The TaC-coated carbon fibers were synthesized by allowing tantalum powder (200 mesh, 99.95% purity, Beijing Mountain Technical Development Center for Non-ferrous Metals in China) to react with carbon fibers at 1:4 (Ta/C) molar ratio in various molten salt media. Salts used as reaction media in this study include pure NaCl, pure KCl, NaCl–LiCl in a molar ratio of 50:50 (eutectic composition), and KCl–LiCl in a molar ratio of 41.2:58.8 (eutectic composition). The weight ratio of salts to reactants (tantalum and carbon fibers) was 14:1. The carbon fibers, covered by a mixture of tantalum powder and the salts, were placed in an alumina crucible and reacted in the temperature range of 850–1200 °C for 1–5 h under a flowing argon atmosphere. After cooling, the crucible was repeatedly boiled in distilled water to remove the salts. The TaC-coated short carbon fiber products were then separated and dried at 80 °C for 2 h. 2.2. Characterization of TaC coated carbon fibers The phases present in the coated short carbon fibers were identified by use of an X-ray diffraction (XRD) instrument (Philips X'Pert Pro MPD) using Cu-Kα radiation (λ = 1.54056 Å). The working voltage and current of the Cu target were 40 kV and 40 mA, respectively. A field emission gun scanning electron microscope (FESEM, NOVA400 NANOSEM) was used to examine surface morphology and to measure the coating thickness on the coated fibers. Fiber samples were cut with scissors to expose a transverse cross-section for SEM observation. The elemental composition of the coating was determined by energy dispersive X-ray spectroscopy (EDS, attachment to the SEM) and by X-ray photoelectron spectroscopy (XPS, VG MultiLab 2000) with a monochromic Al Kα X-ray source operating at 300 W. The photoelectric peak of C 1s located at 284.6 eV was used as the standard for correction of XPS binding energies. 3. Results and discussion 3.1. Influence of the carbon fiber sources on the formation of TaC coatings Fig. 1 shows the XRD patterns of the PAN-based, graphitized PAN-based and pitch-based carbon fiber sources. It can be seen that the intensity and the full width at half maximum (FWHM) of the diffraction peak at around 2θ = 25.5°, corresponding to the (002) reflections of the pseudo-graphite structure, show significant differences between these carbon fibers. The PAN based carbon fibers (curve a) show a broad and weak (002) peak, which is related to their low degree of graphitization and crystallinity [24]. The intensity of the (002) peak for the graphitized PAN-based carbon fibers (curve b) is higher
Fig. 1. XRD patterns of the (a) PAN-based, (b) graphitized PAN-based and (c) pitch-based carbon fibers.
than that of the PAN-based carbon fibers, confirming its higher degree of graphitization and crystallinity. In contrast to the two PAN-based carbon fibers, the pitch-based carbon fibers (curve c) present a strong and sharp (002) peak. This indicates that the pitch based carbon fibers have the highest degree of graphitization and crystallinity among the three types of carbon fibers. For graphitized PAN-based carbon fibers and particularly for pitch-based carbon fibers, two weak bands at around 2θ = 44° and 2θ =53° are evident. The former is usually assigned to the (100) turbostratic band of disordered carbon materials, and the latter corresponds to the (004) reflections of the pseudo-graphite structure [25]. The SEM images of the three types of carbon fiber are presented in Fig. 2. As can be seen from Fig. 2a, PAN-based carbon fibers exhibit groove-like features along the fiber axis and a rough surface. Graphitized PAN-based carbon fibers show a morphology similar to that of PAN-based carbon fibers, but its surfaces appear slightly smoother (shown in Fig. 2c). Both types of carbon fiber exhibit isotropic and featureless transverse texture as shown in Fig. 2b and d. The pitch-based carbon fibers with a diameter of approximately 13 μm display a relatively smoother surface texture (shown in Fig. 2e) and the transverse texture of the cross-sectional area of this carbon fiber under a slightly lower magnification is shown in Fig. 2f, exhibiting a typical radial folded structure. Fig. 3 shows the XRD patterns of the products prepared at 950 °C for 1 h in KCl–LiCl molten salt medium using the various carbon fibers as carbon sources. Only carbon and TaC diffraction peaks can be observed in these XRD patterns. The peaks at about 2θ = 34.9°, 40.5°, 58.7°, 70.1°, 73.8° and 87.8° correspond to the (111), (200), (220), (311), (222) and (400) crystal planes of cubic TaC (JCPDS card no. 0077–0205). The broad peak at about 2θ = 25.5° can be attributed to the carbon fibers. There was no evidence of residual unreacted Ta. The occurrence of carbon and cubic phase TaC indicated that tantalum had reacted with carbon in the molten salt medium and formed TaC on the surface of the carbon fibers. However, the relative intensity and FWHM of the characteristic peaks of TaC derived from the three types of carbon fibers show obvious differences that may result from the differences in thickness and grain size between the TaC coatings. This implies that the degree of graphitization and crystallinity in the carbon fibers may be closely related to the rate of reaction between carbon and tantalum in the molten salt medium. Fig. 4 shows the typical morphologies of the TaC coatings on the various carbon fibers prepared at 950 °C for 1 h in KCl–LiCl molten salts. The SEM images shown in Fig. 4b, d, and f are representative of the cross-sectional morphologies of the TaC-coated PAN-based carbon fibers, graphitized PAN-based carbon fibers and pitch-based carbon
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(a)
(b)
(c)
(d)
(e)
(f)
171
Fig. 2. Typical SEM images of (a–b) PAN-based, (c–d) graphitized PAN-based and (e–f) pitch-based carbon fibers.
Fig. 3. XRD patterns of the products prepared by reaction of Ta in KCl–LiCl molten salts at 950 °C for 1 h with (a) PAN-based carbon fibers, (b) graphitized PAN-based carbon fibers and (c) pitch-based carbon fibers as carbon sources.
fibers, respectively. Continuous and fairly uniform TaC coatings are formed on the surfaces of all three types of carbon fiber, with the most uniform coating being observed on the PAN-based carbon fiber. To obtain information about the elemental composition of the fiber surface, XPS measurements were carried out. As expected, the survey XPS spectrum recorded from the PAN-based carbon fibers reveals the presence of carbon, oxygen and traces of nitrogen (Fig. 5a). For the TaC-coated PAN-based carbon fibers, the survey XPS spectrum shows that carbon, oxygen, tantalum and traces of nitrogen are present in the coatings, and no residual contaminants such as lithium, potassium and chlorine are detected on the surface of the TaC coating (Fig. 5b). The average thickness (measured by SEM scale bar) of the TaC coating formed on PAN-based carbon fibers, graphitized PAN-based carbon fibers and pitch-based carbon fibers is around 180 nm, 100 nm and 40 nm, respectively. It appears that the coating thickness decreases with the increasing degree of graphitization and crystallinity in the carbon fibers, consistent with the XRD results from carbon fibers and carbide-coated carbon fibers shown in Figs. 1 and 3, respectively. The differences in coating thickness between the three types of carbon fiber might be attributed to the different surface reactivities of these
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(a)
(b)
(c)
(d)
(e)
(f)
Fig. 4. Typical SEM images of the surface and cross-section of TaC-coated (a–b) PAN-based carbon fibers, (c–d) graphitized PAN-based carbon fibers and (e–f) pitch based-carbon fibers prepared at 950 °C for 1 h in KCl–LiCl molten salts.
Fig. 5. Survey XPS spectra of the PAN-based carbon fiber (a) and TaC-coated PAN-based carbon fiber (b).
carbon materials, which correlate with their structural ordering or graphitization degree [26]. PAN-based carbon fibers consist mainly of polyaromatic, structurally disordered carbon [27]. In contrast, pitchbased fibers consist mainly of medium or highly textured carbon, where there exist large in-plane crystallites with a high degree of order in three dimensional structures [28]. The structurally disordered PAN-based carbon fibers, especially when ungraphitized, therefore offer many more active carbon sites for reaction with tantalum atoms than the structurally ordered pitch-based carbon fibers and this results in the thicker TaC coating formed on the PAN-based carbon fibers. Images in Fig. 4a, c, and e show the surface morphologies of TaC coatings on PAN-based carbon fibers, graphitized PAN-based carbon fibers and pitch-based carbon fibers, respectively. The SEM observation indicates that the TaC coating formed on PAN-based carbon fibers has a denser, rather more uniform structure and larger grain size than that formed on graphitized PAN-based carbon fibers and pitch-based carbon fibers. This suggests that the grain size and thickness of the TaC coating are distinctively affected by the degree of graphitization and crystallinity of the carbon source.
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3.2. Influence of the molten salt composition on the formation of TaC coatings In order to understand the influence of the molten salt composition on the formation of TaC coatings, TaC-coated carbon fiber products were synthesized in various molten salts. Fig. 6 shows the XRD patterns of the products prepared by reaction of Ta powder at 850 °C for 1 h in four molten salt systems using PAN-based carbon fibers as the carbon source. It can be seen that the products synthesized in LiCl–KCl, NaCl– KCl and pure KCl molten salts show obvious diffraction peaks due to carbon and cubic TaC phase (shown in Fig. 6b, c and d). The intensity of the TaC diffraction peaks for the product prepared in LiCl–KCl molten salts is evidently higher compared to that of the products obtained in other molten salt media. This high intensity of the TaC diffraction peaks can be related to the higher thickness of this TaC coating (shown in Fig. 7). In contrast, no crystalline TaC phase is observed for the product synthesized in pure NaCl medium (shown in Fig. 6a). The further SEM/EDS analysis for the carbon fibers treated in pure NaCl medium indicates that there is no coating formed on the carbon fibers. This suggests that the molten salt composition has a significant influence on the crystal formation and growth of TaC. Fig. 7 shows typical SEM micrographs of the surface and cross-section of each of the products prepared from reaction of PAN-based carbon fibers and Ta at 850 °C for 1 h in LiCl–KCl, NaCl–KCl and KCl molten salt media. As shown in Fig. 7a, c and e, continuous and quite homogeneous coatings on the carbon fibers, with similar surface morphologies, can be observed in each case. The average thickness of the TaC coatings synthesized in LiCl–KCl, NaCl–KCl and pure KCl molten salt media (shown in Fig. 7b, d and f) is about 80 nm, 50 nm and 30 nm, respectively. The SEM observations in terms of coating thickness are consistent with the XRD results in terms of TaC peak intensity. The effect of molten salt composition on TaC coating thickness can be attributed to the different solubilities of tantalum in LiCl–KCl, NaCl–KCl and pure KCl molten salt media and the different melting points and viscosities of these molten salts. The eutectic point of LiCl–KCl is 352 °C, much lower than that of NaCl–KCl (650 °C) and the melting point of KCl (771 °C). In contrast, the melting point of NaCl is 801 °C and this may be so high that it does not facilitate sufficient tantalum solubility or mobility to allow formation of TaC. However, in the low-melting point salts, the reactants could achieve effective dissolution, transport and distribution in the flux [29], thereby enabling formation of TaC coatings. The higher mass transfer rate of tantalum and the consequent faster rate of reaction between tantalum and carbon in the LiCl–KCl molten salt medium result in the formation of a thicker TaC coating. This suggests that LiCl–KCl is a more effective molten salt
173
medium for forming a TaC coating on carbon fibers in comparison to NaCl–KCl, KCl and NaCl molten salt media. 3.3. Influence of reaction temperature on the formation of TaC coatings In order to explore the effect of the reaction temperature on the microstructure of TaC coating, TaC-coated PAN-based carbon fibers were prepared by treatment at 1000 °C, 1100 °C and 1200 °C for 1 h in LiCl– KCl molten salt. Fig. 8 shows the XRD patterns of the products obtained. It can be seen that the intensity of the diffraction peaks from the cubic TaC phase increases and the intensity of the carbon diffraction peaks diminishes to almost nothing with the increase of reaction temperature from 1000 °C to 1200 °C. In addition, the diffraction peaks of TaC are broad at low temperatures (1000 °C) and become narrow at high temperatures (1200 °C), which can be attributed to the growth of the crystal size in the TaC coating with increasing reaction temperature. The SEM images of the TaC-coated carbon fibers prepared by treatment at 1000 °C, 1100 °C and 1200 °C for 1 h in LiCl–KCl molten salts are represented in Fig. 9. The coating thickness estimated from the cross-section of the TaC-coated carbon fibers synthesized at 1000 °C, 1100 °C and 1200 °C (shown in Fig. 9b, e and h) is about 230 nm, 400 nm and 480 nm, respectively, indicating that the coating thickness increases with increasing reaction temperature. Furthermore, it can be seen from Fig. 9a and d that the TaC coatings synthesized at 1000 °C and 1100 °C are uniform along their length and circumferential directions and no rough defects can be found on the surface of these TaC-coated carbon fibers. No cracking or peeling of the coating is observed on the surface of these carbon fibers. However, for the TaC-coated carbon fibers synthesized at 1200 °C, significant cracking of the TaC coating (shown in Fig. 9g) and separation of the TaC coating from the carbon fiber substrate (shown in Fig. 9h) can be seen. This demonstrates that reaction temperature is a very important factor for the controllable fabrication of the adherent, crack-free and continuous TaC coating on carbon fibers. The fibers do not appear to become connected by coating “bridges” in any of the above cases. The grain size of the TaC coatings prepared at the relatively low temperature of 1000 °C and 1100 °C is small and uniform, especially in the former case, as can be seen from Fig. 9c and f. Fine grain size in the nano-range is expected to be beneficial in terms of increasing the strength of the coating and in relaxing residual stresses by grain boundary sliding [30]. Upon increasing the reaction temperature to 1200 °C, the mean grain size of TaC coating increases remarkably, and a great number of large TaC grains with polyhedral shape are visible on the coating surfaces (shown in Fig. 9i). The dependence of grain size in the TaC coating on reaction temperature is attributed to the varying mobility of atoms at different temperatures. High reaction temperatures lead to high atom mobility, which encourages growth and annealing of the TaC resulting in the formation of large grains [14]. The formation of large grains significantly decreases resistance to crack initiation and growth in coating materials [31] and, as a result, cracks and peeling are observed in the surface of TaC-coated carbon fibers prepared at 1200 °C. 3.4. Influence of reaction time on the formation of TaC coatings
Fig. 6. XRD patterns of the products prepared by reaction of Ta with PAN-based carbon fibers, as carbon source, at 850 °C for 1 h in (a) NaCl, (b) KCl, (c) NaCl–KCl and (d) LiCl–KCl molten salt media.
In order to evaluate further the effect of reaction time on the morphology and structure of TaC coatings, TaC-coated PAN-based carbon fibers were synthesized at 900 °C for 1–5 h in LiCl–KCl molten salt mixture. The XRD patterns of the products are presented in Fig. 10a. The relative intensity of the characteristic peaks of TaC increases with the increase of the holding time as it would be expected in the case of increasing coating thickness with the extension of the reaction time. The SEM images shown in Fig. 10b–e show the representative cross-sectional morphology of the TaC coating formed on the PAN-based carbon fibers. The thicknesses of these TaC coatings synthesized at 900 °C for 1, 2, 4 and 5 h in LiCl–KCl molten salts are 130 nm, 180 nm, 380 nm and 560 nm, respectively. This indicates that the TaC coating thickness increases with the
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(a)
(b)
(c)
(d)
(e)
(f)
Fig. 7. Typical SEM images of the surface and cross-section of the products prepared by reaction of tantalum with PAN-based carbon fibers at 850 °C for 1 h in (a–b) LiCl–KCl, (c–d) NaCl–KCl and (e–f) KCl molten salt media.
reaction time, which is in accordance with the XRD patterns shown in Fig. 10a. It is worth noting that, although the coating thickness in Fig. 10e is greater than that in Fig. 9h, almost no cracking or peeling of the former coating can be observed, as shown in Fig. 10f. A careful comparison of Fig. 10f with Fig. 9g reveals that the cracking and breakaway of coating in the latter appear mainly to be caused by the larger grain size rather than excessive thickness of the coating. Thus, reduction of grain size by limiting the reaction temperature is a critical factor for the synthesis of crack-free, adherent and continuous TaC coatings on carbon fibers. From Fig. 10b–e, it can be also observed that the diameter of the TaC-coated carbon fibers increases slightly with increasing coating thickness, which may be caused by volume expansion due to the conversion of hexagonal phase carbon into cubic phase TaC. Furthermore, the diameter of the unreacted carbon fiber core decreases with increasing reaction time as the interface between the TaC coating and carbon moves towards the center of the fiber as carbon is consumed by reaction with tantalum. 3.5. Reaction kinetics of TaC coating formation on carbon fibers Fig. 8. XRD patterns of the TaC-coated carbon fibers prepared by treatment at (a) 1000 °C, (b) 1100 °C and (c) 1200 °C for 1 h in LiCl–KCl molten salt.
In the molten salt medium, carbon fiber and tantalum exist in different states. Tantalum has a slight solubility in molten salts and the
Z.J. Dong et al. / Surface & Coatings Technology 212 (2012) 169–179
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
175
Fig. 9. Typical SEM images of the TaC-coated carbon fibers prepared by treatment at (a–c) 1000 °C, (d–f) 1100 °C and (g–i) 1200 °C for 1 h in LiCl–KCl molten salt.
dissolved tantalum exists as atoms or atomic clusters [32–34]. Carbon does not dissolve in molten salts and remains in a solid state [35]. In the initial stage of the reaction, carbon fibers are immersed in the molten salt solvent containing tantalum atoms formed by the dissolution of metallic tantalum and the reaction between tantalum and carbon occurs at the liquid–solid interface between the molten salts and carbon fibers. After a continuous TaC coating has formed on the carbon fibers, the reaction between tantalum and carbon may involve the following steps:
(1) The diffusion of tantalum atoms through a liquid boundary layer to the outer surface of the TaC coating, i.e. external diffusion; (2) The diffusion of tantalum atoms through the TaC coating to the interface between the TaC coating and unreacted carbon fiber [19], i.e. internal diffusion; (3) The formation of TaC by the interfacial reaction between tantalum and carbon, which leads to the continuous increase of the coating thickness.
(b)
(c)
(e)
(f)
(a)
(d)
Fig. 10. (a) XRD patterns and typical cross-section SEM images of TaC-coated carbon fibers synthesized at 900 °C for (b) 1 h, (c) 2 h, (d) 4 h and (e–f) 5 h in LiCl–KCl molten salts.
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For the abovementioned multi-step process, the slowest step is the rate-determining step that determines the rate of the whole process. Thermodynamic calculations indicate that tantalum metal will react directly with carbon to form TaC even at room temperature but, in practice, this solid-state reaction requires high temperatures up to 1800 °C in order to proceed at an appreciable rate, due to the kinetic limitation [36]. In the molten salt medium, however, tantalum and carbon can react at a relatively low temperature of 850 °C because the molten salt mixture facilitates the dissolution and transport of the tantalum. Therefore, it is reasonable to assume that the interfacial reaction between tantalum and carbon is relatively fast and that the growth of the TaC coating on carbon fibers is governed by the diffusion of tantalum atoms. Fig. 11 shows a geometrical model of the TaC-coated carbon fibers and the concentration distribution of tantalum atoms in the coating and liquid boundary layer, where R0 is the initial radius of the cylindrical carbon fiber (μm), Ri is the radius of the unreacted carbon fiber core (μm), and Rm is the radius of the TaC-coated carbon fiber (μm). CTb denotes the concentration of tantalum atoms in the bulk liquid (mol/m3). Because the amount of tantalum powder present in the molten salts is in great excess cf. what is consumed by reaction and because the dissolution of tantalum powder in the molten salts would reach saturation very quickly owing to its low solubility, CTb can be considered to be a constant. CTm and CTi represent the concentration of tantalum atoms (mol/m 3) at the coating surface and at the reaction interface, respectively. For each mole of TaC generated, one mole of carbon is consumed. The relationship of Ri and Rm can be described as follows: 2 2 π R0 −Ri LρC MC
¼
2 2 π Rm −Ri LρMC
ð1Þ
M MC
where the length of the carbon fiber is L (cm), density of carbon fiber ρC = 1.68 g/cm3, atomic weight of carbon MC = 12 g/mol, density of
formed TaC coating ρMC = 14.5 g/cm3 and atomic weight of formed TaC coating MMC = 193 g/mol. Equation Eq. (1) can be simplified as follows: ffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a R20 −R2i þ R2i M ρ where a ¼ MC C ¼ 1:86: MC ρMC
Rm ¼
ð2Þ
3.5.1. External diffusion control model When the internal diffusion rate of tantalum atoms is far greater than the external diffusion rate of tantalum atoms, the growth of TaC coating is controlled by the external diffusion of tantalum atoms. There is no concentration gradient of tantalum atoms from the coating surface to the reaction interface between the TaC coating and unreacted carbon fiber core, i.e. CTm =CTi, as shown in Fig. 11a. According to mass transfer theory, the mass transfer rate of tantalum atoms, NT (mol/s), through the liquid boundary layer surrounding an individual carbon fiber can be expressed as: NT ¼ 2πRm Lkl ðC Tb −C Tm Þ
ð3Þ
where kl is the mass transfer coefficient of tantalum atoms in the liquid boundary layer, which is influenced by the liquid flow pattern, liquid viscosity and diffusion coefficient of tantalum atoms in molten salt solvent. Considering the irreversibility of the reaction between tantalum and carbon, there is no concentration build-up of tantalum atoms in the coating, namely
C Tm ¼ C Ti ≈0:
ð4Þ
Surface of the coating on an individual carbon fibre
Liquid boundary layer
Unreacted carbon fibre core Reaction interface
Surface of an individual carbon fibre before the coating formed
CT
CTb
CTm
CTb (Bulk liquid concentration)
CTi
(a)
Rm R0 Ri
0
Ri R0 Rm
R
CT CTm
CTi
CTb
CTb
0
(b)
RmR0 Ri
0
Ri R0 Rm
R (Radial position)
Fig. 11. Geometrical model of a TaC-coated carbon fiber and concentration distribution of tantalum atoms in the coating and liquid boundary layer corresponding to (a) external diffusion control and (b) internal diffusion control.
Z.J. Dong et al. / Surface & Coatings Technology 212 (2012) 169–179
Substituting Eq. (4) into Eq. (3) yields: NT ¼ 2πRm Lkl C Tb :
ð5Þ
The rate of interfacial reaction between carbon and tantalum can be expressed in terms of the consumption of carbon in a period of time, which can be written as: vC ¼ −
2πRi LρC dRi MC dt
ð6Þ
where vc is the rate of interfacial reaction (mol/s) and t represents the reaction time. When steady-state conditions have been reached, the mass transfer rate of tantalum atoms through the liquid boundary layer is equal to the rate of interfacial reaction between carbon and tantalum: N T ¼ vC :
ð7Þ
Substituting Eqs. (5) and (6) into Eq. (7) yields, −
2πRi Lρc dRi ¼ 2πRm Lkl C Tb : Mc dt
ð8Þ
Substituting Eq. (2) into Eq. (8) yields, −
ρC Ri dRi ¼ kl C Tb MC dt
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi a R20 −R2i þ R2i :
ð9Þ
Ri R t k C Mc ffidRi ¼ −∫0 l Tb dt ∫Ri0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ρC 2 2 a R0 −Ri þ Ri
ð10Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k ða−1ÞC Tb MC t: aR20 −ða−1ÞR2i −R0 ¼ l ρC
ð11Þ
kl ða−1ÞC Tb M C : ρC
J T ¼ 2πRLD
R
∫Rim
ð15Þ
JT C dR ¼ ∫C TiTm dC T 2πRLD
JT ¼
ð16Þ
2πLD ðC −C Ti Þ: lnðRm =Ri Þ Tm
ð17Þ
Taking into account the irreversibility of the reaction between tantalum and carbon, the tantalum atom concentration at the reaction interface is close to zero, i.e. CTi ≈ 0. Eq. (17) can be simplified as: JT ¼
2πLD 2πLD C ¼ C : lnðRm =Ri Þ Tm lnðRm =Ri Þ Tb
ð19Þ
Substituting Eqs. (6) and (18) into Eq. (19) yields, 2πRi LρC dRi 2πLD ¼ C : lnðRm =Ri Þ Tb MC dt
R
ð12Þ
ð14Þ
From Eq. (14), it can be seen that the reaction coordinate Y is proportional to the reaction time t when the external diffusion of tantalum atom becomes the rate-determining step for the growth of TaC coating. 3.5.2. Internal diffusion control model When the external diffusion rate of tantalum atoms is far greater than the internal diffusion rate of tantalum atoms, the growth of the TaC coating is controlled by the internal diffusion of tantalum atoms. Fig. 11b shows the concentration gradient distribution of tantalum atoms in the TaC coating and liquid boundary layer. The concentration distribution of tantalum atoms is uniform throughout the bulk liquid to the TaC coating surface (CTb = CTm), but for the region from coating surface to the reaction interface, there is a concentration gradient and the tantalum atom concentration at the reaction interface is much less than that at the TaC coating surface, that is CTi b b CTm =
ð20Þ
Separating variable and then integrating Eq. (20) yield, t
−∫Ri0 Ri lnðRm =Ri ÞdRi ¼ ∫0
ð13Þ
ð18Þ
When steady-state conditions have been reached, the internal diffusion rate of tantalum atoms in the TaC coating is equal to the rate of interfacial reaction between carbon and tantalum. Accordingly, the following equation can be obtained.
DMC C Tb dt: ρC
ð21Þ
Substituting Rm according to Eq. (2) yields, a R20 −R2i þ R2i 4ða−1Þ DMC C Tb t: ¼ ρC
Eq. (11) can be simplified as: Y ¼ Kt:
dC T dR
where D is the efficient diffusion coefficient of the tantalum atoms in the TaC coating and R is the radial distance over which diffusion is occurring, resulting in a gradual decrease in the tantalum concentration CT. Separating the variables and then integrating Eq. (15) yield,
−
Denote
K¼
CTb. According to Fick's laws of diffusion, the internal diffusion rate of tantalum atoms, JT (mol/s), in the TaC coating can be described as:
vC ¼ J T
Separating the variables and then integrating Eq. (9) yield,
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Y ¼ aR20 −ða−1ÞR2i −R0
177
h i R2 lnR R2 lnRi −R20 lnR0 2 2 2 0 ln a R0 −Ri þ Ri − 0 þ i 2ða−1Þ 2 ð22Þ
Eq. (22) describes the relationship between the reaction time t and the radius Ri of the unreacted carbon fiber core. Denote ′
Y ¼
′
K ¼
a R20 −R2i þ R2i
h i R2 lnR 2 2 2 0 ln a R0 −Ri þ Ri − 0 4ða−1Þ 2ða−1Þ 2 2 R lnRi −R0 lnR0 þ i 2 DMC C Tb : ρC
ð23Þ ð24Þ
Eq. (22) can be simplified as: ′
′
Y ¼ K t:
ð25Þ
From Eq. (25), it can be seen that the reaction coordinate Y′ is proportional to the reaction time t when the internal diffusion of tantalum
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atoms becomes the rate-determining step for the growth of the TaC coating. To validate further the abovementioned diffusion control model, the diameter of the TaC-coated carbon fibers Dm (=2Rm), the diameter of the unreacted carbon fiber core Di (=2Ri) and the thickness of the TaC coatings δ were measured from Fig. 10. The two variables Y and Y′, which correspond to the external diffusion control model and internal diffusion control model, respectively, are related with Ri and R0 and the latter can be obtained from Rm and Ri according the Eq. (2). Y and Y′ can be calculated from Eqs. (12) and (23). The relationships between Y and Y′ and reaction time t are presented in the scatter point plots in Fig. 12. The linear fitting of these data points has been performed by using the Origin 8 software and the coefficient of determination R 2 has been calculated automatically. The coefficient of determination is the square of the correlation coefficient R, and it is an important tool in determining the degree of linear correlation of variables and the goodness of fit of a model in regression analysis. The value of coefficient of determination R 2 varies from 0 to 1. A higher value means a better fit. In this work, the coefficient of determination R 2 for the linear fitting of Y − t (Fig. 12a) is 0.890, i.e. less than 0.985 for the linear fitting of Y′ − t (Fig. 12b). This indicates that the latter fit is more better and that the internal diffusion control model is therefore more appropriate than the external diffusion control model. Thus, the growth of the TaC coating is controlled by the internal diffusion of tantalum atoms through the TaC coating.
4. Conclusion TaC coatings have been prepared on the surfaces of PAN-based, graphitized PAN-based and pitch-based carbon fibers by synthesis in molten salts. The degree of carbon fiber graphitization, molten salt composition, reaction temperature and reaction time have important influence on the thickness, grain size, adhesion and surface morphology of the TaC coatings on the carbon fibers. In comparison with graphitized PAN-based and pitch-based carbon fibers, PAN-based carbon fibers with a lower degree of graphitization are more reactive towards TaC coating formation, leading to the formation of thicker tantalum carbide coatings. The LiCl–KCl salt mixture has a relatively low melting point compared with NaCl–KCl, KCl and NaCl and is therefore more suitable as a molten salt medium in which to synthesize TaC coatings on carbon fibers. With increasing reaction temperature and reaction time, the thickness and the grain size of the TaC coatings increase noticeably. The formation of excessively large TaC grains on the surfaces of carbon fibers appears to induce the cracking and peeling of the carbide coatings. However, a homogeneous, continuous and crack-free TaC coating can be prepared by limiting the reaction temperature and controlling the reaction time. The experimental results for PAN-based
0.55 0.50
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0.50 0.45
(b)
0.40
R2=0.890
Y'(10-12m2)
0.40
Y(10-6m)
Acknowledgments
(a)
0.45
0.35 0.30 0.25
R2=0.985
0.35 0.30 0.25 0.20
0.20
0.15
0.15 0.10
fibers agree well with the internal diffusion control model, which suggests that the growth of the TaC coating is limited by the internal diffusion of tantalum atoms through the TaC coating.
1.0
1.5
2.0
2.5
t (h)
3.0
3.5
4.0
0.10
1.0
1.5
2.0
2.5
3.0
3.5
4.0
t (h)
Fig. 12. Linear fitting of (a) Y − t and (b) Y′ − t, which corresponds to the external diffusion control model and internal diffusion control model, respectively.
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