Modeling of gas phase diffusion transport during chemical vapor infiltration process

Vol. 12 No. 3Trans. Nonferrous met. Soc. ChinaJun.2002[ Article l]1003-63262002)3-0429-04Modeling of gas phase diffusion transport duringchemical vapor infiltration processXIAO Peng肖鹏y,LID李娣),Ⅹ U Yong-dong徐永东), HUANG Bai-yur(黄伯云(1. State Key Laboratory for Powder Metallurgy Central South University, Changsha 410083, China2. Loudi Agriculture and Agro-machine School, Loudi 417000, China3. State Key Laboratory of Solidification Processing Northwestern Polytechnical UniversityXi an 710072, ChinaAbstract In order to improve the uniformity of both the concentration of gaseous reagent and the deposition of matrixwithin micro-pores during the chemical vapor infiltration( Cvi process a calculation modeling of gas phase diffusiontransport within micro-pores was established. Taken CH3SiCl3 as precursor for depositing Sic as example, the diffusioncoefficient decomposing reaction rate concentration within the reactor and concentration distributing profiling of MTswithin micro-pore were accounted respectively. The results indicate that increasing the ratio of diffusion coefficient todecomposition rate constant of precursor MTS is propitious to decrease the densification gradient of parts and decreasingthe aspect ratio L/D )of micro-pore is favorable to make the concentration uniform within poresL Key words Chemical vapor infiltration modeling diffusion transport compositesCLC number]TQ174I Document code ]AINTRODUCTIONcoating on the surface of pore within the porouspreform,anaseThe chemical vapor infiltration( Cvi ) methodone of the most practical and promising process forto occur namely gaseous reagents diffuses from thesurface of preform into the interior pores. Suchfabrication of ceramic/carbon matrix composites diffusion is driven by a concentration gradient inreinforced by long fibers. In the course of matrixsobaric CVI. Consider a straight cylindrical pore ofdepositing, there is competition between gaseoustial diameter D and length Lreagents consume requirements of deposition chemical Fig. 1, exposed to a gaseous mixture undergoingreaction and gas phase transport rate. The effect of decomposition at a uniform temperature T. As solidspore net structure within preform on gas phase deposit on the inside walls of the pore the poretransport rate and matrix densification tenor is very diameter, D, will decrease as a function of time, timportant. For most parts fabricated by CVmethod, the matrix rapidly deposits on the outerand of the axial position, Z. The relationshipsurface of the preform, because where has a higherbetween concentration profile, CMrs(Z), of MrSgaseous precursor concentration than the pores located precursor along the pore and the initial concentin the interior of the preform. It leads to block theentrance of pore consequently the micro-pores canCMTs(0)matrixnot be perfectly filled in. The rapid and perfectdensification of micro-pore is one of the key issues forlower cost fabrication of desired composites. Tai andLackey et af 2] made some theoretical investigIn present work taking deposition of Sic fromCH3 SiCI( MTS) precursor as an example, bothDmodeling of gas phase diffusion transport and algebrequations of CVI process are established. The effectfactors on gas phase diffusion in CVI process werestudied in a numerical calculation method凵中国煤化工,」F=22 MODELING OF GAS PHASE DIFFUSIONTRANSPORTCNMHGFig 1 Schematic of gas diffusing intoIn CVI process in order to deposit a solidng pore space①[(59772031 supported by the National Natural Science Foundation of China21 Accepted date ]2001-10-31430Trans. Nonferrous met. Soc. ChinaJun.2002ration, CMI(0), on the entrance of pore can be to be 0.0107 cm kPa s K- 3/2). At 1.01 X 10described as follows 3JPa and 1 373 5K in the system, D is thereforeCMI( 2) cosh(1-2/L)](1) estimated to be 5. 38 cm2s 1. From the equalosi1e(5and (6), note that the diffusion coefficientwhere L is the length of pore, z is the axialonal to pressure and indposition and 8 is the Thiele modulus which can be temperature according to a power law with anexpressed as followsexponent 1. 50=(ksL/DD y.5(2When2r≤λ, the gas molecules collide mostlywhere ks is the first-order reaction rate of mTs with the walls of the pore and the flowdecomposition reaction on the surface of pore, cmr Knudsen or molecular regime. As the concentration ofmin-1, and D. is the diffusion coefficient of the the vapor increases the frequencies of a moleculemulti-component gas mixture, MTS H2,cmsliding with other molecules or withallbecome comparable. Therefore, the diffusioncoefficient can be determined from both molecular2.1 Diffusivitydiffusion and Knudsen diffusion. The KnudsenThe diffusion coefficient in the vapor depositiondiffusivity dk can be denote 2asprocess varies with temperature, pressurepore2r(RTy(7)diameter. The effective diffusivity, De oftransport in a porous body includes the FickianAt 2r=10 um and T=1373. 5K, Dk isdiffusivity D and the Kihudsondiffuestimated to be 1. 323 cmrom Egns. (3)is hardly to precisely depict the complex pore size(7), De approximates to be 4.07e(distribution so it is necessary to add a correct item/r. The relationship about them can be typically 2. 2 MiS decomposition ratedescribed byThe decomposition rate, ks( cm' min) isDe=/x(1/D+1/Dk)1(3) defined as the dissipation rate of mTS of unit area onwhere e is the porosity of a porous body and tthe interior surface of pore. It is difficult in directthe tortuosity factor. According to Ref [5], the measuring thealue. Accordinexperimentally determined value of t is usually conservation law the relationship between thebetween 2 and 6, although slightly larger and smallerdecomposition rate ks of mTs and the deposition ratelues have also been observed. An alternate empirical Rd of SiC on the interior surface of pore can becorrelation for Tdeduced as follows(4)ks=( raps MMrs y msSiCPMTS R))×10-4When the pore radius r is much larger than the(8)Knudsen diffusivity Dk can be ignored for the MTS( PMTg)) are 3 12 and 6.672 x10 g cm"omolecular mean free path A, namely 2r>100A, the where the densities for SiC ( Osic )and gas-phaspurposes of obtaining the desired estimate because the respectively and the molecular weights for MrSmolecules collide mostly with each other. The Fickian (Mmrs)and SiC( Msc )are 149.5 and 40 g mol-1diffusivity D can be calculated using the ChapmanEnskog relationship2 given for MTS in H, bycalculated to be 0.075 cm min,em min,ks isT3/2 MMIS+ MHD=0.001858MMIS WHH,2.3 MIS concentration in reaction chamberwhere T is the temperature, Ki p is the pressureulate the mrs concentration1.01X 10Pa, the molecular weights for H2( Mu) CMTs(0 )under kinetic equilibrium state in theand MTS( MMrS )are 2 and 1495g mol Ireaction chamber, it is necessary to compute theresident time t, which can be expressed as 8Jrespectively the overall hard shell diameter, o is anz=273Vp/101325FT(9)average between the H,(2.827A )and the MTS(5.114A), and the collision integral for diffusionwhere v denotes volume of reaction chamber, cmn2 d is estimated from the Leonard-Jones potential off der中国煤化工m, and T and pH, and mts to be 0.8099. At 1.01x 10 Pa andare terespeYHCure( Pa )in chamberCNMHG1373. 5K, the diffusion coefficient D is thereforeSo the mrs concentration CMIs(0) in theestimated to be 5. 1chamber can be deduced asEqn. (5 )can be simplified further as follow[7]CMrO)= CoFt/MMIS V(10)KMr/p6) where C and e denote the volume fraction of MTSFor t5WFuted by H2, the KM approximates in overall mixture gas and the density of MrS vaporVol. 12 No. 3 Modeling of gas phase diffusion transport during chemical vapor infiltration process.431(6.672x10g cm" 3), respectively3.2 Initial length and diameter of poreUnite Egns. (9) and( 10), Cmr 0 ) can also bAs shown in Fig 3, the smaller the aspect ratioexpressed as followsL/D is propitious to make mrS concentration (Z)CMr 0)T101325(11) within pore tend to equal the concentration C(0)onthe entrance of pore. For example, at De/ks=1600cmr(o)is calculate to be 1. 69X 10-6 mol and D=10 um, MTS concentration C(Z) withincm-3 on the condition that the flow rates of h,, any location of pore is equal to CO)when the ratioMTS and Ar are 600, 210 and 300 mL minrespectively, T is 1 373. 5,Ki and p is 1.01 Xwhich only equal the thickness of one layer carbon105Pacloth or carbon tow. In other word, the densificationof matrix is uniform when the length of pore is justEFFECT FACTORS ON GAS-PHASE Based on this, the authors bring forward an improvedCVI method to change the course into that first tobraidform and then to deposit matrix in cvi3. 1 Ratio of De and ksFig 2 denotes the relationship between value ofmethod, and adopt a course that both stacking ofCeyco)and axial position under different ratioarbon cloth and deposition of matrix are conducted iof gas efficient diffusivity De and reaction rate ks ofsimultaneity. It leads to both densification of micro-e andof preform are synchronouMTS decomposition reaction on a determinate lengthaccomplished. In this improved CVI method theof pore L the MTS concentration within the pore length of micro-pore is greatly shorten, therefore,aand therefore the deposition rate of Sic will be moremore uniform part can be rapidly fabricated compareduniform, the larger the gas-phase diffusivity De to traditional CVI methods. More details abcompared to the reaction rate ks. On the other handMTS concentration in location of Z within pore(c improved CVI method were reported 10-12](Z)) will increase with increasing ratio D/ks. Atthe same temperature, that C(Z) tends to equateL/D=20ao) predicts SiC matrix deposition rate within porespace to be more uniform. So it is in favor of makingthe density of sic matrix composites part uniform toboth increase the gas diffusion coefficient D and0.6decrease Mts decomposition reaction rate ks. In2000CVI process a relative lower deposition temperature0.4is usually used to improve the uniformity of partdensity which not only decreases ks but also0.2D/ks=1600D=10mincreases the uniformity of mrS concentration withpr0.4in the system can be adopted to increase the diffusioncoefficient De therefore to quicken gas phase transportFig 3 Relationship between distributing curvesof concentration in pores and L/D1.04 CONCLUSIONTaking the deposition of SiC using CVI process0.as an example tohase diffusiontransport with micro-pores of the preform was0.6established. The calculation results indicated thatD/ks=2000MrS gas-phase concentration within ththerefore the deposition rate of Sic matrix will beD=20 mm1200more中国煤化 Iger the gas efficientdiffusTHreaction rate of mrsCNMHG1.21.6ratIoT REFERENCESFig 2 Calculated values of az yco)with万方蔣瓣 rent ratios of d。toks[1] TaiN H, Chou T W. Modeling of an improved chemicalTrans. Nonferrous met. Soc. 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