SURFACE TENSION CALCULATION OF Si-Zr ALLOYS FOR REACTIVE MELT INFILTRATION OF SiC AND/OR ZrC BASED CERAMIC COMPOSITES

Transcription

1 Research and Revews n Materals Scence and Chemstry Vol. 6, Issue 2, 2016, Pages ISSN Publshed Onlne on August 22, Jyot Academc Press SURFACE TENSION CALCULATION OF S-Zr ALLOYS FOR REACTIVE MELT INFILTRATION OF SC AND/OR ZrC BASED CERAMIC COMPOSITES Y. G. TONG 1,2, H. ZHANG 2, X. B. LIANG 1, C. Y. LEE 3, S. X. BAI 2 and Q. H. QIN 3 1 Natonal Engneerng Research Center of Mechancal Product Remanufacturng Academy of Armored Forces Engneerng Bejng P. R. Chna e-mal: tygaarh419@163.com 2 College of Aerospace Scence and Engneerng Natonal Unversty of Defense Technology Changsha P. R. Chna 3 Research School of Engneerng Australan Natonal Unversty ACT Australa Abstract Surface tenson of slcon based and zrconum based alloys s one of the most mportant parameters for reactve melt nfltraton of SC and/or ZrC based ceramc compostes. However, the hgh meltng ponts and reactvty of these Keywords and phrases: surface tenson, S-Zr system, calculaton, Butler model, reactve melt nfltraton. Communcated by Ana Rosa Slva. Receved March 20, 2016; Revsed July

2 116 Y. G. TONG et al. alloys wth oxygen make t dffcult and expensve to expermentally measure these alloys surface tenson. The am of present work was to calculate the surface tenson of these alloys based on thermodynamc data and Butler model. The surface tenson of slcon based alloys ncreased wth an ncrease n zrconum concentraton whle that of the zrconum based alloys decreased wth an ncrease n slcon concentraton. Both slcon based and zrconum based alloys were found to have negatve coeffcents of temperature for surface tenson. The calculated surface tenson values were n good agreement wth publshed expermental data, whch ndcated that the calculaton model and database were effectve for calculatng surface tenson of slcon based and zrconum based alloys. 1. Introducton Calculaton of phase dagrams base on thermodynamc functons has been wdely used n the last two decades [1]. The general acceptance of the unary data of thermodynamc functons ssued by SGTE (Scentfc Group of Thermodata Europe) [2] makes t possble to create large databases, whch are compatble wth each other and nternally consstent. Such databases can be used for calculatng phase dagrams of bnary and mult component systems. The qualty of the predcton of phase equlbrum and thermodynamc propertes n such mult component systems reflects the qualty of the database and verfes the thermodynamc assessments of lower order systems [3]. It s however also possble to use such relable databases for other purposes such as evaluatng the surface tenson of mxed solutons. Thus, the range of the applcablty of the thermodynamc databases s consderably wdened and the understandng of the surface tenson of molten alloys, salt mxtures, and oxde mxtures s mproved. Ceramc matrx compostes wth SC and/or ZrC based matrx renforced by hgh strength contnuous ceramc fbers have attracted much attenton for hgh temperature applcatons due to ther superor hgh temperature strength, low densty, mproved damage tolerance, good oxdaton, and ablaton resstance [4-7]. Reactve melt nfltraton (RMI) has been demonstrated to be an attractve technque for preparng fber renforced SC and/or ZrC based composte wth many advantages ncludng short fabrcaton perod, low cost, and near net shape [8-12].

3 SURFACE TENSION CALCULATION OF 117 Durng the RMI process, molten slcon based S-Zr alloy or zrconum based Zr-S alloy nfltrates nto a porous carbon fber renforced carbon preform (C/C) n a vacuum or nert atmosphere under the drvng force of capllary. The molten alloy expands to fll the pores and reacts wth the carbon n the porous C/C preform, whch ultmately results n a dense SC and/or ZrC matrx. The capllary force ncreases wth the magnfed surface tenson of the molten alloy accordng to the Young-Laplace equaton: P 2σ cos θ =, (1) r where σ s the surface tenson of the molten alloy, θ s the equlbrum contact angle of the molten alloy on the sold, and r s an effectve pore radus characterstc of the preform. It should be mentoned that the surface tenson of the nfltrated molten alloy s a very mportant parameter n the practcal RMI process and also n the numercal smulaton of the molten alloy nfltraton nto the porous preform. Unfortunately, there s very lttle publshed nformaton about the surface tenson data for S-Zr bnary system. Only Kostkov and Tarabanov [13] measured the surface tenson of slcon based S-Zr alloys and the measured data was lmted to very narrow composton and temperature range. The surface tenson of zrconum based Zr-S alloys s stll unknown and the surface tenson of the slcon based and zrconum based alloys n S-Zr system needs to be systematcally nvestgated n order to further understandng the RMI of SC and/or ZrC based ceramc composte. However, the meltng ponts of these alloys are qute hgh, whch makes t dffcult and expensve to measure these alloys surface tenson by experments. Addtonally, the molten S-Zr alloys are hghly reactve wth oxygen and the substrate materal [14], whch greatly affects the accuracy of the expermentally measured surface tenson values of these alloys. Butler [15] bult a model to calculate surface tenson of molten alloys based on thermodynamc data, provdng a practcal and economcal method to calculate the surface tenson of molten alloys.

4 118 Y. G. TONG et al. In our prevous work [16, 17], hgh performance SC and ZrC based ceramc compostes have been successfully produced by a quck and low cost RMI process usng slcon based S-Zr alloys and zrconum based Zr-S alloys, respectvely. The am of ths contrbuton s to calculate the surface tenson of the slcon based and zrconum based alloys n the S-Zr system, whch should help to mprove the understandng of the RMI producton of the SC and ZrC based ceramc compostes. 2. Calculaton Method Butler provded a theoretcal model to calculate the surface tenson of bnary and ternary alloy systems [18]. In that model, the surface s consdered as an addtonal thermodynamc phase n equlbrum wth the bulk. Based on the Butler s model, the surface tenson of lqud alloys can be descrbed as shown by Equaton (2): E, S E, B ( G G ), = 1, 2, 3,, n, S RT X 1 σ = σ + ln + S B X S (2) where R, T, σ, σ, and S are gas constant, temperature, surface tenson of molten alloys, surface tenson of pure components, and surface area, respectvely. S X and the surface phase and the bulk phase. B X are the mole fracton of a component n E S G, and E B G, are the partal excess Gbbs energes of a component n the surface phase and the bulk phase, respectvely, both as functons of temperature and composton. The surface area of component s calculated by Equaton (3) [19]: S M 2 / 3 = 1.091N ( ), (3) ρ where N 0, M, and ρ are Avogadro s number, the molar mass, and densty, respectvely.

5 SURFACE TENSION CALCULATION OF 119 Assumng that the free energy of an alloy s always proportonal to the number of nteractve contacts between neghbourng atoms, E S G, and E B G, are related to the respectve coordnaton numbers n the surface layer and the bulk phase as [20]: E, S E, B G = β G, (4) where β s the rato between the two coordnaton numbers,.e., a parameter descrbng the reduced coordnaton n the surface phase. Equaton (4) s based on the model proposed by Speser et al. [20]. Ths equaton means that the free energy n the surface phase has the same temperature and composton dependence as that n the bulk phase. In typcal close-packed sold structures, the coordnaton numbers are 12 and 9 for the bulk and the surface phases, respectvely, and thus β = 0.75 [21]. However, n some cases the value of β mght be affected by other factors, such as the relaxaton of the surface structure. In the lteratures, dfferent values rangng from 0.5 β can be found [21]. The thermodynamc data for the Gbbs excess free energes n bnary systems can be gven n the form of Redlch-Kster polynomals as follows [22]: G E n ( k ) k = xx j L ( x x j ), k = 1, 2, 3,, n, k= 0 (5) where ( k L ) s the nteracton parameter. Based on the Gbbs excess free energes of bnary systems, the partal excess energy of component and j n the bnary system can be derved from the standard thermodynamc relaton n the form of Equatons (6) and (7): G E E E G = G + ( 1 x ), (6) x E E E ( G xg ) G j =. (7) x 1

6 120 Y. G. TONG et al. 3. Results and Dscusson 3.1. Surface tenson and densty of pure slcon and zrconum The surface tenson of pure component can be descrbed n terms of [23]: dσ σ = σm + ( T Tm ), (8) dt where σ m s the surface tenson at the meltng pont T m and dσ m / dt s a temperature coeffcent of surface tenson. Table 1 presents the values of the parameters used n Equaton (8) for pure slcon and zrconum as gven n [24, 25]. Based on Equaton (8) and the parameters n Table 1, t s concluded that both the surface tenson of slcon and zrconum decreases wth an ncrease n temperature. Accordng to [26], the densty of pure component can be calculated as follows: dρ ρ = ρm + ( T Tm ), (9) dt n whch ρ m s the densty at the meltng temperature T m and dρ m / dt s a coeffcent. The parameters used n Equaton (9) are obtaned from [25, 27] and also lsted n Table 1. Wth the same varaton trend of surface tenson, the densty of pure slcon and zrconum decreases wth an ncrease n temperature. Table 1. Parameters used n the calculatons Element ρ m 3 ( g cm ) dρ dt 3 ( g cm K ) T m ( K ) σ m ( N m) dσ dt ( N mk) M ( g mol) Slcon Zrconum

7 SURFACE TENSION CALCULATION OF Surface tenson calculaton of slcon based and zrconum based alloys In the present work, the Gbbs excess free energy of the S-Zr bnary system was calculated by usng Redlch-Kster polynomals equaton (6) wth a thermodynamc database created for S-Zr phase dagram calculatons [28]. The optmal nteracton parameters are shown n Table 2. Based on Equaton (5), the Gbbs excess free energy of S-Zr bnary system can be descrbed as Equaton (10): G E n ( k ) k 2 = x1x2 L ( x 1 x 2 ) = 10Tx Zr x S k= 0 + ( T 10TxZr ) xzrxs. (10) Combne and solve Equatons (2)-(9), and the surface tenson of the alloy can be calculated. A smple computer program was wrtten to calculate the surface tenson of slcon based and zrconum alloys n S- Zr system by solvng Equatons (2)-(9) wth a thermodynamc database and parameters from Tables 1 and 2. Seen from the phase dagram of S- Zr system (Fgure 1), there are two eutectc alloys, S-Zr10 and Zr-S8.8 alloys, whch have the lowest meltng pont. In our prevous work [16, 17], both the eutectc slcon based S-Zr10 and zrconum based Zr- S8.8 alloys showed great potental for preparng hgh performance SC and/or ZrC based ceramc compostes by RMI. Thus, our calculaton of surface tenson manly focused on the slcon based S-Zr10 and zrconum based Zr-S8.8 alloys n order to help understandng the nfltraton process of the sad alloys. Even so, the above method can be used to calculate surface tenson of all the alloys n the S-Zr system. Table 2. Interacton parameters n the S-Zr system Interacton Parameters 0 L 1 L Expresson T 10T

8 122 Y. G. TONG et al. Fgure 1. Phase dagram of S-Zr bnary system. Fgure 2 shows the surface tenson of slcon based S-Zr10 alloy calculated at dfferent temperatures. The surface tenson calculated by the mxng rule and the surface tenson of pure slcon were also ncluded for comparson. Surface tenson by mxng rule was calculated usng the followng equaton: σ = x (11) SσS + xzrσzr. As seen n Fgure 2, both the calculated surface tenson of S-Zr10 alloy s larger than that of pure slcon. Wth ncrease n temperatures, both the surface tenson of S-Zr10 alloy and pure slcon decrease lnearly. The calculated surface tenson varaton of zrconum based Zr-S8.8 alloy wth temperature changes (Fgure 3) s smlar to that of S-Zr10 alloy. However, the calculated surface tenson of Zr-S8.8 alloy s smaller than that of pure zrconum, whch ndcates that the addton of slcon nto zrconum can reduce the surface tenson of zrconum based alloys.

9 SURFACE TENSION CALCULATION OF 123 Fgure 2. Surface tenson of S-Zr10 alloy and pure slcon versus temperature. Fgure 3. Surface tenson of Zr-S8.8 alloy and pure zrconum versus temperature.

10 124 Y. G. TONG et al. In order to further understand the effect of slcon addton on the surface tenson of zrconum based alloys and that of zrconum addton on the surface tenson of slcon based alloys, surface tenson of slcon based alloys wth dfferent zrconum content and that of zrconum based alloys wth dfferent slcon content were calculated. The results are shown n Fgure 4 and Fgure 5, respectvely. In the slcon based alloys, the surface tenson ncreases wth an ncrease n zrconum content whle the surface tenson of the zrconum based alloys decreases wth an ncrease n slcon content. It should be noted that the surface tenson varaton wth the alloyed element content changes s non-lnear, whch s dfferent from the lnear surface tenson varaton of pure slcon and zrconum wth temperature changes. Fgure 4. Calculated surface tenson of slcon based S-Zr alloys at 1773K.

11 SURFACE TENSION CALCULATION OF 125 Fgure 5. Calculated surface tenson of zrconum based Zr-S alloys at 2073K. Kostkov and Tarabanov [13] expermentally measured the surface tenson of slcon and slcon based S-Zr alloys n a ntrogen atmosphere. Ther nvestgaton ndcated that the surface tenson of slcon based S-Zr alloys was larger than that of pure slcon. The surface tenson of the slcon based S-Zr alloys ncreased wth an ncrease n zrconum content n the alloy whle the surface tenson of the slcon based alloy decreases wth an ncrease n temperature. Ther expermental conclusons are qute consstent wth the conclusons we got from the above calculaton. In order to further confrm the valdty of the surface tenson calculaton method employed n ths S-Zr system, some publshed expermental surface tenson data was referenced for comparson, whch s shown n Fgure 6. The calculated surface tenson values are n good agreement wth the publshed expermental data, whch ndcates that the calculaton method and thermodynamc data are effectve for calculatng surface tenson of the alloys n S-Zr system. By

12 126 Y. G. TONG et al. contrast, both the calculated value and expermentally measured surface tenson s larger than the surface tenson calculated by the mxed rule. Thus, t s not reasonable to calculate the surface tenson of alloys n the S-Zr bnary system by the smple mxed rule. Fgure 6. Calculated and expermentally measured surface tenson data. Surface tenson of the molten alloys s one of the most mportant parameters for RMI. Accordng to Equaton (1), capllary force vares wth surface tenson of the molten alloys, whch should nfluence the nfltraton process of RMI. In order to further nvestgate the effect of alloys surface tenson on RMI, the capllary force for dfferent alloys were calculated based on the alloys surface tenson calculated n ths work. The contact angle and pore radus n Equaton (1) was assumed as 20 and 10µm, respectvely. The capllary force as a functon of surface tenson of S-Zr alloys s shown n Fgure 7. As can be seen, the capllary force of slcon based and zrconum based alloys greatly ncreases wth the ncrease of surface tenson. It ndcates that ncreasng the surface tenson of alloys greatly helps to mprove the nfltraton of molten alloys durng RMI process.

13 SURFACE TENSION CALCULATION OF 127 Fgure 7. Capllary force as a functon of surface tenson of alloys n S-Zr system (a) slcon based S-Zr alloys, (b) zrconum based Zr-S alloy.

14 128 Y. G. TONG et al. 4. Conclusons (1) The surface tenson of slcon based and zrconum based alloys was calculated based on Butler model and thermodynamc data. (2) The surface tenson of slcon based alloys ncreases wth an ncrease n zrconum concentraton whle that of zrconum-based alloys decreases wth an ncrease of slcon concentraton. (3) Both the surface tenson of slcon based alloys and zrconum based alloys decreases wth an ncrease n temperature. (4) The calculated surface tenson s n good agreement wth some publshed expermental data. References [1] N. Saunders and P. Modownk, Calphad A Comprehensve Gude, Elsever, London, [2] A. T. Dnsdale, SGTE data for pure elements, Calphad 15 (1991), [3] R. Pcha, J. Vrestal and A. Kroupa, Predcton of alloy surface tenson usng a thermodynamc database, Calphad 28 (2004), [4] S. A. Chen, C. R. Zhang, Y. D. Zhang, D. Zhao, H. F. Hu and Z. B. Zhang, Mechansm of ablaton of 3D C/ZrC-SC composte under an oxyacetylene flame, Corros. Sc. 68 (2013), [5] N. Padmavath, S. Kumar, V. V. B. Prasad, J. Subrahmanyama and K. K. Ray, Processng of carbon-fber renforced (SC + ZrC) mn-compostes by soft-soluton approach and ther characterzaton, Ceram. Int. 35 (2009), [6] Y. G. Wang, X. J. Zhu, L. T. Zhang and L. F. Cheng, C/C-SC-ZrC compostes fabrcated by reactve melt nfltraton wth S 0.87Zr0.13 alloy, Ceram. Int. 38 (2012), [7] W. Krenkel, Applcaton of fbre renforced C/C-SC ceramcs, Ceram. Forum Int. 80(8) (2003), [8] J. Yang and O. J. Ilegbus, Knetcs of slcon-metal alloy nfltraton nto porous carbon, Compostes A 1 (2000), [9] M. Sngh and D. R. Behrendt, Reactve melt nfltraton of slcon-molybdenum alloys nto mcroporous carbon preforms, Mater. Sc. Eng. A 194 (1995),

15 SURFACE TENSION CALCULATION OF 129 [10] M. Esfehanan, J. G. Unster, F. Moztarzadeh and J. G. Henrch, Development of a hgh temperature C/XS 2 - SC (X = Mo, T) composte va reactve melt nfltraton, J. Eur. Ceram. Soc. 27 (2007), [11] S. Z. Jang, X. Xong, Z. K. Chen, P. Xao and B. Y. Huang, Influence factors of C/C-SC dual matrx compostes prepared by reactve melt nfltraton, Mater. Des. 30 (2009), [12] S. Kumar, A. Kumar, R. Dev, A. Shukla and A. K. Gupta, Capllary nfltraton studes of lquds nto 3D-sttched C-C preforms Part B: Knetcs of slcon nfltraton, J. Eur. Ceram. Soc. 29 (2009), [13] V. I. Kostkov and A. S. Tarabanov, Metod lssl Svostva Gran Raz Kontakt faz, AN UKR SSR, pp: 79-90, edted by V. N. Eremenko, Naukova Dumka, [14] B. J. Keene, A revew of the surface tenson of slcon and ts bnary alloys wth reference to Marangon flow, Surf. Interface Anal. 10 (1987), [15] J. A. V. Butler, The thermodynamcs of the surfaces of solutons, Proc. R. Soc. 135 (1932), [16] Y. G. Tong, S. X. Ba, H. Zhang and K. Chen, C/C-SC composte prepared by S-10Zr alloyed melt nfltraton, Ceram. Int. 38(4) (2012), [17] Y. G. Tong, S. X. Ba and K. Chen, C/C-ZrC composte prepared by chemcal vapor nfltraton combned wth alloyed reactve melt nfltraton, Ceram. Int. 38(7) (2012), [18] Z. Y. Qao, Z. M. Cao and T. Tanaka, Predcton of surface and nterfacal tenson based on thermodynamc data and Calphad approach, Rare Metals 25(5) (2005), [19] T. Tanaka, K. Hack and S. Hara, Calculaton of surface tenson of lqud B-Sn alloy usng thermochemcal applcaton lbrary ChemApp, Calphad 24(4) (2000), [20] R. Speser, D. R. Pore and K. Yeum, Surface tenson of bnary lqud alloys, Scrpta Metal. 21 (1987), [21] I. Egry, E. Rcc, R. Novakovc and S. Ozawa, Surface tenson of lqud metals and alloys: Recent developments, Adv. Collod Interface Sc. 159 (2010), [22] M. Kucharsk and P. Fma, The surface tenson and densty of lqud Ag-B, Ag-Sn and B-Sn alloys, Monatshefte für Cheme/Chemcal Monthly 136 (2005), [23] B. J. Keene, Revew of data for the surface tenson of pure metals, Int. Mater. Rev. 38(4) (1993), [24] N. Eustathopoulos and B. Drevet, Surface tenson of lqud slcon: Hgh or low value?, J. Cryst. Growth 371 (2013), [25] P. F. Parads and W. K. Rhm, Thermophyscal propertes of zrconum measured usng electrostatc levtaton, Proc. SPIE 3792, Materals Research n Low Gravty II, 1999.

16 130 Y. G. TONG et al. [26] E. A. Brandes and G. B. Brook, Smthhells Metals Reference Book, 7, London: Butterworth Henemann, 1992, [27] W. K. Rhm and K. Ohsaka, Thermophyscal propertes measurement of molten slcon by hgh-temperature electrostatc levtator: Densty, volume expanson, specfc heat capacty, emssvty, surface tenson and vscosty, J. Cryst. Growth 208 (2000), [28] H. M. Chen, F. Zheng, H. S. Lu, L. B. Lu and Z. P. Jn, Thermodynamc assessment of B-Zr and S-Zr bnary systems, J. Alloy Compd. 468 (2009), g